What is chemistry? Simply put, chemistry is the study of the interactions of matter with other matter and with energy. This seems straightforward enough. However, the definition of chemistry includes a wide range of topics that must be understood to gain a mastery of the topic or even take additional courses in chemistry. In this book, we will lay the foundations of chemistry in a topic-by-topic fashion to provide you with the background you need to successfully understand chemistry. The definition of chemistry—the study of the interactions of matter with other matter and with energy—uses some terms that should also be defined. We start the study of chemistry by defining some basic terms. Matter is anything that has mass and takes up space. A book is matter, a computer is matter, food is matter, and dirt in the ground is matter. Sometimes matter may be difficult to identify. For example, air is matter, but because it is so thin compared to other matter (e.g., a book, a computer, food, and dirt), we sometimes forget that air has mass and takes up space. Things that are not matter include thoughts, ideas, emotions, and hopes. To understand matter and how it changes, we need to be able to describe matter. There are two basic ways to describe matter: physical properties and chemical properties. Physical properties are characteristics that describe matter as it exists. Some of many physical characteristics of matter are shape, color, size, and temperature. An important physical property is the phase (or state) of matter. The three fundamental phases of matter are solid, liquid, and gas (see Figure 1.1 "The Phases of Matter"). Chemical properties are characteristics of matter that describe how matter changes form in the presence of other matter. Does a sample of matter burn? Burning is a chemical property. Does it behave violently when put in water? This reaction is a chemical property as well (Figure 1.2 "Chemical Properties"). In the following chapters, we will see how descriptions of physical and chemical properties are important aspects of chemistry. If matter always stayed the same, chemistry would be rather boring. Fortunately, a major part of chemistry involves change. A physical change occurs when a sample of matter changes one or more of its physical properties. For example, a solid may melt (Figure 1.3 "Physical Changes"), or alcohol in a thermometer may change volume as the temperature changes. A physical change does not affect the chemical composition of matter. A chemical change is the process of demonstrating a chemical property, such as the burning match in Figure 1.2 "Chemical Properties". As the matter in the match burns, its chemical composition changes, and new forms of matter with new physical properties are created. Note that chemical changes are frequently accompanied by physical changes, as the new matter will likely have different physical properties from the original matter. A sample of matter that has the same physical and chemical properties throughout is called a substance. Sometimes the phrase pure substance is used, but the word pure isn’t needed. The definition of the term substance is an example of how chemistry has a specific definition for a word that is used in everyday language with a different, vaguer definition. Here, we will use the term substance with its strict chemical definition. Chemistry recognizes two different types of substances: elements and compounds. An element is the simplest type of chemical substance; it cannot be broken down into simpler chemical substances by ordinary chemical means. There are about 115 elements known to science, of which 80 are stable. (The other elements are radioactive, a condition we will consider in Chapter 15 "Nuclear Chemistry".) Each element has its own unique set of physical and chemical properties. Examples of elements include iron, carbon, and gold. A compound is a combination of more than one element. The physical and chemical properties of a compound are different from the physical and chemical properties of its constituent elements; that is, it behaves as a completely different substance. There are over 50 million compounds known, and more are being discovered daily. Examples of compounds include water, penicillin, and sodium chloride (the chemical name for common table salt). Elements and compounds are not the only ways in which matter can be present. We frequently encounter objects that are physical combinations of more than one element or compound. Physical combinations of more than one substance are called mixtures. There are two types of mixtures. A heterogeneous mixture is a mixture composed of two or more substances. It is easy to tell, sometimes by the naked eye, that more than one substance is present. A homogeneous mixture is a combination of two or more substances that is so intimately mixed that the mixture behaves as a single substance. Another word for a homogeneous mixture is solution. Thus, a combination of salt and steel wool is a heterogeneous mixture because it is easy to see which particles of the matter are salt crystals and which are steel wool. On the other hand, if you take salt crystals and dissolve them in water, it is very difficult to tell that you have more than one substance present just by looking—even if you use a powerful microscope. The salt dissolved in water is a homogeneous mixture, or a solution (Figure 1.4 "Types of Mixtures"). There are other descriptors that we can use to describe matter, especially elements. We can usually divide elements into metals and nonmetals, and each set shares certain (but not always all) properties. A metal is an element that is solid at room temperature (although mercury is a well-known exception), is shiny and silvery, conducts electricity and heat well, can be pounded into thin sheets (a property called malleability), and can be drawn into thin wires (a property called ductility). A nonmetal is an element that is brittle when solid, does not conduct electricity or heat very well, and cannot be made into thin sheets or wires (Figure 1.5 "Semimetals"). Nonmetals also exist in a variety of phases and colors at room temperature. Some elements have properties of both metals and nonmetals and are called semimetals (or metalloids). We will see later how these descriptions can be assigned rather easily to various elements. KEY TAKEAWAYS - Chemistry is the study of matter and its interactions with other matter and energy. - Matter is anything that has mass and takes up space. - Matter can be described in terms of physical properties and chemical properties. - Physical properties and chemical properties of matter can change. - Matter is composed of elements and compounds. - Combinations of different substances are called mixtures. - Elements can be described as metals, nonmetals, and semimetals. Chemistry is a branch of science. Although science itself is difficult to define exactly, the following definition can serve as starting point. Science is the process of knowing about the natural universe through observation and experiment. Science is not the only process of knowing (e.g., the ancient Greeks simply sat and thought), but it has evolved over more than 350 years into the best process that humanity has devised to date to learn about the universe around us. The process of science is usually stated as the scientific method, which is rather naïvely described as follows: (1) state a hypothesis, (2) test the hypothesis, and (3) refine the hypothesis. Actually, however, the process is not that simple. (For example, I don’t go into my lab every day and exclaim, “I am going to state a hypothesis today and spend the day testing it!”) The process is not that simple because science and scientists have a body of knowledge that has already been identified as coming from the highest level of understanding, and most scientists build from that body of knowledge. An educated guess about how the natural universe works is called a hypothesis. A scientist who is familiar with how part of the natural universe works—say, a chemist—is interested in furthering that knowledge. That person makes a reasonable guess—a hypothesis—that is designed to see if the universe works in a new way as well. Here’s an example of a hypothesis: “if I mix one part of hydrogen with one part of oxygen, I can make a substance that contains both elements.” Most good hypotheses are grounded in previously understood knowledge and represent a testable extension of that knowledge. The scientist then devises ways to test if that guess is or is not correct. That is, the scientist plans experiments. Experiments are tests of the natural universe to see if a guess (hypothesis) is correct. An experiment to test our previous hypothesis would be to actually mix hydrogen and oxygen and see what happens. Most experiments include observations of small, well-defined parts of the natural universe designed to see results of the experiments. Why do we have to do experiments? Why do we have to test? Because the natural universe is not always so obvious, experiments are necessary. For example, it is fairly obvious that if you drop an object from a height, it will fall. Several hundred years ago (coincidentally, near the inception of modern science), the concept of gravity explained that test. However, is it obvious that the entire natural universe is composed of only about 115 fundamental chemical building blocks called elements? This wouldn’t seem true if you looked at the world around you and saw all the different forms matter can take. In fact, the concept of the element is only about 200 years old, and the last naturally occurring element was identified about 80 years ago. It took decades of tests and millions of experiments to establish what the elements actually are. These are just two examples; a myriad of such examples exists in chemistry and science in general. When enough evidence has been collected to establish a general principle of how the natural universe works, the evidence is summarized in a theory. A theory is a general statement that explains a large number of observations. “All matter is composed of atoms” is a general statement, a theory, that explains many observations in chemistry. A theory is a very powerful statement in science. There are many statements referred to as “the theory of _______” or the “______ theory” in science (where the blanks represent a word or concept). When written in this way, theories indicate that science has an overwhelming amount of evidence of its correctness. We will see several theories in the course of this text. A specific statement that is thought to be never violated by the entire natural universe is called a law. A scientific law is the highest understanding of the natural universe that science has and is thought to be inviolate. For example, the fact that all matter attracts all other matter—the law of gravitation—is one such law. Note that the terms theory and law used in science have slightly different meanings from those in common usage; theory is often used to mean hypothesis (“I have a theory…”), whereas a law is an arbitrary limitation that can be broken but with potential consequences (such as speed limits). Here again, science uses these terms differently, and it is important to apply their proper definitions when you use these words in science. (See Figure 1.8 "Defining a Law".) There is an additional phrase in our definition of science: “the natural universe.” Science is concerned only with the natural universe. What is the natural universe? It’s anything that occurs around us, well, naturally. Stars; planets; the appearance of life on earth; and how animals, plants, and other matter function are all part of the natural universe. Science is concerned with that—and only that. Of course, there are other things that concern us. For example, is the English language part of science? Most of us can easily answer no; English is not science. English is certainly worth knowing (at least for people in predominantly English-speaking countries), but why isn’t it science? English, or any human language, isn’t science because ultimately it is contrived; it is made up. Think of it: the word spelled b-l-u-e represents a certain color, and we all agree what color that is. But what if we used the word h-a-r-d-n-r-f to describe that color? (See Figure 1.9 "English Is Not Science".) That would be fine—as long as everyone agreed. Anyone who has learned a second language must initially wonder why a certain word is used to describe a certain concept; ultimately, the speakers of that language agreed that a particular word would represent a particular concept. It was contrived. How would you describe this color? Blue or hardnrf? Either way, you’re not doing science. That doesn’t mean language isn’t worth knowing. It is very important in society. But it’s not science. Science deals only with what occurs naturally. The field of science has gotten so big that it is common to separate it into more specific fields. First, there is mathematics, the language of science. All scientific fields use mathematics to express themselves—some more than others. Physics and astronomy are scientific fields concerned with the fundamental interactions between matter and energy. Chemistry, as defined previously, is the study of the interactions of matter with other matter and with energy. Biology is the study of living organisms, while geology is the study of the earth. Other sciences can be named as well. Understand that these fields are not always completely separate; the boundaries between scientific fields are not always readily apparent. Therefore, a scientist may be labeled a biochemist if he or she studies the chemistry of biological organisms. Finally, understand that science can be either qualitative or quantitative. Qualitative implies a description of the quality of an object. For example, physical properties are generally qualitative descriptions: sulfur is yellow, your math book is heavy, or that statue is pretty. A quantitative description represents the specific amount of something; it means knowing how much of something is present, usually by counting or measuring it. As such, some quantitative descriptions would include 25 students in a class, 650 pages in a book, or a velocity of 66 miles per hour. Quantitative expressions are very important in science; they are also very important in chemistry. KEY TAKEAWAYS - Science is a process of knowing about the natural universe through observation and experiment. - Scientists go through a rigorous process to determine new knowledge about the universe; this process is generally referred to as the scientific method. - Science is broken down into various fields, of which chemistry is one. - Science, including chemistry, is both qualitative and quantitative. In 1983, an Air Canada airplane had to make an emergency landing because it unexpectedly ran out of fuel; ground personnel had filled the fuel tanks with a certain number of pounds of fuel, not kilograms of fuel. In 1999, the Mars Climate Orbiter spacecraft was lost attempting to orbit Mars because the thrusters were programmed in terms of English units, even though the engineers built the spacecraft using metric units. In 1993, a nurse mistakenly administered 23 units of morphine to a patient rather than the “2–3” units prescribed. (The patient ultimately survived.) These incidents occurred because people weren’t paying attention to quantities. Chemistry, like all sciences, is quantitative. It deals with quantities, things that have amounts and units. Dealing with quantities is very important in chemistry, as is relating quantities to each other. In this chapter, we will discuss how we deal with numbers and units, including how they are combined and manipulated. Quantities have two parts: the number and the unit. The number tells “how many.” It is important to be able to express numbers properly so that the quantities can be communicated properly. Standard notation is the straightforward expression of a number. Numbers such as 17, 101.5, and 0.00446 are expressed in standard notation. For relatively small numbers, standard notation is fine. However, for very large numbers, such as 306,000,000, or for very small numbers, such as 0.000000419, standard notation can be cumbersome because of the number of zeros needed to place nonzero numbers in the proper position. Scientific notation is an expression of a number using powers of 10. Powers of 10 are used to express numbers that have many zeros: and so forth. The raised number to the right of the 10 indicating the number of factors of 10 in the original number is the exponent. (Scientific notation is sometimes called exponential notation.) The exponent’s value is equal to the number of zeros in the number expressed in standard notation. Small numbers can also be expressed in scientific notation but with negative exponents: and so forth. Again, the value of the exponent is equal to the number of zeros in the denominator of the associated fraction. A negative exponent implies a decimal number less than one. A number is expressed in scientific notation by writing the first nonzero digit, then a decimal point, and then the rest of the digits. The part of a number in scientific notation that is multiplied by a power of 10 is called the coefficient. Then determine the power of 10 needed to make that number into the original number and multiply the written number by the proper power of 10. For example, to write 79,345 in scientific notation, 79,345 = 7.9345 × 10,000 = 7.9345 × 10^4 Thus, the number in scientific notation is 7.9345 × 104. For small numbers, the same process is used, but the exponent for the power of 10 is negative: 0.000411 = 4.11 × 1/10,000 = 4.11 × 10^−4 Typically, the extra zero digits at the end or the beginning of a number are not included. (See Figure 2.1 "Using Scientific Notation".) Another way to determine the power of 10 in scientific notation is to count the number of places you need to move the decimal point to get a numerical value between 1 and 10. The number of places equals the power of 10. This number is positive if you move the decimal point to the right and negative if you move the decimal point to the left: 56,900=5.69 × 10^4 0.000028=2.8 × 10−5 Many quantities in chemistry are expressed in scientific notation. When performing calculations, you may have to enter a number in scientific notation into a calculator. Be sure you know how to correctly enter a number in scientific notation into your calculator. Different models of calculators require different actions for properly entering scientific notation. If in doubt, consult your instructor immediately. (See Figure 2.2 "Scientific Notation on a Calculator".) KEY TAKEAWAYS - Standard notation expresses a number normally. - Scientific notation expresses a number as a coefficient times a power of 10. - The power of 10 is positive for numbers greater than 1 and negative for numbers between 0 and 1. A number indicates “how much,” but the unit indicates “of what.” The “of what” is important when communicating a quantity. For example, if you were to ask a friend how close you are to Lake Erie and your friend says “six,” then your friend isn’t giving you complete information. Six what? Six miles? Six inches? Six city blocks? The actual distance to the lake depends on what units you use. Chemistry, like most sciences, uses the International System of Units, or SI for short. (The letters SI stand for the French “le Système International d’unités.”) SI specifies certain units for various types of quantities, based on seven fundamental units for various quantities. We will use most of the fundamental units in chemistry. Initially, we will deal with three fundamental units. The meter (m) is the SI unit of length. It is a little longer than a yard (see Figure 2.3 "The Meter"). The SI unit of mass is the kilogram (kg), which is about 2.2 pounds (lb). The SI unit of time is the second (s). To express a quantity, you need to combine a number with a unit. If you have a length that is 2.4 m, then you express that length as simply 2.4 m. A time of 15,000 s can be expressed as 1.5 × 104 s in scientific notation. Sometimes, a given unit is not an appropriate size to easily express a quantity. For example, the width of a human hair is very small, and it doesn’t make much sense to express it in meters. SI also defines a series of numerical prefixes that refer to multiples or fractions of a fundamental unit to make a unit more conveniently sized for a specific quantity. Table 2.1 "Multiplicative Prefixes for SI Units" lists the prefixes, their abbreviations, and their multiplicative factors. Some of the prefixes, such as kilo-, mega-, and giga-, represent more than one of the fundamental unit, while other prefixes, such as centi-, milli-, and micro-, represent fractions of the original unit. Note, too, that once again we are using powers of 10. Each prefix is a multiple of or fraction of a power of 10. To use the fractions to generate new units, simply combine the prefix with the unit itself; the abbreviation for the new unit is the combination of the abbreviation for the prefix and the abbreviation of the unit. For example, the kilometer (km) is 1,000 × meter, or 1,000 m. Thus, 5 kilometers (5 km) is equal to 5,000 m. Similarly, a millisecond (ms) is 1/1,000 × second, or one-thousandth of a second. Thus, 25 ms is 25 thousandths of a second. You will need to become proficient in combining prefixes and units. (You may recognize that one of our fundamental units, the kilogram, automatically has a prefix-unit combination, the kilogram. The word kilogram means 1,000 g.) In addition to the fundamental units, SI also allows for derived units based on a fundamental unit or units. There are many derived units used in science. For example, the derived unit for area comes from the idea that area is defined as width times height. Because both width and height are lengths, they both have the fundamental unit of meter, so the unit of area is meter × meter, or meter2 (m2). This is sometimes spoken as “square meters.” A unit with a prefix can also be used to derive a unit for area, so we can also have cm2, mm2, or km2 as acceptable units for area. Volume is defined as length times width times height, so it has units of meter × meter × meter or meter3 (m3), sometimes spoken as “cubic meters.” The cubic meter is a rather large unit, however, so another unit is defined that is somewhat more manageable: the liter (L). A liter is 1/1,000th of a cubic meter and is a little more than 1 quart in volume (see Figure 2.4 "The Liter"). Prefixes can also be used with the liter unit, so we can speak of milliliters (1/1,000th of a liter; mL) and kiloliters (1,000 L; kL). Another definition of a liter is one-tenth of a meter cubed. Because one-tenth of a meter is 10 cm, then a liter is equal to 1,000 cm3 (Figure 2.5 "The Size of 1 Liter"). Because 1 L equals 1,000 mL, we conclude that 1 mL equals 1 cm3; thus, these units are interchangeable. Units not only are multiplied together but also can be divided. For example, if you are traveling at one meter for every second of time elapsed, your velocity is 1 meter per second, or 1 m/s. The word per implies division, so velocity is determined by dividing a distance quantity by a time quantity. Other units for velocity include kilometers per hour (km/h) or even micrometers per nanosecond (μm/ns). Later, we will see other derived units that can be expressed as fractions. KEY TAKEAWAYS - Numbers tell “how much,” and units tell “of what.” - Chemistry uses a set of fundamental units and derived units from SI units. - Chemistry uses a set of prefixes that represent multiples or fractions of units. - Units can be multiplied and divided to generate new units for quantities. If you use a calculator to evaluate the expression 337/217, you will get the following: 337/217=1.55299539171... and so on for many more digits. Although this answer is correct, it is somewhat presumptuous. You start with two values that each have three digits, and the answer has twelve digits? That does not make much sense from a strict numerical point of view. Consider using a ruler to measure the width of an object, as shown in Figure 2.6 "Expressing Width". The object is definitely more than 1 cm long, so we know that the first digit in our measurement is 1. We see by counting the tick marks on the ruler that the object is at least three ticks after the 1. If each tick represents 0.1 cm, then we know the object is at least 1.3 cm wide. But our ruler does not have any more ticks between the 0.3 and the 0.4 marks, so we can’t know exactly how much the next decimal place is. But with a practiced eye we can estimate it. Let us estimate it as about six-tenths of the way between the third and fourth tick marks, which estimates our hundredths place as 6, so we identify a measurement of 1.36 cm for the width of the object. Does it make any sense to try to report a thousandths place for the measurement? No, it doesn’t; we are not exactly sure of the hundredths place (after all, it was an estimate only), so it would be fruitless to estimate a thousandths place. Our best measurement, then, stops at the hundredths place, and we report 1.36 cm as proper measurement. This concept of reporting the proper number of digits in a measurement or a calculation is called significant figures. Significant figures (sometimes called significant digits) represent the limits of what values of a measurement or a calculation we are sure of. The convention for a measurement is that the quantity reported should be all known values and the first estimated value. The conventions for calculations are discussed as follows. In many cases, you will be given a measurement. How can you tell by looking what digits are significant? For example, the reported population of the United States is 306,000,000. Does that mean that it is exactly three hundred six million or is some estimation occurring? The following conventions dictate which numbers in a reported measurement are significant and which are not significant: 1. Any nonzero digit is significant. 2. Any zeros between nonzero digits (i.e., embedded zeros) are significant. 3. Zeros at the end of a number without a decimal point (i.e., trailing zeros) are not significant; they serve only to put the significant digits in the correct positions. However, zeros at the end of any number with a decimal point are significant. 4. Zeros at the beginning of a decimal number (i.e., leading zeros) are not significant; again, they serve only to put the significant digits in the correct positions. So, by these rules, the population figure of the United States has only three significant figures: the 3, the 6, and the zero between them. The remaining six zeros simply put the 306 in the millions position. How are significant figures handled in calculations? It depends on what type of calculation is being performed. If the calculation is an addition or a subtraction, the rule is as follows: limit the reported answer to the rightmost column that all numbers have significant figures in common. For example, if you were to add 1.2 and 4.71, we note that the first number stops its significant figures in the tenths column, while the second number stops its significant figures in the hundredths column. We therefore limit our answer to the tenths column. We drop the last digit—the 1—because it is not significant to the final answer. The dropping of positions in sums and differences brings up the topic of rounding. Although there are several conventions, in this text we will adopt the following rule: the final answer should be rounded up if the first dropped digit is 5 or greater and rounded down if the first dropped digit is less than 5. If the operations being performed are multiplication or division, the rule is as follows: limit the answer to the number of significant figures that the data value with the least number of significant figures has. So if we are dividing 23 by 448, which have two and three significant figures each, we should limit the final reported answer to two significant figures (the lesser of two and three significant figures): 23/448=0.051339286...=0.051 The same rounding rules apply in multiplication and division as they do in addition and subtraction. As you have probably realized by now, the biggest issue in determining the number of significant figures in a value is the zero. Is the zero significant or not? One way to unambiguously determine whether a zero is significant or not is to write a number in scientific notation. Scientific notation will include zeros in the coefficient of the number only if they are significant. Thus, the number 8.666 × 106 has four significant figures. However, the number 8.6660 × 106 has five significant figures. That last zero is significant; if it were not, it would not be written in the coefficient. So when in doubt about expressing the number of significant figures in a quantity, use scientific notation and include the number of zeros that are truly significant. KEY TAKEAWAYS - Significant figures in a quantity indicate the number of known values plus one place that is estimated. - There are rules for which numbers in a quantity are significant and which are not significant. - In calculations involving addition and subtraction, limit significant figures based on the rightmost place that all values have in common. - In calculations involving multiplication and division, limit significant figures to the least number of significant figures in all the data values. In Section 2.2 "Expressing Units", we showed some examples of how to replace initial units with other units of the same type to get a numerical value that is easier to comprehend. In this section, we will formalize the process. Consider a simple example: how many feet are there in 4 yards? Most people will almost automatically answer that there are 12 feet in 4 yards. How did you make this determination? Well, if there are 3 feet in 1 yard and there are 4 yards, then there are 4 × 3 = 12 feet in 4 yards. This is correct, of course, but it is informal. Let us formalize it in a way that can be applied more generally. We know that 1 yard (yd) equals 3 feet (ft): 1 yd = 3 ft In math, this expression is called an equality. The rules of algebra say that you can change (i.e., multiply or divide or add or subtract) the equality (as long as you don’t divide by zero) and the new expression will still be an equality. For example, if we divide both sides by 2, we get 1/2 yd=3/2 ft We see that one-half of a yard equals 3/2, or one and a half, feet—something we also know to be true, so the above equation is still an equality. Going back to the original equality, suppose we divide both sides of the equation by 1 yard (number and unit): 1 yd/1 yd=3 ft/1 yd The expression is still an equality, by the rules of algebra. The left fraction equals 1. It has the same quantity in the numerator and the denominator, so it must equal 1. The quantities in the numerator and denominator cancel, both the number and the unit: 1 yd/1 yd=3 ft/1 yd When everything cancels in a fraction, the fraction reduces to 1: 1=3 ft/1 yd We have an expression, 3 ft/1 yd, that equals 1. This is a strange way to write 1, but it makes sense: 3 ft equal 1 yd, so the quantities in the numerator and denominator are the same quantity, just expressed with different units. The expression 3 ft/1 yd is called a conversion factor, and it is used to formally change the unit of a quantity into another unit. (The process of converting units in such a formal fashion is sometimes called dimensional analysis or the factor label method.) To see how this happens, let us start with the original quantity: 4 yd Now let us multiply this quantity by 1. When you multiply anything by 1, you don’t change the value of the quantity. Rather than multiplying by just 1, let us write 1 as 3 ft/1 yd: 4 yd × 3 ft/1 yd The 4 yd term can be thought of as 4 yd/1; that is, it can be thought of as a fraction with 1 in the denominator. We are essentially multiplying fractions. If the same thing appears in the numerator and denominator of a fraction, they cancel. In this case, what cancels is the unit yard: 4 yd × 3 ft/1 yd That is all that we can cancel. Now, multiply and divide all the numbers to get the final answer: 4 × 3 ft/1=12 ft/1=12 ft Again, we get an answer of 12 ft, just as we did originally. But in this case, we used a more formal procedure that is applicable to a variety of problems. How many millimeters are in 14.66 m? To answer this, we need to construct a conversion factor between millimeters and meters and apply it correctly to the original quantity. We start with the definition of a millimeter, which is 1 mm = 1/1,000 m The 1/1,000 is what the prefix milli- means. Most people are more comfortable working without fractions, so we will rewrite this equation by bringing the 1,000 into the numerator of the other side of the equation: 1,000 mm = 1 m Now we construct a conversion factor by dividing one quantity into both sides. But now a question arises: which quantity do we divide by? It turns out that we have two choices, and the two choices will give us different conversion factors, both of which equal 1: 1,000 mm/1,000 mm=1 m/1,000 mm or 1,000 mm/1 m=1 m/1 m 1=1 m/1,000 mm or 1,000 mm/1 m=1 Which conversion factor do we use? The answer is based on what unit you want to get rid of in your initial quantity. The original unit of our quantity is meters, which we want to convert to millimeters. Because the original unit is assumed to be in the numerator, to get rid of it, we want the meter unit in the denominator; then they will cancel. Therefore, we will use the second conversion factor. Canceling units and performing the mathematics, we get 14.66 m × 1,000 mm/1 m=14,660 mm Note how m cancels, leaving mm, which is the unit of interest. The ability to construct and apply proper conversion factors is a very powerful mathematical technique in chemistry. You need to master this technique if you are going to be successful in this and future courses. What if we have a derived unit that is the product of more than one unit, such as m2? Suppose we want to convert square meters to square centimeters? The key is to remember that m2 means m × m, which means we have two meter units in our derived unit. That means we have to include two conversion factors, one for each unit. For example, to convert 17.6 m2 to square centimeters, we perform the conversion as follows: 17.6 m^2=17.6( m ×  m) × (100 cm/1 m) × (100 cm/1 m)=176,000 cm × cm=1.76 × 10^5 Sometimes there will be a need to convert from one unit with one numerical prefix to another unit with a different numerical prefix. How do we handle those conversions? Well, you could memorize the conversion factors that interrelate all numerical prefixes. Or you can go the easier route: first convert the quantity to the base unit, the unit with no numerical prefix, using the definition of the original prefix. Then convert the quantity in the base unit to the desired unit using the definition of the second prefix. You can do the conversion in two separate steps or as one long algebraic step. For example, to convert 2.77 kg to milligrams: 2.77 kg × 1,000 g/1 kg=2,770 g(convert to the base unit of grams) 2,770 g × 1,000 mg/1 g=2,770,000 mg=2.77 × 10^6 mg(convert to desired unit) Alternatively, it can be done in a single multistep process: 2.77 kg × (1,000 g/1 kg) × (1,000 mg/1 g)=2,770,000 mg=2.77 × 10^6 mg You get the same answer either way. When considering the significant figures of a final numerical answer in a conversion, there is one important case where a number does not impact the number of significant figures in a final answer—the so-called exact number. An exact number is a number from a defined relationship, not a measured one. For example, the prefix kilo- means 1,000—exactly 1,000, no more or no less. Thus, in constructing the conversion factor 1,000 g/1 kg neither the 1,000 nor the 1 enter into our consideration of significant figures. The numbers in the numerator and denominator are defined exactly by what the prefix kilo- means. Another way of thinking about it is that these numbers can be thought of as having an infinite number of significant figures, such as 1,000.0000000000… g/1.0000000000… kg The other numbers in the calculation will determine the number of significant figures in the final answer. KEY TAKEAWAYS - Units can be converted to other units using the proper conversion factors. - Conversion factors are constructed from equalities that relate two different units. - Conversions can be a single step or multistep. - Unit conversion is a powerful mathematical technique in chemistry that must be mastered. - Exact numbers do not affect the determination of significant figures. There are other units in chemistry that are important, and we will cover others in the course of the entire book. One of the fundamental quantities in science is temperature. Temperature is a measure of the average amount of energy of motion, or kinetic energy, a system contains. Temperatures are expressed using scales that use units called degrees, and there are several temperature scales in use. In the United States, the commonly used temperature scale is the Fahrenheit scale (symbolized by °F and spoken as “degrees Fahrenheit”). On this scale, the freezing point of liquid water (the temperature at which liquid water turns to solid ice) is 32°F, and the boiling point of water (the temperature at which liquid water turns to steam) is 212°F. Science also uses other scales to express temperature. The Celsius scale (symbolized by °C and spoken as “degrees Celsius”) is a temperature scale where 0°C is the freezing point of water and 100°C is the boiling point of water; the scale is divided into 100 divisions between these two landmarks and extended higher and lower. By comparing the Fahrenheit and Celsius scales, a conversion between the two scales can be determined: °C=(°F–32) × 5/9 °F=(°C × 95)+32 Using these formulas, we can convert from one temperature scale to another. The number 32 in the formulas is exact and does not count in significant figure determination. The fundamental unit of temperature (another fundamental unit of science, bringing us to four) in SI is the kelvin (K). The Kelvin temperature scale (note that the name of the scale capitalizes the word Kelvin, but the unit itself is lowercase) uses degrees that are the same size as the Celsius degree, but the numerical scale is shifted up by 273.15 units. That is, the conversion between the Kelvin and Celsius scales is as follows: K = °C + 273.15 °C = K − 273.15 For most purposes, it is acceptable to use 273 instead of 273.15. Note that the Kelvin scale does not use the word degrees; a temperature of 295 K is spoken of as “two hundred ninety-five kelvins” and not “two hundred ninety-five degrees Kelvin.” The reason that the Kelvin scale is defined this way is because there exists a minimum possible temperature called absolute zero. The Kelvin temperature scale is set so that 0 K is absolute zero, and temperature is counted upward from there. Normal room temperature is about 295 K, as seen in the following example. Figure 2.9 "Fahrenheit, Celsius, and Kelvin Temperatures" compares the three temperature scales. Note that science uses the Celsius and Kelvin scales almost exclusively; virtually no practicing chemist expresses laboratory-measured temperatures with the Fahrenheit scale. (In fact, the United States is one of the few countries in the world that still uses the Fahrenheit scale on a daily basis. The other two countries are Liberia and Myanmar [formerly Burma]. People driving near the borders of Canada or Mexico may pick up local radio stations on the other side of the border that express the daily weather in degrees Celsius, so don’t get confused by their weather reports.) Density is a physical property that is defined as a substance’s mass divided by its volume: density= mass/volume or d=m/V Density is usually a measured property of a substance, so its numerical value affects the significant figures in a calculation. Notice that density is defined in terms of two dissimilar units, mass and volume. That means that density overall has derived units, just like velocity. Common units for density include g/mL, g/cm3, g/L, kg/L, and even kg/m3. Densities for some common substances are listed in Table 2.2 "Densities of Some Common Substances". Because of how it is defined, density can act as a conversion factor for switching between units of mass and volume. For example, suppose you have a sample of aluminum that has a volume of 7.88 cm3. How can you determine what mass of aluminum you have without measuring it? You can use the volume to calculate it. If you multiply the given volume by the known density (from Table 2.2 "Densities of Some Common Substances"), the volume units will cancel and leave you with mass units, telling you the mass of the sample: 7.88 cm^3 × (2.7 g/cm^3)=21 g of aluminum where we have limited our answer to two significant figures. Density can also be used as a conversion factor to convert mass to volume—but care must be taken. We have already demonstrated that the number that goes with density normally goes in the numerator when density is written as a fraction. Take the density of gold, for example: d=19.3 g/mL=19.3 g/mL Although this was not previously pointed out, it can be assumed that there is a 1 in the denominator: d=19.3 g/mL=19.3 g/1 mL That is, the density value tells us that we have 19.3 grams for every 1 milliliter of volume, and the 1 is an exact number. When we want to use density to convert from mass to volume, the numerator and denominator of density need to be switched—that is, we must take the reciprocal of the density. In so doing, we move not only the units but also the numbers: 1/d=1 mL/19.3 g This reciprocal density is still a useful conversion factor, but now the mass unit will cancel and the volume unit will be introduced. Thus, if we want to know the volume of 45.9 g of gold, we would set up the conversion as follows: 45.9 g × (1 mL/19.3 g) =2.38 mL Note how the mass units cancel, leaving the volume unit, which is what we’re looking for. Care must be used with density as a conversion factor. Make sure the mass units are the same, or the volume units are the same, before using density to convert to a different unit. Often, the unit of the given quantity must be first converted to the appropriate unit before applying density as a conversion factor. KEY TAKEAWAYS - Chemistry uses the Celsius and Kelvin scales to express temperatures. - A temperature on the Kelvin scale is the Celsius temperature plus 273.15. - The minimum possible temperature is absolute zero and is assigned 0 K on the Kelvin scale. - Density relates a substance’s mass and volume. - Density can be used to calculate volume from a given mass or mass from a given volume. The basic building block of all matter is the atom. Curiously, the idea of atoms was first proposed in the fifth century BCE, when the Greek philosophers Leucippus and Democritus proposed their existence in a surprisingly modern fashion. However, their ideas never took hold among their contemporaries, and it wasn’t until the early 1800s that evidence amassed to make scientists reconsider the idea. Today, the concept of the atom is central to the study of matter. The smallest piece of an element that maintains the identity of that element is called an atom. Individual atoms are extremely small. It would take about fifty million atoms in a row to make a line that is 1 cm long. The period at the end of a printed sentence has several million atoms in it. Atoms are so small that it is difficult to believe that all matter is made from atoms—but it is. The concept that atoms play a fundamental role in chemistry is formalized by the modern atomic theory, first stated by John Dalton, an English scientist, in 1808. It consists of three parts: 1. All matter is composed of atoms. 2. Atoms of the same element are the same; atoms of different elements are different. 3. Atoms combine in whole-number ratios to form compounds. These concepts form the basis of chemistry. Although the word atom comes from a Greek word that means “indivisible,” we understand now that atoms themselves are composed of smaller parts called subatomic particles. The first part to be discovered was the electron, a tiny subatomic particle with a negative charge. It is often represented as e−, with the right superscript showing the negative charge. Later, two larger particles were discovered. The proton is a more massive (but still tiny) subatomic particle with a positive charge, represented as p+. The neutron is a subatomic particle with about the same mass as a proton but no charge. It is represented as either n or n0. We now know that all atoms of all elements are composed of electrons, protons, and (with one exception) neutrons. Table 3.1 "Properties of the Three Subatomic Particles" summarizes the properties of these three subatomic particles. How are these particles arranged in atoms? They are not arranged at random. Experiments by Ernest Rutherford in England in the 1910s pointed to a nuclear model of the atom. The relatively massive protons and neutrons are collected in the center of an atom, in a region called the nucleus of the atom (plural nuclei). The electrons are outside the nucleus and spend their time orbiting in space about the nucleus. (See Figure 3.1 "The Structure of the Atom".) The modern atomic theory states that atoms of one element are the same, while atoms of different elements are different. What makes atoms of different elements different? The fundamental characteristic that all atoms of the same element share is the number of protons. All atoms of hydrogen have one and only one proton in the nucleus; all atoms of iron have 26 protons in the nucleus. This number of protons is so important to the identity of an atom that it is called the atomic number of the element. Thus, hydrogen has an atomic number of 1, while iron has an atomic number of 26. Each element has its own characteristic atomic number. Atoms of the same element can have different numbers of neutrons, however. Atoms of the same element (i.e., atoms with the same number of protons) with different numbers of neutrons are called isotopes. Most naturally occurring elements exist as isotopes. For example, most hydrogen atoms have a single proton in their nucleus. However, a small number (about one in a million) of hydrogen atoms have a proton and a neutron in their nuclei. This particular isotope of hydrogen is called deuterium. A very rare form of hydrogen has one proton and two neutrons in the nucleus; this isotope of hydrogen is called tritium. The sum of the number of protons and neutrons in the nucleus is called the mass number of the isotope. Neutral atoms have the same number of electrons as they have protons, so their overall charge is zero. However, as we shall see later, this will not always be the case. When referring to an atom, we simply use the element’s name: the term sodium refers to the element as well as an atom of sodium. But it can be unwieldy to use the name of elements all the time. Instead, chemistry defines a symbol for each element. The atomic symbol is a one- or two-letter abbreviation of the name of the element. By convention, the first letter of an element’s symbol is always capitalized, while the second letter (if present) is lowercase. Thus, the symbol for hydrogen is H, the symbol for sodium is Na, and the symbol for nickel is Ni. Most symbols come from the English name of the element, although some symbols come from an element’s Latin name. (The symbol for sodium, Na, comes from its Latin name, natrium.) Table 3.2 "Names and Symbols of Common Elements" lists some common elements and their symbols. You should memorize the symbols in Table 3.2 "Names and Symbols of Common Elements", as this is how we will be representing elements throughout chemistry. The elements are grouped together in a special chart called the periodic table. A simple periodic table is shown in Figure 3.2 "A Simple Periodic Table", while a more extensive one is presented in Chapter 17 "Appendix: Periodic Table of the Elements". The elements on the periodic table are listed in order of ascending atomic number. The periodic table has a special shape that will become important to us when we consider the organization of electrons in atoms (see Chapter 8 "Electronic Structure"). One immediate use of the periodic table helps us identify metals and nonmetals. Nonmetals are in the upper right corner of the periodic table, on one side of the heavy line splitting the right-hand part of the chart. All other elements are metals. There is an easy way to represent isotopes using the atomic symbols. We use the construction where X is the symbol of the element, A is the mass number, and Z is the atomic number. Thus, for the isotope of carbon that has 6 protons and 6 neutrons, the symbol is where C is the symbol for the element, 6 represents the atomic number, and 12 represents the mass number. It is also common to state the mass number after the name of an element to indicate a particular isotope. Carbon-12 represents an isotope of carbon with 6 protons and 6 neutrons, while uranium-238 is an isotope of uranium that has 146 neutrons. KEY TAKEAWAYS - Chemistry is based on the modern atomic theory, which states that all matter is composed of atoms. - Atoms themselves are composed of protons, neutrons, and electrons. - Each element has its own atomic number, which is equal to the number of protons in its nucleus. - Isotopes of an element contain different numbers of neutrons. - Elements are represented by an atomic symbol. - The periodic table is a chart that organizes all the elements. There are many substances that exist as two or more atoms connected together so strongly that they behave as a single particle. These multiatom combinations are called molecules. A molecule is the smallest part of a substance that has the physical and chemical properties of that substance. In some respects, a molecule is similar to an atom. A molecule, however, is composed of more than one atom. Some elements exist naturally as molecules. For example, hydrogen and oxygen exist as two-atom molecules. Other elements also exist naturally as diatomic molecules (see Table 3.3 "Elements That Exist as Diatomic Molecules"). As with any molecule, these elements are labeled with a molecular formula, a formal listing of what and how many atoms are in a molecule. (Sometimes only the word formula is used, and its meaning is inferred from the context.) For example, the molecular formula for elemental hydrogen is H2, with H being the symbol for hydrogen and the subscript 2 implying that there are two atoms of this element in the molecule. Other diatomic elements have similar formulas: O2, N2, and so forth. Other elements exist as molecules—for example, sulfur normally exists as an eight-atom molecule, S8, while phosphorus exists as a four-atom molecule, P4 (see Figure 3.3 "Molecular Art of S"). Otherwise, we will assume that elements exist as individual atoms, rather than molecules. It is assumed that there is only one atom in a formula if there is no numerical subscript on the right side of an element’s symbol. Figure 3.3 "Molecular Art of S" shows two examples of how we will be representing molecules in this text. An atom is represented by a small ball or sphere, which generally indicates where the nucleus is in the molecule. A cylindrical line connecting the balls represents the connection between the atoms that make this collection of atoms a molecule. This connection is called a chemical bond. In Chapter 9 "Chemical Bonds", we will explore the origin of chemical bonds. You will see other examples of this “ball and cylinder” representation of molecules throughout this book. Many compounds exist as molecules. In particular, when nonmetals connect with other nonmetals, the compound typically exists as molecules. (Compounds between a metal and a nonmetal are different and will be considered in Section 3.4 "Ions and Ionic Compounds".) Furthermore, in some cases there are many different kinds of molecules that can be formed between any given elements, with all the different molecules having different chemical and physical properties. How do we tell them apart? The answer is a very specific system of naming compounds, called chemical nomenclature. By following the rules of nomenclature, each and every compound has its own unique name, and each name refers to one and only one compound. Here, we will start with relatively simple molecules that have only two elements in them, the so-called binary compounds: 1. Identify the elements in the molecule from its formula. This is why you need to know the names and symbols of the elements in Table 3.2 "Names and Symbols of Common Elements". 2. Begin the name with the element name of the first element. If there is more than one atom of this element in the molecular formula, use a numerical prefix to indicate the number of atoms, as listed in Table 3.4 "Numerical Prefixes Used in Naming Molecular Compounds". Do not use the prefix mono- if there is only one atom of the first element. 3. Name the second element by using three pieces: a. a numerical prefix indicating the number of atoms of the second element, plus b. the stem of the element name (e.g., ox for oxygen, chlor for chlorine, etc.), plus c. the suffix -ide. 4. Combine the two words, leaving a space between them. Let us see how these steps work for a molecule whose molecular formula is SO2, which has one sulfur atom and two oxygen atoms—this completes step 1. According to step 2, we start with the name of the first element—sulfur. Remember, we don’t use the mono- prefix for the first element. Now for step 3, we combine the numerical prefix di- (see Table 3.4 "Numerical Prefixes Used in Naming Molecular Compounds") with the stem ox- and the suffix -ide, to make dioxide. Bringing these two words together, we have the unique name for this compound—sulfur dioxide. Why all this trouble? There is another common compound consisting of sulfur and oxygen whose molecular formula is SO3, so the compounds need to be distinguished. SO3 has three oxygen atoms in it, so it is a different compound with different chemical and physical properties. The system of chemical nomenclature is designed to give this compound its own unique name. Its name, if you go through all the steps, is sulfur trioxide. Different compounds have different names. In some cases, when a prefix ends in a or o and the element name begins with o we drop the a or o on the prefix. So we see monoxide or pentoxide rather than monooxide or pentaoxide in molecule names. One great thing about this system is that it works both ways. From the name of a compound, you should be able to determine its molecular formula. Simply list the element symbols, with a numerical subscript if there is more than one atom of that element, in the order of the name (we do not use a subscript 1 if there is only one atom of the element present; 1 is implied). From the name nitrogen trichloride, you should be able to get NCl3 as the formula for this molecule. From the name diphosphorus pentoxide, you should be able to get the formula P2O5 (note the numerical prefix on the first element, indicating there is more than one atom of phosphorus in the formula). Some simple molecules have common names that we use as part of the formal system of chemical nomenclature. For example, H2O is given the name water, not dihydrogen monoxide. NH3 is called ammonia, while CH4 is called methane. We will occasionally see other molecules that have common names; we will point them out as they occur. KEY TAKEAWAYS - Molecules are groups of atoms that behave as a single unit. - Some elements exist as molecules: hydrogen, oxygen, sulfur, and so forth. - There are rules that can express a unique name for any given molecule, and a unique formula for any given name. Because matter is defined as anything that has mass and takes up space, it should not be surprising to learn that atoms and molecules have mass. Individual atoms and molecules, however, are very small, and the masses of individual atoms and molecules are also very small. For macroscopic objects, we use units such as grams and kilograms to state their masses, but these units are much too big to comfortably describe the masses of individual atoms and molecules. Another scale is needed. The atomic mass unit (u; some texts use amu, but this older style is no longer accepted) is defined as one-twelfth of the mass of a carbon-12 atom, an isotope of carbon that has six protons and six neutrons in its nucleus. By this scale, the mass of a proton is 1.00728 u, the mass of a neutron is 1.00866 u, and the mass of an electron is 0.000549 u. There will not be much error if you estimate the mass of an atom by simply counting the total number of protons and neutrons in the nucleus (i.e., identify its mass number) and ignore the electrons. Thus, the mass of carbon-12 is about 12 u, the mass of oxygen-16 is about 16 u, and the mass of uranium-238 is about 238 u. More exact masses are found in scientific references—for example, the exact mass of uranium-238 is 238.050788 u, so you can see that we are not far off by using the whole-number value as the mass of the atom. What is the mass of an element? This is somewhat more complicated because most elements exist as a mixture of isotopes, each of which has its own mass. Thus, although it is easy to speak of the mass of an atom, when talking about the mass of an element, we must take the isotopic mixture into account. The atomic mass of an element is a weighted average of the masses of the isotopes that compose an element. What do we mean by a weighted average? Well, consider an element that consists of two isotopes, 50% with mass 10 u and 50% with mass 11 u. A weighted average is found by multiplying each mass by its fractional occurrence (in decimal form) and then adding all the products. The sum is the weighted average and serves as the formal atomic mass of the element. In this example, we have the following: Note that no atom in our hypothetical element has a mass of 10.5 u; rather, that is the average mass of the atoms, weighted by their percent occurrence. This example is similar to a real element. Boron exists as about 20% boron-10 (five protons and five neutrons in the nuclei) and about 80% boron-11 (five protons and six neutrons in the nuclei). The atomic mass of boron is calculated similarly to what we did for our hypothetical example, but the percentages are different: Thus, we use 10.8 u for the atomic mass of boron. Virtually all elements exist as mixtures of isotopes, so atomic masses may vary significantly from whole numbers. Table 3.5 "Selected Atomic Masses of Some Elements" lists the atomic masses of some elements; a more expansive table is in Chapter 17 "Appendix: Periodic Table of the Elements". The atomic masses in Table 3.5 "Selected Atomic Masses of Some Elements" are listed to three decimal places where possible, but in most cases, only one or two decimal places are needed. Note that many of the atomic masses, especially the larger ones, are not very close to whole numbers. This is, in part, the effect of an increasing number of isotopes as the atoms increase in size. (The record number is 10 isotopes for tin.) Now that we understand that atoms have mass, it is easy to extend the concept to the mass of molecules. The molecular mass is the sum of the masses of the atoms in a molecule. This may seem like a trivial extension of the concept, but it is important to count the number of each type of atom in the molecular formula. Also, although each atom in a molecule is a particular isotope, we use the weighted average, or atomic mass, for each atom in the molecule. For example, if we were to determine the molecular mass of dinitrogen trioxide, N2O3, we would need to add the atomic mass of nitrogen two times with the atomic mass of oxygen three times: We would not be far off if we limited our numbers to one or even two decimal places. KEY TAKEAWAYS - The atomic mass unit (u) is a unit that describes the masses of individual atoms and molecules. - The atomic mass is the weighted average of the masses of all isotopes of an element. - The molecular mass is the sum of the masses of the atoms in a molecule. So far, we have discussed elements and compounds that are electrically neutral. They have the same number of electrons as protons, so the negative charges of the electrons is balanced by the positive charges of the protons. However, this is not always the case. Electrons can move from one atom to another; when they do, species with overall electric charges are formed. Such species are called ions. Species with overall positive charges are termed cations, while species with overall negative charges are called anions. Remember that ions are formed only when electrons move from one atom to another; a proton never moves from one atom to another. Compounds formed from positive and negative ions are called ionic compounds. Individual atoms can gain or lose electrons. When they do, they become monatomic ions. When atoms gain or lose electrons, they usually gain or lose a characteristic number of electrons and so take on a characteristic overall charge. Table 3.6 "Monatomic Ions of Various Charges" lists some common ions in terms of how many electrons they lose (making cations) or gain (making anions). There are several things to notice about the ions in Table 3.6 "Monatomic Ions of Various Charges". First, each element that forms cations is a metal, except for one (hydrogen), while each element that forms anions is a nonmetal. This is actually one of the chemical properties of metals and nonmetals: metals tend to form cations, while nonmetals tend to form anions. Second, most atoms form ions of a single characteristic charge. When sodium atoms form ions, they always form a 1+ charge, never a 2+ or 3+ or even 1− charge. Thus, if you commit the information in Table 3.6 "Monatomic Ions of Various Charges" to memory, you will always know what charges most atoms form. (In Chapter 9 "Chemical Bonds", we will discuss why atoms form the charges they do.) Third, there are some exceptions to the previous point. A few elements, all metals, can form more than one possible charge. For example, iron atoms can form 2+ cations or 3+ cations. Cobalt is another element that can form more than one possible charged ion (2+ and 3+), while lead can form 2+ or 4+ cations. Unfortunately, there is little understanding which two charges a metal atom may take, so it is best to just memorize the possible charges a particular element can have. Note the convention for indicating an ion. The magnitude of the charge is listed as a right superscript next to the symbol of the element. If the charge is a single positive or negative one, the number 1 is not written; if the magnitude of the charge is greater than 1, then the number is written before the + or − sign. An element symbol without a charge written next to it is assumed to be the uncharged atom. Naming an ion is straightforward. For a cation, simply use the name of the element and add the word ion (or if you want to be more specific, add cation) after the element’s name. So Na+ is the sodium ion; Ca2+ is the calcium ion. If the element has more than one possible charge, the value of the charge comes after the element name and before the word ion. Thus, Fe2+ is the iron two ion, while Fe3+ is the iron three ion. In print, we use roman numerals in parentheses to represent the charge on the ion, so these two iron ions would be represented as the iron(II) cation and the iron(III) cation, respectively. For a monatomic anion, use the stem of the element name and append the suffix -ide to it, and then add ion. This is similar to how we named molecular compounds. Thus, Cl− is the chloride ion, and N3− is the nitride ion. Chemical formulas for ionic compounds are called ionic formulas. A proper ionic formula has a cation and an anion in it; an ionic compound is never formed between two cations only or two anions only. The key to writing proper ionic formulas is simple: the total positive charge must balance the total negative charge. Because the charges on the ions are characteristic, sometimes we have to have more than one of a cation or an anion to balance the overall positive and negative charges. It is conventional to use the lowest ratio of ions that are needed to balance the charges. For example, consider the ionic compound between Na+ and Cl−. Each ion has a single charge, one positive and one negative, so we need only one ion of each to balance the overall charge. When writing the ionic formula, we follow two additional conventions: (1) write the formula for the cation first and the formula for the anion next, but (2) do not write the charges on the ions. Thus, for the compound between Na+ and Cl−, we have the ionic formula NaCl (Figure 3.5 "NaCl = Table Salt"). The formula Na2Cl2 also has balanced charges, but the convention is to use the lowest ratio of ions, which would be one of each. (Remember from our conventions for writing formulas that we don’t write a 1 subscript if there is only one atom of a particular element present.) For the ionic compound between magnesium cations (Mg2+) and oxide anions (O2−), again we need only one of each ion to balance the charges. By convention, the formula is MgO. For the ionic compound between Mg2+ ions and Cl− ions, we now consider the fact that the charges have different magnitudes, 2+ on the magnesium ion and 1− on the chloride ion. To balance the charges with the lowest number of ions possible, we need to have two chloride ions to balance the charge on the one magnesium ion. Rather than write the formula MgClCl, we combine the two chloride ions and write it with a 2 subscript: MgCl2. What is the formula MgCl2 telling us? There are two chloride ions in the formula. Although chlorine as an element is a diatomic molecule, Cl2, elemental chlorine is not part of this ionic compound. The chlorine is in the form of a negatively charged ion, not the neutral element. The 2 subscript is in the ionic formula because we need two Cl− ions to balance the charge on one Mg2+ ion. Naming ionic compounds is simple: combine the name of the cation and the name of the anion, in both cases omitting the word ion. Do not use numerical prefixes if there is more than one ion necessary to balance the charges. NaCl is sodium chloride, a combination of the name of the cation (sodium) and the anion (chloride). MgO is magnesium oxide. MgCl2 is magnesium chloride—not magnesium dichloride. In naming ionic compounds whose cations can have more than one possible charge, we must also include the charge, in parentheses and in roman numerals, as part of the name. Hence FeS is iron(II) sulfide, while Fe2S3 is iron(III) sulfide. Again, no numerical prefixes appear in the name. The number of ions in the formula is dictated by the need to balance the positive and negative charges. How do you know whether a formula—and by extension, a name—is for a molecular compound or for an ionic compound? Molecular compounds form between nonmetals and nonmetals, while ionic compounds form between metals and nonmetals. The periodic table (Figure 3.2 "A Simple Periodic Table") can be used to determine which elements are metals and nonmetals. There also exists a group of ions that contain more than one atom. These are called polyatomic ions. Table 3.7 "Common Polyatomic Ions" lists the formulas, charges, and names of some common polyatomic ions. Only one of them, the ammonium ion, is a cation; the rest are anions. Most of them also contain oxygen atoms, so sometimes they are referred to as oxyanions. Some of them, such as nitrate and nitrite, and sulfate and sulfite, have very similar formulas and names, so care must be taken to get the formulas and names correct. Note that the -ite polyatomic ion has one less oxygen atom in its formula than the -ate ion but with the same ionic charge. The naming of ionic compounds that contain polyatomic ions follows the same rules as the naming for other ionic compounds: simply combine the name of the cation and the name of the anion. Do not use numerical prefixes in the name if there is more than one polyatomic ion; the only exception to this is if the name of the ion itself contains a numerical prefix, such as dichromate or triiodide. Writing the formulas of ionic compounds has one important difference. If more than one polyatomic ion is needed to balance the overall charge in the formula, enclose the formula of the polyatomic ion in parentheses and write the proper numerical subscript to the right and outside the parentheses. Thus, the formula between calcium ions, Ca2+, and nitrate ions, NO3−, is properly written Ca(NO3)2, not CaNO32 or CaN2O6. Use parentheses where required. The name of this ionic compound is simply calcium nitrate. KEY TAKEAWAYS - Ions form when atoms lose or gain electrons. - Ionic compounds have positive ions and negative ions. - Ionic formulas balance the total positive and negative charges. - Ionic compounds have a simple system of naming. - Groups of atoms can have an overall charge and make ionic compounds. There is one other group of compounds that is important to us—acids—and these compounds have interesting chemical properties. Initially, we will define an acid as an ionic compound of the H+ cation dissolved in water. (We will expand on this definition in Chapter 12 "Acids and Bases".) To indicate that something is dissolved in water, we will use the phase label (aq) next to a chemical formula (where aq stands for “aqueous,” a word that describes something dissolved in water). If the formula does not have this label, then the compound is treated as a molecular compound rather than an acid. Acids have their own nomenclature system. If an acid is composed of only hydrogen and one other element, the name is hydro- + the stem of the other element + -ic acid. For example, the compound HCl(aq) is hydrochloric acid, while H2S(aq) is hydrosulfuric acid. (If these acids were not dissolved in water, the compounds would be called hydrogen chloride and hydrogen sulfide, respectively. Both of these substances are well known as molecular compounds; when dissolved in water, however, they are treated as acids.) If a compound is composed of hydrogen ions and a polyatomic anion, then the name of the acid is derived from the stem of the polyatomic ion’s name. Typically, if the anion name ends in -ate, the name of the acid is the stem of the anion name plus -ic acid; if the related anion’s name ends in -ite, the name of the corresponding acid is the stem of the anion name plus -ous acid. Table 3.9 "Names and Formulas of Acids" lists the formulas and names of a variety of acids that you should be familiar with. You should recognize most of the anions in the formulas of the acids. All acids have some similar properties. For example, acids have a sour taste; in fact, the sour taste of some of our foods, such as citrus fruits and vinegar, is caused by the presence of acids in food. Many acids react with some metallic elements to form metal ions and elemental hydrogen. Acids make certain plant pigments change colors; indeed, the ripening of some fruits and vegetables is caused by the formation or destruction of excess acid in the plant. In Chapter 12 "Acids and Bases", we will explore the chemical behavior of acids. Acids are very prevalent in the world around us. We have already mentioned that citrus fruits contain acid; among other compounds, they contain citric acid, H3C6H5O7(aq). Oxalic acid, H2C2O4(aq), is found in spinach and other green leafy vegetables. Hydrochloric acid not only is found in the stomach (stomach acid) but also can be bought in hardware stores as a cleaner for concrete and masonry. Phosphoric acid is an ingredient in some soft drinks. KEY TAKEAWAYS - An acid is a compound of the H+ ion dissolved in water. - Acids have their own naming system. - Acids have certain chemical properties that distinguish them from other compounds. Chemistry is largely about chemical changes. Indeed, if there were no chemical changes, chemistry as such would not exist! Chemical changes are a fundamental part of chemistry. Because chemical changes are so central, it may be no surprise that chemistry has developed some special ways of presenting them. A chemical reaction expresses a chemical change. For example, one chemical property of hydrogen is that it will react with oxygen to make water. We can write that as follows: hydrogen reacts with oxygen to make water We can represent this chemical change more succinctly as hydrogen + oxygen → water where the + sign means that the two substances interact chemically with each other and the → symbol implies that a chemical reaction takes place. But substances can also be represented by chemical formulas. Remembering that hydrogen and oxygen both exist as diatomic molecules, we can rewrite our chemical change as H2 + O2 → H2O This is an example of a chemical equation, which is a concise way of representing a chemical reaction. The initial substances are called reactants, and the final substances are called products. Unfortunately, it is also an incomplete chemical equation. The law of conservation of matter says that matter cannot be created or destroyed. In chemical equations, the number of atoms of each element in the reactants must be the same as the number of atoms of each element in the products. If we count the number of hydrogen atoms in the reactants and products, we find two hydrogen atoms. But if we count the number of oxygen atoms in the reactants and products, we find that there are two oxygen atoms in the reactants but only one oxygen atom in the products. What can we do? Can we change the subscripts in the formula for water so that it has two oxygen atoms in it? No; you cannot change the formulas of individual substances because the chemical formula for a given substance is characteristic of that substance. What you can do, however, is to change the number of molecules that react or are produced. We do this one element at a time, going from one side of the reaction to the other, changing the number of molecules of a substance until all elements have the same number of atoms on each side. To accommodate the two oxygen atoms as reactants, let us assume that we have two water molecules as products: H2 + O2 → 2H2O The 2 in front of the formula for water is called a coefficient. Now there is the same number of oxygen atoms in the reactants as there are in the product. But in satisfying the need for the same number of oxygen atoms on both sides of the reaction, we have also changed the number of hydrogen atoms on the product side, so the number of hydrogen atoms is no longer equal. No problem—simply go back to the reactant side of the equation and add a coefficient in front of the H2. The coefficient that works is 2: 2H2 + O2 → 2H2O There are now four hydrogen atoms in the reactants and also four atoms of hydrogen in the product. There are two oxygen atoms in the reactants and two atoms of oxygen in the product. The law of conservation of matter has been satisfied. When the reactants and products of a chemical equation have the same number of atoms of all elements present, we say that an equation is balanced. All proper chemical equations are balanced. If a substance does not have a coefficient written in front of it, it is assumed to be 1. Also, the convention is to use all whole numbers when balancing chemical equations. This sometimes makes us do a bit more “back and forth” work when balancing a chemical equation. Many chemical equations also include phase labels for the substances: (s) for solid, (ℓ) for liquid, (g) for gas, and (aq) for aqueous (i.e., dissolved in water). Special conditions, such as temperature, may also be listed above the arrow. For example, 2NaHCO3(s) −200°C→ Na2CO3(s)+CO2(g)+H2O(ℓ) KEY TAKEAWAYS - A chemical equation is a concise description of a chemical reaction. - Proper chemical equations are balanced. Up to now, we have presented chemical reactions as a topic, but we have not discussed how the products of a chemical reaction can be predicted. Here we will begin our study of certain types of chemical reactions that allow us to predict what the products of the reaction will be. A single-replacement reaction is a chemical reaction in which one element is substituted for another element in a compound, generating a new element and a new compound as products. For example, 2HCl(aq) + Zn(s) → ZnCl2(aq) + H2(g) is an example of a single-replacement reaction. The hydrogen atoms in HCl are replaced by Zn atoms, and in the process a new element—hydrogen—is formed. Another example of a single-replacement reaction is 2NaCl(aq) + F2(g) → 2NaF(s) + Cl2(g) Here the negatively charged ion changes from chloride to fluoride. A typical characteristic of a single-replacement reaction is that there is one element as a reactant and another element as a product. Not all proposed single-replacement reactions will occur between two given reactants. This is most easily demonstrated with fluorine, chlorine, bromine, and iodine. Collectively, these elements are called the halogens and are in the next-to-last column on the periodic table (see Figure 4.1 "Halogens on the Periodic Table"). The elements on top of the column will replace the elements below them on the periodic table but not the other way around. Thus, the reaction represented by CaI2(s) + Cl2(g) → CaCl2(s) + I2(s) will occur, but the reaction CaF2(s) + Br2(ℓ) → CaBr2(s) + F2(g) will not because bromine is below fluorine on the periodic table. This is just one of many ways the periodic table helps us understand chemistry. Chemical reactivity trends are easy to predict when replacing anions in simple ionic compounds—simply use their relative positions on the periodic table. However, when replacing the cations, the trends are not as straightforward. This is partly because there are so many elements that can form cations; an element in one column on the periodic table may replace another element nearby, or it may not. A list called the activity series does the same thing the periodic table does for halogens: it lists the elements that will replace elements below them in single-replacement reactions. A simple activity series is shown below. Using the activity series is similar to using the positions of the halogens on the periodic table. An element on top will replace an element below it in compounds undergoing a single-replacement reaction. Elements will not replace elements above them in compounds. A double-replacement reaction occurs when parts of two ionic compounds are exchanged, making two new compounds. A characteristic of a double-replacement equation is that there are two compounds as reactants and two different compounds as products. An example is CuCl2(aq) + 2AgNO3(aq) → Cu(NO3)2(aq) + 2AgCl(s) There are two equivalent ways of considering a double-replacement equation: either the cations are swapped, or the anions are swapped. (You cannot swap both; you would end up with the same substances you started with.) Either perspective should allow you to predict the proper products, as long as you pair a cation with an anion and not a cation with a cation or an anion with an anion. Predicting whether a double-replacement reaction occurs is somewhat more difficult than predicting a single-replacement reaction. However, there is one type of double-replacement reaction that we can predict: the precipitation reaction. A precipitation reaction occurs when two ionic compounds are dissolved in water and form a new ionic compound that does not dissolve; this new compound falls out of solution as a solid precipitate. The formation of a solid precipitate is the driving force that makes the reaction proceed. To judge whether double-replacement reactions will occur, we need to know what kinds of ionic compounds form precipitates. For this, we use solubility rules, which are general statements that predict which ionic compounds dissolve (are soluble) and which do not (are not soluble or insoluble). Table 4.1 "Some Useful Solubility Rules" lists some general solubility rules. We need to consider each ionic compound (both the reactants and the possible products) in light of the solubility rules in Table 4.1 "Some Useful Solubility Rules". If a compound is soluble, we use the (aq) label with it, indicating it dissolves. If a compound is not soluble, we use the (s) label with it and assume that it will precipitate out of solution. If everything is soluble, then no reaction will be expected. For example, consider the possible double-replacement reaction between Na2SO4 and SrCl2. The solubility rules say that all ionic sodium compounds are soluble and all ionic chloride compounds are soluble except for Ag+, Hg22+, and Pb2+, which are not being considered here. Therefore, Na2SO4 and SrCl2 are both soluble. The possible double-replacement reaction products are NaCl and SrSO4. Are these soluble? NaCl is (by the same rule we just quoted), but what about SrSO4? Compounds of the sulfate ion are generally soluble, but Sr2+ is an exception: we expect it to be insoluble—a precipitate. Therefore, we expect a reaction to occur, and the balanced chemical equation would be Na2SO4(aq) + SrCl2(aq) → 2NaCl(aq) + SrSO4(s) You would expect to see a visual change corresponding to SrSO4 precipitating out of solution Some double-replacement reactions are obvious because you can see a solid precipitate coming out of solution. KEY TAKEAWAYS - A single-replacement reaction replaces one element for another in a compound. - The periodic table or an activity series can help predict whether single-replacement reactions occur. - A double-replacement reaction exchanges the cations (or the anions) of two ionic compounds. - A precipitation reaction is a double-replacement reaction in which one product is a solid precipitate. - Solubility rules are used to predict whether some double-replacement reactions will occur. For single-replacement and double-replacement reactions, many of the reactions included ionic compounds: compounds between metals and nonmetals or compounds that contained recognizable polyatomic ions. Now we take a closer look at reactions that include ionic compounds. One important aspect about ionic compounds that differs from molecular compounds has to do with dissolving in a liquid, such as water. When molecular compounds, such as sugar, dissolve in water, the individual molecules drift apart from each other. When ionic compounds dissolve, the ions physically separate from each other. We can use a chemical equation to represent this process—for example, with NaCl: NaCl(s) −H2O→ (Na^+(aq))+(Cl^−(aq)) When NaCl dissolves in water, the ions separate and go their own way in solution; the ions are now written with their respective charges, and the (aq) phase label emphasizes that they are dissolved (Figure 4.3 "Ionic Solutions"). This process is called dissociation; we say that the ions dissociate. When an ionic compound dissociates in water, water molecules surround each ion and separate it from the rest of the solid. Each ion goes its own way in solution. All ionic compounds that dissolve behave this way. (This behavior was first suggested by the Swedish chemist Svante August Arrhenius [1859–1927] as part of his PhD dissertation in 1884. Interestingly, his PhD examination team had a hard time believing that ionic compounds would behave like this, so they gave Arrhenius a barely passing grade. Later, this work was cited when Arrhenius was awarded the Nobel Prize in Chemistry.) Keep in mind that when the ions separate, all the ions separate. Thus, when CaCl2 dissolves, the one Ca2+ ion and the two Cl− ions separate from each other: CaCl2(s) −H2O→ (Ca^2+(aq))+(Cl^−(aq))+(Cl^−(aq)) or CaCl2(s) −H2O→ (Ca^2+(aq))+(2Cl^−(aq)) That is, the two chloride ions go off on their own. They do not remain as Cl2 (that would be elemental chlorine; these are chloride ions); they do not stick together to make Cl2− or Cl22−. They become dissociated ions in their own right. Polyatomic ions also retain their overall identity when they are dissolved. When chemicals in solution react, the proper way of writing the chemical formulas of the dissolved ionic compounds is in terms of the dissociated ions, not the complete ionic formula. A complete ionic equation is a chemical equation in which the dissolved ionic compounds are written as separated ions. Solubility rules are very useful in determining which ionic compounds are dissolved and which are not. For example, when NaCl(aq) reacts with AgNO3(aq) in a double-replacement reaction to precipitate AgCl(s) and form NaNO3(aq), the complete ionic equation includes NaCl, AgNO3, and NaNO3 written as separated ions: (Na^+(aq)) + (Cl^−(aq)) + (Ag^+(aq)) + (NO3^−(aq)) → AgCl(s) + (Na^+(aq)) + (NO3^−(aq)) This is more representative of what is occurring in the solution. You may notice that in a complete ionic equation, some ions do not change their chemical form; they stay exactly the same on the reactant and product sides of the equation. For example, in (Na^+(aq)) + (Cl^−(aq)) + (Ag^+(aq)) + (NO3^−(aq)) → AgCl(s) + Na+(aq) + (NO3^−(aq)) the Ag+(aq) and Cl−(aq) ions become AgCl(s), but the Na+(aq) ions and the NO3−(aq) ions stay as Na+(aq) ions and NO3−(aq) ions. These two ions are examples of spectator ions, ions that do nothing in the overall course of a chemical reaction. They are present, but they do not participate in the overall chemistry. It is common to cancel spectator ions (something also done with algebraic quantities) on the opposite sides of a chemical equation: (Na^+(aq))+(Cl^−(aq))+(Ag^+(aq))+ (NO3^−(aq))→AgCl(s)+(Na^+(aq))+(NO3^−(aq)) What remains when the spectator ions are removed is called the net ionic equation, which represents the actual chemical change occurring between the ionic compounds: (Cl^−(aq)) + (Ag^+(aq)) → AgCl(s) It is important to reiterate that the spectator ions are still present in solution, but they don’t experience any net chemical change, so they are not written in a net ionic equation. KEY TAKEAWAYS - Ionic compounds that dissolve separate into individual ions. - Complete ionic equations show dissolved ionic solids as separated ions. - Net ionic equations show only the ions and other substances that change in a chemical reaction. Three classifications of chemical reactions will be reviewed in this section. Predicting the products in some of them may be difficult, but the reactions are still easy to recognize. A composition reaction (sometimes also called a combination reaction or a synthesis reaction) produces a single substance from multiple reactants. A single substance as a product is the key characteristic of the composition reaction. There may be a coefficient other than one for the substance, but if the reaction has only a single substance as a product, it can be called a composition reaction. In the reaction 2H2(g) + O2(g) → 2H2O(ℓ) water is produced from hydrogen and oxygen. Although there are two molecules of water being produced, there is only one substance—water—as a product. So this is a composition reaction. A decomposition reaction starts from a single substance and produces more than one substance; that is, it decomposes. One substance as a reactant and more than one substance as the products is the key characteristic of a decomposition reaction. For example, in the decomposition of sodium hydrogen carbonate (also known as sodium bicarbonate), 2NaHCO3(s) → Na2CO3(s) + CO2(g) + H2O(ℓ) sodium carbonate, carbon dioxide, and water are produced from the single substance sodium hydrogen carbonate. Composition and decomposition reactions are difficult to predict; however, they should be easy to recognize. A combustion reaction occurs when a reactant combines with oxygen, many times from the atmosphere, to produce oxides of all other elements as products; any nitrogen in the reactant is converted to elemental nitrogen, N2. Many reactants, called fuels, contain mostly carbon and hydrogen atoms, reacting with oxygen to produce CO2 and H2O. For example, the balanced chemical equation for the combustion of methane, CH4, is as follows: CH4 + 2O2 → CO2 + 2H2O Kerosene can be approximated with the formula C12H26, and its combustion equation is 2C12H26 + 37O2 → 24CO2 + 26H2O Sometimes fuels contain oxygen atoms, which must be counted when balancing the chemical equation. One common fuel is ethanol, C2H5OH, whose combustion equation is C2H5OH + 3O2 → 2CO2 + 3H2O If nitrogen is present in the original fuel, it is converted to N2, not to a nitrogen-oxygen compound. Thus, for the combustion of the fuel dinitroethylene, whose formula is C2H2N2O4, we have 2C2H2N2O4 + O2 → 4CO2 + 2H2O + 2N2 KEY TAKEAWAYS - A composition reaction produces a single substance from multiple reactants. - A decomposition reaction produces multiple products from a single reactant. - Combustion reactions are the combination of some compound with oxygen to make oxides of the other elements as products (although nitrogen atoms react to make N2). In Chapter 3 "Atoms, Molecules, and Ions", Section 3.5 "Acids", we defined an acid as an ionic compound that contains H+ as the cation. This is slightly incorrect, but until additional concepts were developed, a better definition needed to wait. Now we can redefine an acid: an acid is any compound that increases the amount of hydrogen ion (H+) in an aqueous solution. The chemical opposite of an acid is a base. The equivalent definition of a base is that a base is a compound that increases the amount of hydroxide ion (OH−) in an aqueous solution. These original definitions were proposed by Arrhenius (the same person who proposed ion dissociation) in 1884, so they are referred to as the Arrhenius definition of an acid and a base, respectively. You may recognize that, based on the description of a hydrogen atom, an H+ ion is a hydrogen atom that has lost its lone electron; that is, H+ is simply a proton. Do we really have bare protons moving about in aqueous solution? No. What is more likely is that the H+ ion has attached itself to one (or more) water molecule(s). To represent this chemically, we define the hydronium ion as H3O+, which represents an additional proton attached to a water molecule. We use the hydronium ion as the more logical way a hydrogen ion appears in an aqueous solution, although in many chemical reactions H+ and H3O+ are treated equivalently. The reaction of an acid and a base is called a neutralization reaction. Although acids and bases have their own unique chemistries, the acid and base cancel each other’s chemistry to produce a rather innocuous substance—water. In fact, the general reaction between an acid and a base is acid + base → water + salt where the term salt is generally used to define any ionic compound (soluble or insoluble) that is formed from a reaction between an acid and a base. (In chemistry, the word salt refers to more than just table salt.) For example, the balanced chemical equation for the reaction between HCl(aq) and KOH(aq) is HCl(aq) + KOH(aq) → H2O(ℓ) + KCl(aq) where the salt is KCl. By counting the number of atoms of each element, we find that only one water molecule is formed as a product. However, in the reaction between HCl(aq) and Mg(OH)2(aq), additional molecules of HCl and H2O are required to balance the chemical equation: 2HCl(aq) + Mg(OH)2(aq) → 2H2O(ℓ) + MgCl2(aq) Here, the salt is MgCl2. (This is one of several reactions that take place when a type of antacid—a base—is used to treat stomach acid.) Neutralization reactions are one type of chemical reaction that proceeds even if one reactant is not in the aqueous phase. For example, the chemical reaction between HCl(aq) and Fe(OH)3(s) still proceeds according to the equation 3HCl(aq) + Fe(OH)3(s) → 3H2O(ℓ) + FeCl3(aq) even though Fe(OH)3 is not soluble. When one realizes that Fe(OH)3(s) is a component of rust, this explains why some cleaning solutions for rust stains contain acids—the neutralization reaction produces products that are soluble and wash away. (Washing with acids like HCl is one way to remove rust and rust stains, but HCl must be used with caution!) Complete and net ionic reactions for neutralization reactions will depend on whether the reactants and products are soluble, even if the acid and base react. For example, in the reaction of HCl(aq) and NaOH(aq), HCl(aq) + NaOH(aq) → H2O(ℓ) + NaCl(aq) the complete ionic reaction is (H^+(aq))+(Cl^−(aq))+( Na^+(aq))+(OH^−(aq))→ H2O(ℓ) +(Na^+(aq) )+(Cl^−(aq)) The Na+(aq) and Cl−(aq) ions are spectator ions, so we can remove them to have (H^+(aq)) + (OH^−(aq)) → H2O(ℓ) as the net ionic equation. If we wanted to write this in terms of the hydronium ion, H3O+(aq), we would write it as (H3O^+(aq)) + (OH^−(aq)) → 2H2O(ℓ) With the exception of the introduction of an extra water molecule, these two net ionic equations are equivalent. However, for the reaction between HCl(aq) and Cr(OH)2(s), because chromium(II) hydroxide is insoluble, we cannot separate it into ions for the complete ionic equation: (2H^+(aq)) + (2Cl^−(aq)) + Cr(OH)2(s) → 2H2O(ℓ) + (Cr^2+(aq)) + (2Cl^−(aq)) The chloride ions are the only spectator ions here, so the net ionic equation is (2H^+(aq)) + Cr(OH)2(s) → 2H2O(ℓ) + (Cr^2+(aq)) KEY TAKEAWAYS - The Arrhenius definition of an acid is a substance that increases the amount of H+ in an aqueous solution. - The Arrhenius definition of a base is a substance that increases the amount of OH− in an aqueous solution. - Neutralization is the reaction of an acid and a base, which forms water and a salt. - Net ionic equations for neutralization reactions may include solid acids, solid bases, solid salts, and water. Consider this chemical reaction: 2Na(s) + Cl2(g) → 2NaCl The reactants are elements, and it is assumed that they are electrically neutral; they have the same number of electrons as protons. The product, however, is ionic; it is composed of Na+ and Cl− ions. Somehow, the individual sodium atoms as reactants had to lose an electron to make the Na+ ion, while the chlorine atoms as reactants had to each gain an electron to become the Cl− ion. This reaction involves the transfer of electrons between atoms. In reality, electrons are lost by some atoms and gained by other atoms simultaneously. However, mentally we can separate the two processes. Oxidation is defined as the loss of one or more electrons by an atom. Reduction is defined as the gain of one or more electrons by an atom. In reality, oxidation and reduction always occur together; it is only mentally that we can separate them. Chemical reactions that involve the transfer of electrons are called oxidation-reduction (or redox) reactions. Redox reactions require that we keep track of the electrons assigned to each atom in a chemical reaction. How do we do that? We use an artificial count called the oxidation number to keep track of electrons in atoms. Oxidation numbers are assigned to atoms based on a series of rules. Oxidation numbers are not necessarily equal to the charge on the atom; we must keep the concepts of charge and oxidation numbers separate. The rules for assigning oxidation numbers to atoms are as follows: 1. Atoms in their elemental state are assigned an oxidation number of 0. 2. Atoms in monatomic (i.e., one-atom) ions are assigned an oxidation number equal to their charge. Oxidation numbers are usually written with the sign first, then the magnitude, which differentiates them from charges. 3. In compounds, fluorine is assigned a −1 oxidation number; oxygen is usually assigned a −2 oxidation number (except in peroxide compounds [where it is −1] and in binary compounds with fluorine [where it is positive]); and hydrogen is usually assigned a +1 oxidation number (except when it exists as the hydride ion, H−, in which case rule 2 prevails). 4. In compounds, all other atoms are assigned an oxidation number so that the sum of the oxidation numbers on all the atoms in the species equals the charge on the species (which is zero if the species is neutral). Let us work through a few examples for practice. In H2, both hydrogen atoms have an oxidation number of 0, by rule 1. In NaCl, sodium has an oxidation number of +1, while chlorine has an oxidation number of −1, by rule 2. In H2O, the hydrogen atoms each have an oxidation number of +1, while the oxygen has an oxidation number of −2, even though hydrogen and oxygen do not exist as ions in this compound as per rule 3. By contrast, by rule 3 in hydrogen peroxide (H2O2), each hydrogen atom has an oxidation number of +1, while each oxygen atom has an oxidation number of −1. We can use rule 4 to determine oxidation numbers for the atoms in SO2. Each oxygen atom has an oxidation number of −2; for the sum of the oxidation numbers to equal the charge on the species (which is zero), the sulfur atom is assigned an oxidation number of +4. Does this mean that the sulfur atom has a 4+ charge on it? No, it only means that the sulfur atom is assigned a +4 oxidation number by our rules of apportioning electrons among the atoms in a compound. All redox reactions occur with a simultaneous change in the oxidation numbers of some atoms. At least two elements must change their oxidation numbers. When an oxidation number of an atom is increased in the course of a redox reaction, that atom is being oxidized. When an oxidation number of an atom is decreased in the course of a redox reaction, that atom is being reduced. Oxidation and reduction are thus also defined in terms of increasing or decreasing oxidation numbers, respectively. In this introduction to oxidation-reduction reactions, we are using straightforward examples. However, oxidation reactions can become quite complex; the following equation represents a redox reaction: To demonstrate that this is a redox reaction, the oxidation numbers of the species being oxidized and reduced are listed; can you determine what is being oxidized and what is being reduced? This is also an example of a net ionic reaction; spectator ions that do not change oxidation numbers are not displayed in the equation. KEY TAKEAWAYS - Oxidation-reduction (redox) reactions involve the transfer of electrons from one atom to another. - Oxidation numbers are used to keep track of electrons in atoms. - There are rules for assigning oxidation numbers to atoms. - Oxidation is an increase of oxidation number (a loss of electrons); reduction is a decrease in oxidation number (a gain of electrons). We have already established that quantities are important in science, especially in chemistry. It is important to make accurate measurements of a variety of quantities when performing experiments. However, it is also important to be able to relate one measured quantity to another, unmeasured quantity. In this chapter, we will consider how we manipulate quantities to relate them to each other. Consider a classic recipe for pound cake: 1 pound of eggs, 1 pound of butter, 1 pound of flour, and 1 pound of sugar. (That’s why it’s called “pound cake.”) If you have 4 pounds of butter, how many pounds of sugar, flour, and eggs do you need? You would need 4 pounds each of sugar, flour, and eggs. Now suppose you have 1.00 g H2. If the chemical reaction follows the balanced chemical equation 2H2(g) + O2(g) → 2H2O(ℓ) then what mass of oxygen do you need to make water? Curiously, this chemical reaction question is very similar to the pound cake question. Both of them involve relating a quantity of one substance to a quantity of another substance or substances. The relating of one chemical substance to another using a balanced chemical reaction is called stoichiometry. Using stoichiometry is a fundamental skill in chemistry; it greatly broadens your ability to predict what will occur and, more importantly, how much is produced. Let us consider a more complicated example. A recipe for pancakes calls for 2 cups (c) of pancake mix, 1 egg, and 1/2 c of milk. We can write this in the form of a chemical equation: 2 c mix + 1 egg + 1/2 c milk → 1 batch of pancakes If you have 9 c of pancake mix, how many eggs and how much milk do you need? It might take a little bit of work, but eventually you will find you need 4½ eggs and 2¼ c milk. How can we formalize this? We can make a conversion factor using our original recipe and use that conversion factor to convert from a quantity of one substance to a quantity of another substance, similar to the way we constructed a conversion factor between feet and yards in Chapter 2 "Measurements". Because one recipe’s worth of pancakes requires 2 c of pancake mix, 1 egg, and 1/2 c of milk, we actually have the following mathematical relationships that relate these quantities: 2 c pancake mix ⇔ 1 egg ⇔ 1/2 c milk where ⇔ is the mathematical symbol for “is equivalent to.” This does not mean that 2 c of pancake mix equal 1 egg. However, as far as this recipe is concerned, these are the equivalent quantities needed for a single recipe of pancakes. So, any possible quantities of two or more ingredients must have the same numerical ratio as the ratios in the equivalence. We can deal with these equivalences in the same way we deal with equalities in unit conversions: we can make conversion factors that essentially equal 1. For example, to determine how many eggs we need for 9 c of pancake mix, we construct the conversion factor 1 egg/2 c pancake mix This conversion factor is, in a strange way, equivalent to 1 because the recipe relates the two quantities. Starting with our initial quantity and multiplying by our conversion factor, 9 c pancake mix×(1 egg/2 c pancake mix)=4.5 eggs Note how the units cups pancake mix canceled, leaving us with units of eggs. This is the formal, mathematical way of getting our amounts to mix with 9 c of pancake mix. We can use a similar conversion factor for the amount of milk: 9 c pancake mix×(1/2 c milk/2 c pancake mix)=2.25 c milk Again, units cancel, and new units are introduced. A balanced chemical equation is nothing more than a recipe for a chemical reaction. The difference is that a balanced chemical equation is written in terms of atoms and molecules, not cups, pounds, and eggs. For example, consider the following chemical equation: 2H2(g) + O2(g) → 2H2O(ℓ) We can interpret this as, literally, “two hydrogen molecules react with one oxygen molecule to make two water molecules.” That interpretation leads us directly to some equivalences, just as our pancake recipe did: 2H2 molecules ⇔ 1O2 molecule ⇔ 2H2O molecules These equivalences allow us to construct conversion factors: 2 molecules H2/1 molecule O2 2 molecules H2/2 molecules H2 O1 molecule O2/2 molecules H2O and so forth. These conversions can be used to relate quantities of one substance to quantities of another. For example, suppose we need to know how many molecules of oxygen are needed to react with 16 molecules of H2. As we did with converting units, we start with our given quantity and use the appropriate conversion factor: 16 molecules H2×(1 molecule O2/2 molecules H2)=8 molecules O2 Note how the unit molecules H2 cancels algebraically, just as any unit does in a conversion like this. The conversion factor came directly from the coefficients in the balanced chemical equation. This is another reason why a properly balanced chemical equation is important. Chemical equations also allow us to make conversions regarding the number of atoms in a chemical reaction because a chemical formula lists the number of atoms of each element in a compound. The formula H2O indicates that there are two hydrogen atoms and one oxygen atom in each molecule, and these relationships can be used to make conversion factors: 2 atoms H/1 molecule H2O 1 molecule H2O/1 atom O Conversion factors like this can also be used in stoichiometry calculations. KEY TAKEAWAY - Quantities of substances can be related to each other using balanced chemical equations. So far, we have been talking about chemical substances in terms of individual atoms and molecules. Yet we don’t typically deal with substances an atom or a molecule at a time; we work with millions, billions, and trillions of atoms and molecules at a time. What we need is a way to deal with macroscopic, rather than microscopic, amounts of matter. We need a unit of amount that relates quantities of substances on a scale that we can interact with. Chemistry uses a unit called mole. A mole (mol) is a number of things equal to the number of atoms in exactly 12 g of carbon-12. Experimental measurements have determined that this number is very large: 1 mol = 6.02214179 × 10^23 things Understand that a mole means a number of things, just like a dozen means a certain number of things—twelve, in the case of a dozen. But a mole is a much larger number of things. These things can be atoms, or molecules, or eggs; however, in chemistry, we usually use the mole to refer to the amounts of atoms or molecules. Although the number of things in a mole is known to eight decimal places, it is usually fine to use only two or three decimal places in calculations. The numerical value of things in a mole is often called Avogadro’s number (NA), which is also known as the Avogadro constant, after Amadeo Avogadro, an Italian chemist who first proposed its importance. How big is a mole? It is very large. Suppose you had a mole of dollar bills that need to be counted. If everyone on earth (about 6 billion people) counted one bill per second, it would take about 3.2 million years to count all the bills. A mole of sand would fill a cube about 32 km on a side. A mole of pennies stacked on top of each other would have about the same diameter as our galaxy, the Milky Way. A mole is a lot of things—but atoms and molecules are very tiny. One mole of carbon atoms would make a cube that is 1.74 cm on a side, small enough to carry in your pocket. Why is the mole unit so important? It represents the link between the microscopic and the macroscopic, especially in terms of mass. A mole of a substance has the same mass in grams as one unit (atom or molecules) has in atomic mass units. The mole unit allows us to express amounts of atoms and molecules in visible amounts that we can understand. For example, we already know that, by definition, a mole of carbon has a mass of exactly 12 g. This means that exactly 12 g of C has 6.022 × 10^23 atoms: 12 g C = 6.022 × 10^23 atoms C We can use this equality as a conversion factor between the number of atoms of carbon and the number of grams of carbon. How many grams are there, say, in 1.50 × 10^25 atoms of carbon? This is a one-step conversion: 1.50 × 10^25 atoms C × (12.0000 g C /(6.022 × 10^23 atoms C))=299 g C But it also goes beyond carbon. Previously we defined atomic and molecular masses as the number of atomic mass units per atom or molecule. Now we can do so in terms of grams. The atomic mass of an element is the number of grams in 1 mol of atoms of that element, while the molecular mass of a compound is the number of grams in 1 mol of molecules of that compound. Sometimes these masses are called molar masses to emphasize the fact that they are the mass for 1 mol of things. (The term molar is the adjective form of mole and has nothing to do with teeth.) Here are some examples. The mass of a hydrogen atom is 1.0079 u; the mass of 1 mol of hydrogen atoms is 1.0079 g. Elemental hydrogen exists as a diatomic molecule, H2. One molecule has a mass of 1.0079 + 1.0079 = 2.0158 u, while 1 mol H2 has a mass of 2.0158 g. A molecule of H2O has a mass of about 18.01 u; 1 mol H2O has a mass of 18.01 g. A single unit of NaCl has a mass of 58.45 u; NaCl has a molar mass of 58.45 g. In each of these moles of substances, there are 6.022 × 1023 units: 6.022 × 1023 atoms of H, 6.022 × 1023 molecules of H2 and H2O, 6.022 × 1023 units of NaCl ions. These relationships give us plenty of opportunities to construct conversion factors for simple calculations. Knowing the molar mass of a substance, we can calculate the number of moles in a certain mass of a substance and vice versa, as these examples illustrate. The molar mass is used as the conversion factor. Other conversion factors can be combined with the definition of mole—density, for example. KEY TAKEAWAYS - The mole is a key unit in chemistry. - The molar mass of a substance, in grams, is numerically equal to one atom’s or molecule’s mass in atomic mass units. Consider this balanced chemical equation: 2H2 + O2 → 2H2O We interpret this as “two molecules of hydrogen react with one molecule of oxygen to make two molecules of water.” The chemical equation is balanced as long as the coefficients are in the ratio 2:1:2. For instance, this chemical equation is also balanced: 100H2 + 50O2 → 100H2O This equation is not conventional—because convention says that we use the lowest ratio of coefficients—but it is balanced. So is this chemical equation: 5,000H2 + 2,500O2 → 5,000H2O Again, this is not conventional, but it is still balanced. Suppose we use a much larger number: 12.044 × 10^23 H2 + 6.022 × 10^23 O2 → 12.044 × 10^23 H2O These coefficients are also in the ratio of 2:1:2. But these numbers are related to the number of things in a mole: the first and last numbers are two times Avogadro’s number, while the second number is Avogadro’s number. That means that the first and last numbers represent 2 mol, while the middle number is just 1 mol. Well, why not just use the number of moles in balancing the chemical equation? 2H2 + O2 → 2H2O is the same balanced chemical equation we started with! What this means is that chemical equations are not just balanced in terms of molecules; they are also balanced in terms of moles. We can just as easily read this chemical equation as “two moles of hydrogen react with one mole of oxygen to make two moles of water.” All balanced chemical reactions are balanced in terms of moles. In Chapter 4 "Chemical Reactions and Equations", Section 4.1 "The Chemical Equation", we stated that a chemical equation is simply a recipe for a chemical reaction. As such, chemical equations also give us equivalences—equivalences between the reactants and the products. However, now we understand that these equivalences are expressed in terms of moles. Consider the chemical equation 2H2 + O2 → 2H2O This chemical reaction gives us the following equivalences: 2 mol H2 ⇔ 1 mol O2 ⇔ 2 mol H2O Any two of these quantities can be used to construct a conversion factor that lets us relate the number of moles of one substance to an equivalent number of moles of another substance. If, for example, we want to know how many moles of oxygen will react with 17.6 mol of hydrogen, we construct a conversion factor between 2 mol of H2 and 1 mol of O2 and use it to convert from moles of one substance to moles of another: 17.6 mol H2 × (1 mol O2/2 mol H2)=8.80 mol O2 Note how the mol H2 unit cancels, and mol O2 is the new unit introduced. This is an example of a mole-mole calculation, when you start with moles of one substance and convert to moles of another substance by using the balanced chemical equation. The example may seem simple because the numbers are small, but numbers won’t always be so simple! It is important to reiterate that balanced chemical equations are balanced in terms of moles. Not grams, kilograms, or liters—but moles. Any stoichiometry problem will likely need to work through the mole unit at some point, especially if you are working with a balanced chemical reaction. KEY TAKEAWAYS - Balanced chemical reactions are balanced in terms of moles. - A balanced chemical reaction gives equivalences in moles that allow stoichiometry calculations to be performed. Mole-mole calculations are not the only type of calculations that can be performed using balanced chemical equations. Recall that the molar mass can be determined from a chemical formula and used as a conversion factor. We can add that conversion factor as another step in a calculation to make a mole-mass calculation, where we start with a given number of moles of a substance and calculate the mass of another substance involved in the chemical equation, or vice versa. For example, suppose we have the balanced chemical equation 2Al + 3Cl2 → 2AlCl3 Suppose we know we have 123.2 g of Cl2. How can we determine how many moles of AlCl3 we will get when the reaction is complete? First and foremost, chemical equations are not balanced in terms of grams; they are balanced in terms of moles. So to use the balanced chemical equation to relate an amount of Cl2 to an amount of AlCl3, we need to convert the given amount of Cl2 into moles. We know how to do this by simply using the molar mass of Cl2 as a conversion factor. The molar mass of Cl2 (which we get from the atomic mass of Cl from the periodic table) is 70.90 g/mol. We must invert this fraction so that the units cancel properly: 123.2 g Cl2 × (1 mol Cl2/70.90 g Cl2)=1.738 mol Cl2 Now that we have the quantity in moles, we can use the balanced chemical equation to construct a conversion factor that relates the number of moles of Cl2 to the number of moles of AlCl3. The numbers in the conversion factor come from the coefficients in the balanced chemical equation: 2 mol AlCl3/3 mol Cl2 Using this conversion factor with the molar quantity we calculated above, we get 1.738 mol Cl2 × (2 mol AlCl3/3 mol Cl2)=1.159 mol AlCl3 So, we will get 1.159 mol of AlCl3 if we react 123.2 g of Cl2. In this last example, we did the calculation in two steps. However, it is mathematically equivalent to perform the two calculations sequentially on one line: 123.2 g Cl2 × (1 mol Cl2/70.90 g Cl2) × (2 mol AlCl3/3 mol Cl2)=1.159 mol AlCl3 The units still cancel appropriately, and we get the same numerical answer in the end. Sometimes the answer may be slightly different from doing it one step at a time because of rounding of the intermediate answers, but the final answers should be effectively the same. A variation of the mole-mass calculation is to start with an amount in moles and then determine an amount of another substance in grams. The steps are the same but are performed in reverse order. It should be a trivial task now to extend the calculations to mass-mass calculations, in which we start with a mass of some substance and end with the mass of another substance in the chemical reaction. For this type of calculation, the molar masses of two different substances must be used—be sure to keep track of which is which. Again, however, it is important to emphasize that before the balanced chemical reaction is used, the mass quantity must first be converted to moles. Then the coefficients of the balanced chemical reaction can be used to convert to moles of another substance, which can then be converted to a mass. For example, let us determine the number of grams of SO3 that can be produced by the reaction of 45.3 g of SO2 and O2: 2SO2(g) + O2(g) → 2SO3(g) First, we convert the given amount, 45.3 g of SO2, to moles of SO2 using its molar mass (64.06 g/mol): 45.3 g SO2 × (1 mol SO2/64.06 g SO2)=0.707 mol SO2 Second, we use the balanced chemical reaction to convert from moles of SO2 to moles of SO3: 0.707 mol SO2 × (2 mol SO3/2 mol SO2)=0.707 mol SO3 Finally, we use the molar mass of SO3 (80.06 g/mol) to convert to the mass of SO3: 0.707 mol SO3 × (80.06 g SO3/1 mol SO3)=56.6 g SO3 We can also perform all three steps sequentially, writing them on one line as 45.3 g SO2 × (1 mol SO2/64.06 g SO2) × (2 mol SO3/2 mol SO2) × (80.06 g SO3/1 mol SO3)=56.6 g SO3 We get the same answer. Note how the initial and all the intermediate units cancel, leaving grams of SO3, which is what we are looking for, as our final answer. KEY TAKEAWAYS - Mole quantities of one substance can be related to mass quantities using a balanced chemical equation. - Mass quantities of one substance can be related to mass quantities using a balanced chemical equation. - In all cases, quantities of a substance must be converted to moles before the balanced chemical equation can be used to convert to moles of another substance. In all the previous calculations we have performed involving balanced chemical equations, we made two assumptions: (1) the reaction goes exactly as written, and (2) the reaction proceeds completely. In reality, such things as side reactions occur that make some chemical reactions rather messy. For example, in the actual combustion of some carbon-containing compounds, such as methane, some CO is produced as well as CO2. However, we will continue to ignore side reactions, unless otherwise noted. The second assumption, that the reaction proceeds completely, is more troublesome. Many chemical reactions do not proceed to completion as written, for a variety of reasons (some of which we will consider in Chapter 13 "Chemical Equilibrium"). When we calculate an amount of product assuming that all the reactant reacts, we calculate the theoretical yield, an amount that is theoretically produced as calculated using the balanced chemical reaction. In many cases, however, this is not what really happens. In many cases, less—sometimes much less—of a product is made during the course of a chemical reaction. The amount that is actually produced in a reaction is called the actual yield. By definition, the actual yield is less than or equal to the theoretical yield. If it is not, then an error has been made. Both theoretical yields and actual yields are expressed in units of moles or grams. It is also common to see something called a percent yield. The percent yield is a comparison between the actual yield and the theoretical yield and is defined as percent yield=(actual yield/theoretical yield) × 100% It does not matter whether the actual and theoretical yields are expressed in moles or grams, as long as they are expressed in the same units. However, the percent yield always has units of percent. Proper percent yields are between 0% and 100%—again, if percent yield is greater than 100%, an error has been made. KEY TAKEAWAYS - Theoretical yield is what you calculate the yield will be using the balanced chemical reaction. - Actual yield is what you actually get in a chemical reaction. - Percent yield is a comparison of the actual yield with the theoretical yield. One additional assumption we have made about chemical reactions—in addition to the assumption that reactions proceed all the way to completion—is that all the reactants are present in the proper quantities to react to products. This is not always the case. Consider Figure 5.2 "Making Water". Here we are taking hydrogen atoms and oxygen atoms (left) to make water molecules (right). However, there are not enough oxygen atoms to use up all the hydrogen atoms. We run out of oxygen atoms and cannot make any more water molecules, so the process stops when we run out of oxygen atoms. A similar situation exists for many chemical reactions: you usually run out of one reactant before all of the other reactant has reacted. The reactant you run out of is called the limiting reagent; the other reactant or reactants are considered to be in excess. A crucial skill in evaluating the conditions of a chemical process is to determine which reactant is the limiting reagent and which is in excess. The key to recognizing which reactant is the limiting reagent is based on a mole-mass or mass-mass calculation: whichever reactant gives the lesser amount of product is the limiting reagent. What we need to do is determine an amount of one product (either moles or mass) assuming all of each reactant reacts. Whichever reactant gives the least amount of that particular product is the limiting reagent. It does not matter which product we use, as long as we use the same one each time. It does not matter whether we determine the number of moles or grams of that product; however, we will see shortly that knowing the final mass of product can be useful. For example, consider this reaction: 4As(s) + 3O2(g) → 2As2O3(s) Suppose we start a reaction with 50.0 g of As and 50.0 g of O2. Which one is the limiting reagent? We need to perform two mole-mass calculations, each assuming that each reactant reacts completely. Then we compare the amount of the product produced by each and determine which is less. The calculations are as follows: 50.0 g As × (1 mol As/74.92 g As) ×( 2 mol As2O3/4 mol As)=0.334 mol As2O3 50.0 g O2 × (1 mol O2/ 32.00 g O2) × (2 mol As2O3/3 mol O2)=1.04 mol As2O3 Comparing these two answers, it is clear that 0.334 mol of As2O3 is less than 1.04 mol of As2O3, so arsenic is the limiting reagent. If this reaction is performed under these initial conditions, the arsenic will run out before the oxygen runs out. We say that the oxygen is “in excess.” Identifying the limiting reagent, then, is straightforward. However, there are usually two associated questions: (1) what mass of product (or products) is then actually formed? and (2) what mass of what reactant is left over? The first question is straightforward to answer: simply perform a conversion from the number of moles of product formed to its mass, using its molar mass. For As2O3, the molar mass is 197.84 g/mol; knowing that we will form 0.334 mol of As2O3 under the given conditions, we will get 0.334 mol As2O3 × (197.84 g As2O3/1 mol As2O3)=66.1 g As2O3 The second question is somewhat more convoluted to answer. First, we must do a mass-mass calculation relating the limiting reagent (here, As) to the other reagent (O2). Once we determine the mass of O2 that reacted, we subtract that from the original amount to determine the amount left over. According to the mass-mass calculation, 50.0 g As × (1 mol As/74.92 g As)×(3 mol O2/4 mol As)×(32.00 g O2/1 mol O2)=16.0 g O2 reacted Because we reacted 16.0 g of our original O2, we subtract that from the original amount, 50.0 g, to get the mass of O2 remaining: 50.0 g O2 − 16.0 g O2 reacted = 34.0 g O2 left over You must remember to perform this final subtraction to determine the amount remaining; a common error is to report the 16.0 g as the amount remaining. KEY TAKEAWAYS - The limiting reagent is that reactant that produces the least amount of product. - Mass-mass calculations can determine how much product is produced and how much of the other reactants remain. Of the three basic phases of matter—solids, liquids, and gases—only one of them has predictable physical properties: gases. In fact, the study of the properties of gases was the beginning of the development of modern chemistry from its alchemical roots. The interesting thing about some of these properties is that they are independent of the identity of the gas. That is, it doesn’t matter if the gas is helium gas, oxygen gas, or sulfur vapors; some of their behavior is predictable and, as we will find, very similar. In this chapter, we will review some of the common behaviors of gases. Let us start by reviewing some properties of gases. Gases have no definite shape or volume; they tend to fill whatever container they are in. They can compress and expand, sometimes to a great extent. Gases have extremely low densities, one-thousandth or less the density of a liquid or solid. Combinations of gases tend to mix together spontaneously; that is, they form solutions. Air, for example, is a solution of mostly nitrogen and oxygen. Any understanding of the properties of gases must be able to explain these characteristics. Gases were among the first substances studied in terms of the modern scientific method, which was developed in the 1600s. It did not take long to recognize that gases all shared certain physical behaviors, suggesting that all gases could be described by one all-encompassing theory. Today, that theory is the kinetic theory of gases. It is based on the following statements: 1. Gases consist of tiny particles of matter that are in constant motion. 2. Gas particles are constantly colliding with each other and the walls of a container. These collisions are elastic; that is, there is no net loss of energy from the collisions. 3. Gas particles are separated by large distances, with the size of a gas particle tiny compared to the distances that separate them. 4. There are no interactive forces (i.e., attraction or repulsion) between the particles of a gas. 5. The average speed of gas particles is dependent on the temperature of the gas. This model of gases explains some of the physical properties of gases. Because most of a gas is empty space, a gas has a low density and can expand or contract under the appropriate influence. The fact that gas particles are in constant motion means that two or more gases will always mix, as the particles from the individual gases move and collide with each other. An ideal gas is a gas that exactly follows the statements of the kinetic theory. Unfortunately, real gases are not ideal. Many gases deviate slightly from agreeing perfectly with the kinetic theory of gases. However, most gases adhere to the statements so well that the kinetic theory of gases is well accepted by the scientific community. KEY TAKEAWAYS - The physical behavior of gases is explained by the kinetic theory of gases. - An ideal gas adheres exactly to the kinetic theory of gases. The kinetic theory of gases indicates that gas particles are always in motion and are colliding with other particles and the walls of the container holding them. Although collisions with container walls are elastic (i.e., there is no net energy gain or loss because of the collision), a gas particle does exert a force on the wall during the collision. The accumulation of all these forces distributed over the area of the walls of the container causes something we call pressure. Pressure (P) is defined as the force of all the gas particle/wall collisions divided by the area of the wall: pressure=force/area All gases exert pressure; it is one of the fundamental measurable quantities of this phase of matter. Even our atmosphere exerts pressure—in this case, the gas is being “held in” by the earth’s gravity, rather than the gas being in a container. The pressure of the atmosphere is about 14.7 pounds of force for every square inch of surface area: 14.7 lb/in2. Pressure has a variety of units. The formal, SI-approved unit of pressure is the pascal (Pa), which is defined as 1 N/m2 (one newton of force over an area of one square meter). However, this is usually too small in magnitude to be useful. A common unit of pressure is the atmosphere (atm), which was originally defined as the average atmospheric pressure at sea level. However, “average atmospheric pressure at sea level” is difficult to pinpoint because of atmospheric pressure variations. A more reliable and common unit is millimeters of mercury (mmHg), which is the amount of pressure exerted by a column of mercury exactly 1 mm high. An equivalent unit is the torr, which equals 1 mmHg. (The torr is named after Evangelista Torricelli, a seventeenth-century Italian scientist who invented the mercury barometer.) With these definitions of pressure, the atmosphere unit is redefined: 1 atm is defined as exactly 760 mmHg, or 760 torr. We thus have the following equivalences: 1 atm=760 mmHg=760 torr We can use these equivalences as with any equivalences—to perform conversions from one unit to another. Relating these to the formal SI unit of pressure, 1 atm = 101,325 Pa. KEY TAKEAWAYS - Pressure is a force exerted over an area. - Pressure has several common units that can be converted. When seventeenth-century scientists began studying the physical properties of gases, they noticed some simple relationships between some of the measurable properties of the gas. Take pressure (P) and volume (V), for example. Scientists noted that for a given amount of a gas (usually expressed in units of moles [n]), if the temperature (T) of the gas was kept constant, pressure and volume were related: As one increases, the other decreases. As one decreases, the other increases. We say that pressure and volume are inversely related. There is more to it, however: pressure and volume of a given amount of gas at constant temperature are numerically related. If you take the pressure value and multiply it by the volume value, the product is a constant for a given amount of gas at a constant temperature: P × V = constant at constant n and T If either volume or pressure changes while amount and temperature stay the same, then the other property must change so that the product of the two properties still equals that same constant. That is, if the original conditions are labeled P1 and V1 and the new conditions are labeled P2 and V2, we have P1V1 = constant = P2V2 where the properties are assumed to be multiplied together. Leaving out the middle part, we have simply P1V1 = P2V2 at constant n and T This equation is an example of a gas law. A gas law is a simple mathematical formula that allows you to model, or predict, the behavior of a gas. This particular gas law is called Boyle’s law, after the English scientist Robert Boyle, who first announced it in 1662. Figure 6.2 "Boyle’s Law" shows two representations of how Boyle’s law works. Boyle’s law is an example of a second type of mathematical problem we see in chemistry—one based on a mathematical formula. Tactics for working with mathematical formulas are different from tactics for working with conversion factors. First, most of the questions you will have to answer using formulas are word-type questions, so the first step is to identify what quantities are known and assign them to variables. Second, in most formulas, some mathematical rearrangements (i.e., algebra) must be performed to solve for an unknown variable. The rule is that to find the value of the unknown variable, you must mathematically isolate the unknown variable by itself and in the numerator of one side of the equation. Finally, units must be consistent. For example, in Boyle’s law there are two pressure variables; they must have the same unit. There are also two volume variables; they also must have the same unit. In most cases, it won’t matter what the unit is, but the unit must be the same on both sides of the equation. As mentioned, you can use any units for pressure or volume, but both pressures must be expressed in the same units, and both volumes must be expressed in the same units. There are other measurable characteristics of a gas. One of them is temperature (T). Perhaps one can vary the temperature of a gas sample and note what effect it has on the other properties of the gas. Early scientists did just this, discovering that if the amount of a gas and its pressure are kept constant, then changing the temperature changes the volume (V). As temperature increases, volume increases; as temperature decreases, volume decreases. We say that these two characteristics are directly related. A mathematical relationship between V and T should be possible except for one thought: what temperature scale should we use? We know from Chapter 2 "Measurements" that science uses several possible temperature scales. Experiments show that the volume of a gas is related to its absolute temperature in Kelvin, not its temperature in degrees Celsius. If the temperature of a gas is expressed in kelvins, then experiments show that the ratio of volume to temperature is a constant: V/T=constant We can modify this equation as we modified Boyle’s law: the initial conditions V1 and T1 have a certain value, and the value must be the same when the conditions of the gas are changed to some new conditions V2 and T2, as long as pressure and the amount of the gas remain constant. Thus, we have another gas law: V1/T1=V2/T2 at constant P and n This gas law is commonly referred to as Charles’s law, after the French scientist Jacques Charles, who performed experiments on gases in the 1780s. The tactics for using this mathematical formula are similar to those for Boyle’s law. To determine an unknown quantity, use algebra to isolate the unknown variable by itself and in the numerator; the units of similar variables must be the same. But we add one more tactic: all temperatures must be expressed in the absolute temperature scale (Kelvin). As a reminder, we review the conversion between the absolute temperature scale and the Celsius temperature scale: K = °C + 273 where K represents the temperature in kelvins, and °C represents the temperature in degrees Celsius. It is more mathematically complicated if a final temperature must be calculated because the T variable is in the denominator of Charles’s law. There are several mathematical ways to work this, but perhaps the simplest way is to take the reciprocal of Charles’s law. That is, rather than write it as V1/T1=V2/T2 write the equation as T1/V1=T2/V2 It is still an equality and a correct form of Charles’s law, but now the temperature variable is in the numerator, and the algebra required to predict a final temperature is simpler. KEY TAKEAWAYS - The behavior of gases can be modeled with gas laws. - Boyle’s law relates a gas’s pressure and volume at constant temperature and amount. - Charles’s law relates a gas’s volume and temperature at constant pressure and amount. - In gas laws, temperatures must always be expressed in kelvins. You may notice in Boyle’s law and Charles’s law that we actually refer to four physical properties of a gas: pressure (P), volume (V), temperature (T), and amount (in moles; n). We do this because these are the only four independent physical properties of a gas. There are other physical properties, but they are all related to one (or more) of these four properties. Boyle’s law is written in terms of two of these properties, with the other two being held constant. Charles’s law is written in terms of two different properties, with the other two being held constant. It may not be surprising to learn that there are other gas laws that relate other pairs of properties—as long as the other two are held constant. Here we will mention a few. Gay-Lussac’s law relates pressure with absolute temperature. In terms of two sets of data, Gay-Lussac’s law is P1/T1=P2/T2 at constant V and n Note that it has a structure very similar to that of Charles’s law, only with different variables—pressure instead of volume. Avogadro’s law introduces the last variable for amount. The original statement of Avogadro’s law states that equal volumes of different gases at the same temperature and pressure contain the same number of particles of gas. Because the number of particles is related to the number of moles (1 mol = 6.022 × 1023 particles), Avogadro’s law essentially states that equal volumes of different gases at the same temperature and pressure contain the same amount (moles, particles) of gas. Put mathematically into a gas law, Avogadro’s law is V1/n1=V2/n2 at constant P and T (First announced in 1811, it was Avogadro’s proposal that volume is related to the number of particles that eventually led to naming the number of things in a mole as Avogadro’s number.) Avogadro’s law is useful because for the first time we are seeing amount, in terms of the number of moles, as a variable in a gas law. The variable n in Avogadro’s law can also stand for the number of moles of gas in addition to number of particles. One thing we notice about all the gas laws is that, collectively, volume and pressure are always in the numerator, and temperature is always in the denominator. This suggests that we can propose a gas law that combines pressure, volume, and temperature. This gas law is known as the combined gas law, and its mathematical form is P1V1/T1=P2V2/T2 at constant n This allows us to follow changes in all three major properties of a gas. Again, the usual warnings apply about how to solve for an unknown algebraically (isolate it on one side of the equation in the numerator), units (they must be the same for the two similar variables of each type), and units of temperature must be in kelvins. As with other gas laws, if you need to determine the value of a variable in the denominator of the combined gas law, you can either cross-multiply all the terms or just take the reciprocal of the combined gas law. Remember, the variable you are solving for must be in the numerator and all by itself on one side of the equation. KEY TAKEAWAYS - There are other gas laws that relate any two physical properties of a gas. - The combined gas law relates pressure, volume, and temperature of a gas. So far, the gas laws we have considered have all required that the gas change its conditions; then we predict a resulting change in one of its properties. Are there any gas laws that relate the physical properties of a gas at any given time? Consider a further extension of the combined gas law to include n. By analogy to Avogadro’s law, n is positioned in the denominator of the fraction, opposite the volume. So PV/nT=constant Because pressure, volume, temperature, and amount are the only four independent physical properties of a gas, the constant in the above equation is truly a constant; indeed, because we do not need to specify the identity of a gas to apply the gas laws, this constant is the same for all gases. We define this constant with the symbol R, so the previous equation is written as PV/nT=R which is usually rearranged as PV = nRT This equation is called the ideal gas law. It relates the four independent properties of a gas at any time. The constant R is called the ideal gas law constant. Its value depends on the units used to express pressure and volume. Table 6.1 "Values of the Ideal Gas Law Constant " lists the numerical values of R. The ideal gas law is used like any other gas law, with attention paid to the unit and making sure that temperature is expressed in Kelvin. However, the ideal gas law does not require a change in the conditions of a gas sample. The ideal gas law implies that if you know any three of the physical properties of a gas, you can calculate the fourth property. The ideal gas law can also be used in stoichiometry problems. It should be obvious by now that some physical properties of gases depend strongly on the conditions. What we need is a set of standard conditions so that properties of gases can be properly compared to each other. Standard temperature and pressure (STP) is defined as exactly 100 kPa of pressure (0.986 atm) and 273 K (0°C). For simplicity, we will use 1 atm as standard pressure. Defining STP allows us to compare more directly the properties of gases that differ from each other. One property shared among gases is a molar volume. The molar volume is the volume of 1 mol of a gas. At STP, the molar volume of a gas can be easily determined by using the ideal gas law: (1 atm)V=(1 mol)(0.08205⋅ (L⋅atm/mol⋅K))(273 K) All the units cancel except for L, the unit of volume. So V = 22.4 L Note that we have not specified the identity of the gas; we have specified only that the pressure is 1 atm and the temperature is 273 K. This makes for a very useful approximation: any gas at STP has a volume of 22.4 L per mole of gas; that is, the molar volume at STP is 22.4 L/mol (Figure 6.4 "Molar Volume"). This molar volume makes a useful conversion factor in stoichiometry problems if the conditions are at STP. If the conditions are not at STP, a molar volume of 22.4 L/mol is not applicable. However, if the conditions are not at STP, the combined gas law can be used to calculate what the volume of the gas would be if at STP; then the 22.4 L/mol molar volume can be used. The ideal gas law can also be used to determine the densities of gases. Density, recall, is defined as the mass of a substance divided by its volume: d=m/V Assume that you have exactly 1 mol of a gas. If you know the identity of the gas, you can determine the molar mass of the substance. Using the ideal gas law, you can also determine the volume of that mole of gas, using whatever the temperature and pressure conditions are. Then you can calculate the density of the gas by using density = molar mass/molar volume KEY TAKEAWAYS - The ideal gas law relates the four independent physical properties of a gas at any time. - The ideal gas law can be used in stoichiometry problems whose chemical reactions involve gases. - Standard temperature and pressure (STP) are a useful set of benchmark conditions to compare other properties of gases. - At STP, gases have a volume of 22.4 L per mole. - The ideal gas law can be used to determine densities of gases. One of the properties of gases is that they mix with each other. When they do so, they become a solution—a homogeneous mixture. Some of the properties of gas mixtures are easy to determine if we know the composition of the gases in the mix. In gas mixtures, each component in the gas phase can be treated separately. Each component of the mixture shares the same temperature and volume. (Remember that gases expand to fill the volume of their container; gases in a mixture continue to do that as well.) However, each gas has its own pressure. The partial pressure of a gas, Pi, is the pressure that an individual gas in a mixture has. Partial pressures are expressed in torr, millimeters of mercury, or atmospheres like any other gas pressure; however, we use the term pressure when talking about pure gases and the term partial pressure when we are talking about the individual gas components in a mixture. Dalton’s law of partial pressures states that the total pressure of a gas mixture, Ptot, is equal to the sum of the partial pressures of the components, Pi: Ptot=P1+P2+P3+…=∑(# of gases) Pi Although this may seem to be a trivial law, it reinforces the idea that gases behave independently of each other. One of the reasons we have to deal with Dalton’s law of partial pressures is because gases are frequently collected by bubbling through water. As we will see in Chapter 10 "Solids and Liquids", liquids are constantly evaporating into a vapor until the vapor achieves a partial pressure characteristic of the substance and the temperature. This partial pressure is called a vapor pressure. Table 6.2 "Vapor Pressure of Water versus Temperature" lists the vapor pressures of H2O versus temperature. Note that if a substance is normally a gas under a given set of conditions, the term partial pressure is used; the term vapor pressure is reserved for the partial pressure of a vapor when the liquid is the normal phase under a given set of conditions. Any time a gas is collected over water, the total pressure is equal to the partial pressure of the gas plus the vapor pressure of water. This means that the amount of gas collected will be less than the total pressure suggests. Finally, we introduce a new unit that can be useful, especially for gases. The mole fraction, χi, is the ratio of the number of moles of component i in a mixture divided by the total number of moles in the sample: χi=moles of component i/total number of moles (χ is the lowercase Greek letter chi.) Note that mole fraction is not a percentage; its values range from 0 to 1. For example, consider the combination of 4.00 g of He and 5.0 g of Ne. Converting both to moles, we get 4.00 g He × (1 mol He/4.00 g He)=1.00 mol He and 5.0 g Ne × (1 mol Ne/20.0 g Ne)=0.25 mol Ne The total number of moles is the sum of the two mole amounts: total moles = 1.00 mol + 0.025 mol = 1.25 mol The mole fractions are simply the ratio of each mole amount and the total number of moles, 1.25 mol: χHe=1.00 mol/1.25 mol=0.800 χNe=0.25 mol/1.25 mol=0.200 The sum of the mole fractions equals exactly 1. For gases, there is another way to determine the mole fraction. When gases have the same volume and temperature (as they would in a mixture of gases), the number of moles is proportional to partial pressure, so the mole fractions for a gas mixture can be determined by taking the ratio of partial pressure to total pressure: χi=Pi/Ptot This expression allows us to determine mole fractions without calculating the moles of each component directly. KEY TAKEAWAYS - The pressure of a gas in a gas mixture is termed the partial pressure. - Dalton’s law of partial pressure says that the total pressure in a gas mixture is the sum of the individual partial pressures. - Collecting gases over water requires that we take the vapor pressure of water into account. - Mole fraction is another way to express the amounts of components in a mixture. Energy is a very important quantity in science and the world around us. Although most of our energy ultimately comes from the sun, much of the energy we use on a daily basis is rooted in chemical reactions. The gasoline in your car, the electricity in your house, the food in your diet—all provide substances for chemical reactions to provide energy (gasoline, food) or are produced from chemical reactions (electricity, about 50% of which is generated by burning coal). As such, it is only natural that the study of chemistry involves energy. Energy is the ability to do work. Think about it: when you have a lot of energy, you can do a lot of work; but if you’re low on energy, you don’t want to do much work. Work (w) itself is defined as a force (F) operating over a distance (Δx): w = F × Δx In SI, force has units of newtons (N), while distance has units of meters. Therefore, work has units of N·m. This compound unit is redefined as a joule (J): 1 joule = 1 newton·meter 1 J = 1 N·m Because energy is the ability to do work, energy is also measured in joules. This is the primary unit of energy we will use here. How much is 1 J? It is enough to warm up about one-fourth of a gram of water by 1°C. It takes about 12,000 J to warm a cup of coffee from room temperature to 50°C. So a joule is not a lot of energy. It will not be uncommon to measure energies in thousands of joules, so the kilojoule (kJ) is a common unit of energy, with 1 kJ equal to 1,000 J. An older—but still common—unit of energy is the calorie. The calorie (cal) was originally defined in terms of warming up a given quantity of water. The modern definition of calorie equates it to joules: 1 cal = 4.184 J One area where the calorie is used is in nutrition. Energy contents of foods are often expressed in calories. However, the calorie unit used for foods is actually the kilocalorie (kcal). Most foods indicate this by spelling the word with a capital C—Calorie. Figure 7.1 "Calories on Food Labels" shows one example. So be careful counting calories when you eat! In the study of energy, we use the term system to describe the part of the universe under study: a beaker, a flask, or a container whose contents are being observed and measured. An isolated system is a system that does not allow a transfer of energy or matter into or out of the system. A good approximation of an isolated system is a closed, insulated thermos-type bottle. The fact that the thermos-type bottle is closed keeps matter from moving in or out, and the fact that it is insulated keeps energy from moving in or out. One of the fundamental ideas about the total energy of an isolated system is that is does not increase or decrease. When this happens to a quantity, we say that the quantity is conserved. The statement that the total energy of an isolated system does not change is called the law of conservation of energy. As a scientific law, this concept occupies the highest level of understanding we have about the natural universe. KEY TAKEAWAYS - Energy is the ability to do work and uses the unit joule. - The law of conservation of energy states that the total energy of an isolated system does not increase or decrease. We have already defined work as a force acting through a distance. It turns out that there are other equivalent definitions of work that are also important in chemistry. When a certain volume of a gas expands, it works against an external pressure to expand (Figure 7.2 "Volume versus Pressure"). That is, the gas must perform work. Assuming that the external pressure Pext is constant, the amount of work done by the gas is given by the equation w = −Pext × ΔV where ΔV is the change in volume of the gas. This term is always the final volume minus the initial volume, ΔV = Vfinal − Vinitial and can be positive or negative, depending on whether Vfinal is larger (is expanding) or smaller (is contracting) than Vinitial. The negative sign in the equation for work is important and implies that as volume expands (ΔV is positive), the gas in the system is losing energy as work. On the other hand, if the gas is contracting, ΔV is negative, and the two negative signs make the work positive, so energy is being added to the system. Finally, let us consider units. Volume changes are usually expressed in units like liters, while pressures are usually expressed in atmospheres. When we use the equation to determine work, the unit for work comes out as liter·atmospheres, or L·atm. This is not a very common unit for work. However, there is a conversion factor between L·atm and the common unit of work, joules: 1 L·atm = 101.32 J Using this conversion factor and the previous equation for work, we can calculate the work performed when a gas expands or contracts. Heat is another aspect of energy. Heat is the transfer of energy from one body to another due to a difference in temperature. For example, when we touch something with our hands, we interpret that object as either hot or cold depending on how energy is transferred: If energy is transferred into your hands, the object feels hot. If energy is transferred from your hands to the object, your hands feel cold. Because heat is a measure of energy transfer, heat is also measured in joules. For a given object, the amount of heat (q) involved is proportional to two things: the mass of the object (m) and the temperature change (ΔT) evoked by the energy transfer. We can write this mathematically as q∝m × ΔT where ∝ means “is proportional to.” To make a proportionality an equality, we include a proportionality constant. In this case, the proportionality constant is labeled c and is called the specific heat capacity, or, more succinctly, specific heat: q = mcΔT where the mass, specific heat, and change in temperature are multiplied together. Specific heat is a measure of how much energy is needed to change the temperature of a substance; the larger the specific heat, the more energy is needed to change the temperature. The units for specific heat are J/(g⋅°C) or J/(g⋅K), depending on what the unit of ΔT is. You may note a departure from the insistence that temperature be expressed in Kelvin. That is because a change in temperature has the same value whether the temperatures are expressed in degrees Celsius or kelvins. As with any equation, when you know all but one variable in the expression for q, you can determine the remaining variable by using algebra. Table 7.1 "Specific Heats of Various Substances" lists the specific heats of some substances. Specific heat is a physical property of substances, so it is a characteristic of the substance. The general idea is that the lower the specific heat, the less energy is required to change the temperature of the substance by a certain amount. KEY TAKEAWAYS - Work can be defined as a gas changing volume against a constant external pressure. - Heat is the transfer of energy due to temperature differences. - Heat can be calculated in terms of mass, temperature change, and specific heat. Now that we have shown how energy, work, and heat are related, we are ready to consider energy changes in chemical reactions. A fundamental concept is that every chemical reaction occurs with a concurrent change in energy. Now we need to learn how to properly express these energy changes. Our study of gases in Chapter 6 "Gases" and our definition of work in Section 7.2 "Work and Heat" indicate that conditions like pressure, volume, and temperature affect the energy content of a system. What we need is a definition of energy that holds when some of these conditions are specified (somewhat similar to our definition of standard temperature and pressure in our study of gases). We define the enthalpy change (ΔH) as the heat of a process when pressure is held constant: ΔH≡q at constant pressure The letter H stands for “enthalpy,” a kind of energy, while the Δ implies a change in the quantity. We will always be interested in the change in H, rather than the absolute value of H itself. When a chemical reaction occurs, there is a characteristic change in enthalpy. The enthalpy change for a reaction is typically written after a balanced chemical equation and on the same line. For example, when two moles of hydrogen react with one mole of oxygen to make two moles of water, the characteristic enthalpy change is 570 kJ. We write the equation as 2H2(g) + O2(g) → 2H2O(ℓ) ΔH = −570 kJ A chemical equation that includes an enthalpy change is called a thermochemical equation. A thermochemical equation is assumed to refer to the equation in molar quantities, which means it must be interpreted in terms of moles, not individual molecules. You may have noticed that the ΔH for a chemical reaction may be positive or negative. The number is assumed to be positive if it has no sign; a + sign can be added explicitly to avoid confusion. A chemical reaction that has a positive ΔH is said to be endothermic, while a chemical reaction that has a negative ΔH is said to be exothermic. What does it mean if the ΔH of a process is positive? It means that the system in which the chemical reaction is occurring is gaining energy. If one considers the energy of a system as being represented as a height on a vertical energy plot, the enthalpy change that accompanies the reaction can be diagrammed as in part (a) in Figure 7.3 "Reaction Energy": the energy of the reactants has some energy, and the system increases its energy as it goes to products. The products are higher on the vertical scale than the reactants. Endothermic, then, implies that the system gains, or absorbs, energy. An opposite situation exists for an exothermic process, as shown in part (b) in Figure 7.3 "Reaction Energy". If the enthalpy change of a reaction is negative, the system is losing energy, so the products have less energy than the reactants, and the products are lower on the vertical energy scale than the reactants are. Exothermic, then, implies that the system loses, or gives off, energy. (a) In an endothermic reaction, the energy of the system increases (i.e., moves higher on the vertical scale of energy). (b) In an exothermic reaction, the energy of the system decreases (i.e., moves lower on the vertical scale of energy). How are ΔH values measured experimentally? Actually, ΔH is not measured; q is measured. But the measurements are performed under conditions of constant pressure, so ΔH is equal to the q measured. Experimentally, q is measured by taking advantage of the equation q = mcΔT We premeasure the mass of the chemicals in a system. Then we let the chemical reaction occur and measure the change in temperature (ΔT) of the system. If we know the specific heat of the materials in the system (typically, we do), we can calculate q. That value of q is numerically equal to the ΔH of the process, which we can scale up to a molar scale. The container in which the system resides is typically insulated, so any energy change goes into changing the temperature of the system, rather than being leaked from the system. The container is referred to as a calorimeter, and the process of measuring changes in enthalpy is called calorimetry. For example, suppose 4.0 g of NaOH, or 0.10 mol of NaOH, are dissolved to make 100.0 mL of aqueous solution, while 3.65 g of HCl, or 0.10 mol of HCl, are dissolved to make another 100.0 mL of aqueous solution. The two solutions are mixed in an insulated calorimeter, a thermometer is inserted, and the calorimeter is covered (see Figure 7.4 "Calorimeters" for an example setup). The thermometer measures the temperature change as the following chemical reaction occurs: NaOH (aq) + HCl(aq) → NaCl(aq) + H2O(ℓ) An observer notes that the temperature increases from 22.4°C to 29.1°C. Assuming that the heat capacities and densities of the solutions are the same as those of pure water, we now have the information we need to determine the enthalpy change of the chemical reaction. The total amount of solution is 200.0 mL, and with a density of 1.00 g/mL, we thus have 200.0 g of solution. Using the equation for q, we substitute for our experimental measurements and the specific heat of water (Table 7.1 "Specific Heats of Various Substances"): q=(200.0 g)⎛⎝4.184 J g⋅°C⎞⎠(6.7°C) Solving for q, we get q=5,600 J≡ΔH for the reaction The heat q is equal to the ΔH for the reaction because the chemical reaction occurs at constant pressure. However, the reaction is giving off this amount of energy, so the actual sign on ΔH is negative: ΔH = −5,600 J for the reaction Thus, we have the following thermochemical equation for the chemical reaction that occurred in the calorimeter: (1/10) NaOH(aq)+(1/10) HCl(aq)→(1/10) NaCl(aq)+(1/10) H2O(ℓ) ΔH=−5,600 J The 1/10 coefficients are present to remind us that we started with one-tenth of a mole of each reactant, so we make one-tenth of a mole of each product. Typically, however, we report thermochemical equations in terms of moles, not one-tenth of a mole. To scale up to molar quantities, we must multiply the coefficients by 10. However, when we do this, we get 10 times as much energy. Thus, we have NaOH (aq) + HCl(aq) → NaCl(aq) + H2O(ℓ) ΔH = −56,000 J The ΔH can be converted into kJ units, so our final thermochemical equation is NaOH (aq) + HCl(aq) → NaCl(aq) + H2O(ℓ) ΔH = −56 kJ We have just taken our experimental data from calorimetry and determined the enthalpy change of a chemical reaction. Similar measurements on other chemical reactions can determine the ΔH values of any chemical reaction you want to study. KEY TAKEAWAYS - Every chemical reaction occurs with a concurrent change in energy. - The change in enthalpy equals heat at constant pressure. - Enthalpy changes can be expressed by using thermochemical equations. - Enthalpy changes are measured by using calorimetry. In Chapter 5 "Stoichiometry and the Mole", we related quantities of one substance to another in a chemical equation by performing calculations that used the balanced chemical equation; the balanced chemical equation provided equivalences that we used to construct conversion factors. For example, in the balanced chemical equation 2H2(g) + O2(g) → 2H2O(ℓ) we recognized the equivalences 2 mol H2 ⇔ 1 mol O2 ⇔ 2 mol H2O where ⇔ is the mathematical symbol for “is equivalent to.” In our thermochemical equation, however, we have another quantity—energy change: 2H2(g) + O2(g) → 2H2O(ℓ) ΔH = −570 kJ This new quantity allows us to add another equivalence to our list: 2 mol H2 ⇔ 1 mol O2 ⇔ 2 mol H2O ⇔ −570 kJ That is, we can now add an energy amount to the equivalences—the enthalpy change of a balanced chemical reaction. This equivalence can also be used to construct conversion factors so that we can relate enthalpy change to amounts of substances reacted or produced. Note that these equivalences address a concern. When an amount of energy is listed for a balanced chemical reaction, what amount(s) of reactants or products does it refer to? The answer is that relates to the number of moles of the substance as indicated by its coefficient in the balanced chemical reaction. Thus, 2 mol of H2 are related to −570 kJ, while 1 mol of O2 is related to −570 kJ. This is why the unit on the energy change is kJ, not kJ/mol. For example, consider the thermochemical equation H2(g) + Cl2(g) → 2HCl(g) ΔH = −184.6 kJ The equivalences for this thermochemical equation are 1 mol H2 ⇔ 1 mol Cl2 ⇔ 2 mol HCl ⇔ −184.6 kJ Suppose we asked how much energy is given off when 8.22 mol of H2 react. We would construct a conversion factor between the number of moles of H2 and the energy given off, −184.6 kJ: 8.22 mol H2×(−184.6 kJ/1 mol H2)=−1,520 kJ The negative sign means that this much energy is given off. Like any stoichiometric quantity, we can start with energy and determine an amount, rather than the other way around. KEY TAKEAWAY - The energy change of a chemical reaction can be used in stoichiometry calculations. Now that we understand that chemical reactions occur with a simultaneous change in energy, we can apply the concept more broadly. To start, remember that some chemical reactions are rather difficult to perform. For example, consider the combustion of carbon to make carbon monoxide: 2C(s) + O2(g) → 2CO(g) ΔH = ? In reality, this is extremely difficult to do; given the opportunity, carbon will react to make another compound, carbon dioxide: 2C(s) + O2(g) → 2CO2(g) ΔH = −393.5 kJ Is there a way around this? Yes. It comes from the understanding that chemical equations can be treated like algebraic equations, with the arrow acting like the equals sign. Like algebraic equations, chemical equations can be combined, and if the same substance appears on both sides of the arrow, it can be canceled out (much like a spectator ion in ionic equations). For example, consider these two reactions: 2C(s) + 2O2(g) → 2CO2(g) 2CO2(g) → 2CO(g) + O2(g) If we added these two equations by combining all the reactants together and all the products together, we would get 2C(s) + 2O2(g) + 2CO2(g) → 2CO2(g) + 2CO(g) + O2(g) We note that 2CO2(g) appears on both sides of the arrow, so they cancel: 2C(s)+2O2(g)+ 2CO2(g)→ 2CO2(g)+2CO(g)+O2(g) We also note that there are 2 mol of O2 on the reactant side, and 1 mol of O2 on the product side. We can cancel 1 mol of O2 from both sides: 2C(s)+ 2O2(g)→2CO(g)+ O2(g) What do we have left? 2C(s) + O2(g) → 2CO(g) This is the reaction we are looking for! So by algebraically combining chemical equations, we can generate new chemical equations that may not be feasible to perform. What about the enthalpy changes? Hess’s law states that when chemical equations are combined algebraically, their enthalpies can be combined in exactly the same way. Two corollaries immediately present themselves: 1. If a chemical reaction is reversed, the sign on ΔH is changed. 2. If a multiple of a chemical reaction is taken, the same multiple of the ΔH is taken as well. What are the equations being combined? The first chemical equation is the combustion of C, which produces CO2: 2C(s) + 2O2(g) → 2CO2(g) This reaction is two times the reaction to make CO2 from C(s) and O2(g), whose enthalpy change is known: C(s) + O2(g) → CO2(g) ΔH = −393.5 kJ According to the first corollary, the first reaction has an energy change of two times −393.5 kJ, or −787.0 kJ: 2C(s) + 2O2(g) → 2CO2(g) ΔH = −787.0 kJ The second reaction in the combination is related to the combustion of CO(g): 2CO(g) + O2(g) → 2CO2(g) ΔH = −566.0 kJ The second reaction in our combination is the reverse of the combustion of CO. When we reverse the reaction, we change the sign on the ΔH: 2CO2(g) → 2CO(g) + O2(g) ΔH = +566.0 kJ Now that we have identified the enthalpy changes of the two component chemical equations, we can combine the ΔH values and add them: Hess’s law is very powerful. It allows us to combine equations to generate new chemical reactions whose enthalpy changes can be calculated, rather than directly measured. KEY TAKEAWAY - Hess’s law allows us to combine reactions algebraically and then combine their enthalpy changes the same way. Hess’s law allows us to construct new chemical reactions and predict what their enthalpies of reaction will be. This is a very useful tool because now we don’t have to measure the enthalpy changes of every possible reaction. We need measure only the enthalpy changes of certain benchmark reactions and then use these reactions to algebraically construct any possible reaction and combine the enthalpies of the benchmark reactions accordingly. But what are the benchmark reactions? We need to have some agreed-on sets of reactions that provide the central data for any thermochemical equation. Formation reactions are chemical reactions that form one mole of a substance from its constituent elements in their standard states. By standard states we mean as a diatomic molecule if that is how the element exists and the proper phase at normal temperatures (typically room temperature). The product is one mole of substance, which may require that coefficients on the reactant side be fractional (a change from our normal insistence that all coefficients be whole numbers). For example, the formation reaction for methane (CH4) is C(s) + 2H2(g) → CH4(g) The formation reaction for carbon dioxide (CO2) is C(s) + O2(g) → CO2(g) In both cases, one of the elements is a diatomic molecule because that is the standard state for that particular element. The formation reaction for H2O— 2H2(g) + O2(g) → 2H2O(ℓ) —is not in a standard state because the coefficient on the product is 2; for a proper formation reaction, only one mole of product is formed. Thus, we have to divide all coefficients by 2: H2(g) + 1/2O2(g) → H2O(ℓ) On a molecular scale, we are using half of an oxygen molecule, which may be problematic to visualize. However, on a molar level, it implies that we are reacting only half of a mole of oxygen molecules, which should be an easy concept for us to understand. Given the formula of any substance, you should be able to write the proper formation reaction for that substance. The enthalpy change for a formation reaction is called the enthalpy of formation and is given the symbol ΔHf. The subscript f is the clue that the reaction of interest is a formation reaction. Thus, for the formation of FeO(s), Fe(s)+(1/2)O2(g)→FeO(s) ΔH≡ΔHf=−272 kJ/mol Note that now we are using kJ/mol as the unit because it is understood that the enthalpy change is for one mole of substance. Note, too, by definition, that the enthalpy of formation of an element is exactly zero because making an element from an element is no change. For example, H2(g) → H2(g) ΔHf = 0 Formation reactions and their enthalpies are important because these are the thermochemical data that are tabulated for any chemical reaction. Table 7.2 "Enthalpies of Formation for Various Substances" lists some enthalpies of formation for a variety of substances; in some cases, however, phases can be important (e.g., for H2O). It is easy to show that any general chemical equation can be written in terms of the formation reactions of its reactants and products, some of them reversed (which means the sign must change in accordance with Hess’s law). For example, consider 2NO2(g) → N2O4(g) We can write it in terms of the (reverse) formation reaction of NO2 and the formation reaction of N2O4: We must multiply the first reaction by 2 to get the correct overall balanced equation. We are simply using Hess’s law in combining the ΔHf values of the formation reactions. Now that we have established formation reactions as the major type of thermochemical reaction we will be interested in, do we always need to write all the formation reactions when we want to determine the enthalpy change of any random chemical reaction? No. There is an easier way. You may have noticed in all our examples that we change the signs on all the enthalpies of formation of the reactants, and we don’t change the signs on the enthalpies of formation of the products. We also multiply the enthalpies of formation of any substance by its coefficient—technically, even when it is just 1. This allows us to make the following statement: the enthalpy change of any chemical reaction is equal to the sum of the enthalpies of formation of the products minus the sum of the enthalpies of formation of the reactants. In mathematical terms, ΔHrxn=∑npΔHf,p−∑nrΔHf,r where np and nr are the number of moles of products and reactants, respectively (even if they are just 1 mol), and ΔHf,p and ΔHf,r are the enthalpies of formation of the product and reactant species, respectively. This products-minus-reactants scheme is very useful in determining the enthalpy change of any chemical reaction, if the enthalpy of formation data are available. Because the mol units cancel when multiplying the amount by the enthalpy of formation, the enthalpy change of the chemical reaction has units of energy (joules or kilojoules) only. KEY TAKEAWAYS - A formation reaction is the formation of one mole of a substance from its constituent elements. - Enthalpies of formation are used to determine the enthalpy change of any given reaction. Atoms act the way they do because of their structure. We already know that atoms are composed of protons, neutrons, and electrons. Protons and neutrons are located in the nucleus, and electrons orbit around the nucleus. But we need to know the structural details to understand why atoms react the way they do. Virtually everything we know about atoms ultimately comes from light. Before we can understand the composition of atoms (especially electrons), we need to understand the properties of light. What we know as light is more properly called electromagnetic radiation. We know from experiments that light acts as a wave. As such, it can be described as having a frequency and a wavelength. The wavelength of light is the distance between corresponding points in two adjacent light cycles, and the frequency of light is the number of cycles of light that pass a given point in one second. Wavelength is typically represented by λ, the lowercase Greek letter lambda, while frequency is represented by ν, the lowercase Greek letter nu (although it looks like a Roman “vee,” it is actually the Greek equivalent of the letter “en”). Wavelength has units of length (meters, centimeters, etc.), while frequency has units of per second, written as s−1 and sometimes called a hertz (Hz). Figure 8.1 "Characteristics of Light Waves" shows how these two characteristics are defined. Light acts as a wave and can be described by a wavelength λ and a frequency ν. One property of waves is that their speed is equal to their wavelength times their frequency. That means we have speed=λν For light, however, speed is actually a universal constant when light is traveling through a vacuum (or, to a very good approximation, air). The measured speed of light (c) in a vacuum is 2.9979 × 108 m/s, or about 3.00 × 108 m/s. Thus, we have c=λν Because the speed of light is a constant, the wavelength and the frequency of light are related to each other: as one increases, the other decreases and vice versa. We can use this equation to calculate what one property of light has to be when given the other property. Light also behaves like a package of energy. It turns out that for light, the energy of the “package” of energy is proportional to its frequency. (For most waves, energy is proportional to wave amplitude, or the height of the wave.) The mathematical equation that relates the energy (E) of light to its frequency is E=hν where ν is the frequency of the light, and h is a constant called Planck’s constant. Its value is 6.626 × 10−34 J·s—a very small number that is another fundamental constant of our universe, like the speed of light. The units on Planck’s constant may look unusual, but these units are required so that the algebra works out. Because a light wave behaves like a little particle of energy, light waves have a particle-type name: the photon. It is not uncommon to hear light described as photons. Wavelengths, frequencies, and energies of light span a wide range; the entire range of possible values for light is called the electromagnetic spectrum. We are mostly familiar with visible light, which is light having a wavelength range between about 400 nm and 700 nm. Light can have much longer and much shorter wavelengths than this, with corresponding variations in frequency and energy. Figure 8.2 "The Electromagnetic Spectrum" shows the entire electromagnetic spectrum and how certain regions of the spectrum are labeled. You may already be familiar with some of these regions; they are all light—with different frequencies, wavelengths, and energies. KEY TAKEAWAYS - Light acts like a wave, with a frequency and a wavelength. - The frequency and wavelength of light are related by the speed of light, a constant. - Light acts like a particle of energy, whose value is related to the frequency of light. There are two fundamental ways of generating light: either heat an object up so hot it glows or pass an electrical current through a sample of matter (usually a gas). Incandescent lights and fluorescent lights generate light via these two methods, respectively. A hot object gives off a continuum of light. We notice this when the visible portion of the electromagnetic spectrum is passed through a prism: the prism separates light into its constituent colors, and all colors are present in a continuous rainbow (part (a) in Figure 8.3 "Prisms and Light"). This image is known as a continuous spectrum. However, when electricity is passed through a gas and light is emitted and this light is passed though a prism, we see only certain lines of light in the image (part (b) in Figure 8.3 "Prisms and Light"). This image is called a line spectrum. It turns out that every element has its own unique, characteristic line spectrum. (a) A glowing object gives off a full rainbow of colors, which are noticed only when light is passed through a prism to make a continuous spectrum. (b) However, when electricity is passed through a gas, only certain colors of light are emitted. Here are the colors of light in the line spectrum of Hg. Why does the light emitted from an electrically excited gas have only certain colors, while light given off by hot objects has a continuous spectrum? For a long time, it was not well explained. Particularly simple was the spectrum of hydrogen gas, which could be described easily by an equation; no other element has a spectrum that is so predictable (Figure 8.4 "Hydrogen Spectrum"). Late-nineteenth-century scientists found that the positions of the lines obeyed a pattern given by the equation 1λ=(109,700 cm^−1)(1/4−1/n^2) where n = 3, 4, 5, 6,…, but they could not explain why this was so. The spectrum of hydrogen was particularly simple and could be predicted by a simple mathematical expression. In 1913, the Danish scientist Niels Bohr suggested a reason why the hydrogen atom spectrum looked this way. He suggested that the electron in a hydrogen atom could not have any random energy, having only certain fixed values of energy that were indexed by the number n (the same n in the equation above and now called a quantum number). Quantities that have certain specific values are called quantized values. Bohr suggested that the energy of the electron in hydrogen was quantized because it was in a specific orbit. Because the energies of the electron can have only certain values, the changes in energies can have only certain values (somewhat similar to a staircase: not only are the stair steps set at specific heights but the height between steps is fixed). Finally, Bohr suggested that the energy of light emitted from electrified hydrogen gas was equal to the energy difference of the electron’s energy states: Elight=hν=ΔEelectron This means that only certain frequencies (and thus, certain wavelengths) of light are emitted. Figure 8.5 "Bohr’s Model of the Hydrogen Atom" shows a model of the hydrogen atom based on Bohr’s ideas. Bohr’s description of the hydrogen atom had specific orbits for the electron, which had quantized energies. Bohr’s ideas were useful but were applied only to the hydrogen atom. However, later researchers generalized Bohr’s ideas into a new theory called quantum mechanics, which explains the behavior of electrons as if they were acting as a wave, not as particles. Quantum mechanics predicts two major things: quantized energies for electrons of all atoms (not just hydrogen) and an organization of electrons within atoms. Electrons are no longer thought of as being randomly distributed around a nucleus or restricted to certain orbits (in that regard, Bohr was wrong). Instead, electrons are collected into groups and subgroups that explain much about the chemical behavior of the atom. In the quantum-mechanical model of an atom, the state of an electron is described by four quantum numbers, not just the one predicted by Bohr. The first quantum number is called the principal quantum number (n). The principal quantum number largely determines the energy of an electron. Electrons in the same atom that have the same principal quantum number are said to occupy an electron shell of the atom. The principal quantum number can be any nonzero positive integer: 1, 2, 3, 4,…. Within a shell, there may be multiple possible values of the next quantum number, the angular momentum quantum number (ℓ). The ℓ quantum number has a minor effect on the energy of the electron but also affects the spatial distribution of the electron in three-dimensional space—that is, the shape of an electron’s distribution in space. The value of the ℓ quantum number can be any integer between 0 and n − 1: ℓ = 0, 1, 2,…, n − 1 Thus, for a given value of n, there are different possible values of ℓ: and so forth. Electrons within a shell that have the same value of ℓ are said to occupy a subshell in the atom. Commonly, instead of referring to the numerical value of ℓ, a letter represents the value of ℓ (to help distinguish it from the principal quantum number): The next quantum number is called the magnetic quantum number (mℓ). For any value of ℓ, there are 2ℓ + 1 possible values of mℓ, ranging from −ℓ to ℓ: −ℓ ≤ mℓ ≤ ℓ or |mℓ|≤ ℓ The following explicitly lists the possible values of mℓ for the possible values of ℓ: The particular value of mℓ dictates the orientation of an electron’s distribution in space. When ℓ is zero, mℓ can be only zero, so there is only one possible orientation. When ℓ is 1, there are three possible orientations for an electron’s distribution. When ℓ is 2, there are five possible orientations of electron distribution. This goes on and on for other values of ℓ, but we need not consider any higher values of ℓ here. Each value of mℓ designates a certain orbital. Thus, there is only one orbital when ℓ is zero, three orbitals when ℓ is 1, five orbitals when ℓ is 2, and so forth. The mℓ quantum number has no effect on the energy of an electron unless the electrons are subjected to a magnetic field—hence its name. The ℓ quantum number dictates the general shape of electron distribution in space (Figure 8.6 "Electron Orbitals"). Any s orbital is spherically symmetric (part (a) in Figure 8.6 "Electron Orbitals"), and there is only one orbital in any s subshell. Any p orbital has a two-lobed, dumbbell-like shape (part (b) in Figure 8.6 "Electron Orbitals"); because there are three of them, we normally represent them as pointing along the x-, y-, and z-axes of Cartesian space. The d orbitals are four-lobed rosettes (part (c) in Figure 8.6 "Electron Orbitals"); they are oriented differently in space (the one labeled dz2 has two lobes and a torus instead of four lobes, but it is equivalent to the other orbitals). When there is more than one possible value of mℓ, each orbital is labeled with one of the possible values. It should be noted that the diagrams in Figure 8.6 "Electron Orbitals" are estimates of the electron distribution in space, not surfaces electrons are fixed on. (a) The lone s orbital is spherical in distribution. (b) The three p orbitals are shaped like dumbbells, and each one points in a different direction. (c) The five d orbitals are rosette in shape, except for the dz2 orbital, which is a “dumbbell + torus” combination. They are all oriented in different directions. The final quantum number is the spin quantum number (ms). Electrons and other subatomic particles behave as if they are spinning (we cannot tell if they really are, but they behave as if they are). Electrons themselves have two possible spin states, and because of mathematics, they are assigned the quantum numbers +1/2 and −1/2. These are the only two possible choices for the spin quantum number of an electron. KEY TAKEAWAYS - Electrons in atoms have quantized energies. - The state of electrons in atoms is described by four quantum numbers. Now that you know that electrons have quantum numbers, how are they arranged in atoms? The key to understanding electronic arrangement is summarized in the Pauli exclusion principle: no two electrons in an atom can have the same set of four quantum numbers. This dramatically limits the number of electrons that can exist in a shell or a subshell. Electrons are typically organized around an atom by starting at the lowest possible quantum numbers first, which are the shells-subshells with lower energies. Consider H, an atom with a single electron only. Under normal conditions, the single electron would go into the n = 1 shell, which has only a single s subshell with one orbital (because mℓ can equal only 0). The convention is to label the shell-subshell combination with the number of the shell and the letter that represents the subshell. Thus, the electron goes in the 1s shell-subshell combination. It is usually not necessary to specify the mℓ or ms quantum numbers, but for the H atom, the electron has mℓ = 0 (the only possible value) and an ms of either +1/2 or −1/2. The He atom has two electrons. The second electron can also go into the 1s shell-subshell combination but only if its spin quantum number is different from the first electron’s spin quantum number. Thus, the sets of quantum numbers for the two electrons are {1, 0, 0, +1/2} and {1, 0, 0, −1/2}. Notice that the overall set is different for the two electrons, as required by the Pauli exclusion principle. The next atom is Li, with three electrons. However, now the Pauli exclusion principle implies that we cannot put that electron in the 1s shell-subshell because no matter how we try, this third electron would have the same set of four quantum numbers as one of the first two electrons. So this third electron must be assigned to a different shell-subshell combination. However, the n = 1 shell doesn’t have another subshell; it is restricted to having just ℓ = 0, or an s subshell. Therefore, this third electron has to be assigned to the n = 2 shell, which has an s (ℓ = 0) subshell and a p (ℓ = 1) subshell. Again, we usually start with the lowest quantum number, so this third electron is assigned to the 2s shell-subshell combination of quantum numbers. The Pauli exclusion principle has the net effect of limiting the number of electrons that can be assigned a shell-subshell combination of quantum numbers. For example, in any s subshell, no matter what the shell number, there can be a maximum of only two electrons. Once the s subshell is filled up, any additional electrons must go to another subshell in the shell (if it exists) or to higher-numbered shell. A similar analysis shows that a p subshell can hold a maximum of six electrons. A d subshell can hold a maximum of 10 electrons, while an f subshell can have a maximum of 14 electrons. By limiting subshells to these maxima, we can distribute the available electrons to their shells and subshells. Now that we see how electrons are partitioned among the shells and subshells, we need a more concise way of communicating this partitioning. Chemists use an electron configuration to represent the organization of electrons in shells and subshells in an atom. An electron configuration simply lists the shell and subshell labels, with a right superscript giving the number of electrons in that subshell. The shells and subshells are listed in the order of filling. For example, an H atom has a single electron in the 1s subshell. Its electron configuration is H: 1s^1 He has two electrons in the 1s subshell. Its electron configuration is He: 1s^2 The three electrons for Li are arranged in the 1s subshell (two electrons) and the 2s subshell (one electron). The electron configuration of Li is Li: (1s^2)×(2s^1) Be has four electrons, two in the 1s subshell and two in the 2s subshell. Its electron configuration is Be: (1s^2)×(2s^2) Now that the 2s subshell is filled, electrons in larger atoms must go into the 2p subshell, which can hold a maximum of six electrons. The next six elements progressively fill up the 2p subshell: B: (1s^2)×(2s^2)×(2p^1) C: (1s^2)×(2s^2)×(2p^2) N: (1s^2)×(2s^2)×(2p^3) O: (1s^2)×(2s^2)×(2p^4) F: (1s^2)×(2s^2)×(2p^5) Ne: (1s^2)×(2s^2)×(2p^6) Now that the 2p subshell is filled (all possible subshells in the n = 2 shell), the next electron for the next-larger atom must go into the n = 3 shell, s subshell. For larger atoms, the electron arrangement becomes more complicated. This is because after the 3p subshell is filled, filling the 4s subshell first actually leads to a lesser overall energy than filling the 3d subshell. Recall that while the principal quantum number largely dictates the energy of an electron, the angular momentum quantum number also has an impact on energy; by the time we get to the 3d and 4s subshells, we see overlap in the filling of the shells. Thus, after the 3p subshell is completely filled (which occurs for Ar), the next electron for K occupies the 4s subshell, not the 3d subshell: K: (1s^2)×(2s^2)×(2p^6)×(3s^2)×(3p^6)×(4s^1), not (1s^2)×(2s^2)×(2p^6)×(3s^2)×(3p^6)×(3d^1) For larger and larger atoms, the order of filling the shells and subshells seems to become even more complicated. There are some useful ways to remember the order, like that shown in Figure 8.7 "Electron Shell Filling Order". If you follow the arrows in order, they pass through the subshells in the order that they are filled with electrons in larger atoms. Initially, the order is the same as the expected shell-subshell order, but for larger atoms, there is some shifting around of the principal quantum numbers. However, Figure 8.7 "Electron Shell Filling Order" gives a valid ordering of filling subshells with electrons for most atoms. As the previous example demonstrated, electron configurations can get fairly long. An abbreviated electron configuration uses one of the elements from the last column of the periodic table, which contains what are called the noble gases, to represent the core of electrons up to that element. Then the remaining electrons are listed explicitly. For example, the abbreviated electron configuration for Li, which has three electrons, would be Li: [He]2s^1 where [He] represents the two-electron core that is equivalent to He’s electron configuration. The square brackets represent the electron configuration of a noble gas. This is not much of an abbreviation. However, consider the abbreviated electron configuration for W, which has 74 electrons: W: [Xe](6s^2)×(4f^14)×(5d^4) This is a significant simplification over an explicit listing of all 74 electrons. So for larger elements, the abbreviated electron configuration can be a very useful shorthand. There are some exceptions to the rigorous filling of subshells by electrons. In many cases, an electron goes from a higher-numbered shell to a lower-numbered but later-filled subshell to fill the later-filled subshell. One example is Ag. With 47 electrons, its electron configuration is predicted to be Ag: [Kr](5s^2)×(4d^9) However, experiments have shown that the electron configuration is actually Ag: [Kr](5s^1)×(4d^10) This, then, qualifies as an exception to our expectations. At this point, you do not need to memorize the exceptions; but if you come across one, understand that it is an exception to the normal rules of filling subshells with electrons, which can happen. KEY TAKEAWAYS - The Pauli exclusion principle limits the number of electrons in the subshells and shells. - Electrons in larger atoms fill shells and subshells in a regular pattern that we can follow. - Electron configurations are a shorthand method of indicating what subshells electrons occupy in atoms. - Abbreviated electron configurations are a simpler way of representing electron configurations for larger atoms. - Exceptions to the strict filling of subshells with electrons occur. In Chapter 3 "Atoms, Molecules, and Ions", we introduced the periodic table as a tool for organizing the known chemical elements. A periodic table is shown in Figure 8.8 "The Periodic Table". The elements are listed by atomic number (the number of protons in the nucleus), and elements with similar chemical properties are grouped together in columns. Why does the periodic table have the structure it does? The answer is rather simple, if you understand electron configurations: the shape of the periodic table mimics the filling of the subshells with electrons. Let us start with H and He. Their electron configurations are 1s1 and 1s2, respectively; with He, the n = 1 shell is filled. These two elements make up the first row of the periodic table (see Figure 8.9 "The 1"). The next two electrons, for Li and Be, would go into the 2s subshell. Figure 8.10 "The 2" shows that these two elements are adjacent on the periodic table. For the next six elements, the 2p subshell is being occupied with electrons. On the right side of the periodic table, these six elements (B through Ne) are grouped together (Figure 8.11 "The 2"). The next subshell to be filled is the 3s subshell. The elements when this subshell is being filled, Na and Mg, are back on the left side of the periodic table (Figure 8.12 "The 3"). Next, the 3p subshell is filled with the next six elements (Figure 8.13 "The 3"). Instead of filling the 3d subshell next, electrons go into the 4s subshell (Figure 8.14 "The 4"). After the 4s subshell is filled, the 3d subshell is filled with up to 10 electrons. This explains the section of 10 elements in the middle of the periodic table (Figure 8.15 "The 3"). And so forth. As we go across the rows of the periodic table, the overall shape of the table outlines how the electrons are occupying the shells and subshells. The first two columns on the left side of the periodic table are where the s subshells are being occupied. Because of this, the first two rows of the periodic table are labeled the s block. Similarly, the p block are the right-most six columns of the periodic table, the d block is the middle 10 columns of the periodic table, while the f block is the 14-column section that is normally depicted as detached from the main body of the periodic table. It could be part of the main body, but then the periodic table would be rather long and cumbersome. Figure 8.16 "Blocks on the Periodic Table" shows the blocks of the periodic table. The electrons in the highest-numbered shell, plus any electrons in the last unfilled subshell, are called valence electrons; the highest-numbered shell is called the valence shell. (The inner electrons are called core electrons.) The valence electrons largely control the chemistry of an atom. If we look at just the valence shell’s electron configuration, we find that in each column, the valence shell’s electron configuration is the same. For example, take the elements in the first column of the periodic table: H, Li, Na, K, Rb, and Cs. Their electron configurations (abbreviated for the larger atoms) are as follows, with the valence shell electron configuration highlighted: H: 1s1 Li: 1s22s1 Na: [Ne]3s1 K: [Ar]4s1 Rb: [Kr]5s1 Cs: [Xe]6s1 They all have a similar electron configuration in their valence shells: a single s electron. Because much of the chemistry of an element is influenced by valence electrons, we would expect that these elements would have similar chemistry—and they do. The organization of electrons in atoms explains not only the shape of the periodic table but also the fact that elements in the same column of the periodic table have similar chemistry. The same concept applies to the other columns of the periodic table. Elements in each column have the same valence shell electron configurations, and the elements have some similar chemical properties. This is strictly true for all elements in the s and p blocks. In the d and f blocks, because there are exceptions to the order of filling of subshells with electrons, similar valence shells are not absolute in these blocks. However, many similarities do exist in these blocks, so a similarity in chemical properties is expected. Similarity of valence shell electron configuration implies that we can determine the electron configuration of an atom solely by its position on the periodic table. Consider Se, as shown in Figure 8.17 "Selenium on the Periodic Table". It is in the fourth column of the p block. This means that its electron configuration should end in a p4 electron configuration. Indeed, the electron configuration of Se is [Ar](4s^2)×(3d^10)×(4p^4), as expected. KEY TAKEAWAYS - The arrangement of electrons in atoms is responsible for the shape of the periodic table. - Electron configurations can be predicted by the position of an atom on the periodic table. One of the reasons the periodic table is so useful is because its structure allows us to qualitatively determine how some properties of the elements vary versus their position on the periodic table. The variation of properties versus position on the periodic table is called periodic trends. There is no other tool in science that allows us to judge relative properties of a class of objects like this, which makes the periodic table a very useful tool. Many periodic trends are general. There may be a few points where an opposite trend is seen, but there is an overall trend when considered across a whole row or down a whole column of the periodic table. The first periodic trend we will consider atomic radius. The atomic radius is an indication of the size of an atom. Although the concept of a definite radius of an atom is a bit fuzzy, atoms behave as if they have a certain radius. Such radii can be estimated from various experimental techniques, such as the x-ray crystallography of crystals. As you go down a column of the periodic table, the atomic radii increase. This is because the valence electron shell is getting a larger and there is a larger principal quantum number, so the valence shell lies physically farther away from the nucleus. This trend can be summarized as follows: as↓PT, atomic radius↑ where PT stands for periodic table. Going across a row on the periodic table, left to right, the trend is different. This is because although the valence shell maintains the same principal quantum number, the number of protons—and hence the nuclear charge—is increasing as you go across the row. The increasing positive charge casts a tighter grip on the valence electrons, so as you go across the periodic table, the atomic radii decrease. Again, we can summarize this trend as follows: as→PT, atomic radius↓ Figure 8.19 "Atomic Radii Trends on the Periodic Table" shows spheres representing the atoms of the s and p blocks from the periodic table to scale, showing the two trends for the atomic radius. Although there are some reversals in the trend (e.g., see Po in the bottom row), atoms generally get smaller as you go across the periodic table and larger as you go down any one column. Numbers are the radii in pm. Ionization energy (IE) is the amount of energy required to remove an electron from an atom in the gas phase: A(g)→A^+(g)+e− ΔH≡IE\ IE is usually expressed in kJ/mol of atoms. It is always positive because the removal of an electron always requires that energy be put in (i.e., it is endothermic). IE also shows periodic trends. As you go down the periodic table, it becomes easier to remove an electron from an atom (i.e., IE decreases) because the valence electron is farther away from the nucleus. Thus, as↓PT, IE↓ However, as you go across the periodic table and the electrons get drawn closer in, it takes more energy to remove an electron; as a result, IE increases: as→PT, IE↑ Figure 8.20 "Ionization Energy on the Periodic Table" shows values of IE versus position on the periodic table. Again, the trend isn’t absolute, but the general trends going across and down the periodic table should be obvious. IE also shows an interesting trend within a given atom. This is because more than one IE can be defined by removing successive electrons (if the atom has them to begin with): A(g) → A^+(g) + e^− IE1 A^+(g) → A^2+(g) + e^− IE2 A^2+(g) → A^3+(g) + e^− IE3 and so forth. Each successive IE is larger than the previous because an electron is being removed from an atom with a progressively larger positive charge. However, IE takes a large jump when a successive ionization goes down into a new shell. For example, the following are the first three IEs for Mg, whose electron configuration is 1s22s22p63s2: Mg(g) → Mg^+(g) + e^− IE1 = 738 kJ/mol Mg+(g) → Mg^2+(g) + e^− IE2 = 1,450 kJ/mol Mg2+(g) → Mg^3+(g) + e^− IE3 = 7,734 kJ/mol The second IE is twice the first, which is not a surprise: the first IE involves removing an electron from a neutral atom, while the second one involves removing an electron from a positive ion. The third IE, however, is over five times the previous one. Why is it so much larger? Because the first two electrons are removed from the 3s subshell, but the third electron has to be removed from the n = 2 shell (specifically, the 2p subshell, which is lower in energy than the n = 3 shell). Thus, it takes much more energy than just overcoming a larger ionic charge would suggest. It is trends like this that demonstrate that electrons are organized in atoms in groups. The opposite of IE is described by electron affinity (EA), which is the energy change when a gas-phase atom accepts an electron: A(g) + e^−→A^−(g) ΔH≡EA EA is also usually expressed in kJ/mol. EA also demonstrates some periodic trends, although they are less obvious than the other periodic trends discussed previously. Generally, as you go across the periodic table, EA increases its magnitude: as→PT, EA↑ There is not a definitive trend as you go down the periodic table; sometimes EA increases, sometimes it decreases. Figure 8.21 "Electron Affinity on the Periodic Table" shows EA values versus position on the periodic table for the s- and p-block elements. The trend isn’t absolute, especially considering the large positive EA values for the second column. However, the general trend going across the periodic table should be obvious. KEY TAKEAWAY - Certain properties—notably atomic radius, IE, and EA—can be qualitatively understood by the positions of the elements on the periodic table. How do atoms make compounds? Typically they join together in such a way that they lose their identities as elements and adopt a new identity as a compound. These joins are called chemical bonds. But how do atoms join together? Ultimately, it all comes down to electrons. Before we discuss how electrons interact, we need to introduce a tool to simply illustrate electrons in an atom. In almost all cases, chemical bonds are formed by interactions of valence electrons in atoms. To facilitate our understanding of how valence electrons interact, a simple way of representing those valence electrons would be useful. A Lewis electron dot diagram (or electron dot diagram or a Lewis diagram or a Lewis structure) is a representation of the valence electrons of an atom that uses dots around the symbol of the element. The number of dots equals the number of valence electrons in the atom. These dots are arranged to the right and left and above and below the symbol, with no more than two dots on a side. (It does not matter what order the positions are used.) For example, the Lewis electron dot diagram for hydrogen is simply Because the side is not important, the Lewis electron dot diagram could also be drawn as follows: The electron dot diagram for helium, with two valence electrons, is as follows: By putting the two electrons together on the same side, we emphasize the fact that these two electrons are both in the 1s subshell; this is the common convention we will adopt, although there will be exceptions later. The next atom, lithium, has an electron configuration of 1s22s1, so it has only one electron in its valence shell. Its electron dot diagram resembles that of hydrogen, except the symbol for lithium is used: Beryllium has two valence electrons in its 2s shell, so its electron dot diagram is like that of helium: The next atom is boron. Its valence electron shell is 2s22p1, so it has three valence electrons. The third electron will go on another side of the symbol: Again, it does not matter on which sides of the symbol the electron dots are positioned. For carbon, there are four valence electrons, two in the 2s subshell and two in the 2p subshell. As usual, we will draw two dots together on one side, to represent the 2s electrons. However, conventionally, we draw the dots for the two p electrons on different sides. As such, the electron dot diagram for carbon is as follows: With N, which has three p electrons, we put a single dot on each of the three remaining sides: For oxygen, which has four p electrons, we now have to start doubling up on the dots on one other side of the symbol. When doubling up electrons, make sure that a side has no more than two electrons. Fluorine and neon have seven and eight dots, respectively: With the next element, sodium, the process starts over with a single electron because sodium has a single electron in its highest-numbered shell, the n = 3 shell. By going through the periodic table, we see that the Lewis electron dot diagrams of atoms will never have more than eight dots around the atomic symbol. For atoms with partially filled d or f subshells, these electrons are typically omitted from Lewis electron dot diagrams. For example, the electron dot diagram for iron (valence shell configuration 4s23d6) is as follows: Elements in the same column of the periodic table have similar Lewis electron dot diagrams because they have the same valence shell electron configuration. Thus the electron dot diagrams for the first column of elements are as follows: Monatomic ions are atoms that have either lost (for cations) or gained (for anions) electrons. Electron dot diagrams for ions are the same as for atoms, except that some electrons have been removed for cations, while some electrons have been added for anions. Thus in comparing the electron configurations and electron dot diagrams for the Na atom and the Na+ ion, we note that the Na atom has a single valence electron in its Lewis diagram, while the Na+ ion has lost that one valence electron: Technically, the valence shell of the Na+ ion is now the n = 2 shell, which has eight electrons in it. So why do we not put eight dots around Na+? Conventionally, when we show electron dot diagrams for ions, we show the original valence shell of the atom, which in this case is the n = 3 shell and empty in the Na+ ion. In making cations, electrons are first lost from the highest numbered shell, not necessarily the last subshell filled. For example, in going from the neutral Fe atom to the Fe2+ ion, the Fe atom loses its two 4s electrons first, not its 3d electrons, despite the fact that the 3d subshell is the last subshell being filled. Thus we have Anions have extra electrons when compared to the original atom. Here is a comparison of the Cl atom with the Cl− ion: KEY TAKEAWAYS - Lewis electron dot diagrams use dots to represent valence electrons around an atomic symbol. - Lewis electron dot diagrams for ions have less (for cations) or more (for anions) dots than the corresponding atom. In Section 9.1 "Lewis Electron Dot Diagrams", we saw how ions are formed by losing electrons to make cations or by gaining electrons to form anions. The astute reader may have noticed something: Many of the ions that form have eight electrons in their valence shell. Either atoms gain enough electrons to have eight electrons in the valence shell and become the appropriately charged anion, or they lose the electrons in their original valence shell; the lower shell, now the valence shell, has eight electrons in it, so the atom becomes positively charged. For whatever reason, having eight electrons in a valence shell is a particularly energetically stable arrangement of electrons. The trend that atoms like to have eight electrons in their valence shell is called the octet rule. When atoms form compounds, the octet rule is not always satisfied for all atoms at all times, but it is a very good rule of thumb for understanding the kinds of bonding arrangements that atoms can make. It is not impossible to violate the octet rule. Consider sodium: in its elemental form, it has one valence electron and is stable. It is rather reactive, however, and does not require a lot of energy to remove that electron to make the Na+ ion. We could remove another electron by adding even more energy to the ion, to make the Na2+ ion. However, that requires much more energy than is normally available in chemical reactions, so sodium stops at a 1+ charge after losing a single electron. It turns out that the Na+ ion has a complete octet in its new valence shell, the n = 2 shell, which satisfies the octet rule. The octet rule is a result of trends in energies and is useful in explaining why atoms form the ions that they do. Now consider an Na atom in the presence of a Cl atom. The two atoms have these Lewis electron dot diagrams and electron configurations: For the Na atom to obtain an octet, it must lose an electron; for the Cl atom to gain an octet, it must gain an electron. An electron transfers from the Na atom to the Cl atom: resulting in two ions—the Na+ ion and the Cl− ion: Both species now have complete octets, and the electron shells are energetically stable. From basic physics, we know that opposite charges attract. This is what happens to the Na+ and Cl− ions: where we have written the final formula (the formula for sodium chloride) as per the convention for ionic compounds, without listing the charges explicitly. The attraction between oppositely charged ions is called an ionic bond, and it is one of the main types of chemical bonds in chemistry. Ionic bonds are caused by electrons transferring from one atom to another. In electron transfer, the number of electrons lost must equal the number of electrons gained. We saw this in the formation of NaCl. A similar process occurs between Mg atoms and O atoms, except in this case two electrons are transferred: The two ions each have octets as their valence shell, and the two oppositely charged particles attract, making an ionic bond: Remember, in the final formula for the ionic compound, we do not write the charges on the ions. What about when an Na atom interacts with an O atom? The O atom needs two electrons to complete its valence octet, but the Na atom supplies only one electron: The O atom still does not have an octet of electrons. What we need is a second Na atom to donate a second electron to the O atom: These three ions attract each other to give an overall neutral-charged ionic compound, which we write as Na2O. The need for the number of electrons lost being equal to the number of electrons gained explains why ionic compounds have the ratio of cations to anions that they do. This is required by the law of conservation of matter as well. The strength of ionic bonding depends on two major characteristics: the magnitude of the charges and the size of the ion. The greater the magnitude of the charge, the stronger the ionic bond. The smaller the ion, the stronger the ionic bond (because a smaller ion size allows the ions to get closer together). The measured strength of ionic bonding is called the lattice energy. Some lattice energies are given in Table 9.1 "Lattice Energies of Some Ionic Compounds". KEY TAKEAWAYS - The tendency to form species that have eight electrons in the valence shell is called the octet rule. - The attraction of oppositely charged ions caused by electron transfer is called an ionic bond. - The strength of ionic bonding depends on the magnitude of the charges and the sizes of the ions. Ionic bonding typically occurs when it is easy for one atom to lose one or more electrons and another atom to gain one or more electrons. However, some atoms won’t give up or gain electrons easily. Yet they still participate in compound formation. How? There is another mechanism for obtaining a complete valence shell: sharing electrons. When electrons are shared between two atoms, they make a bond called a covalent bond. Let us illustrate a covalent bond by using H atoms, with the understanding that H atoms need only two electrons to fill the 1s subshell. Each H atom starts with a single electron in its valence shell: The two H atoms can share their electrons: We can use circles to show that each H atom has two electrons around the nucleus, completely filling each atom’s valence shell: Because each H atom has a filled valence shell, this bond is stable, and we have made a diatomic hydrogen molecule. (This explains why hydrogen is one of the diatomic elements.) For simplicity’s sake, it is not unusual to represent the covalent bond with a dash, instead of with two dots: H–H Because two atoms are sharing one pair of electrons, this covalent bond is called a single bond. As another example, consider fluorine. F atoms have seven electrons in their valence shell: These two atoms can do the same thing that the H atoms did; they share their unpaired electrons to make a covalent bond. Note that each F atom has a complete octet around it now: We can also write this using a dash to represent the shared electron pair: There are two different types of electrons in the fluorine diatomic molecule. The bonding electron pair makes the covalent bond. Each F atom has three other pairs of electrons that do not participate in the bonding; they are called lone electron pairs. Each F atom has one bonding pair and three lone pairs of electrons. Covalent bonds can be made between different elements as well. One example is HF. Each atom starts out with an odd number of electrons in its valence shell: The two atoms can share their unpaired electrons to make a covalent bond: We note that the H atom has a full valence shell with two electrons, while the F atom has a complete octet of electrons. More than two atoms can participate in covalent bonding, although any given covalent bond will be between two atoms only. Consider H and O atoms: The H and O atoms can share an electron to form a covalent bond: The H atom has a complete valence shell. However, the O atom has only seven electrons around it, which is not a complete octet. We fix this by including a second H atom, whose single electron will make a second covalent bond with the O atom: (It does not matter on what side the second H atom is positioned.) Now the O atom has a complete octet around it, and each H atom has two electrons, filling its valence shell. This is how a water molecule, H2O, is made. There is a simple set of steps for determining the Lewis electron dot diagram of a simple molecule. First, you must identify the central atom and the surrounding atoms. The central atom is the atom in the center of the molecule, while the surrounding atoms are the atoms making bonds to the central atom. The central atom is usually written first in the formula of the compound (H2O is the notable exception). After the central and surrounding atoms have been identified, follow these steps: 1. Count the total number of valence electrons. Add extra if the species has negative charges and remove some for every positive charge on the species. 2. Write the central atom and surround it with the surrounding atoms. 3. Put a pair of electrons between the central atom and each surrounding atom. 4. Complete the octets around the surrounding atoms (except for H). 5. Put remaining electrons, if any, around the central atom. 6. Check that every atom has a full valence shell. Let us try these steps to determine the electron dot diagram for BF4−. The B atom is the central atom, and the F atoms are the surrounding atoms. There is a negative sign on the species, so we have an extra electron to consider. 1. Count the total number of electrons. B has 3, each F has 7, and there is one extra electron: 3 + 7 + 7 + 7 + 7 + 1 = 32. 2. Write the central atom surrounded by surrounding atoms. 3. Put a pair of electrons between the central atom and each surrounding atom. This uses up eight electrons, so we have 32 − 8 = 24 electrons left. 4. Complete the octets around the surrounding atoms (except for H). This uses up 24 more electrons, leaving 24 − 24 = 0 electrons left. 5. Put remaining electrons, if any, around the central atom. There are no additional electrons to add to the central atom. 6. Check. The B atom has eight electrons around it, as does each F atom. Each atom has a complete octet. This is a good Lewis electron dot diagram for BF4−. Sometimes, however, these steps don’t work. If we were to follow these steps for the compound formaldehyde (CH2O), we would get the following: The H and O atoms have the proper number of electrons, but the C atom has only six electrons around it, not the eight electrons for an octet. How do we fix this? We fix this by recognizing that two atoms can share more than one pair of electrons. In the case of CH2O, the O and C atoms share two pairs of electrons, with the following Lewis electron dot diagram as a result: By circling the electrons around each atom, we can now see that the O and C atoms have octets, while each H atom has two electrons: Each valence shell is full, so this is an acceptable Lewis electron dot diagram. If we were to use lines to represent the bonds, we would use two lines between the C and O atoms: The bond between the C and O atoms is a double bond and represents two bonding pairs of electrons between the atoms. If using the rules for drawing Lewis electron dot diagrams don’t work as written, a double bond may be required. It is also possible to have a triple bond, in which there are three pairs of electrons between two atoms. Good examples of this are elemental nitrogen (N2) and acetylene (C2H2): Acetylene is an interesting example of a molecule with two central atoms, which are both C atoms. Polyatomic ions are bonded together with covalent bonds. Because they are ions, however, they participate in ionic bonding with other ions. So both major types of bonding can occur at the same time. KEY TAKEAWAYS - Covalent bonds are formed when atoms share electrons. - Lewis electron dot diagrams can be drawn to illustrate covalent bond formation. - Double bonds or triple bonds between atoms may be necessary to properly illustrate the bonding in some molecules. Consider the H2 molecule: Because the nuclei of each H atom contain protons, the electrons in the bond are attracted to the nuclei (opposite charges attract). But because the two atoms involved in the covalent bond are both H atoms, each nucleus attracts the electrons by the same amount. Thus the electron pair is equally shared by the two atoms. The equal sharing of electrons in a covalent bond is called a nonpolar covalent bond. Now consider the HF molecule: There are two different atoms involved in the covalent bond. The H atom has one proton in its nucleus that is attracting the bonding pair of electrons. However, the F atom has nine protons in its nucleus, with nine times the attraction of the H atom. The F atom attracts the electrons so much more strongly that the electrons remain closer to the F atom than to the H atom; the electrons are no longer equally balanced between the two nuclei. Instead of representing the HF molecule as it may be more appropriate to draw the covalent bond as with the electrons in the bond being nearer to the F atom than the H atom. Because the electrons in the bond are nearer to the F atom, this side of the molecule takes on a partial negative charge, which is represented by δ− (δ is the lowercase Greek letter delta). The other side of the molecule, the H atom, adopts a partial positive charge, which is represented by δ+: A covalent bond between different atoms that attract the shared electrons by different amounts and cause an imbalance of electron distribution is called a polar covalent bond. Technically, any covalent bond between two different elements is polar. However, the degree of polarity is important. A covalent bond between two different elements may be so slightly imbalanced that the bond is, essentially, nonpolar. A bond may be so polar that an electron actually transfers from one atom to another, forming a true ionic bond. How do we judge the degree of polarity? Scientists have devised a scale called electronegativity, a scale for judging how much atoms of any element attract electrons. Electronegativity is a unitless number; the higher the number, the more an atom attracts electrons. A common scale for electronegativity is shown in Figure 9.2 "Electronegativities of the Elements". The polarity of a covalent bond can be judged by determining the difference of the electronegativities of the two atoms involved in the covalent bond, as summarized in the following table: The polarity of a covalent bond can have significant influence on the properties of the substance. If the overall molecule is polar, the substance may have a higher melting point and boiling point than expected; also, it may or may not be soluble in various other substances, such as water or hexane. It should be obvious that covalent bonds are stable because molecules exist. However, they can be broken if enough energy is supplied to a molecule. For most covalent bonds between any two given atoms, a certain amount of energy must be supplied. Although the exact amount of energy depends on the molecule, the approximate amount of energy to be supplied is similar if the atoms in the bond are the same. The approximate amount of energy needed to break a covalent bond is called the bond energy of the covalent bond. Table 9.2 "Bond Energies of Covalent Bonds" lists the bond energies of some covalent bonds. A few trends are obvious from Table 9.2 "Bond Energies of Covalent Bonds". For bonds that involve the same two elements, a double bond is stronger than a single bond, and a triple bond is stronger than a double bond. The energies of multiple bonds are not exact multiples of the single bond energy; for carbon-carbon bonds, the energy increases somewhat less than double or triple the C–C bond energy, while for nitrogen-nitrogen bonds the bond energy increases at a rate greater than the multiple of the N–N single bond energy. The bond energies in Table 9.2 "Bond Energies of Covalent Bonds" are average values; the exact value of the covalent bond energy will vary slightly among molecules with these bonds but should be close to these values. To be broken, covalent bonds always require energy; that is, covalent bond breaking is always an endothermic process. Thus the ΔH for this process is positive: Molecule–O–H → Molecule–O + H ΔH ≈ +463 kJ/mol However, when making a covalent bond, energy is always given off; covalent bond making is always an exothermic process. Thus ΔH for this process is negative: Molecule–S + H → Molecule–S–H ΔH ≈ −339 kJ/mol Bond energies can be used to estimate the energy change of a chemical reaction. When bonds are broken in the reactants, the energy change for this process is endothermic. When bonds are formed in the products, the energy change for this process is exothermic. We combine the positive energy change with the negative energy change to estimate the overall energy change of the reaction. For example, in 2H2 + O2 → 2H2O we can draw Lewis electron dot diagrams for each substance to see what bonds are broken and what bonds are formed: (The lone electron pairs on the O atoms are omitted for clarity.) We are breaking two H–H bonds and one O–O double bond and forming four O–H single bonds. The energy required for breaking the bonds is as follows: 2 H–H bonds: 2(+436 kJ/mol) 1 O=O bond: +498 kJ/mol Total: +1,370 kJ/mol The energy given off when the four O–H bonds are made is as follows: 4 O–H bonds: 4(−463 kJ/mol) Total: −1,852 kJ/mol Combining these two numbers: +1,370 kJ/mol + (−1,852 kJ/mol) Net Change: −482 kJ/mol ≈ ΔH The actual ΔH is −572 kJ/mol; we are off by about 16%—although not ideal, a 16% difference is reasonable because we used estimated, not exact, bond energies. KEY TAKEAWAYS - Covalent bonds can be nonpolar or polar, depending on the electronegativities of the atoms involved. - Covalent bonds can be broken if energy is added to a molecule. - The formation of covalent bonds is accompanied by energy given off. - Covalent bond energies can be used to estimate the enthalpy changes of chemical reactions. As important and useful as the octet rule is in chemical bonding, there are some well-known violations. This does not mean that the octet rule is useless—quite the contrary. As with many rules, there are exceptions, or violations. There are three violations to the octet rule. Odd-electron molecules represent the first violation to the octet rule. Although they are few, some stable compounds have an odd number of electrons in their valence shells. With an odd number of electrons, at least one atom in the molecule will have to violate the octet rule. Examples of stable odd-electron molecules are NO, NO2, and ClO2. The Lewis electron dot diagram for NO is as follows: Although the O atom has an octet of electrons, the N atom has only seven electrons in its valence shell. Although NO is a stable compound, it is very chemically reactive, as are most other odd-electron compounds. Electron-deficient molecules represent the second violation to the octet rule. These stable compounds have less than eight electrons around an atom in the molecule. The most common examples are the covalent compounds of beryllium and boron. For example, beryllium can form two covalent bonds, resulting in only four electrons in its valence shell: Boron commonly makes only three covalent bonds, resulting in only six valence electrons around the B atom. A well-known example is BF3: The third violation to the octet rule is found in those compounds with more than eight electrons assigned to their valence shell. These are called expanded valence shell molecules. Such compounds are formed only by central atoms in the third row of the periodic table or beyond that have empty d orbitals in their valence shells that can participate in covalent bonding. One such compound is PF5. The only reasonable Lewis electron dot diagram for this compound has the P atom making five covalent bonds: Formally, the P atom has 10 electrons in its valence shell. KEY TAKEAWAY - There are three violations to the octet rule: odd-electron molecules, electron-deficient molecules, and expanded valence shell molecules. Molecules have shapes. There is an abundance of experimental evidence to that effect—from their physical properties to their chemical reactivity. Small molecules—molecules with a single central atom—have shapes that can be easily predicted. The basic idea in molecular shapes is called valence shell electron pair repulsion (VSEPR). It basically says that electron pairs, being composed of negatively charged particles, repel each other to get as far away from each other as possible. VSEPR makes a distinction between electron group geometry, which expresses how electron groups (bonds and nonbonding electron pairs) are arranged, and molecular geometry, which expresses how the atoms in a molecule are arranged. However, the two geometries are related. There are two types of electron groups: any type of bond—single, double, or triple—and lone electron pairs. When applying VSEPR to simple molecules, the first thing to do is to count the number of electron groups around the central atom. Remember that a multiple bond counts as only one electron group. Any molecule with only two atoms is linear. A molecule whose central atom contains only two electron groups orients those two groups as far apart from each other as possible—180° apart. When the two electron groups are 180° apart, the atoms attached to those electron groups are also 180° apart, so the overall molecular shape is linear. Examples include BeH2 and CO2: A molecule with three electron groups orients the three groups as far apart as possible. They adopt the positions of an equilateral triangle—120° apart and in a plane. The shape of such molecules is trigonal planar. An example is BF3: Some substances have a trigonal planar electron group distribution but have atoms bonded to only two of the three electron groups. An example is GeF2: From an electron group geometry perspective, GeF2 has a trigonal planar shape, but its real shape is dictated by the positions of the atoms. This shape is called bent or angular. A molecule with four electron groups about the central atom orients the four groups in the direction of a tetrahedron, as shown in Figure 9.3 "Tetrahedral Geometry". If there are four atoms attached to these electron groups, then the molecular shape is also tetrahedral. Methane (CH4) is an example. This diagram of CH4 illustrates the standard convention of displaying a three-dimensional molecule on a two-dimensional surface. The straight lines are in the plane of the page, the solid wedged line is coming out of the plane toward the reader, and the dashed wedged line is going out of the plane away from the reader. NH3 is an example of a molecule whose central atom has four electron groups but only three of them are bonded to surrounding atoms. Although the electron groups are oriented in the shape of a tetrahedron, from a molecular geometry perspective, the shape of NH3 is trigonal pyramidal. H2O is an example of a molecule whose central atom has four electron groups but only two of them are bonded to surrounding atoms. Although the electron groups are oriented in the shape of a tetrahedron, the shape of the molecule is bent or angular. A molecule with four electron groups about the central atom but only one electron group bonded to another atom is linear because there are only two atoms in the molecule. Double or triple bonds count as a single electron group. CH2O has the following Lewis electron dot diagram. The central C atom has three electron groups around it because the double bond counts as one electron group. The three electron groups repel each other to adopt a trigonal planar shape: (The lone electron pairs on the O atom are omitted for clarity.) The molecule will not be a perfect equilateral triangle because the C–O double bond is different from the two C–H bonds, but both planar and triangular describe the appropriate approximate shape of this molecule. KEY TAKEAWAY - The approximate shape of a molecule can be predicted from the number of electron groups and the number of surrounding atoms. In Chapter 6 "Gases", we discussed the properties of gases. Here, we consider some properties of liquids and solids. As a review, Table 10.1 "Properties of the Three Phases of Matter" lists some general properties of the three phases of matter. Why does a substance have the phase it does? The preferred phase of a substance at a given set of conditions is a balance between the energy of the particles and intermolecular forces (or intermolecular interactions) between the particles. If the forces between particles are strong enough, the substance is a liquid or, if stronger, a solid. If the forces between particles are weak and sufficient energy is present, the particles separate from each other, so the gas phase is the preferred phase. The energy of the particles is mostly determined by temperature, so temperature is the main variable that determines what phase is stable at any given point. What forces define intermolecular interactions? There are several. A force present in all substances with electrons is the dispersion force (sometimes called the London dispersion force, after the physicist Fritz London, who first described this force in the early 1900s). This interaction is caused by the instantaneous position of an electron in a molecule, which temporarily makes that point of the molecule negatively charged and the rest of the molecule positively charged. In an instant, the electron is now somewhere else, but the fleeting imbalance of electric charge in the molecule allows molecules to interact with each other. As you might expect, the greater the number of electrons in a species, the stronger the dispersion force; this partially explains why smaller molecules are gases and larger molecules are liquids and solids at the same temperature. (Mass is a factor as well.) Molecules with a permanent dipole moment experience dipole-dipole interactions, which are generally stronger than dispersion forces if all other things are equal. The oppositely charged ends of a polar molecule, which have partial charges on them, attract each other (Figure 10.1 "Dipole-Dipole Interactions"). Thus a polar molecule such CH2Cl2 has a significantly higher boiling point (313 K, or 40°C) than a nonpolar molecule like CF4 (145 K, or −128°C), even though it has a lower molar mass (85 g/mol vs. 88 g/mol). An unusually strong form of dipole-dipole interaction is called hydrogen bonding. Hydrogen bonding is found in molecules with an H atom bonded to an N atom, an O atom, or an F atom. Such covalent bonds are very polar, and the dipole-dipole interaction between these bonds in two or more molecules is strong enough to create a new category of intermolecular force. Hydrogen bonding is the reason water has unusual properties. For such a small molecule (its molar mass is only 18 g/mol), H2O has relatively high melting and boiling points. Its boiling point is 373 K (100°C), while the boiling point of a similar molecule, H2S, is 233 K (−60°C). This is because H2O molecules experience hydrogen bonding, while H2S molecules do not. This strong attraction between H2O molecules requires additional energy to separate the molecules in the condensed phase, so its boiling point is higher than would be expected. Hydrogen bonding is also responsible for water’s ability as a solvent, its high heat capacity, and its ability to expand when freezing; the molecules line up in such a way that there is extra space between the molecules, increasing its volume in the solid state (Figure 10.2 "Hydrogen Bonding"). When water solidifies, hydrogen bonding between the molecules forces the molecules to line up in a way that creates empty space between the molecules, increasing the overall volume of the solid. This is why ice is less dense than liquid water. The preferred phase a substance adopts can change with temperature. At low temperatures, most substances are solids (only helium is predicted to be a liquid at absolute zero). As the temperature increases, those substances with very weak intermolecular forces become gases directly (in a process called sublimation, which will be discussed in Section 10.2 "Phase Transitions: Melting, Boiling, and Subliming"). Substances with weak interactions can become liquids as the temperature increases. As the temperature increases even more, the individual particles will have so much energy that the intermolecular forces are overcome, so the particles separate from each other, and the substance becomes a gas (assuming that their chemical bonds are not so weak that the compound decomposes from the high temperature). Although is it difficult to predict the temperature ranges for which solid, liquid, or gas is the preferred phase for any random substance, all substances progress from solid to liquid to gas in that order as temperature increases. KEY TAKEAWAYS - All substances experience dispersion forces between their particles. - Substances that are polar experience dipole-dipole interactions. - Substances with covalent bonds between an H atom and N, O, or F atoms experience hydrogen bonding. - The preferred phase of a substance depends on the strength of the intermolecular force and the energy of the particles. Substances can change phase—often because of a temperature change. At low temperatures, most substances are solid; as the temperature increases, they become liquid; at higher temperatures still, they become gaseous. The process of a solid becoming a liquid is called melting (an older term that you may see sometimes is fusion). The opposite process, a liquid becoming a solid, is called solidification. For any pure substance, the temperature at which melting occurs—known as the melting point—is a characteristic of that substance. It requires energy for a solid to melt into a liquid. Every pure substance has a certain amount of energy it needs to change from a solid to a liquid. This amount is called the enthalpy of fusion (or heat of fusion) of the substance, represented as ΔHfus. Some ΔHfus values are listed in Table 10.2 "Enthalpies of Fusion for Various Substances"; it is assumed that these values are for the melting point of the substance. Note that the unit of ΔHfus is kilojoules per mole, so we need to know the quantity of material to know how much energy is involved. The ΔHfus is always tabulated as a positive number. However, it can be used for both the melting and the solidification processes as long as you keep in mind that melting is always endothermic (so ΔH will be positive), while solidification is always exothermic (so ΔH will be negative). During melting, energy goes exclusively to changing the phase of a substance; it does not go into changing the temperature of a substance. Hence melting is an isothermal process because a substance stays at the same temperature. Only when all of a substance is melted does any additional energy go to changing its temperature. What happens when a solid becomes a liquid? In a solid, individual particles are stuck in place because the intermolecular forces cannot be overcome by the energy of the particles. When more energy is supplied (e.g., by raising the temperature), there comes a point at which the particles have enough energy to move around but not enough energy to separate. This is the liquid phase: particles are still in contact but are able to move around each other. This explains why liquids can assume the shape of their containers: the particles move around and, under the influence of gravity, fill the lowest volume possible (unless the liquid is in a zero-gravity environment—see Figure 10.3 "Liquids and Gravity"). The phase change between a liquid and a gas has some similarities to the phase change between a solid and a liquid. At a certain temperature, the particles in a liquid have enough energy to become a gas. The process of a liquid becoming a gas is called boiling (or vaporization), while the process of a gas becoming a liquid is called condensation. However, unlike the solid/liquid conversion process, the liquid/gas conversion process is noticeably affected by the surrounding pressure on the liquid because gases are strongly affected by pressure. This means that the temperature at which a liquid becomes a gas, the boiling point, can change with surrounding pressure. Therefore, we define the normal boiling point as the temperature at which a liquid changes to a gas when the surrounding pressure is exactly 1 atm, or 760 torr. Unless otherwise specified, it is assumed that a boiling point is for 1 atm of pressure. Like the solid/liquid phase change, the liquid/gas phase change involves energy. The amount of energy required to convert a liquid to a gas is called the enthalpy of vaporization (or heat of vaporization), represented as ΔHvap. Some ΔHvap values are listed in Table 10.3 "Enthalpies of Vaporization for Various Substances"; it is assumed that these values are for the normal boiling point temperature of the substance, which is also given in the table. The unit for ΔHvap is also kilojoules per mole, so we need to know the quantity of material to know how much energy is involved. The ΔHvap is also always tabulated as a positive number. It can be used for both the boiling and the condensation processes as long as you keep in mind that boiling is always endothermic (so ΔH will be positive), while condensation is always exothermic (so ΔH will be negative). As with melting, the energy in boiling goes exclusively to changing the phase of a substance; it does not go into changing the temperature of a substance. So boiling is also an isothermal process. Only when all of a substance has boiled does any additional energy go to changing its temperature. What happens when a liquid becomes a gas? We have already established that a liquid is composed of particles in contact with each other. When a liquid becomes a gas, the particles separate from each other, with each particle going its own way in space. This is how gases tend to fill their containers. Indeed, in the gas phase most of the volume is empty space; only about 1/1,000th of the volume is actually taken up by matter (Figure 10.4 "Liquids and Gases"). It is this property of gases that explains why they can be compressed, a fact that is considered in Chapter 6 "Gases". In (a), the particles are a liquid; the particles are in contact but are also able to move around each other. In (b), the particles are a gas, and most of the volume is actually empty space. The particles are not to scale; in reality, the dots representing the particles would be about 1/100th the size as depicted. Under some circumstances, the solid phase can transition directly to the gas phase without going through a liquid phase, and a gas can directly become a solid. The solid-to-gas change is called sublimation, while the reverse process is called deposition. Sublimation is isothermal, like the other phase changes. There is a measurable energy change during sublimation; this energy change is called the enthalpy of sublimation, represented as ΔHsub. The relationship between the ΔHsub and the other enthalpy changes is as follows: ΔHsub = ΔHfus + ΔHvap As such, ΔHsub is not always tabulated because it can be simply calculated from ΔHfus and ΔHvap. There are several common examples of sublimation. A well-known product—dry ice—is actually solid CO2. Dry ice is dry because it sublimes, with the solid bypassing the liquid phase and going straight to the gas phase. The sublimation occurs at temperature of −77°C, so it must be handled with caution. If you have ever noticed that ice cubes in a freezer tend to get smaller over time, it is because the solid water is very slowly subliming. “Freezer burn” isn’t actually a burn; it occurs when certain foods, such as meats, slowly lose solid water content because of sublimation. The food is still good but looks unappetizing. Reducing the temperature of a freezer will slow the sublimation of solid water. Chemical equations can be used to represent a phase change. In such cases, it is crucial to use phase labels on the substances. For example, the chemical equation for the melting of ice to make liquid water is as follows: H2O(s) → H2O(ℓ) No chemical change is taking place; however, a physical change is taking place. KEY TAKEAWAYS - Phase changes can occur between any two phases of matter. - All phase changes occur with a simultaneous change in energy. - All phase changes are isothermal. There are some properties that all liquids have. The liquid that we are most familiar with is probably water, and it has these properties. Other liquids have them as well, which is something to keep in mind. All liquids have a certain portion of their particles having enough energy to enter the gas phase, and if these particles are at the surface of the liquid, they do so (Figure 10.5 "Evaporation"). The formation of a gas from a liquid at temperatures below the boiling point is called evaporation. At these temperatures, the material in the gas phase is called vapor, rather than gas; the term gas is reserved for when the gas phase is the stable phase. Some particles of a liquid have enough energy to escape the liquid phase to become a vapor. If the available volume is large enough, eventually all the liquid will become vapor. But if the available volume is not enough, eventually some of the vapor particles will reenter the liquid phase (Figure 10.6 "Equilibrium"). At some point, the number of particles entering the vapor phase will equal the number of particles leaving the vapor phase, so there is no net change in the amount of vapor in the system. We say that the system is at equilibrium. The partial pressure of the vapor at equilibrium is called the vapor pressure of the liquid. At some point, the number of particles entering the vapor phase will be balanced by the number of particles returning to the liquid. This point is called equilibrium. Understand that the liquid has not stopped evaporating. The reverse process—condensation—is occurring as fast as evaporation is, so there is no net change in the amount of vapor in the system. The term dynamic equilibrium represents a situation in which a process still occurs, but the opposite process also occurs at the same rate so that there is no net change in the system. The vapor pressure for a substance is dependent on the temperature of the substance; as the temperature increases, so does the vapor pressure. Figure 10.7 "Plots of Vapor Pressure versus Temperature for Several Liquids" is a plot of vapor pressure versus temperature for several liquids. Having defined vapor pressure, we can also redefine the boiling point of a liquid: the temperature at which the vapor pressure of a liquid equals the surrounding environmental pressure. The normal vapor pressure, then, is the temperature at which the vapor pressure is 760 torr, or exactly 1 atm. Thus boiling points vary with surrounding pressure, a fact that can have large implications on cooking foods at lower- or higher-than-normal elevations. Atmospheric pressure varies significantly with altitude. The vapor pressure of a liquid depends on the identity of the liquid and the temperature, as this plot shows. The vapor pressure curve for water is not exactly zero at the melting point—0°C. Even ice has a vapor pressure; that is why it sublimes over time. However, the vapor pressures of solids are typically much lower than that of liquids. At −1°C, the vapor pressure of ice is 4.2 torr. At a freezer temperature of 0°F (−17°C), the vapor pressure of ice is only 1.0 torr; so-called deep freezers can get down to −23°C, where the vapor pressure of ice is only 0.6 torr. All liquids share some other properties as well. Surface tension is an effect caused by an imbalance of forces on the atoms at the surface of a liquid, as shown in Figure 10.9 "Surface Tension". The blue particle in the bulk of the liquid experiences intermolecular forces from all around, as illustrated by the arrows. However, the yellow particle on the surface does not experience any forces above it because there are no particles above it. This leads to an imbalance of forces that we call surface tension. Surface tension comes from the fact that particles at the surface of a liquid do not experience interactions from all directions, leading to an imbalance of forces on the surface. Surface tension is responsible for several well-known behaviors of liquids, including water. Liquids with high surface tension tend to bead up when present in small amounts (Figure 10.10 "Effects of Surface Tension"). Surface tension causes liquids to form spheres in free fall or zero gravity (see Figure 10.3 "Liquids and Gravity": the “floating” water isn’t in the shape of a sphere by accident; it is the result of surface tension). Surface tension is also responsible for the fact that small insects can “walk” on water. Because of surface tension, it takes energy to break the surface of a liquid, and if an object (such as an insect) is light enough, there is not enough force due to gravity for the object to break through the surface, so the object stays on top of the water (Figure 10.11 "Walking on Water"). Carefully done, this phenomenon can also be illustrated with a thin razor blade or a paper clip. The fact that small droplets of water bead up on surfaces does not mean that water—or any other liquid—does not interact with other substances. Sometimes the attraction can be very strong. Adhesion is the tendency of a substance to interact with other substances because of intermolecular forces, while cohesion is the tendency of a substance to interact with itself. If cohesive forces within a liquid are stronger than adhesive forces between a liquid and another substance, then the liquid tends to keep to itself; it will bead up. However, if adhesive forces between a liquid and another substance are stronger than cohesive forces, then the liquid will spread out over the other substance, trying to maximize the interface between the other substance and the liquid. We say that the liquid wets the other substance. Adhesion and cohesion are important for other phenomena as well. In particular, if adhesive forces are strong, then when a liquid is introduced to a small-diameter tube of another substance, the liquid moves up or down in the tube, as if ignoring gravity. Because tiny tubes are called capillaries, this phenomenon is called capillary action. For example, one type of capillary action—capillary rise—is seen when water or water-based liquids rise up in thin glass tubes (like the capillaries sometimes used in blood tests), forming an upwardly curved surface called a meniscus. Capillary action is also responsible for the “wicking” effect that towels and sponges use to dry wet objects; the matting of fibers forms tiny capillaries that have good adhesion with water. Cotton is a good material for this; polyester and other synthetic fabrics do not display similar capillary action, which is why you seldom find rayon bath towels. A similar effect is observed with liquid fuels or melted wax and their wicks. Capillary action is thought to be at least partially responsible for transporting water from the roots to the tops of trees, even tall ones. On the other hand, some liquids have stronger cohesive forces than adhesive forces. In this case, in the presence of a capillary, the liquid is forced down from its surface; this is an example of a type of capillary action called capillary depression. In this case, the meniscus curves downward. Mercury has very strong cohesive forces; when a capillary is placed in a pool of mercury, the surface of the mercury liquid is depressed (Figure 10.12 "Capillary Action"). (a) Capillary rise is seen when adhesion is strong, such as with water in a thin glass tube. (b) Capillary depression is seen when cohesive forces are stronger than adhesive forces, such as with mercury and thin glass tubes. KEY TAKEAWAYS - All liquids evaporate. - If volume is limited, evaporation eventually reaches a dynamic equilibrium, and a constant vapor pressure is maintained. - All liquids experience surface tension, an imbalance of forces at the surface of the liquid. - All liquids experience capillary action, demonstrating either capillary rise or capillary depression in the presence of other substances. A solid is like a liquid in that particles are in contact with each other. Solids are unlike liquids in that the intermolecular forces are strong enough to hold the particles in place. At low enough temperatures, all substances are solids (helium is the lone exception), but the temperature at which the solid state becomes the stable phase varies widely among substances, from 20 K (−253°C) for hydrogen to over 3,900 K (3,600°C) for carbon. The solid phase has several characteristics. First, solids maintain their shape. They do not fill their entire containers like gases do, and they do not adopt the shape of their containers like liquids do. They cannot be easily compressed like gases can, and they have relatively high densities. Solids may also demonstrate a variety of properties. For example, many metals can be beaten into thin sheets or drawn into wires, while compounds such as NaCl will shatter if they are struck. Some metals, such as sodium and potassium, are rather soft, while others, such as diamond, are very hard and can easily scratch other substances. Appearances differ as well: most metals are shiny and silvery, but sulfur (a nonmetal) is yellow, and ionic compounds can take on a rainbow of colors. Solid metals conduct electricity and heat, while ionic solids do not. Many solids are opaque, but some are transparent. Some dissolve in water, but some do not. Figure 10.13 "Properties of Solids" shows two solids that exemplify the similar and dissimilar properties of solids. (a) Sodium metal is silvery, soft, and opaque and conducts electricity and heat well. (b) NaCl is transparent, hard, and colorless and does not conduct electricity or heat well in the solid state. These two substances illustrate the range of properties that solids can have. Solids can have a wide variety of physical properties because there are different types of solids. Here we will review the different types of solids and the bonding that gives them their properties. First, we must distinguish between two general types of solids. An amorphous solid is a solid with no long-term structure or repetition. Examples include glass and many plastics, both of which are composed of long chains of molecules with no order from one molecule to the next. A crystalline solid is a solid that has a regular, repeating three-dimensional structure. A crystal of NaCl (see Figure 10.13 "Properties of Solids") is one example: at the atomic level, NaCl is composed of a regular three-dimensional array of Na+ ions and Cl− ions. There is only one type of amorphous solid. However, there are several different types of crystalline solids, depending on the identity of the units that compose the crystal. An ionic solid is a crystalline solid composed of ions (even if the ions are polyatomic). NaCl is an example of an ionic solid (Figure 10.14 "An Ionic Solid"). The Na+ ions and Cl− ions alternate in three dimensions, repeating a pattern that goes on throughout the sample. The ions are held together by the attraction of opposite charges—a very strong force. Hence most ionic solids have relatively high melting points; for example, the melting point of NaCl is 801°C. Ionic solids are typically very brittle. To break them, the very strong ionic attractions need to be broken; a displacement of only about 1 × 10−10 m will move ions next to ions of the same charge, which results in repulsion. Ionic solids do not conduct electricity in their solid state; however, in the liquid state and when dissolved in some solvent, they do conduct electricity. This fact originally promoted the idea that some substances exist as ionic particles. A molecular solid is a crystalline solid whose components are covalently bonded molecules. Many molecular substances, especially when carefully solidified from the liquid state, form solids where the molecules line up with a regular fashion similar to an ionic crystal, but they are composed of molecules instead of ions. Because the intermolecular forces between molecules are typically less strong than in ionic solids, molecular solids typically melt at lower temperatures and are softer than ionic solids. Ice is an example of a molecular solid. In the solid state, the molecules line up in a regular pattern (Figure 10.15 "Molecular Solids"). Some very large molecules, such as biological molecules, will form crystals only if they are very carefully solidified from the liquid state or, more usually, from a dissolved state; otherwise, they will form amorphous solids. Water molecules line up in a regular pattern to form molecular solids. The dotted lines show how the polar O–H covalent bonds in one molecule engage in hydrogen bonding with other molecules. The O atoms are red, and the H atoms are white. Some solids are composed of atoms of one or more elements that are covalently bonded together in a seemingly never-ending fashion. Such solids are called covalent network solids. Each piece of the substance is essentially one huge molecule, as the covalent bonding in the crystal extends throughout the entire crystal. The two most commonly known covalent network solids are carbon in its diamond form and silicon dioxide (SiO2). Figure 10.16 "Covalent Network Solids" shows the bonding in a covalent network solid. Generally, covalent network solids are poor conductors of electricity, although their ability to conduct heat is variable: diamond is one of the most thermally conductive substances known, while SiO2 is about 100 times less thermally conductive. Most covalent network solids are very hard, as exemplified by diamond, which is the hardest known substance. Covalent network solids have high melting points by virtue of their network of covalent bonds, all of which would have to be broken for them to transform into a liquid. Indeed, covalent network solids are among the highest-melting substances known: the melting point of diamond is over 3,500°C, while the melting point of SiO2 is around 1,650°C. These characteristics are explained by the network of covalent bonds throughout the sample. Diamond is a covalent network solid, with each C atom making four covalent bonds to four other C atoms. A diamond is essentially one huge molecule. A metallic solid is a solid with the characteristic properties of a metal: shiny and silvery in color and a good conductor of heat and electricity. A metallic solid can also be hammered into sheets and pulled into wires. A metallic solid exhibits metallic bonding, a type of intermolecular interaction caused by the sharing of the s valence electrons by all atoms in the sample. It is the sharing of these valence electrons that explains the ability of metals to conduct electricity and heat well. It is also relatively easy for metals to lose these valence electrons, which explains why metallic elements usually form cations when they make compounds. KEY TAKEAWAYS - Solids can be divided into amorphous solids and crystalline solids. - Crystalline solids can be ionic, molecular, covalent network, or metallic. A solution is a homogeneous mixture—a mixture of two or more substances that are so intimately mixed that the mixture behaves in many ways like a single substance. Many chemical reactions occur when the reactants are dissolved in solution. In this chapter, we will introduce concepts that are applicable to solutions and the chemical reactions that occur in them. The major component of a solution is called the solvent. The minor component of a solution is called the solute. By major and minor we mean whichever component has the greater presence by mass or by moles. Sometimes this becomes confusing, especially with substances with very different molar masses. However, here we will confine the discussion to solutions for which the major component and the minor component are obvious. Solutions exist for every possible phase of the solute and the solvent. Salt water, for example, is a solution of solid NaCl in liquid water; soda water is a solution of gaseous CO2 in liquid water, while air is a solution of a gaseous solute (O2) in a gaseous solvent (N2). In all cases, however, the overall phase of the solution is the same phase as the solvent. One important concept of solutions is in defining how much solute is dissolved in a given amount of solvent. This concept is called concentration. Various words are used to describe the relative amounts of solute. Dilute describes a solution that has very little solute, while concentrated describes a solution that has a lot of solute. One problem is that these terms are qualitative; they describe more or less but not exactly how much. In most cases, only a certain maximum amount of solute can be dissolved in a given amount of solvent. This maximum amount is called the solubility of the solute. It is usually expressed in terms of the amount of solute that can dissolve in 100 g of the solvent at a given temperature. Table 11.2 "Solubilities of Some Ionic Compounds" lists the solubilities of some simple ionic compounds. These solubilities vary widely: NaCl can dissolve up to 31.6 g per 100 g of H2O, while AgCl can dissolve only 0.00019 g per 100 g of H2O. When the maximum amount of solute has been dissolved in a given amount of solvent, we say that the solution is saturated with solute. When less than the maximum amount of solute is dissolved in a given amount of solute, the solution is unsaturated. These terms are also qualitative terms because each solute has its own solubility. A solution of 0.00019 g of AgCl per 100 g of H2O may be saturated, but with so little solute dissolved, it is also rather dilute. A solution of 36.1 g of NaCl in 100 g of H2O is also saturated but rather concentrated. Ideally, we need more precise ways of specifying the amount of solute in a solution. We will introduce such ways in Section 11.2 "Quantitative Units of Concentration". In some circumstances, it is possible to dissolve more than the maximum amount of a solute in a solution. Usually, this happens by heating the solvent, dissolving more solute than would normally dissolve at regular temperatures, and letting the solution cool down slowly and carefully. Such solutions are called supersaturated solutions and are not stable; given an opportunity (such as dropping a crystal of solute in the solution), the excess solute will precipitate from the solution. It should be obvious that some solutes dissolve in certain solvents but not others. NaCl, for example, dissolves in water but not in vegetable oil. Beeswax dissolves in liquid hexane but not water. What is it that makes a solute soluble in some solvents but not others? The answer is intermolecular interactions. The intermolecular interactions include London dispersion forces, dipole-dipole interactions, and hydrogen bonding (as described in Chapter 10 "Solids and Liquids"). From experimental studies, it has been determined that if molecules of a solute experience the same intermolecular forces that the solvent does, the solute will likely dissolve in that solvent. So, NaCl—a very polar substance because it is composed of ions—dissolves in water, which is very polar, but not in oil, which is generally nonpolar. Nonpolar wax dissolves in nonpolar hexane but not in polar water. This concept leads to the general rule that “like dissolves like” for predicting whether a solute is soluble in a given solvent. However, this is a general rule, not an absolute statement, so it must be applied with care. KEY TAKEAWAYS - Solutions are composed of a solvent (major component) and a solute (minor component). - Concentration is the expression of the amount of solute in a given amount of solvent and can be described by several qualitative terms. - Solubility is a specific amount of solute that can dissolve in a given amount of solvent. - “Like dissolves like” is a useful rule for deciding if a solute will be soluble in a solvent. Rather than qualitative terms (Section 11.1 "Some Definitions"), we need quantitative ways to express the amount of solute in a solution; that is, we need specific units of concentration. In this section, we will introduce several common and useful units of concentration. Molarity (M) is defined as the number of moles of solute divided by the number of liters of solution: molarity = moles of solute/liters of solution which can be simplified as M=mol/L, or mol/L As with any mathematical equation, if you know any two quantities, you can calculate the third, unknown, quantity. For example, suppose you have 0.500 L of solution that has 0.24 mol of NaOH dissolved in it. The concentration of the solution can be calculated as follows: molarity=0.24 mol NaOH/0.500 L=0.48 M NaOH The concentration of the solution is 0.48 M, which is spoken as “zero point forty-eight molarity” or “zero point forty-eight molar.” If the quantity of the solute is given in mass units, you must convert mass units to mole units before using the definition of molarity to calculate concentration. For example, what is the molar concentration of a solution of 22.4 g of HCl dissolved in 1.56 L? First, convert the mass of solute to moles using the molar mass of HCl (36.5 g/mol): 22.4 g HCl×(1 mol HCl/36.5 g HCl)=0.614 mol HCl Now we can use the definition of molarity to determine a concentration: M=(0.614 mol HCl/1.56 L)=0.394 M The definition of molarity can be used to determine the amount of solute or the volume of solution, if the other information is given. Example 4 illustrates this situation. If you need to determine volume, remember the rule that the unknown quantity must be by itself and in the numerator to determine the correct answer. Thus rearrangement of the definition of molarity is required. A similar unit of concentration is molality (m), which is defined as the number of moles of solute per kilogram of solvent, not per liter of solution: molality=moles solute/kilograms solvent Mathematical manipulation of molality is the same as with molarity. Another way to specify an amount is percentage composition by mass (or mass percentage, % m/m). It is defined as follows: % m/m=(mass of solute/mass of entire sample)×100% It is not uncommon to see this unit used on commercial products (Figure 11.1 "Concentration in Commercial Applications"). Related concentration units are parts per thousand (ppth), parts per million (ppm), and parts per billion (ppb). Parts per thousand is defined as follows: ppth=(mass of solute/mass of sample)×1,000 There are similar definitions for parts per million and parts per billion: ppm=(mass of solute/mass of sample)×1,000,000 and ppb=(mass of solute/mass of sample)×1,000,000,000 Each unit is used for progressively lower and lower concentrations. The two masses must be expressed in the same unit of mass, so conversions may be necessary. As with molarity and molality, algebraic rearrangements may be necessary to answer certain questions. For ionic solutions, we need to differentiate between the concentration of the salt versus the concentration of each individual ion. Because the ions in ionic compounds go their own way when a compound is dissolved in a solution, the resulting concentration of the ion may be different from the concentration of the complete salt. For example, if 1 M NaCl were prepared, the solution could also be described as a solution of 1 M Na+(aq) and 1 M Cl−(aq) because there is one Na+ ion and one Cl− ion per formula unit of the salt. However, if the solution were 1 M CaCl2, there are two Cl−(aq) ions for every formula unit dissolved, so the concentration of Cl−(aq) would be 2 M, not 1 M. In addition, the total ion concentration is the sum of the individual ion concentrations. Thus for the 1 M NaCl, the total ion concentration is 2 M; for the 1 M CaCl2, the total ion concentration is 3 M. KEY TAKEAWAY - Quantitative units of concentration include molarity, molality, mass percentage, parts per thousand, parts per million, and parts per billion. Often, a worker will need to change the concentration of a solution by changing the amount of solvent. Dilution is the addition of solvent, which decreases the concentration of the solute in the solution. Concentration is the removal of solvent, which increases the concentration of the solute in the solution. (Do not confuse the two uses of the word concentration here!) In both dilution and concentration, the amount of solute stays the same. This gives us a way to calculate what the new solution volume must be for the desired concentration of solute. From the definition of molarity, molarity=moles of solute/liters of solution we can solve for the number of moles of solute: moles of solute = (molarity)(liters of solution) A simpler way of writing this is to use M to represent molarity and V to represent volume. So the equation becomes moles of solute = MV Because this quantity does not change before and after the change in concentration, the product MV must be the same before and after the concentration change. Using numbers to represent the initial and final conditions, we have M1V1 = M2V2 as the dilution equation. The volumes must be expressed in the same units. Note that this equation gives only the initial and final conditions, not the amount of the change. The amount of change is determined by subtraction. Concentrating solutions involves removing solvent. Usually this is done by evaporating or boiling, assuming that the heat of boiling does not affect the solute. The dilution equation is used in these circumstances as well. KEY TAKEAWAY - Calculate the new concentration or volume for a dilution or concentration of a solution. Concentration can be a conversion factor between the amount of solute and the amount of solution or solvent (depending on the definition of the concentration unit). As such, concentrations can be useful in a variety of stoichiometry problems. In many cases, it is best to use the original definition of the concentration unit; it is that definition that provides the conversion factor. A simple example of using a concentration unit as a conversion factor is one in which we use the definition of the concentration unit and rearrange; we can do the calculation again as a unit conversion, rather than as a definition. For example, suppose we ask how many moles of solute are present in 0.108 L of a 0.887 M NaCl solution. Because 0.887 M means 0.887 mol/L, we can use this second expression for the concentration as a conversion factor: 0.108 L NaCl×(0.887 mol NaCl / L NaCl)=0.0958 mol NaCl (There is an understood 1 in the denominator of the conversion factor.) If we used the definition approach, we get the same answer, but now we are using conversion factor skills. Like any other conversion factor that relates two different types of units, the reciprocal of the concentration can be also used as a conversion factor. Of course, once quantities in moles are available, another conversion can give the mass of the substance, using molar mass as a conversion factor. More complex stoichiometry problems using balanced chemical reactions can also use concentrations as conversion factors. For example, suppose the following equation represents a chemical reaction: 2AgNO3(aq) + CaCl2(aq) → 2AgCl(s) + Ca(NO3)2(aq) If we wanted to know what volume of 0.555 M CaCl2 would react with 1.25 mol of AgNO3, we first use the balanced chemical equation to determine the number of moles of CaCl2 that would react and then use concentration to convert to liters of solution: 1.25 mol AgNO3×(1 mol CaCl2/2 mol AgNO3)×(1 L solution/0.555 mol CaCl2)=1.13 L CaCl2 This can be extended by starting with the mass of one reactant, instead of moles of a reactant. We can extend our skills even further by recognizing that we can relate quantities of one solution to quantities of another solution. Knowing the volume and concentration of a solution containing one reactant, we can determine how much of another solution of another reactant will be needed using the balanced chemical equation. We have used molarity exclusively as the concentration of interest, but that will not always be the case. The next example shows a different concentration unit being used. KEY TAKEAWAY - Know how to apply concentration units as conversion factors. The properties of solutions are very similar to the properties of their respective pure solvents. This makes sense because the majority of the solution is the solvent. However, some of the properties of solutions differ from pure solvents in measurable and predictable ways. The differences are proportional to the fraction that the solute particles occupy in the solution. These properties are called colligative properties; the word colligative comes from the Greek word meaning “related to the number,” implying that these properties are related to the number of solute particles, not their identities. Before we introduce the first colligative property, we need to introduce a new concentration unit. The mole fraction of the ith component in a solution, χi, is the number of moles of that component divided by the total number of moles in the sample: χi=moles of ith component/total moles (χ is the lowercase Greek letter chi.) The mole fraction is always a number between 0 and 1 (inclusive) and has no units; it is just a number. A useful thing to note is that the sum of the mole fractions of all substances in a mixture equals 1. Thus the mole fraction of C6H6 in Example 15 could be calculated by evaluating the definition of mole fraction a second time, or—because there are only two substances in this particular mixture—we can subtract the mole fraction of the C10H8 from 1 to get the mole fraction of C6H6. Now that this new concentration unit has been introduced, the first colligative property can be considered. As was mentioned in Chapter 10 "Solids and Liquids", all pure liquids have a characteristic vapor pressure in equilibrium with the liquid phase, the partial pressure of which is dependent on temperature. Solutions, however, have a lower vapor pressure than the pure solvent has, and the amount of lowering is dependent on the fraction of solute particles, as long as the solute itself does not have a significant vapor pressure (the term nonvolatile is used to describe such solutes). This colligative property is called vapor pressure depression (or lowering). The actual vapor pressure of the solution can be calculated as follows: P soln=χ solv P∗ solv where Psoln is the vapor pressure of the solution, χsolv is the mole fraction of the solvent particles, and P∗solv is the vapor pressure of the pure solvent at that temperature (which is data that must be provided). This equation is known as Raoult’s law (the approximate pronunciation is rah-OOLT). Vapor pressure depression is rationalized by presuming that solute particles take positions at the surface in place of solvent particles, so not as many solvent particles can evaporate. Two colligative properties are related to solution concentration as expressed in molality. As a review, recall the definition of molality: molality=moles solute/kilograms solvent Because the vapor pressure of a solution with a nonvolatile solute is depressed compared to that of the pure solvent, it requires a higher temperature for the solution’s vapor pressure to reach 1.00 atm (760 torr). Recall that this is the definition of the normal boiling point: the temperature at which the vapor pressure of the liquid equals 1.00 atm. As such, the normal boiling point of the solution is higher than that of the pure solvent. This property is called boiling point elevation. The change in boiling point (ΔTb) is easily calculated: ΔTb = mKb where m is the molality of the solution and Kb is called the boiling point elevation constant, which is a characteristic of the solvent. Several boiling point elevation constants (as well as boiling point temperatures) are listed in Table 11.3 "Boiling Point Data for Various Liquids". Remember that what is initially calculated is the change in boiling point temperature, not the new boiling point temperature. Once the change in boiling point temperature is calculated, it must be added to the boiling point of the pure solvent—because boiling points are always elevated—to get the boiling point of the solution. The boiling point of a solution is higher than the boiling point of the pure solvent, but the opposite occurs with the freezing point. The freezing point of a solution is lower than the freezing point of the pure solvent. Think of this by assuming that solute particles interfere with solvent particles coming together to make a solid, so it takes a lower temperature to get the solvent particles to solidify. This is called freezing point depression. The equation to calculate the change in the freezing point for a solution is similar to the equation for the boiling point elevation: ΔTf = mKf where m is the molality of the solution and Kf is called the freezing point depression constant, which is also a characteristic of the solvent. Several freezing point depression constants (as well as freezing point temperatures) are listed in Table 11.4 "Freezing Point Data for Various Liquids". Remember that this equation calculates the change in the freezing point, not the new freezing point. What is calculated needs to be subtracted from the normal freezing point of the solvent because freezing points always go down. Freezing point depression is one colligative property we use in everyday life. Many antifreezes used in automobile radiators use solutions that have a lower freezing point than normal so that automobile engines can operate at subfreezing temperatures. We also take advantage of freezing point depression when we sprinkle various compounds on ice to thaw it in the winter for safety (Figure 11.2 "Salt and Safety"). The compounds make solutions that have a lower freezing point, so rather than forming slippery ice, any ice is liquefied and runs off, leaving a safer pavement behind. Before we introduce the final colligative property, we need to present a new concept. A semipermeable membrane is a thin membrane that will pass certain small molecules but not others. A thin sheet of cellophane, for example, acts as a semipermeable membrane. Consider the system in Figure 11.3 "Osmosis"a. A semipermeable membrane separates two solutions having the different concentrations marked. Curiously, this situation is not stable; there is a tendency for water molecules to move from the dilute side (on the left) to the concentrated side (on the right) until the concentrations are equalized, as in Figure 11.3 "Osmosis"b. This tendency is called osmosis. In osmosis, the solute remains in its original side of the system; only solvent molecules move through the semipermeable membrane. In the end, the two sides of the system will have different volumes. Because a column of liquid exerts a pressure, there is a pressure difference Π on the two sides of the system that is proportional to the height of the taller column. This pressure difference is called the osmotic pressure, which is a colligative property. (a) Two solutions of differing concentrations are placed on either side of a semipermeable membrane. (b) When osmosis occurs, solvent molecules selectively pass through the membrane from the dilute solution to the concentrated solution, diluting it until the two concentrations are the same. The pressure exerted by the different height of the solution on the right is called the osmotic pressure. The osmotic pressure of a solution is easy to calculate: Π = MRT where Π is the osmotic pressure of a solution, M is the molarity of the solution, R is the ideal gas law constant, and T is the absolute temperature. This equation is reminiscent of the ideal gas law we considered in Chapter 6 "Gases". Osmotic pressure is important in biological systems because cell walls are semipermeable membranes. In particular, when a person is receiving intravenous (IV) fluids, the osmotic pressure of the fluid needs to be approximately the same as blood serum; otherwise bad things can happen. Figure 11.4 "Osmotic Pressure and Red Blood Cells" shows three red blood cells: Figure 11.4 "Osmotic Pressure and Red Blood Cells"a shows a healthy red blood cell. Figure 11.4 "Osmotic Pressure and Red Blood Cells"b shows a red blood cell that has been exposed to a lower concentration than normal blood serum (a so-called hypotonic solution); the cell has plumped up as solvent moves into the cell to dilute the solutes inside. Figure 11.4 "Osmotic Pressure and Red Blood Cells"c shows a red blood cell exposed to a higher concentration than normal blood serum (hypertonic); water leaves the red blood cell, so it collapses onto itself. Only when the solutions inside and outside the cell are the same (isotonic) will the red blood cell be able to do its job. (a) This is what a normal red blood cell looks like. (b) When a red blood cell is exposed to a hypotonic solution, solvent goes through the cell membrane and dilutes the inside of the cell. (c) When a red blood cell is exposed to a hypertonic solution, solvent goes from the cell to the surrounding solution, diluting the hypertonic solution and collapsing the cell. Neither of these last two cases is desirable, so IV solutions must be isotonic with blood serum to not cause deleterious effects. Osmotic pressure is also the reason you should not drink seawater if you’re stranded in a lifeboat on an ocean; seawater has a higher osmotic pressure than most of the fluids in your body. You can drink the water, but ingesting it will pull water out of your cells as osmosis works to dilute the seawater. Ironically, your cells will die of thirst, and you will also die. (It is OK to drink the water if you are stranded on a body of freshwater, at least from an osmotic pressure perspective.) Osmotic pressure is also thought to be important—in addition to capillary action—in getting water to the tops of tall trees. KEY TAKEAWAYS - Colligative properties depend only on the number of dissolved particles (that is, the concentration), not their identity. - Raoult’s law is concerned with the vapor pressure depression of solutions. - The boiling points of solutions are always higher, and the freezing points of solutions are always lower, than those of the pure solvent. - Osmotic pressure is caused by concentration differences between solutions separated by a semipermeable membrane and is an important biological issue. In Section 11.5 "Colligative Properties of Solutions", we considered the colligative properties of solutions with molecular solutes. What about solutions with ionic solutes? Do they exhibit colligative properties? There is a complicating factor: ionic solutes separate into ions when they dissolve. This increases the total number of particles dissolved in solution and increases the impact on the resulting colligative property. Historically, this greater-than-expected impact on colligative properties was one main piece of evidence for ionic compounds separating into ions (increased electrical conductivity was another piece of evidence). For example, when NaCl dissolves, it separates into two ions: NaCl(s) → Na+(aq) + Cl−(aq) This means that a 1 M solution of NaCl actually has a net particle concentration of 2 M. The observed colligative property will then be twice as large as expected for a 1 M solution. It is easy to incorporate this concept into our equations to calculate the respective colligative property. We define the van’t Hoff factor (i) as the number of particles each solute formula unit breaks apart into when it dissolves. Previously, we have always tacitly assumed that the van’t Hoff factor is simply 1. But for some ionic compounds, i is not 1, as shown in Table 11.5 "Ideal van’t Hoff Factors for Ionic Compounds". The ideal van’t Hoff factor is equal to the number of ions that form when an ionic compound dissolves. It is the “ideal” van’t Hoff factor because this is what we expect from the ionic formula. However, this factor is usually correct only for dilute solutions (solutions less than 0.001 M). At concentrations greater than 0.001 M, there are enough interactions between ions of opposite charge that the net concentration of the ions is less than expected—sometimes significantly. The actual van’t Hoff factor is thus less than the ideal one. Here, we will use ideal van’t Hoff factors. Revised equations to calculate the effect of ionization are then easily produced: ΔTb = imKb ΔTf = imKg Π = iMRT where all variables have been previously defined. To calculate vapor pressure depression according to Raoult’s law, the mole fraction of solvent particles must be recalculated to take into account the increased number of particles formed on ionization. KEY TAKEAWAYS - For ionic solutes, the calculation of colligative properties must include the fact that the solutes separate into multiple particles when they dissolve. - The equations for calculating colligative properties of solutions of ionic solvents include the van’t Hoff factor, i. Acids and bases are important classes of chemical compounds. They are part of the foods and beverages we ingest, they are present in medicines and other consumer products, and they are prevalent in the world around us. In this chapter, we will focus on acids and bases and their chemistry. Historically, the first chemical definition of an acid and a base was put forward by Svante Arrhenius, a Swedish chemist, in 1884. An Arrhenius acid is a compound that increases the H+ ion concentration in aqueous solution. The H+ ion is just a bare proton, and it is rather clear that bare protons are not floating around in an aqueous solution. Instead, chemistry has defined the hydronium ion (H3O+) as the actual chemical species that represents an H+ ion. H+ ions and H3O+ ions are often considered interchangeable when writing chemical equations (although a properly balanced chemical equation should also include the additional H2O). Classic Arrhenius acids can be considered ionic compounds in which H+ is the cation. Table 12.1 "Some Arrhenius Acids" lists some Arrhenius acids and their names. An Arrhenius base is a compound that increases the OH− ion concentration in aqueous solution. Ionic compounds of the OH− ion are classic Arrhenius bases. Acids have some properties in common. They turn litmus, a plant extract, red. They react with some metals to give off H2 gas. They react with carbonate and hydrogen carbonate salts to give off CO2 gas. Acids that are ingested typically have a sour, sharp taste. (The name acid comes from the Latin word acidus, meaning “sour.”) Bases also have some properties in common. They are slippery to the touch, turn litmus blue, and have a bitter flavor if ingested. Acids and bases have another property: they react with each other to make water and an ionic compound called a salt. A salt, in chemistry, is any ionic compound made by combining an acid with a base. A reaction between an acid and a base is called a neutralization reaction and can be represented as follows: acid + base → H2O + salt The stoichiometry of the balanced chemical equation depends on the number of H+ ions in the acid and the number of OH− ions in the base. KEY TAKEAWAYS - An Arrhenius acid is a compound that increases the H+ ion concentration in aqueous solution. - An Arrhenius base is a compound that increases the OH− ion concentration in aqueous solution. - The reaction between an Arrhenius acid and an Arrhenius base is called neutralization and results in the formation of water and a salt. The Arrhenius definition of acid and base is limited to aqueous (that is, water) solutions. Although this is useful because water is a common solvent, it is limited to the relationship between the H+ ion and the OH− ion. What would be useful is a more general definition that would be more applicable to other chemical reactions and, importantly, independent of H2O. In 1923, Danish chemist Johannes Brønsted and English chemist Thomas Lowry independently proposed new definitions for acids and bases, ones that focus on proton transfer. A Brønsted-Lowry acid is any species that can donate a proton (H+) to another molecule. A Brønsted-Lowry base is any species that can accept a proton from another molecule. In short, a Brønsted-Lowry acid is a proton donor (PD), while a Brønsted-Lowry base is a proton acceptor (PA). It is easy to see that the Brønsted-Lowry definition covers the Arrhenius definition of acids and bases. Consider the prototypical Arrhenius acid-base reaction: H^+(aq)acid+OH^−(aq)base → H2O(ℓ) The acid species and base species are marked. The proton, however, is (by definition) a proton donor (labeled PD), while the OH− ion is acting as the proton acceptor (labeled PA): H^+(aq)PD+OH^−(aq)PA → H2O(ℓ) The proton donor is a Brønsted-Lowry acid, and the proton acceptor is the Brønsted-Lowry base: H^+(aq)BL acid+OH^−(aq)BL base → H2O(ℓ) Thus H+ is an acid by both definitions, and OH− is a base by both definitions. Ammonia (NH3) is a base even though it does not contain OH− ions in its formula. Instead, it generates OH− ions as the product of a proton-transfer reaction with H2O molecules; NH3 acts like a Brønsted-Lowry base, and H2O acts like a Brønsted-Lowry acid: A reaction with water is called hydrolysis; we say that NH3 hydrolyzes to make NH4+ ions and OH− ions. Even the dissolving of an Arrhenius acid in water can be considered a Brønsted-Lowry acid-base reaction. Consider the process of dissolving HCl(g) in water to make an aqueous solution of hydrochloric acid. The process can be written as follows: HCl(g) + H2O(ℓ) → H3O^+(aq) + Cl^−(aq) HCl(g) is the proton donor and therefore a Brønsted-Lowry acid, while H2O is the proton acceptor and a Brønsted-Lowry base. These two examples show that H2O can act as both a proton donor and a proton acceptor, depending on what other substance is in the chemical reaction. A substance that can act as a proton donor or a proton acceptor is called amphiprotic. Water is probably the most common amphiprotic substance we will encounter, but other substances are also amphiprotic. In the reaction between NH3 and H2O, the chemical reaction does not go to completion; rather, the reverse process occurs as well, and eventually the two processes cancel out any additional change. At this point, we say the chemical reaction is at equilibrium. Both processes still occur, but any net change by one process is countered by the same net change by the other process; it is a dynamic, rather than a static, equilibrium. Because both reactions are occurring, it makes sense to use a double arrow instead of a single arrow: What do you notice about the reverse reaction? The NH4+ ion is donating a proton to the OH− ion, which is accepting it. This means that the NH4+ ion is acting as the proton donor, or Brønsted-Lowry acid, while OH− ion, the proton acceptor, is acting as a Brønsted-Lowry base. The reverse reaction is also a Brønsted-Lowry acid base reaction: This means that both reactions are acid-base reactions by the Brønsted-Lowry definition. If you consider the species in this chemical reaction, two sets of similar species exist on both sides. Within each set, the two species differ by a proton in their formulas, and one member of the set is a Brønsted-Lowry acid, while the other member is a Brønsted-Lowry base. These sets are marked here: The two sets—NH3/NH4+ and H2O/OH−—are called conjugate acid-base pairs. We say that NH4+ is the conjugate acid of NH3, OH− is the conjugate base of H2O, and so forth. Every Brønsted-Lowry acid-base reaction can be labeled with two conjugate acid-base pairs. KEY TAKEAWAYS - A Brønsted-Lowry acid is a proton donor; a Brønsted-Lowry base is a proton acceptor. - Acid-base reactions include two sets of conjugate acid-base pairs. The reaction of an acid with a base to make a salt and water is a common reaction in the laboratory, partly because so many compounds can act as acids or bases. Another reason that acid-base reactions are so prevalent is because they are often used to determine quantitative amounts of one or the other. Performing chemical reactions quantitatively to determine the exact amount of a reagent is called a titration. A titration can be performed with almost any chemical reaction for which the balanced chemical equation is known. Here, we will consider titrations that involve acid-base reactions. In a titration, one reagent has a known concentration or amount, while the other reagent has an unknown concentration or amount. Typically, the known reagent (the titrant) is added to the unknown quantity and is dissolved in solution. The unknown amount of substance (the analyte) may or may not be dissolved in solution (but usually is). The titrant is added to the analyte using a precisely calibrated volumetric delivery tube called a burette (also spelled buret; see Figure 12.1 "Equipment for Titrations"). The burette has markings to determine how much volume of solution has been added to the analyte. When the reaction is complete, it is said to be at the equivalence point; the number of moles of titrant can be calculated from the concentration and the volume, and the balanced chemical equation can be used to determine the number of moles (and then concentration or mass) of the unknown reactant. For example, suppose 25.66 mL (or 0.02566 L) of 0.1078 M HCl was used to titrate an unknown sample of NaOH. What mass of NaOH was in the sample? We can calculate the number of moles of HCl reacted: # mol HCl = (0.02566 L)(0.1078 M) = 0.002766 mol HCl We also have the balanced chemical reaction between HCl and NaOH: HCl + NaOH → NaCl + H2O So we can construct a conversion factor to convert to number of moles of NaOH reacted: 0.002766 mol HCl×(1 mol NaOH/1 mol HCl)=0.002766 mol NaOH Then we convert this amount to mass, using the molar mass of NaOH (40.00 g/mol): 0.002766 mol NaOH×(40.00 g NaOH/1 mol NaOH)=0.1106 g NaOH This is type of calculation is performed as part of a titration. How does one know if a reaction is at its equivalence point? Usually, the person performing the titration adds a small amount of an indicator, a substance that changes color depending on the acidity or basicity of the solution. Because different indicators change colors at different levels of acidity, choosing the correct one is important in performing an accurate titration. KEY TAKEAWAYS - A titration is the quantitative reaction of an acid and a base. - Indicators are used to show that all the analyte has reacted with the titrant. Except for their names and formulas, so far we have treated all acids as equals, especially in a chemical reaction. However, acids can be very different in a very important way. Consider HCl(aq). When HCl is dissolved in H2O, it completely dissociates into H+(aq) and Cl−(aq) ions; all the HCl molecules become ions: HCl −100%→H^+(aq) + Cl^−(aq) Any acid that dissociates 100% into ions is called a strong acid. If it does not dissociate 100%, it is a weak acid. HC2H3O2 is an example of a weak acid: HC2H3O2−~5%→H^+(aq) + C2H3O2^−(aq) Because this reaction does not go 100% to completion, it is more appropriate to write it as an equilibrium: HC2H3O2⇄H+(aq) + C2H3O2^−(aq) As it turns out, there are very few strong acids, which are given in Table 12.2 "Strong Acids and Bases". If an acid is not listed here, it is a weak acid. It may be 1% ionized or 99% ionized, but it is still classified as a weak acid. The issue is similar with bases: a strong base is a base that is 100% ionized in solution. If it is less than 100% ionized in solution, it is a weak base. There are very few strong bases (see Table 12.2 "Strong Acids and Bases"); any base not listed is a weak base. All strong bases are OH– compounds. So a base based on some other mechanism, such as NH3 (which does not contain OH− ions as part of its formula), will be a weak base. Certain salts will also affect the acidity or basicity of aqueous solutions because some of the ions will undergo hydrolysis, just like NH3 does to make a basic solution. The general rule is that salts with ions that are part of strong acids or bases will not hydrolyze, while salts with ions that are part of weak acids or bases will hydrolyze. Consider NaCl. When it dissolves in an aqueous solution, it separates into Na+ ions and Cl− ions: NaCl → Na^+(aq) + Cl^−(aq) Will the Na+(aq) ion hydrolyze? If it does, it will interact with the OH− ion to make NaOH: Na^+(aq) + H2O → NaOH + H^+(aq) However, NaOH is a strong base, which means that it is 100% ionized in solution: NaOH → Na^+(aq) + OH^−(aq) The free OH−(aq) ion reacts with the H+(aq) ion to remake a water molecule: H^+(aq) + OH^−(aq) → H2O The net result? There is no change, so there is no effect on the acidity or basicity of the solution from the Na+(aq) ion. What about the Cl− ion? Will it hydrolyze? If it does, it will take an H+ ion from a water molecule: Cl^−(aq) + H2O → HCl + OH^− However, HCl is a strong acid, which means that it is 100% ionized in solution: HCl → H^+(aq) + Cl^−(aq) The free H+(aq) ion reacts with the OH−(aq) ion to remake a water molecule: H^+(aq) + OH^−(aq) → H2O The net result? There is no change, so there is no effect on the acidity or basicity of the solution from the Cl−(aq) ion. Because neither ion in NaCl affects the acidity or basicity of the solution, NaCl is an example of a neutral salt. Things change, however, when we consider a salt like NaC2H3O2. We already know that the Na+ ion won’t affect the acidity of the solution. What about the acetate ion? If it hydrolyzes, it will take an H+ from a water molecule: C2H3O2^−(aq) + H2O → HC2H3O2 + OH^−(aq) Does this happen? Yes, it does. Why? Because HC2H3O2 is a weak acid. Any chance a weak acid has to form, it will (the same with a weak base). As some C2H3O2− ions hydrolyze with H2O to make the molecular weak acid, OH− ions are produced. OH− ions make solutions basic. Thus NaC2H3O2 solutions are slightly basic, so such a salt is called a basic salt. There are also salts whose aqueous solutions are slightly acidic. NH4Cl is an example. When NH4Cl is dissolved in H2O, it separates into NH4+ ions and Cl− ions. We have already seen that the Cl− ion does not hydrolyze. However, the NH4+ ion will: NH4^+(aq) + H2O → NH3(aq) + H3O^+(aq) Recall from Section 12.1 "Arrhenius Acids and Bases" that H3O+ ion is the hydronium ion, the more chemically proper way to represent the H+ ion. This is the classic acid species in solution, so a solution of NH4+(aq) ions is slightly acidic. NH4Cl is an example of an acid salt. The molecule NH3 is a weak base, and it will form when it can, just like a weak acid will form when it can. So there are two general rules: (1) If an ion derives from a strong acid or base, it will not affect the acidity of the solution. (2) If an ion derives from a weak acid, it will make the solution basic; if an ion derives from a weak base, it will make the solution acidic. Some salts are composed of ions that come from both weak acids and weak bases. The overall effect on an aqueous solution depends on which ion exerts more influence on the overall acidity. We will not consider such salts here. KEY TAKEAWAYS - Strong acids and bases are 100% ionized in aqueous solution. - Weak acids and bases are less than 100% ionized in aqueous solution. - Salts of weak acids or bases can affect the acidity or basicity of their aqueous solutions. We have already seen that H2O can act as an acid or a base: NH3 + H2O → NH4^+ + OH^− (H2O acts as an acid) HCl + H2O → H3O^+ + Cl^− (H2O acts as a base) It may not surprise you to learn, then, that within any given sample of water, some H2O molecules are acting as acids, and other H2O molecules are acting as bases. The chemical equation is as follows: H2O + H2O → H3O^+ + OH^− This occurs only to a very small degree: only about 6 in 108 H2O molecules are participating in this process, which is called the autoionization of water. At this level, the concentration of both H+(aq) and OH−(aq) in a sample of pure H2O is about 1.0 × 10−7 M. If we use square brackets—[ ]—around a dissolved species to imply the molar concentration of that species, we have [H^+] = [OH^−] = 1.0 × 10^(−7) M for any sample of pure water because H2O can act as both an acid and a base. The product of these two concentrations is 1.0 × 10−14: [H^+] × [OH^−] = (1.0 × 10^(−7))(1.0 × 10^(−7)) = 1.0 × 10^(−14) In acids, the concentration of H+(aq)—[H+]—is greater than 1.0 × 10−7 M, while for bases the concentration of OH−(aq)—[OH−]—is greater than 1.0 × 10−7 M. However, the product of the two concentrations—[H+][OH−]—is always equal to 1.0 × 10−14, no matter whether the aqueous solution is an acid, a base, or neutral: [H^+][OH^−] = 1.0 × 10^(−14) This value of the product of concentrations is so important for aqueous solutions that it is called the autoionization constant of water and is denoted Kw: Kw = [H^+][OH^−] = 1.0 × 10^(−14) This means that if you know [H+] for a solution, you can calculate what [OH−] has to be for the product to equal 1.0 × 10−14, or if you know [OH−], you can calculate [H+]. This also implies that as one concentration goes up, the other must go down to compensate so that their product always equals the value of Kw. When you have a solution of a particular acid or base, you need to look at the formula of the acid or base to determine the number of H+ or OH− ions in the formula unit because [H+] or [OH−] may not be the same as the concentration of the acid or base itself. For strong acids and bases, [H+] and [OH−] can be determined directly from the concentration of the acid or base itself because these ions are 100% ionized by definition. However, for weak acids and bases, this is not so. The degree, or percentage, of ionization would need to be known before we can determine [H+] and [OH−]. KEY TAKEAWAY - In any aqueous solution, the product of [H+] and [OH−] equals 1.0 × 10−14. As we have seen, [H+] and [OH−] values can be markedly different from one aqueous solution to another. So chemists defined a new scale that succinctly indicates the concentrations of either of these two ions. pH is a logarithmic function of [H+]: pH = −log[H^+] pH is usually (but not always) between 0 and 14. Knowing the dependence of pH on [H+], we can summarize as follows: - If pH < 7, then the solution is acidic. - If pH = 7, then the solution is neutral. - If pH > 7, then the solution is basic. This is known as the pH scale. You can use pH to make a quick determination whether a given aqueous solution is acidic, basic, or neutral. pH is a logarithmic scale. A solution that has a pH of 1.0 has 10 times the [H+] as a solution with a pH of 2.0, which in turn has 10 times the [H+] as a solution with a pH of 3.0 and so forth. Using the definition of pH, it is also possible to calculate [H+] (and [OH−]) from pH and vice versa. The general formula for determining [H+] from pH is as follows: [H^+] = 10^(−pH) You need to determine how to evaluate the above expression on your calculator. Ask your instructor if you have any questions. The other issue that concerns us here is significant figures. Because the number(s) before the decimal point in a logarithm relate to the power on 10, the number of digits after the decimal point is what determines the number of significant figures in the final answer: There is an easier way to relate [H+] and [OH−]. We can also define pOH similar to pH: pOH = −log[OH^−] (In fact, p“anything” is defined as the negative logarithm of that anything.) This also implies that [OH^−] = 10^(−pOH) A simple and useful relationship is that for any aqueous solution, pH + pOH = 14 This relationship makes it simple to determine pH from pOH or pOH from pH and then calculate the resulting ion concentration. KEY TAKEAWAYS - pH is a logarithmic function of [H^+]. - [H^+] can be calculated directly from pH. - pOH is related to pH and can be easily calculated from pH. As indicated in Section 12.4 "Strong and Weak Acids and Bases and Their Salts", weak acids are relatively common, even in the foods we eat. But we occasionally encounter a strong acid or base, such as stomach acid, which has a strongly acidic pH of 1.7. By definition, strong acids and bases can produce a relatively large amount of H+ or OH− ions and consequently have marked chemical activities. In addition, very small amounts of strong acids and bases can change the pH of a solution very quickly. If 1 mL of stomach acid [approximated as 0.1 M HCl(aq)] were added to the bloodstream and no correcting mechanism were present, the pH of the blood would decrease from about 7.4 to about 4.7—a pH that is not conducive to continued living. Fortunately, the body has a mechanism for minimizing such dramatic pH changes. The mechanism involves a buffer, a solution that resists dramatic changes in pH. Buffers do so by being composed of certain pairs of solutes: either a weak acid plus a salt derived from that weak acid or a weak base plus a salt of that weak base. For example, a buffer can be composed of dissolved HC2H3O2 (a weak acid) and NaC2H3O2 (the salt derived from that weak acid). Another example of a buffer is a solution containing NH3 (a weak base) and NH4Cl (a salt derived from that weak base). Let us use an HC2H3O2/NaC2H3O2 buffer to demonstrate how buffers work. If a strong base—a source of OH−(aq) ions—is added to the buffer solution, those OH− ions will react with the HC2H3O2 in an acid-base reaction: HC2H3O2(aq) + OH^−(aq) → H2O(ℓ) + C2H3O2^−(aq) Rather than changing the pH dramatically by making the solution basic, the added OH− ions react to make H2O, so the pH does not change much. If a strong acid—a source of H+ ions—is added to the buffer solution, the H+ ions will react with the anion from the salt. Because HC2H3O2 is a weak acid, it is not ionized much. This means that if lots of H+ ions and C2H3O2− ions are present in the same solution, they will come together to make HC2H3O2: H+(aq) + C2H3O2^−(aq) → HC2H3O2(aq) Rather than changing the pH dramatically and making the solution acidic, the added H+ ions react to make molecules of a weak acid. Figure 12.2 "The Actions of Buffers" illustrates both actions of a buffer. Buffers can react with both strong acids (top) and strong bases (side) to minimize large changes in pH. Buffers made from weak bases and salts of weak bases act similarly. For example, in a buffer containing NH3 and NH4Cl, NH3 molecules can react with any excess H+ ions introduced by strong acids: NH3(aq) + H^+(aq) → NH4^+(aq) while the NH4+(aq) ion can react with any OH− ions introduced by strong bases: NH4+^(aq) + OH^−(aq) → NH3(aq) + H2O(ℓ) Buffers work well only for limited amounts of added strong acid or base. Once either solute is completely reacted, the solution is no longer a buffer, and rapid changes in pH may occur. We say that a buffer has a certain capacity. Buffers that have more solute dissolved in them to start with have larger capacities, as might be expected. Human blood has a buffering system to minimize extreme changes in pH. One buffer in blood is based on the presence of HCO3− and H2CO3 [the second compound is another way to write CO2(aq)]. With this buffer present, even if some stomach acid were to find its way directly into the bloodstream, the change in the pH of blood would be minimal. Inside many of the body’s cells, there is a buffering system based on phosphate ions. KEY TAKEAWAY - A buffer is a solution that resists sudden changes in pH. So far in this text, when we present a chemical reaction, we have implicitly assumed that the reaction goes to completion. Indeed, our stoichiometric calculations were based on this; when we asked how much of a product is produced when so much of a reactant reacts, we are assuming that all of a reactant reacts. However, this is usually not the case; many reactions do not go to completion, and many chemists have to deal with that. In this chapter, we will study this phenomenon and see ways in which we can affect the extent of chemical reactions. Consider the following reaction occurring in a closed container (so that no material can go in or out): H2 + I2 → 2HI This is simply the reaction between elemental hydrogen and elemental iodine to make hydrogen iodide. The way the equation is written, we are led to believe that the reaction goes to completion, that all the H2 and the I2 react to make HI. However, this is not the case. The reverse chemical reaction is also taking place: 2HI → H2 + I2 It acts to undo what the first reaction does. Eventually, the reverse reaction proceeds so quickly that it matches the speed of the forward reaction. When that happens, any continued overall reaction stops: the reaction has reached chemical equilibrium (sometimes just spoken as equilibrium; plural equilibria), the point at which the forward and reverse processes balance each other’s progress. Because two opposing processes are occurring at once, it is conventional to represent an equilibrium using a double arrow, like this: H2+ I2⇄2HI The double arrow implies that the reaction is going in both directions. Note that the reaction must still be balanced. One thing to note about equilibrium is that the reactions do not stop; both the forward reaction and the reverse reaction continue to occur. They both occur at the same rate, so any overall change by one reaction is cancelled by the reverse reaction. We say that chemical equilibrium is dynamic, rather than static. Also, because both reactions are occurring simultaneously, the equilibrium can be written backward. For example, representing an equilibrium as H2+ I2⇄2HI is the same thing as representing the same equilibrium as 2HI⇄H2+ I2 The reaction must be at equilibrium for this to be the case, however. KEY TAKEAWAYS - Chemical reactions eventually reach equilibrium, a point at which forward and reverse reactions balance each other’s progress. - Chemical equilibria are dynamic: the chemical reactions are always occurring; they just cancel each other’s progress. In the mid 1860s, Norwegian scientists C. M. Guldberg and P. Waage noted a peculiar relationship between the amounts of reactants and products in an equilibrium. No matter how many reactants they started with, a certain ratio of reactants and products was achieved at equilibrium. Today, we call this observation the law of mass action. It relates the amounts of reactants and products at equilibrium for a chemical reaction. For a general chemical reaction occurring in solution, aA + bB⇄cC + dD the equilibrium constant, also known as Keq, is defined by the following expression: Keq=([C]^c[D]^d)/([A]^a[B]^b) where [A] is the molar concentration of species A at equilibrium, and so forth. The coefficients a, b, c, and d in the chemical equation become exponents in the expression for Keq. The Keq is a characteristic numerical value for a given reaction at a given temperature; that is, each chemical reaction has its own characteristic Keq. The concentration of each reactant and product in a chemical reaction at equilibrium is related; the concentrations cannot be random values, but they depend on each other. The numerator of the expression for Keq has the concentrations of every product (however many products there are), while the denominator of the expression for Keq has the concentrations of every reactant, leading to the common products over reactants definition for the Keq. Let us consider a simple example. Suppose we have this equilibrium: A⇄B There is one reactant, one product, and the coefficients on each are just 1 (assumed, not written). The Keq expression for this equilibrium is Keq=[B][A] (Exponents of 1 on each concentration are understood.) Suppose the numerical value of Keq for this chemical reaction is 2.0. If [B] = 4.0 M, then [A] must equal 2.0 M so that the value of the fraction equals 2.0: Keq=[B]/[A]=4.0/2.0=2.0 By convention, the units are understood to be M and are omitted from the Keq expression. Suppose [B] were 6.0 M. For the Keq value to remain constant (it is, after all, called the equilibrium constant), then [A] would have to be 3.0 M at equilibrium: Keq=[B]/[A]=6.0/3.0=2.0 If [A] were not equal to 3.0 M, the reaction would not be at equilibrium, and a net reaction would occur until that ratio was indeed 2.0. At that point, the reaction is at equilibrium, and any net change would cease. (Recall, however, that the forward and reverse reactions do not stop because chemical equilibrium is dynamic.) The issue is the same with more complex expressions for the Keq; only the mathematics becomes more complex. Generally speaking, given a value for the Keq and all but one concentration at equilibrium, the missing concentration can be calculated. In some types of equilibrium problems, square roots, cube roots, or even higher roots need to be analyzed to determine a final answer. Make sure you know how to perform such operations on your calculator; if you do not know, ask your instructor for assistance. The Keq was defined earlier in terms of concentrations. For gas-phase reactions, the Keq can also be defined in terms of the partial pressures of the reactants and products, Pi. For the gas-phase reaction aA(g) + bB(g)⇄cC(g) + dD(g) the pressure-based equilibrium constant, KP, is defined as follows: KP=(PC^cPD^d)/(PA^aPB^b) where PA is the partial pressure of substance A at equilibrium in atmospheres, and so forth. As with the concentration-based equilibrium constant, the units are omitted when substituting into the expression for KP. There is a simple relationship between Keq (based on concentration units) and KP (based on pressure units): KP=Keq⋅(RT)^(Δn) where R is the ideal gas law constant (in units of L·atm/mol·K), T is the absolute temperature, and Δn is the change in the number of moles of gas in the balanced chemical equation, defined as ngas,prods − ngas,rcts. Note that this equation implies that if the number of moles of gas are the same in reactants and products, Keq = KP. Finally, we recognize that many chemical reactions involve substances in the solid or liquid phases. For example, a particular chemical reaction is represented as follows: 2NaHCO3(s)⇄Na2CO3(s) + CO2(g) + H2O(ℓ) This chemical equation includes all three phases of matter. This kind of equilibrium is called a heterogeneous equilibrium because there is more than one phase present. The rule for heterogeneous equilibria is as follows: Do not include the concentrations of pure solids and pure liquids in Keq expressions. Only partial pressures for gas-phase substances or concentrations in solutions are included in the expressions of equilibrium constants. As such, the equilibrium constant expression for this reaction would simply be KP = PCO2 because the two solids and one liquid would not appear in the expression. KEY TAKEAWAYS - Every chemical equilibrium can be characterized by an equilibrium constant, known as Keq. - The Keq and KP expressions are formulated as amounts of products divided by amounts of reactants; each amount (either a concentration or a pressure) is raised to the power of its coefficient in the balanced chemical equation. - Solids and liquids do not appear in the expression for the equilibrium constant. Once equilibrium is established, the reaction is over, right? Not exactly. An experimenter has some ability to affect the equilibrium. Chemical equilibria can be shifted by changing the conditions that the system experiences. We say that we “stress” the equilibrium. When we stress the equilibrium, the chemical reaction is no longer at equilibrium, and the reaction starts to move back toward equilibrium in such a way as to decrease the stress. The formal statement is called Le Chatelier’s principle: If an equilibrium is stressed, then the reaction shifts to reduce the stress. There are several ways to stress an equilibrium. One way is to add or remove a product or a reactant in a chemical reaction at equilibrium. When additional reactant is added, the equilibrium shifts to reduce this stress: it makes more product. When additional product is added, the equilibrium shifts to reactants to reduce the stress. If reactant or product is removed, the equilibrium shifts to make more reactant or product, respectively, to make up for the loss. It is worth noting that when reactants or products are added or removed, the value of the Keq does not change. The chemical reaction simply shifts, in a predictable fashion, to reestablish concentrations so that the Keq expression reverts to the correct value. How does an equilibrium react to a change in pressure? Pressure changes do not markedly affect the solid or liquid phases. However, pressure strongly impacts the gas phase. Le Chatelier’s principle implies that a pressure increase shifts an equilibrium to the side of the reaction with the fewer number of moles of gas, while a pressure decrease shifts an equilibrium to the side of the reaction with the greater number of moles of gas. If the number of moles of gas is the same on both sides of the reaction, pressure has no effect. What is the effect of temperature changes on an equilibrium? It depends on whether the reaction is endothermic or exothermic. Recall that endothermic means that energy is absorbed by a chemical reaction, while exothermic means that energy is given off by the reaction. As such, energy can be thought of as a reactant or a product, respectively, of a reaction: endothermic: energy + reactants → products exothermic: reactants → products + energy Because temperature is a measure of the energy of the system, increasing temperature can be thought of as adding energy. The reaction will react as if a reactant or a product is being added and will act accordingly by shifting to the other side. For example, if the temperature is increased for an endothermic reaction, essentially a reactant is being added, so the equilibrium shifts toward products. Decreasing the temperature is equivalent to decreasing a reactant (for endothermic reactions) or a product (for exothermic reactions), and the equilibrium shifts accordingly. In the case of temperature, the value of the equilibrium has changed because the Keq is dependent on temperature. That is why equilibria shift with changes in temperature. A catalyst is a substance that increases the speed of a reaction. Overall, a catalyst is not a reactant and is not used up, but it still affects how fast a reaction proceeds. However, a catalyst does not affect the extent or position of a reaction at equilibrium. It helps a reaction achieve equilibrium faster. KEY TAKEAWAYS - Le Chatelier’s principle addresses how an equilibrium shifts when the conditions of an equilibrium are changed. - The direction of shift can be predicted for changes in concentrations, temperature, or pressure. - Catalysts do not affect the position of an equilibrium; they help reactions achieve equilibrium faster. There are some circumstances in which, given some initial amounts and the Keq, you will have to determine the concentrations of all species when equilibrium is achieved. Such calculations are not difficult to do, especially if a consistent approach is applied. We will consider such an approach here. Suppose we have this simple equilibrium. Its associated Keq is 4.0, and the initial concentration of each reactant is 1.0 M: H2(g)1.0 M+Cl2(g)1.0 M⇄2HCl(g)  Keq=4.0 Because we have concentrations for the reactants but not the products, we presume that the reaction will proceed in the forward direction to make products. But by how much will it proceed? We don’t know, so let us assign it a variable. Let us assume that x M H2 reacts as the reaction goes to equilibrium. This means that at equilibrium, we have (1.0 − x) M H2 left over. According to the balanced chemical equation, H2 and Cl2 react in a 1:1 ratio. How do we know that? The coefficients of these two species in the balanced chemical equation are 1 (unwritten, of course). This means that if x M H2 reacts, x M Cl2 reacts as well. If we start with 1.0 M Cl2 at the beginning and we react x M, we have (1.0 − x) M Cl2 left at equilibrium. How much HCl is made? We start with zero, but we also see that 2 mol of HCl are made for every mole of H2 (or Cl2) that reacts (from the coefficients in the balanced chemical equation), so if we lose x M H2, we gain 2x M HCl. So now we know the equilibrium concentrations of our species: H2(g)(1.0−x) M+Cl2(g)(1.0−x) M⇄2HCl(g)2x M  Keq=4.0 We can substitute these concentrations into the Keq expression for this reaction and combine it with the known value of Keq: Keq=[HCl]^2/([H2][Cl2])=(2x)^2/((1−x)(1−x))=4.0 This is an equation in one variable, so we should be able to solve for the unknown value. This expression may look formidable, but first we can simplify the denominator and write it as a perfect square as well: (2x)^2/(1−x)^2=4.0 The fraction is a perfect square, as is the 4.0 on the right. So we can take the square root of both sides: 2x/1−x=2.0 Now we rearrange and solve (be sure you can follow each step): 2x=2.0−2.0x 4x=2.0 x=0.50 Now we have to remind ourselves what x is—the amount of H2 and Cl2 that reacted—and 2x is the equilibrium [HCl]. To determine the equilibrium concentrations, we need to go back and evaluate the expressions 1 − x and 2x to get the equilibrium concentrations of our species: 1.0 − x = 1.0 − 0.50 = 0.50 M = [H2] = [Cl2] 2x = 2(0.50) = 1.0 M = [HCl] The units are assumed to be molarity. To check, we simply substitute these concentrations and verify that we get the numerical value of the Keq, in this case 4.0: (1.0)^2/((0.50)(0.50))=4.0  We formalize this process by introducing the ICE chart, where ICE stands for initial, change, and equilibrium. The initial values go in the first row of the chart. The change values, usually algebraic expressions because we do not yet know their exact numerical values, go in the next row. However, the change values must be in the proper stoichiometric ratio as indicated by the balanced chemical equation. Finally, the equilibrium expressions in the last row are a combination of the initial value and the change value for each species. The expressions in the equilibrium row are substituted into the Keq expression, which yields an algebraic equation that we try to solve. The ICE chart for the above example would look like this: Substituting the last row into the expression for the Keq yields Keq=[HCl]^2/([H2][Cl2])=(2x)^2/((1−x)(1−x))=4.0 which, of course, is the same expression we have already solved and yields the same answers for the equilibrium concentrations. The ICE chart is a more formalized way to do these types of problems. The + sign is included explicitly in the change row of the ICE chart to avoid any confusion. Sometimes when an ICE chart is set up and the Keq expression is constructed, a more complex algebraic equation will result. One of the more common equations has an x2 term in it and is called a quadratic equation. There will be two values possible for the unknown x, and for a quadratic equation with the general formula ax2 + bx + c = 0 (where a, b, and c are the coefficients of the quadratic equation), the two possible values are as follows: x=(−b±√(b2−4ac))/2a One value of x is the + sign used in the numerator, and the other value of x is the − sign used in the numerator. In this case, one value of x typically makes no sense as an answer and can be discarded as physically impossible, leaving only one possible value and the resulting set of concentrations. Example 9 illustrates this. KEY TAKEAWAY - An ICE chart is a convenient way to determine equilibrium concentrations from starting amounts. In one sense, all chemical equilibria are treated the same. However, there are several classes of reactions that are noteworthy because of either the identities of the reactants and products or the form of the Keq expression. In Chapter 12 "Acids and Bases", we noted how some acids and bases are strong and some are weak. If an acid or base is strong, it is ionized 100% in H2O. HCl(aq) is an example of a strong acid: HCl(aq) −100%→ H^+(aq) + Cl^−(aq) However, if an acid or base is weak, it may dissolve in H2O but does not ionize completely. This means that there is an equilibrium between the unionized acid or base and the ionized form. HC2H3O2 is an example of a weak acid: HC2H3O2(aq)⇄H^+(aq) + C2H3O2^–(aq) HC2H3O2 is soluble in H2O (in fact, it is the acid in vinegar), so the reactant concentration will appear in the equilibrium constant expression. But not all the molecules separate into ions. This is the case for all weak acids and bases. An acid dissociation constant, Ka, is the equilibrium constant for the dissociation of a weak acid into ions. Note the a subscript on the K; it implies that the substance is acting as an acid. The larger Ka is, the stronger the acid is. Table 13.1 "Acid Dissociation Constants for Some Weak Acids" lists several acid dissociation constants. Keep in mind that they are just equilibrium constants. Note also that the acid dissociation constant refers to one H+ ion coming off the initial reactant. Thus the acid dissociation constant for H3PO4 refers to this equilibrium: H3PO4(aq)⇄H^+(aq) + H2PO4^–(aq) Ka=7.5×10^(−3) The H2PO4− ion, called the dihydrogen phosphate ion, is also a weak acid with its own acid dissociation constant: H2PO4^–(aq)⇄H^+(aq) + HPO4^(2–)(aq) Ka=6.2×10^(−8) Thus for so-called polyprotic acids, each H+ ion comes off in sequence, and each H+ ion that ionizes does so with its own characteristic Ka. The Ka is used in equilibrium constant problems just like other equilibrium constants are. However, in some cases, we can simplify the mathematics if the numerical value of the Ka is small, much smaller than the concentration of the acid itself. Example 11 illustrates this. Weak bases also have dissociation constants, labeled Kb (the b subscript stands for base). However, values of Kb are rarely tabulated because there is a simple relationship between the Kb of a base and the Ka of its conjugate acid: Ka × Kb = 1.0 × 10^(−14) Thus it is simple to calculate the Kb of a base from the Ka of its conjugate acid. In Chapter 12 "Acids and Bases", we introduced the autoionization of water—the idea that water can act as a proton donor and proton acceptor simultaneously. Because water is not a strong acid (Table 12.2 "Strong Acids and Bases"), it must be a weak acid, which means that its behavior as an acid must be described as an equilibrium. That equilibrium is as follows: H2O(ℓ) + H2O(ℓ)⇄H3O^+(aq) + OH^–(aq) The equilibrium constant includes [H3O+] and [OH−] but not [H2O(ℓ)] because it is a pure liquid. Hence the expression does not have any terms in its denominator: K = [H3O^+][OH^−] ≡ Kw = 1.0 × 10^(−14) This is the same Kw that was introduced in Chapter 12 "Acids and Bases" and the same 1.0 × 10−14 that appears in the relationship between the Ka and the Kb of a conjugate acid-base pair. In fact, we can rewrite this relationship as follows: Ka × Kb = Kw In Chapter 4 "Chemical Reactions and Equations", Section 4.2 "Types of Chemical Reactions: Single- and Double-Displacement Reactions", on chemical reactions, the concept of soluble and insoluble compounds was introduced. Solubility rules were presented that allow a person to predict whether certain simple ionic compounds will or will not dissolve. Describing a substance as soluble or insoluble is a bit misleading because virtually all substances are soluble; they are just soluble to different extents. In particular for ionic compounds, what we typically describe as an insoluble compound can actually be ever so slightly soluble; an equilibrium is quickly established between the solid compound and the ions that do form in solution. Thus the hypothetical compound MX does in fact dissolve but only very slightly. That means we can write an equilibrium for it: MX(s)⇄M^+(aq) + X^–(aq) The equilibrium constant for a compound normally considered insoluble is called a solubility product constant and is labeled Ksp (with the subscript sp, meaning “solubility product”). Because the reactant is a solid, its concentration does not appear in the Ksp expression, so like Kw, expressions for Ksp do not have denominators. For example, the chemical equation and the expression for the Ksp for AgCl, normally considered insoluble, are as follows: AgCl(s)⇄Ag^+(aq) + Cl^–(aq) Ksp=[Ag^+][Cl^–] Equilibrium problems involving the Ksp can also be done, and they are usually more straightforward than other equilibrium problems because there is no denominator in the Ksp expression. Care must be taken, however, in completing the ICE chart and evaluating exponential expressions. KEY TAKEAWAY - Equilibrium constants exist for certain groups of equilibria, such as weak acids, weak bases, the autoionization of water, and slightly soluble salts. One important type of chemical reaction is the oxidation-reduction reaction, also known as the redox reaction. Although we introduced redox reactions in Chapter 4 "Chemical Reactions and Equations", Section 4.6 "Oxidation-Reduction Reactions", it is worth reviewing some basic concepts. Consider this chemical reaction: Mg(s) + Cl2(g) → MgCl2 The reactants are two electrically neutral elements; they have the same number of electrons as protons. The product, however, is ionic; it is composed of Mg2+ and Cl− ions. Somehow, the individual Mg atoms lose two electrons to make the Mg2+ ion, while the Cl atoms gain an electron to become Cl− ions. This reaction involves the transfer of electrons between atoms. The process of losing and gaining electrons occurs simultaneously. However, mentally we can separate the two processes. Oxidation is defined as the loss of one or more electrons by an atom. Reduction is defined as the gain of one or more electrons by an atom. So oxidation and reduction always occur together; it is only mentally that we can separate them. Chemical reactions that involve the transfer of electrons are called oxidation-reduction (or redox) reactions. Redox reactions require that we keep track of the electrons assigned to each atom in a chemical reaction. How do we do that? We use oxidation numbers to keep track of electrons in atoms. Oxidation numbers are assigned to atoms based on four rules. Oxidation numbers are not necessarily equal to the charge on the atom (although sometimes they can be); we must keep the concepts of charge and oxidation numbers separate. The rules for assigning oxidation numbers to atoms are as follows: 1. Atoms in their elemental state are assigned an oxidation number of 0. 2. Atoms in monatomic (i.e., one-atom) ions are assigned an oxidation number equal to their charge. Oxidation numbers are usually written with the sign first, then the magnitude, to differentiate them from charges. 3. In compounds, fluorine is assigned a −1 oxidation number; oxygen is usually assigned a −2 oxidation number [except in peroxide compounds (where it is −1) and in binary compounds with fluorine (where it is positive)]; and hydrogen is usually assigned a +1 oxidation number [except when it exists as the hydride ion (H−), in which case rule 2 prevails]. 4. In compounds, all other atoms are assigned an oxidation number so that the sum of the oxidation numbers on all the atoms in the species equals the charge on the species (which is zero if the species is neutral). Here are some examples for practice. In H2, both H atoms have an oxidation number of 0 by rule 1. In MgCl2, magnesium has an oxidation number of +2, while chlorine has an oxidation number of −1 by rule 2. In H2O, the H atoms each have an oxidation number of +1, while the O atom has an oxidation number of −2, even though hydrogen and oxygen do not exist as ions in this compound (rule 3). By contrast, by rule 3, each H atom in hydrogen peroxide (H2O2) has an oxidation number of +1, while each O atom has an oxidation number of −1. We can use rule 4 to determine oxidation numbers for the atoms in SO2. Each O atom has an oxidation number of −2; for the sum of the oxidation numbers to equal the charge on the species (which is zero), the S atom is assigned an oxidation number of +4. Does this mean that the sulfur atom has a 4+ charge on it? No, it means only that the S atom is assigned a +4 oxidation number by our rules of apportioning electrons among the atoms in a compound. All redox reactions occur with a simultaneous change in the oxidation numbers of some atoms. At least two elements must change their oxidation numbers. When an oxidation number of an atom is increased in the course of a redox reaction, that atom is being oxidized. When an oxidation number of an atom is decreased in the course of a redox reaction, that atom is being reduced. Thus oxidation and reduction can also be defined in terms of increasing or decreasing oxidation numbers, respectively. Oxidation reactions can become quite complex, as attested by the following redox reaction: 6H^+(aq)+2Mn+7O4^−(aq)+5H2O2−1(ℓ) →2Mn^2++2(aq)+5O20(g)+8H2O(ℓ) To demonstrate that this is a redox reaction, the oxidation numbers of the species being oxidized and reduced are listed; can you determine what is being oxidized and what is being reduced? This is also an example of a net ionic reaction; spectator ions that do not change oxidation numbers are not displayed in the equation. Eventually, we will need to learn techniques for writing correct (i.e., balanced) redox reactions. KEY TAKEAWAYS - Oxidation-reduction (redox) reactions involve the transfer of electrons from one atom to another. - Oxidation numbers are used to keep track of electrons in atoms. - There are rules for assigning oxidation numbers to atoms. - Oxidation is an increase in oxidation number (loss of electrons); reduction is a decrease in oxidation number (gain of electrons). Balancing simple redox reactions can be a straightforward matter of going back and forth between products and reactants. For example, in the redox reaction of Na and Cl2: Na + Cl2 → NaCl it should be immediately clear that the Cl atoms are not balanced. We can fix this by putting the coefficient 2 in front of the product: Na + Cl2 → 2NaCl However, now the sodium is unbalanced. This can be fixed by including the coefficient 2 in front of the Na reactant: 2Na + Cl2 → 2NaCl This reaction is now balanced. That was fairly straightforward; we say that we are able to balance the reaction by inspection. Many simple redox reactions can be balanced by inspection. The first thing you should do when encountering an unbalanced redox reaction is to try to balance it by inspection. Some redox reactions are not easily balanced by inspection. Consider this redox reaction: Al + Ag^+ → Al^(3+) + Ag At first glance, this equation seems balanced: there is one Ag atom on both sides and one Al atom on both sides. However, if you look at the total charge on each side, there is a charge imbalance: the reactant side has a total charge of 1+, while the product side has a total charge of 3+. Something is amiss with this chemical equation; despite the equal number of atoms on each side, it is not balanced. A fundamental point about redox reactions that has not arisen previously is that the total number of electrons being lost must equal the total number of electrons being gained for a redox reaction to be balanced. This is not the case for the aluminum and silver reaction: the Al atom loses three electrons to become the Al3+ ion, while the Ag+ ion gains only one electron to become elemental silver. To balance this, we will write each oxidation and reduction reaction separately, listing the number of electrons explicitly in each. Individually, the oxidation and reduction reactions are called half reactions. We will then take multiples of each reaction until the number of electrons on each side cancels completely and combine the half reactions into an overall reaction, which should then be balanced. This method of balancing redox reactions is called the half reaction method. (There are other ways of balancing redox reactions, but this is the only one that will be used in this text. The reason for this will be seen in Chapter 14 "Oxidation and Reduction", Section 14.3 "Applications of Redox Reactions: Voltaic Cells".) The oxidation half reaction involves aluminum, which is being oxidized: Al → Al^(3+) This half reaction is not completely balanced because the overall charges on each side are not equal. When an Al atom is oxidized to Al3+, it loses three electrons. We can write these electrons explicitly as products: Al → Al^(3+) + 3e^− Now this half reaction is balanced—in terms of both atoms and charges. The reduction half reaction involves silver: Ag^+ → Ag The overall charge is not balanced on both sides. But we can fix this by adding one electron to the reactant side because the Ag+ ion must accept one electron to become the neutral Ag atom: Ag^+ + e^− → Ag This half reaction is now also balanced. When combining the two half reactions into a balanced chemical equation, the key is that the total number of electrons must cancel, so the number of electrons lost by atoms are equal to the number of electrons gained by other atoms. This may require we multiply one or both half reaction(s) by an integer to make the number of electrons on each side equal. With three electrons as products and one as reactant, the least common multiple of these two numbers is three: we can use a single aluminum reaction but must take three times the silver reaction: Al → Al^(3+) + 3e^− 3 × [Ag^+ + e^− → Ag] The 3 on the second reaction is distributed to all species in the reaction: Al → Al^3+ + 3e^− 3Ag^+ + 3e^− → 3Ag Now the two half reactions can be combined just like two algebraic equations, with the arrow serving as the equals sign. The same species on opposite sides of the arrow can be canceled: Al + 3Ag^++ 3e^−→Al^(3+)+ 3Ag + 3e^− The net balanced redox reaction is as follows: Al + 3Ag^+ → Al^(3+) + 3Ag There is still only one Al atom on each side of the chemical equation, but there are now three Ag atoms, and the total charge on each side of the equation is the same (3+ for both sides). This redox reaction is balanced. It took more effort to use the half reaction method than by inspection, but the correct balanced redox reaction was obtained. Many redox reactions occur in aqueous solution—in water. Because of this, in many cases H2O or a fragment of an H2O molecule (H+ or OH−, in particular) can participate in the redox reaction. As such, we need to learn how to incorporate the solvent into a balanced redox equation. Consider the following oxidation half reaction in aqueous solution, which has one Cr atom on each side: Cr^(3+) → CrO4^− Here, the Cr atom is going from the +3 to the +7 oxidation state. To do this, the Cr atom must lose four electrons. Let us start by listing the four electrons as products: Cr^(3+) → CrO4^− + 4e^− But where do the O atoms come from? They come from water molecules or a common fragment of a water molecule that contains an O atom: the OH− ion. When we balance this half reaction, we should feel free to include either of these species in the reaction to balance the elements. Let us use H2O to balance the O atoms; we need to include four water molecules to balance the four O atoms in the products: 4H2O + Cr^(3+) → CrO4^− + 4e^− This balances the O atoms, but now introduces hydrogen to the reaction. We can balance the H atoms by adding an H+ ion, which is another fragment of the water molecule. We need to add eight H+ ions to the product side: 4H2O + Cr^(3+) → CrO4^− + 4e^− + 8H^+ The Cr atoms are balanced, the O atoms are balanced, and the H atoms are balanced; if we check the total charge on both sides of the chemical equation, they are the same (3+, in this case). This half reaction is now balanced, using water molecules and parts of water molecules as reactants and products. Reduction reactions can be balanced in a similar fashion. When oxidation and reduction half reactions are individually balanced, they can be combined in the same fashion as before: by taking multiples of each half reaction as necessary to cancel all electrons. Other species, such as H+, OH−, and H2O, may also have to be canceled in the final balanced reaction. Unless otherwise noted, it does not matter if you add H2O or OH− as a source of O atoms, although a reaction may specify acidic solution or basic solution as a hint of what species to use or what species to avoid. OH− ions are not very common in acidic solutions, so they should be avoided in those circumstances. KEY TAKEAWAYS - Redox reactions can be balanced by inspection or by the half reaction method. - A solvent may participate in redox reactions; in aqueous solutions, H2O, H+, and OH− may be reactants or products. Consider this redox reaction: Zn + Cu^(2+) → Zn^(2+) + Cu If you were to mix zinc metal and copper ions in a container, this reaction would proceed by itself; we say that this reaction is spontaneous. Suppose, however, we set up this reaction in a way depicted in Figure 14.1 "A Redox Reaction in Which the Two Half Reactions Are Physically Separated". Zinc and zinc ions are on one side of the system, while copper and copper ions are on the other side of the system. The two parts are connected with a wire. Even though the two half reactions are physically separated, a spontaneous redox reaction still occurs. However, in this case, the electrons transfer through the wire connecting the two half reactions; that is, this setup becomes a source of electricity. Useful work can be extracted from the electrons as they transfer from one side to the other—for example, a light bulb can be lit, or a motor can be operated. The apparatus as a whole, which allows useful electrical work to be extracted from a redox reaction, is called a voltaic (galvanic) cell. Each individual system that contains a half reaction is called a half cell. The half cell that contains the oxidation reaction is called the anode, while the half cell that contains the reduction reaction is called the cathode. The cathode and anode collectively are the electrodes of the voltaic cell. Because electrons are coming from the anode, the anode is considered the negative electrode of the cell, while the cathode is considered the positive electrode of the cell. Finally, because electrons are moving from one half cell to the other, a charge imbalance builds up as the reaction proceeds. To counter that, a salt bridge is used; the salt bridge contains a solution of some ionic compound whose ions migrate to either side of the voltaic cell to maintain the charge balance. The tendency for electrons to go from one half cell to another is called the voltage of the voltaic cell, represented by E. Sometimes the term potential is used to represent the voltage of a cell. Voltage is expressed in volts (V). The voltage of a voltaic cell is determined by the difference in the tendencies of the individual half cells and is characteristic of a given redox reaction when concentrations are specific (1.0 M for dissolved species and 1.0 atm for gases). Because the voltage of a redox reaction is determined by the difference of the tendencies of the individual half reactions, absolute voltages are unnecessary; only relative voltages of each half reaction are needed. The relative voltage of each half cell is represented as E1/2 and is based on the standard that the E1/2 for the reaction H^+ + e^− → 1/2H2 is assigned to be exactly 0.000 V under standard conditions of pressure and concentration. Table 14.1 "Standard Reduction Potentials of Half Reactions" lists some relative E1/2 values for some half reactions. Note that all half reactions are listed as reduction reactions, so these values are called the standard reduction potentials of each half reaction. Table 14.1 "Standard Reduction Potentials of Half Reactions" lists only reduction reactions, but a redox reaction has a reduction and an oxidation. To make the oxidation reaction, simply reverse the reduction reaction in Table 14.1 "Standard Reduction Potentials of Half Reactions" and change the sign on the E1/2 value. If the reduction potential is negative, make the voltage for the oxidation positive; if the reduction potential is positive, make the voltage for the oxidation negative. To determine the overall voltage of a particular voltaic cell, simply combine the voltages of the oxidation and reduction half reactions. Even if you need to take a multiple of a half reaction for the electrons to cancel, do not take the multiple of the E1/2. Use the values directly as is from Table 14.1 "Standard Reduction Potentials of Half Reactions". Spontaneous redox reactions have positive overall voltages. If the voltage of the reaction as written is negative, it is not spontaneous in that direction. Rather, the reverse reaction is the spontaneous redox reaction. Technically, any redox reaction can be set up to make a voltaic cell. In modern society, however, only certain redox reactions are put to practical use. A portable voltaic cell that generates electricity to power devices for our convenience is called a battery. All batteries are based on redox reactions. The first battery (called a “voltaic pile”) was constructed by the Italian scientist Alessandro Volta in 1800 and was based on the copper/zinc reaction depicted in Figure 14.1 "A Redox Reaction in Which the Two Half Reactions Are Physically Separated". Unfortunately, it was messy, requiring quantities of copper and zinc salts dissolved in water. In 1866, the French scientist Georges Leclanché invented the dry cell, a precursor to today’s modern battery. A schematic of a dry cell is shown in Figure 14.2 "Dry Cells". The zinc case and the central carbon rod serve as the anode and cathode, respectively. The other reactants are combined into a moist paste that minimizes free liquid, so the battery is less messy (hence the name dry cell). The actual redox reaction is complex but can be represented by the following redox reaction: Zn + 2MnO2 + 2NH4^+ → Zn^(2+) + Mn2O3 + 2NH3 + H2O A dry cell has a voltage of about 1.56 V. While common and useful, dry cells have relatively short lifetimes and contain acidic components. They also cannot be recharged, so they are one-use only. Batteries that can be used only once are called primary batteries. The Leclanché dry cell is a common type of battery. In the late 1950s, Lewis Urry of the Eveready Battery Company in Ohio invented the alkaline battery (still marketed today under the trade name Energizer). Alkaline batteries are similar to dry cells, but they use a basic moist paste rather than an acidic one. Moreover, the net amount of base does not change during the course of the redox reaction. The overall redox reaction is as follows: Zn + 2MnO2 → ZnO + Mn2O3 Alkaline batteries have the advantage of being longer lasting and holding their voltage better—about 1.54 V—throughout their lifetime. A common type of battery, especially with the increased popularity of personal electronic devices, is the button battery (Figure 14.3 "Button Batteries"). A button battery is a small battery that can power small electronic devices; the batteries can be as small as 5 mm across. Two popular redox reactions used for button batteries are the alkaline dry-cell reaction and a silver oxide-based reaction: Zn + Ag2O → ZnO + 2Ag Some button batteries use a lithium-based redox reaction, typified by this anode reaction: Li → Li^+ + e^− E1/2 = 3.045 V The actual redox reaction depends on the composition of the cathode and is variable depending on voltage. Lithium batteries can also be used for applications that require more energy, such as portable computers and electric vehicles. Some lithium-based batteries are rechargeable and can be used over and over again; such batteries are called secondary batteries. An important secondary battery is the lead storage battery, shown in Figure 14.4 "Lead Storage Batteries". The lead storage battery is based on this redox reaction: Pb + PbO2 + 4H^+ + SO4^(2−) → 2PbSO4 + 2H2O The redox reaction produces about 2 V, but it is typical to tie several individual batteries together to generate a larger voltage. The lead storage battery has the distinction that the product of both half reactions is PbSO4, which as a solid accumulates on the many plates within each cell (Figure 14.4 "Lead Storage Batteries"). The lead storage battery is a secondary battery, as it can be recharged and reused many times. Because it is based on lead, these batteries are rather heavy. They should also be recycled when replaced so that potentially dangerous lead does not escape into the environment. Because of their characteristics, lead storage batteries are used to start large engines in automobiles, boats, and airplanes. KEY TAKEAWAYS - A voltaic cell produces electricity as a redox reaction occurs. - The voltage of a voltaic cell can be determined by the reduction potentials of the half reactions. - Voltaic cells are fashioned into batteries, which are a convenient source of electricity. Up to this point, we have considered redox reactions for processes that are spontaneous. When set up as a voltaic cell or battery, such reactions can be used as a source of electricity. However, it is possible to go in the other direction. By forcing electricity into a cell, we can make a redox reaction occur that normally would not be spontaneous. Under these circumstances, the cell is called an electrolytic cell, and the process that occurs in the cell is called electrolysis (Figure 14.5 "Electrolysis"). In an electrolytic cell, electricity is forced through the cell to induce a nonspontaneous redox reaction. Here, the redox reaction 2H2O → 2H2 + O2 is being caused by the introduction of electricity, which is supplied by the battery. Electrolysis has many applications. For example, if NaCl is melted at about 800°C in an electrolytic cell and an electric current is passed through it, elemental sodium will appear at the cathode and elemental chlorine will appear at the anode as the following two reactions occur: Na^+ + e^− → Na 2Cl^− → Cl2 + 2e^− Normally we expect elemental sodium and chlorine to react spontaneously to make NaCl. However, by using an input of electricity, we can force the opposite reaction to occur and generate the elements. Lithium, potassium, and magnesium can also be isolated from compounds by electrolysis. Another element that is isolated by electrolysis is aluminum. Aluminum formerly was a difficult metal to isolate in its elemental form; in fact, the top of the Washington Monument has a 2.8 kg cap of aluminum metal, which at the time—1884—was the largest piece of elemental aluminum ever isolated. However, in 1886 the American Charles Hall and the Frenchman Paul Héroult almost simultaneously worked out an electrolytic process for isolating aluminum from bauxite, an ore of aluminum whose chemical formula is AlOx(OH)3 − 2x. The basic reactions are as follows: Al^(3+) + 3e^− → Al 2O^(2−) → O2 + 4e^− With the development of the Hall-Héroult process, the price of aluminum dropped by a factor of over 200, and aluminum metal became common. So much elemental aluminum is produced in the United States each year that it has been estimated that the electrolysis of aluminum uses 5% of all the electricity in the country. (Recycling aluminum requires about 1/70th the energy of refining aluminum from ore, which illustrates the tremendous energy savings that recycling provides.) Another application of electrolysis is electroplating, which is the deposition of a thin layer of metal on an object for protective or decorative purposes (Figure 14.6). Essentially, a metal object is connected to the cathode of an electrolytic cell and immersed in a solution of a particular metal cation. When the electrolytic cell is operated, a thin coating of the metal cation is reduced to the elemental metal on the surface of the object; the thickness of the coating can be as little as a few micrometers (10−6 m). Jewelry, eating utensils, electrical contacts, and car parts like bumpers are common items that are electroplated. Gold, silver, nickel, copper, and chromium are common metals used in electroplating. KEY TAKEAWAYS - Electrolysis is the forcing of a nonspontaneous redox reaction to occur by the introduction of electricity into a cell from an outside source. - Electrolysis is used to isolate elements and electroplate objects. Most chemists pay little attention to the nucleus of an atom except to consider the number of protons it contains because that determines an element’s identity. However, in nuclear chemistry, the composition of the nucleus and the changes that occur there are very important. Applications of nuclear chemistry may be more widespread than you realize. Many people are aware of nuclear power plants and nuclear bombs, but nuclear chemistry also has applications ranging from smoke detectors to medicine, from the sterilization of food to the analysis of ancient artifacts. In this chapter, we will examine some of the basic concepts of nuclear chemistry and some of the nuclear reactions that are important in our everyday lives. We saw in Chapter 3 "Atoms, Molecules, and Ions" that atoms are composed of subatomic particles—protons, neutrons, and electrons. Protons and neutrons are located in the nucleus and provide most of the mass of an atom, while electrons circle the nucleus in shells and subshells and account for an atom’s size. We also introduced in Chapter 3 "Atoms, Molecules, and Ions" the notation for succinctly representing an isotope of a particular atom: 12 6 C The element in this example, represented by the symbol C, is carbon. Its atomic number, 6, is the subscript next to the symbol and is the number of protons in the atom. The mass number, the superscript next to the symbol, is the sum of the number of protons and neutrons in the nucleus of this particular isotope. In this case, the mass number is 12, which means that the number of neutrons in the atom is 12 − 6 = 6 (that is, the mass number of the atom minus the number of protons in the nucleus equals the number of neurons). Occasionally, the atomic number is omitted in this notation because the symbol of the element itself conveys its characteristic atomic number. The two isotopes of hydrogen—2H and 3H—are given their own names and symbols: deuterium (D) and tritium (T), respectively. Atomic theory in the nineteenth century presumed that nuclei had fixed compositions. But in 1896, the French scientist Henri Becquerel found that a uranium compound placed near a photographic plate made an image on the plate, even if the compound was wrapped in black cloth. He reasoned that the uranium compound was emitting some kind of radiation that passed through the cloth to expose the photographic plate. Further investigations showed that the radiation was a combination of particles and electromagnetic rays, with its ultimate source being the atomic nucleus. These emanations were ultimately called, collectively, radioactivity. There are three main forms of radioactive emissions. The first is called an alpha particle, which is symbolized by the Greek letter α. An alpha particle is composed of two protons and two neutrons and is the same as a helium nucleus. (We often use H24e to represent an alpha particle.) It has a 2+ charge. When a radioactive atom emits an alpha particle, the original atom’s atomic number decreases by two (because of the loss of two protons), and its mass number decreases by four (because of the loss of four nuclear particles). We can represent the emission of an alpha particle with a chemical equation—for example, the alpha-particle emission of uranium-235 is as follows: 235 92 U→4 2 He+231 90 Th Rather than calling this equation a chemical equation, we call it a nuclear equation to emphasize that the change occurs in an atomic nucleus. How do we know that a product of this reaction is T90231h ? We use the law of conservation of matter, which says that matter cannot be created or destroyed. This means we must have the same number of protons and neutrons on both sides of the nuclear equation. If our uranium nucleus loses 2 protons, there are 90 protons remaining, identifying the element as thorium. Moreover, if we lose four nuclear particles of the original 235, there are 231 remaining. Thus we use subtraction to identify the isotope of the Th atom—in this case, T90231h. Chemists often use the names parent isotope and daughter isotope to represent the original atom and the product other than the alpha particle. In the previous example, U92235 is the parent isotope, and T90231h is the daughter isotope. When one element changes into another in this manner, it undergoes radioactive decay. The second major type of radioactive emission is called a beta particle, symbolized by the Greek letter β. A beta particle is an electron ejected from the nucleus (not from the shells of electrons about the nucleus) and has a 1− charge. We can also represent a beta particle as e−10. The net effect of beta particle emission on a nucleus is that a neutron is converted to a proton. The overall mass number stays the same, but because the number of protons increases by one, the atomic number goes up by one. Carbon-14 decays by emitting a beta particle: 14 6 C→14 7 N+0 −1 e Again, the sum of the atomic numbers is the same on both sides of the equation, as is the sum of the mass numbers. (Note that the electron is assigned an “atomic number” of –1, equal to its charge.) The third major type of radioactive emission is not a particle but rather a very energetic form of electromagnetic radiation called gamma rays, symbolized by the Greek letter γ. Gamma rays themselves do not carry an overall electrical charge, but they may knock electrons out of atoms in a sample of matter and make it electrically charged (for which gamma rays are termed ionizing radiation). For example, in the radioactive decay of radon-222, both alpha and gamma radiation are emitted, with the latter having an energy of 8.2 × 10−14 J per nucleus decayed: 222 86 Rn→218 84 Po+4 2 He+γ This may not seem like much energy, but if 1 mol of Rn atoms were to decay, the gamma ray energy would be 4.9 × 107 kJ! Alpha, beta, and gamma emissions have different abilities to penetrate matter. The relatively large alpha particle is easily stopped by matter (although it may impart a significant amount of energy to the matter it contacts). Beta particles penetrate slightly into matter, perhaps a few centimeters at most. Gamma rays can penetrate deeply into matter and can impart a large amount of energy into the surrounding matter. Table 15.1 "The Three Main Forms of Radioactive Emissions" summarizes the properties of the three main types of radioactive emissions. Occasionally, an atomic nucleus breaks apart into smaller pieces in a radioactive process called spontaneous fission (or fission). Typically, the daughter isotopes produced by fission are a varied mix of products, rather than a specific isotope as with alpha and beta particle emission. Often, fission produces excess neutrons that will sometimes be captured by other nuclei, possibly inducing additional radioactive events. Uranium-235 undergoes spontaneous fission to a small extent. One typical reaction is 235 92 U→139 56 Ba+94 36 Kr+2(1 0 n) where 1 0 n is a neutron. As with any nuclear process, the sums of the atomic numbers and mass numbers must be the same on both sides of the equation. Spontaneous fission is found only in large nuclei. The smallest nucleus that exhibits spontaneous fission is lead-208. (Fission is the radioactive process used in nuclear power plants and one type of nuclear bomb.) KEY TAKEAWAYS - The major types of radioactivity include alpha particles, beta particles, and gamma rays. - Fission is a type of radioactivity in which large nuclei spontaneously break apart into smaller nuclei. Whether or not a given isotope is radioactive is a characteristic of that particular isotope. Some isotopes are stable indefinitely, while others are radioactive and decay through a characteristic form of emission. As time passes, less and less of the radioactive isotope will be present, and the level of radioactivity decreases. An interesting and useful aspect of radioactive decay is half-life, which is the amount of time it takes for one-half of a radioactive isotope to decay. The half-life of a specific radioactive isotope is constant; it is unaffected by conditions and is independent of the initial amount of that isotope. Consider the following example. Suppose we have 100.0 g of tritium (a radioactive isotope of hydrogen). It has a half-life of 12.3 y. After 12.3 y, half of the sample will have decayed from hydrogen-3 to helium-3 by emitting a beta particle, so that only 50.0 g of the original tritium remains. After another 12.3 y—making a total of 24.6 y—another half of the remaining tritium will have decayed, leaving 25.0 g of tritium. After another 12.3 y—now a total of 36.9 y—another half of the remaining tritium will have decayed, leaving 12.5 g. This sequence of events is illustrated in Figure 15.1 "Radioactive Decay". During each successive half-life, half of the initial amount will radioactively decay. We can determine the amount of a radioactive isotope remaining after a given number half-lives by using the following expression: amount remaining=initial amount×(1/2)^n where n is the number of half-lives. This expression works even if the number of half-lives is not a whole number. Half-lives of isotopes range from fractions of a microsecond to billions of years. Table 15.2 "Half-Lives of Various Isotopes" lists the half-lives of some isotopes. What if the elapsed time is not an exact number of half-lives? We can still calculate the amount of material we have left, but the equation is more complicated. The equation is amount remaining = (amount initially) × e^(−0.693t/t1/2) where e is the base of natural logarithms (2.71828182…), t is the elapsed time, and t1/2 is the half-life of the radioactive isotope. The variables t and t1/2 should have the same units of time, and you may need to make sure you know how to evaluate natural-logarithm powers on your calculator (for many calculators, there is an “inverse logarithm” function that you can use; consult your instructor if you are not sure how to use your calculator). Although this is a more complicated formula, the length of time t need not be an exact multiple of half-lives. KEY TAKEAWAYS - Natural radioactive processes are characterized by a half-life, the time it takes for half of the material to decay radioactively. - The amount of material left over after a certain number of half-lives can be easily calculated. In Chapter 15 "Nuclear Chemistry", Section 15.2 "Half-Life", we used mass to indicate the amount of radioactive substance present. This is only one of several units used to express amounts of radiation. Some units describe the number of radioactive events occurring per unit time, while others express the amount of a person’s exposure to radiation. Perhaps the direct way of reporting radioactivity is the number of radioactive decays per second. One decay per second is called one becquerel (Bq). Even in a small mass of radioactive material, however, there are thousands upon thousands of decays or disintegrations per second. The unit curie (Ci), now defined as 3.7 × 1010 decays/s, was originally defined as the number of decays per second in 1 g of radium. Many radioactive samples have activities that are on the order of microcuries (µCi) or more. Both the becquerel and the curie can be used in place of grams to describe quantities of radioactive material. As an example, the amount of americium in an average smoke detector has an activity of 0.9 µCi. (The curie is named after Polish scientist Marie Curie, who performed some of the initial investigations into radioactive phenomena in the early 1900s; the becquerel is named after Henri Becquerel, who discovered radioactivity in 1896.) Other measures of radioactivity are based on the effects it has on living tissue. Radioactivity can transfer energy to tissues in two ways: through the kinetic energy of the particles hitting the tissue and through the electromagnetic energy of the gamma rays being absorbed by the tissue. Either way, the transferred energy—like the thermal energy from boiling water—can damage the tissue. The rad (an acronym for radiation absorbed dose) is a unit equivalent to 1 g of tissue absorbing 0.01 J: 1 rad = 0.01 J/g Another unit of radiation absorption is the gray (Gy): 1 Gy = 100 rad The rad is more common. To get an idea of the amount of energy this represents, consider that the absorption of 1 rad by 70,000 g of water (approximately the same mass as a 150 lb person) would increase the temperature of the water by only 0.002°C. This may not seem like a lot, but it is enough energy to break about 1 × 1021 molecular C–C bonds in a person’s body. That amount of damage would not be desirable. Predicting the effects of radiation is complicated by the fact that different types of emissions affect various tissues differently. To quantify these effects, the unit rem (an acronym for röntgen equivalent man) is defined as rem = rad × factor where factor is a number greater than or equal to 1 that takes into account the type of radioactive emission and sometimes the type of tissue being exposed. For beta particles, the factor equals 1. For alpha particles striking most tissues, the factor is 10, but for eye tissue the factor is 30. Most radioactive emissions that people are exposed to are on the order of a few dozen millirems (mrem) or less; a medical X-ray is about 20 mrem. A sievert (Sv) is a related unit and is defined as 100 rem. What is a person’s annual exposure to radioactivity and radiation? Table 15.3 "Average Annual Radiation Exposure (Approximate)" lists the sources and annual amounts of radiation exposure. It may surprise you to learn that fully 82% of the radioactivity and radiation exposure we receive is from natural sources—sources we cannot avoid. Fully 10% of the exposure comes from our own bodies—largely from carbon-14 and potassium-40. The actual effects of radioactivity and radiation exposure on a person’s health depend on the type of radioactivity, the length of exposure, and the tissues exposed. Table 15.4 "Effects of Short-Term Exposure to Radioactivity and Radiation" lists the potential threats to health at various amounts of exposure over short periods of time (hours or days). One of the simplest ways of detecting radioactivity is by using a piece of photographic film embedded in a badge or a pen. On a regular basis, the film is developed and checked for exposure. Comparing the exposure level of the film with a set of standard exposures indicates the amount of radiation a person was exposed to. Another means of detecting radioactivity is an electrical device called a Geiger counter (Figure 15.2 "Detecting Radioactivity"). It contains a gas-filled chamber with a thin membrane on one end that allows radiation emitted from radioactive nuclei to enter the chamber and knock electrons off atoms of gas (usually argon). The presence of electrons and positively charged ions causes a small current, which is detected by the Geiger counter and converted to a signal on a meter or, commonly, an audio circuit to produce an audible “click.” KEY TAKEAWAY - Radioactivity can be expressed in a variety of units, including rems, rads, and curies. Radioactive isotopes have a variety of applications. Generally, however, they are useful because either we can detect their radioactivity or we can use the energy they release. Radioactive isotopes are effective tracers because their radioactivity is easy to detect. A tracer is a substance that can be used to follow the pathway of that substance through some structure. For instance, leaks in underground water pipes can be discovered by running some tritium-containing water through the pipes and then using a Geiger counter to locate any radioactive tritium subsequently present in the ground around the pipes. (Recall that tritium is a radioactive isotope of hydrogen.) Tracers can also be used to follow the steps of a complex chemical reaction. After incorporating radioactive atoms into reactant molecules, scientists can track where the atoms go by following their radioactivity. One excellent example of this is the use of carbon-14 to determine the steps involved in photosynthesis in plants. We know these steps because researchers followed the progress of carbon-14 throughout the process. Radioactive isotopes are useful for establishing the ages of various objects. The half-life of radioactive isotopes is unaffected by any environmental factors, so the isotope acts like an internal clock. For example, if a rock is analyzed and is found to contain a certain amount of uranium-235 and a certain amount of its daughter isotope, we can conclude that a certain fraction of the original uranium-235 has radioactively decayed. If half of the uranium has decayed, then the rock has an age of one half-life of uranium-235, or about 4.5 × 109 y. Many analyses like this, using a wide variety of isotopes, have indicated that age of the earth itself is over 4 × 109 y. In another interesting example of radioactive dating, hydrogen-3 dating has been used to verify the stated vintages of some old fine wines. One isotope, carbon-14, is particularly useful in determining the age of once-living artifacts. A tiny amount of carbon-14 is produced naturally in the upper reaches of the atmosphere, and living things incorporate some of it into their tissues, building up to a constant, albeit very low, level. Once a living thing dies, it no longer acquires carbon-14; as time passes the carbon-14 that was in the tissues decays. (The half-life of carbon-14 is 5,370 y.) If a once-living artifact is discovered and analyzed many years after its death and the remaining carbon-14 is compared to the known constant level, an approximate age of the artifact can be determined. Using such methods, scientists determined that the age of the Shroud of Turin (Figure 15.3 "Shroud of Turin"; purported by some to be the burial cloth of Jesus Christ and composed of flax fibers, a type of plant) is about 600–700 y, not 2,000 y as claimed by some. Scientists were also able to use radiocarbon dating to show that the age of a mummified body found in the ice of the Alps was 5,300 y. In 1989, several groups of scientists used carbon-14 dating to demonstrate that the Shroud of Turin was only 600–700 y. Many people still cling to a different notion, despite the scientific evidence. The radiation emitted by some radioactive substances can be used to kill microorganisms on a variety of foodstuffs, extending the shelf life of these products. Produce such as tomatoes, mushrooms, sprouts, and berries are irradiated with the emissions from cobalt-60 or cesium-137. This exposure kills a lot of the bacteria that cause spoilage, so the produce stays fresh longer. Eggs and some meat, such as beef, pork, and poultry, can also be irradiated. Contrary to the belief of some people, irradiation of food does not make the food itself radioactive. Radioactive isotopes have numerous medical applications—diagnosing and treating illness and diseases. One example of a diagnostic application is using radioactive iodine-131 to test for thyroid activity (Figure 15.4 "Medical Diagnostics"). The thyroid gland in the neck is one of the few places in the body with a significant concentration of iodine. To evaluate thyroid activity, a measured dose of 131I is administered to a patient, and the next day a scanner is used to measure the amount of radioactivity in the thyroid gland. The amount of radioactive iodine that collects there is directly related to the activity of the thyroid, allowing trained physicians to diagnose both hyperthyroidism and hypothyroidism. Iodine-131 has a half-life of only 8 d, so the potential for damage due to exposure is minimal. Technetium-99 can also be used to test thyroid function. Bones, the heart, the brain, the liver, the lungs, and many other organs can be imaged in similar ways by using the appropriate radioactive isotope. Very little radioactive material is needed in these diagnostic techniques because the radiation emitted is so easy to detect. However, therapeutic applications usually require much larger doses because their purpose is to preferentially kill diseased tissues. For example, if a thyroid tumor were detected, a much larger infusion (thousands of rem, as opposed to a diagnostic dose of less than 40 rem) of iodine-131 could help destroy the tumor cells. Similarly, radioactive strontium is used to not only detect but also ease the pain of bone cancers. Table 15.5 "Some Radioactive Isotopes with Medical Applications" lists several radioactive isotopes and their medical uses. In addition to the direct application of radioactive isotopes to diseased tissue, the gamma ray emissions of some isotopes can be directed toward the tissue to be destroyed. Cobalt-60 is a useful isotope for this kind of procedure. KEY TAKEAWAY - Radioactivity has several practical applications, including tracers, medical applications, dating once-living objects, and preservation of food. Nuclear changes occur with a simultaneous release of energy. Where does this energy come from? If we could precisely measure the masses of the reactants and products of a nuclear reaction, we would notice that the amount of mass drops slightly in the conversion from reactants to products. Consider the following nuclear equation, in which the molar mass of each species is indicated to four decimal places: 235U235.0439→139Ba138.9088 +94Kr93.9343 +2^1n2 × 1.0087 If we compare the mass of the reactant (235.0439) to the masses of the products (sum = 234.8605), we notice a mass difference of −0.1834 g, or −0.0001834 kg. Where did this mass go? According to Albert Einstein’s theory of relativity, energy (E) and mass (m) are related by the following equation: E = mc^2 where c is the speed of light, or 3.00 × 108 m/s. In the course of the chemical reaction for uranium, the mass difference is converted to energy, which is given off by the reaction: E = (−0.0001834 kg)(3.00 × 10^8 m/s)^2 = −1.65 × 10^(13) J = −1.65 × 10^(10) kJ (For the units to work out, mass must be expressed in units of kilograms.) That is, 16.5 billion kJ of energy is given off every time 1 mol of uranium-235 undergoes this nuclear reaction. This is an extraordinary amount of energy. Compare it to combustion reactions of hydrocarbons, which give off about 650 kJ/mol of energy for every CH2 unit in the hydrocarbon—on the order of hundreds of kilojoules per mole. Nuclear reactions give off billions of kilojoules per mole. If this energy could be properly harvested, it would be a significant source of energy for our society. Nuclear energy involves the controlled harvesting of energy from fission reactions. The reaction can be controlled because the fission of uranium-235 (and a few other isotopes, such as plutonium-239) can be artificially initiated by injecting a neutron into a uranium nucleus. The overall nuclear equation, with energy included as a product, is then as follows: 235U + 1n → 139Ba + 94Kr + 3^(1)n + energy Thus by the careful addition of extra neutrons into a sample of uranium, we can control the fission process and obtain energy that can be used for other purposes. (Artificial or induced radioactivity, in which neutrons are injected into a sample of matter that subsequently cause fission, was first demonstrated in 1934 by Irène Joliot-Curie and Frédéric Joliot, the daughter and son-in-law of Marie Curie.) A nuclear reactor is an apparatus designed to carefully control the progress of a nuclear reaction and extract the resulting energy for useful purposes. Figure 15.5 "A Diagram of a Nuclear Power Plant for Generating Electricity" shows a simplified diagram of a nuclear reactor. The energy from the controlled nuclear reaction converts water into high-pressure steam, which is used to run turbines that generate electricity. The two main components of the power plant are the nuclear reactor itself and the steam-driven turbine and electricity generator. Although the fission of large nuclei can produce different products, on average the fission of uranium produces two more free neutrons than were present to begin with. These neutrons can themselves stimulate other uranium nuclei to undergo fission, releasing yet more energy and even more neutrons, which can in turn induce even more uranium fission. A single neutron can thus begin a process that grows exponentially in a phenomenon called a chain reaction: 1 → 2 → 4 → 8 → 16 → 32 → 64 → 128 → 256 → 512 → 1,024 → 2,048 → 4,096 → 8,192 → 16,384 →… Because energy is produced with each fission event, energy is also produced exponentially and in an uncontrolled fashion. The quick production of energy creates an explosion. This is the mechanism behind the atomic bomb. (The first controlled chain reaction was achieved on December 2, 1942, in an experiment supervised by Enrico Fermi in a laboratory underneath the football stadium at the University of Chicago.) Although fairly simple in theory, an atomic bomb is difficult to produce, in part because uranium-235, the isotope that undergoes fission, makes up only 0.7% of natural uranium; the rest is mostly uranium-238, which does not undergo fission. (Remember that the radioactive process that a nucleus undergoes is characteristic of the isotope.) To make uranium useful for nuclear reactors, the uranium in uranium-235 must be enriched to about 3%. The enrichment of uranium is a laborious and costly series of physical and chemical separations. To be useful in an atomic bomb, uranium must be enriched to 70% or more. At lesser concentrations, the chain reaction cannot sustain itself, so no explosion is produced. Fusion is another nuclear process that can be used to produce energy. In this process, smaller nuclei are combined to make larger nuclei, with an accompanying release of energy. One example is hydrogen fusion, which makes helium: 4^(1)H → 4He + 2.58 × 10^(12) J Notice that the amount of energy given off per mole of reactant is only one-tenth of the amount given off by the fission of 1 mol of uranium-235. On a mass (per gram) basis, however, hydrogen fusion gives off 10 times more energy than fission does. In addition, the product of fission is helium gas, not a wide range of isotopes (some of which are also radioactive) produced by fission. Fusion occurs in nature: The sun and other stars use fusion as their ultimate energy source. Fusion is also the basis of very destructive weapons that have been developed by several countries around the world. However, one current goal is to develop a source of controlled fusion for use as an energy source. The practical problem is that to perform fusion, extremely high pressures and temperatures are necessary. Currently, the only known stable systems undergoing fusion are the interiors of stars. The conditions necessary for fusion can be created using an atomic bomb, but the resulting fusion is uncontrollable (and the basis for another type of bomb, a hydrogen bomb). Currently, researchers are looking for safe, controlled ways for producing useful energy using fusion. KEY TAKEAWAYS - Nuclear energy comes from tiny mass changes in nuclei as radioactive processes occur. - In fission, large nuclei break apart and release energy; in fusion, small nuclei merge together and release energy. Organic chemistry is the study of the chemistry of carbon compounds. Why focus on carbon? Carbon has properties that give its chemistry unparalleled complexity. It forms four covalent bonds, which give it great flexibility in bonding. It makes fairly strong bonds with itself (a characteristic called catenation), allowing for the formation of large molecules; it also forms fairly strong bonds with other elements, allowing for the possibility of a wide variety of substances. No other element demonstrates the versatility of carbon when it comes to making compounds. So an entire field of chemistry is devoted to the study of the compounds and reactivity of one element. Because of the potential for complexity, chemists have defined a rather rigorous system to describe the chemistry of carbon. We will introduce some of that system in this chapter. Should you continue your study of chemistry beyond this text, you will find a much larger world of organic chemistry than we can cover in a single chapter. The simplest organic compounds are those composed of only two elements: carbon and hydrogen. These compounds are called hydrocarbons. Hydrocarbons themselves are separated into two types: aliphatic hydrocarbons and aromatic hydrocarbons. Aliphatic hydrocarbons are hydrocarbons based on chains of C atoms. There are three types of aliphatic hydrocarbons. Alkanes are aliphatic hydrocarbons with only single covalent bonds. Alkenes are hydrocarbons that contain at least one C–C double bond, and alkynes are hydrocarbons that contain a C–C triple bond. Occasionally, we find an aliphatic hydrocarbon with a ring of C atoms; these hydrocarbons are called cycloalkanes (or cycloalkenes or cycloalkynes). Aromatic hydrocarbons have a special six-carbon ring called a benzene ring. Electrons in the benzene ring have special energetic properties that give benzene physical and chemical properties that are markedly different from alkanes. Originally, the term aromatic was used to describe this class of compounds because they were particularly fragrant. However, in modern chemistry the term aromatic denotes the presence of a six-membered ring that imparts different and unique properties to a molecule. The simplest alkanes have their C atoms bonded in a straight chain; these are called normal alkanes. They are named according to the number of C atoms in the chain. The smallest alkane is methane: To make four covalent bonds, the C atom bonds to four H atoms, making the molecular formula for methane CH4. The diagram for methane is misleading, however; the four covalent bonds that the C atom makes are oriented three dimensionally toward the corners of a tetrahedron. A better representation of the methane molecule is shown in Figure 16.1 "Three-Dimensional Representation of Methane". The next-largest alkane has two C atoms that are covalently bonded to each other. For each C atom to make four covalent bonds, each C atom must be bonded to three H atoms. The resulting molecule, whose formula is C2H6, is ethane: Propane has a backbone of three C atoms surrounded by H atoms. You should be able to verify that the molecular formula for propane is C3H8: The diagrams representing alkanes are called structural formulas because they show the structure of the molecule. As molecules get larger, structural formulas become more and more complex. One way around this is to use a condensed structural formula, which lists the formula of each C atom in the backbone of the molecule. For example, the condensed structural formula for ethane is CH3CH3, while for propane it is CH3CH2CH3. Table 16.1 "The First 10 Alkanes" gives the molecular formulas, the condensed structural formulas, and the names of the first 10 alkanes. Because alkanes have the maximum number of H atoms possible according to the rules of covalent bonds, alkanes are also referred to as saturated hydrocarbons. Alkenes have a C–C double bond. Because they have less than the maximum number of H atoms possible, they are called unsaturated hydrocarbons. The smallest alkene—ethene—has two C atoms and is also known by its common name ethylene: The next largest alkene—propene—has three C atoms with a C–C double bond between two of the C atoms. It is also known as propylene: What do you notice about the names of alkanes and alkenes? The names of alkenes are the same as their corresponding alkanes except that the ending is -ene, rather than -ane. Using a stem to indicate the number of C atoms in a molecule and an ending to represent the type of organic compound is common in organic chemistry, as we shall see. With the introduction of the next alkene, butene, we begin to see a major issue with organic molecules: choices. With four C atoms, the C–C double bond can go between the first and second C atoms or between the second and third C atoms: (A double bond between the third and fourth C atoms is the same as having it between the first and second C atoms, only flipped over.) The rules of naming in organic chemistry require that these two substances have different names. The first molecule is named 1-butene, while the second molecule is named 2-butene. The number at the beginning of the name indicates where the double bond originates. The lowest possible number is used to number a feature in a molecule; hence, calling the second molecule 3-butene would be incorrect. Numbers are common parts of organic chemical names because they indicate which C atom in a chain contains a distinguishing feature. The compounds 1-butene and 2-butene have different physical and chemical properties, even though they have the same molecular formula—C4H8. Different molecules with the same molecular formula are called isomers. Isomers are common in organic chemistry and contribute to its complexity. Alkynes, with a C–C triple bond, are named similarly to alkenes except their names end in -yne. The smallest alkyne is ethyne, which is also known as acetylene: Propyne has the structure With butyne, we need to start numbering the position of the triple bond, just as we did with alkenes: Aromatic compounds contain the benzene unit. Benzene itself is composed of six C atoms in a ring, with alternating single and double C–C bonds: The alternating single and double C–C bonds give the benzene ring a special stability, and it does not react like an alkene as might be suspected. Benzene has the molecular formula C6H6; in larger aromatic compounds, a different atom replaces one or more of the H atoms. As fundamental as hydrocarbons are to organic chemistry, their properties and chemical reactions are rather mundane. Most hydrocarbons are nonpolar because of the close electronegativities of the C and H atoms. As such, they dissolve only sparingly in H2O and other polar solvents. Small hydrocarbons, such as methane and ethane, are gases at room temperature, while larger hydrocarbons, such as hexane and octane, are liquids. Even larger hydrocarbons are solids at room temperature and have a soft, waxy consistency. Hydrocarbons are rather unreactive, but they do participate in some classic chemical reactions. One common reaction is substitution with a halogen atom by combining a hydrocarbon with an elemental halogen. Light is sometimes used to promote the reaction, such as this one between methane and chlorine: CH4+Cl2−light→ CH3Cl+HCl Halogens can also react with alkenes and alkynes, but the reaction is different. In these cases, the halogen reacts with the C–C double or triple bond and inserts itself onto each C atom involved in the multiple bonds. This reaction is called an addition reaction. One example is The reaction conditions are usually mild; in many cases, the halogen reacts spontaneously with an alkene or an alkyne. Hydrogen can also be added across a multiple bond; this reaction is called a hydrogenation reaction. In this case, however, the reaction conditions may not be mild; high pressures of H2 gas may be necessary. A platinum or palladium catalyst is usually employed to get the reaction to proceed at a reasonable pace: CH2=CH2+H2−metal catalyst→ CH3CH3 By far the most common reaction of hydrocarbons is combustion, which is the combination of a hydrocarbon with O2 to make CO2 and H2O. The combustion of hydrocarbons is accompanied by a release of energy and is a primary source of energy production in our society (Figure 16.2 "Combustion"). The combustion reaction for gasoline, for example, which can be represented by C8H18, is as follows: 2C8H18 + 25O2 → 16CO2 + 18H2O + ~5060 kJ KEY TAKEAWAYS - The simplest organic compounds are hydrocarbons and are composed of carbon and hydrogen. - Hydrocarbons can be aliphatic or aromatic; aliphatic hydrocarbons are divided into alkanes, alkenes, and alkynes. - The combustion of hydrocarbons is a primary source of energy for our society. Not all hydrocarbons are straight chains. Many hydrocarbons have branches of C atoms attached to a chain. These branched alkanes are isomers of straight-chain alkanes having the same number of C atoms. However, they are different compounds with different physical and chemical properties. As such, they need different names. How do we name branched hydrocarbons? There are a series of rules for naming branched alkanes (and, ultimately, for all organic compounds). These rules make up the system of nomenclature for naming organic molecules. Worldwide, the International Union of Pure and Applied Chemistry (IUPAC) has developed the system of nomenclature for organic compounds. So these rules are sometimes called the IUPAC rules of nomenclature. By learning and applying these rules, you can name any organic compound when given its structure or determine the unique structure of a molecule from its name. You have already learned the basics of nomenclature—the names of the first 10 normal hydrocarbons. Here, we will add some steps to the procedure so you can name branched hydrocarbons. First, given the structure of an alkane, identify the longest continuous chain of C atoms. Note that the longest chain may not be drawn in a straight line. The longest chain determines the parent name of the hydrocarbon. For example, in the molecule the longest chain of carbons has six C atoms. Therefore, it will be named as a hexane. However, in the molecule the longest chain of C atoms is not six, but seven, as shown. So this molecule will be named as a heptane. The next step is to identify the branches, or substituents, on the main chain. The names of the substituents, or alkyl groups, are derived from the names of the parent hydrocarbons; however, rather than having the ending -ane, the substituent name has the ending -yl. Table 16.2 "Substituent Names" lists the substituent names for the five smallest substituents. In naming the branched hydrocarbon, the name of the substituent is combined with the parent name of the hydrocarbon without spaces. However, there is likely one more step. The longest chain of the hydrocarbon must be numbered, and the numerical position of the substituent must be included to account for possible isomers. As with double and triple bonds, the main chain is numbered to give the substituent the lowest possible number. For example, in this alkane the longest chain is five C atoms long, so it is a pentane. There is a one-carbon substituent on the third C atom, so there is a methyl group at position 3. We indicate the position using the number, which is followed by a hyphen, the substituent name, and the parent hydrocarbon name—in this case, 3-methylpentane. That name is specific to that particular hydrocarbon and no other molecule. Organic chemistry nomenclature is very specific! It is common to write the structural formula of a hydrocarbon without the H atoms, for clarity. So we can also represent 3-methylpentane as where it is understood that any unwritten covalent bonds are bonds with H atoms. With this understanding, we recognize that the structural formula for 3-methylpentane refers to a molecule with the formula of C6H14. Branched hydrocarbons may have more than one substituent. If the substituents are different, then give each substituent a number (using the smallest possible numbers) and list the substituents in alphabetical order, with the numbers separated by hyphens and with no spaces in the name. So the molecule is 3-ethyl-2-methylpentane. If the substituents are the same, then use the name of the substituent only once, but use more than one number, separated by a comma. Also, put a numerical prefix before the substituent name that indicates the number of substituents of that type. The numerical prefixes are listed in Table 16.3 "Numerical Prefixes to Use for Multiple Substituents". The number of the position values must agree with the numerical prefix before the substituent. Consider this molecule: The longest chain has four C atoms, so it is a butane. There are two substituents, each of which consists of a single C atom; they are methyl groups. The methyl groups are on the second and third C atoms in the chain (no matter which end the numbering starts from), so we would name this molecule 2,3-dimethylbutane. Note the comma between the numbers, the hyphen between the numbers and the substituent name, and the presence of the prefix di- before the methyl. Other molecules—even with larger numbers of substituents—can be named similarly. Alkenes and alkynes are named in a similar fashion. The biggest difference is that when identifying the longest carbon chain, it must contain the C–C double or triple bond. Furthermore, when numbering the main chain, the double or triple bond gets the lowest possible number. This means that there may be longer or higher-numbered substituents than may be allowed if the molecule were an alkane. For example, this molecule is 2,4-dimethyl-3-heptene (note the number and the hyphens that indicate the position of the double bond). Once you master naming hydrocarbons from their given structures, it is rather easy to draw a structure from a given name. Just draw the parent chain with the correct number of C atoms (putting the double or triple bond in the right position, as necessary) and add the substituents in the proper positions. If you start by drawing the C atom backbone, you can go back and complete the structure by adding H atoms to give each C atom four covalent bonds. From the name 2,3-dimethyl-4-propyl-2-heptene, we start by drawing the seven-carbon parent chain with a double bond starting at the third carbon: We add to this structure two one-carbon substituents on the second and third C atoms: We finish the carbon backbone by adding a three-carbon propyl group to the fourth C atom in the parent chain: If we so choose, we can add H atoms to each C atom to give each carbon four covalent bonds, being careful to note that the C atoms in the double bond already have an additional covalent bond. (How many H atoms do you think are required?There will need to be 24 H atoms to complete the molecule.) Naming substituted benzene molecules is straightforward. If there is only one substituent, the substituent is named as a side chain on a benzene molecule, like this: If there are two or more substituents on a benzene molecule, the relative positions must be numbered, just as an aliphatic chain of C atoms is numbered. The substituent that is first alphabetically is assigned position 1, and the ring is numbered in a circle to give the other substituents the lowest possible number(s). If a benzene ring is treated as a substituent, it is given the name phenyl-. The following molecule is 3-phenylpentane: where the H atoms have been omitted for clarity. KEY TAKEAWAYS - A unique name can be given to branched hydrocarbons. - A unique structure can be drawn for the name of a hydrocarbon. A functional group is any collection of atoms and/or bonds with certain characteristic chemical reactions. We have already seen two functional groups: the C–C double bond and the C–C triple bond. They undergo certain characteristic chemical reactions—for example, the addition of a halogen across the multiple bond. The presence of a halogen atom (F, Cl, Br, or I; also, X is used to represent any halogen atom) is one of the simplest functional groups. Organic compounds that contain a halogen atom are called alkyl halides. We have already seen some examples of alkyl halides when the addition of halogens across double and triple bonds was introduced in Chapter 16 "Organic Chemistry", Section 16.2 "Branched Hydrocarbons"; the products of these reactions were alkyl halides. A simple alkyl halide can be named like an ionic salt, first by stating the name of the parent alkane as a substituent group (with the -yl suffix) and then the name of the halogen as if it were the anion. So CH3Cl has the common name of methyl chloride, while CH3CH2Br is ethyl bromide and CH3CH2CH2I is propyl iodide. However, this system is not ideal for more complicated alkyl halides. The systematic way of naming alkyl halides is to name the halogen as a substituent, just like an alkyl group, and use numbers to indicate the position of the halogen atom on the main chain. The name of the halogen as a substituent comes from the stem of the element’s name plus the ending -o, so the substituent names are fluoro-, chloro-, bromo- and iodo-. If there is more than one of a certain halogen, we use numerical prefixes to indicate the number of each kind, just as with alkyl groups. For example, this molecule is 2-bromobutane, while this molecule is 2,3-dichloropentane. If alkyl groups are present, the substituents are listed alphabetically. Numerical prefixes are ignored when determining the alphabetical ordering of substituent groups. Another simple functional group is the covalently bonded OH group. This is the alcohol functional group. It is not the hydroxide ion; rather than being present as a negatively charged species, in organic chemistry it is a covalently bonded functional group. Like alkyl halides, alcohols have a common naming system and a more formal system. The common system is similar to that of alkyl halides: name the alkyl group attached to the OH group, ending with the suffix -yl, and add the word alcohol as a second word. So CH3OH is methyl alcohol; CH3CH2OH is ethyl alcohol, and CH3CH2CH2OH is propyl alcohol. As with alkyl halides, though, this system is limited (although for smaller alcohols, it is very common in everyday usage). The formal system of naming uses the name of the hydrocarbon containing the OH group and having the correct number of C atoms, dropping the final -e of the name and appending the suffix -ol. Thus CH3OH is methanol and CH3CH2OH is ethanol. For larger alcohol molecules, we use a number to indicate the position of the OH group on the longest carbon chain, similar to the number needed for alkenes and alkynes. Again, the carbon chain is numbered to give the OH group the lowest number, no matter how large the other numbers are. So CH3CH2CH2OH is 1-propanol, while CH3CHOHCH3 is 2-propanol. (A common component in many medicine cabinets, 2‑propanol is also known as isopropanol or isopropyl alcohol [Figure 16.3 "Isopropyl Alcohol"]). Another acceptable way of naming an alcohol—especially a more complicated molecule—is to name the OH group as the hydroxy substituent and give it a numerical position like an alkyl group or a halogen atom. Thus 2-propanol would be called 2-hydroxypropane by this convention. What you find labeled isopropyl alcohol in a medicine cabinet is more formally called 2-propanol. Most alkyl halides are insoluble in H2O. Smaller alcohols, however, are very soluble in H2O because these molecules can engage in hydrogen bonding with H2O molecules. For larger molecules, however, the polar OH group is overwhelmed by the nonpolar alkyl part of the molecule. While methanol is soluble in H2O in all proportions, only about 2.6 g of pentanol will dissolve in 100 g of H2O. Larger alcohols have an even lower solubility in H2O. One reaction common to alcohols and alkyl halides is elimination, the removal of the functional group (either X or OH) and an H atom from an adjacent carbon. The general reaction can be written as follows: where Z represents either the X or the OH group. The biggest difference between elimination in alkyl halides and elimination in alcohols is the identity of the catalyst: for alkyl halides, the catalyst is a strong base; for alcohols, the catalyst is a strong acid. For compounds in which there are H atoms on more than one adjacent carbon, a mixture of products results. KEY TAKEAWAYS - Alkyl halides have a halogen atom as a functional group. - Alcohols have an OH group as a functional group. - Nomenclature rules allow us to name alkyl halides and alcohols. - In an elimination reaction, a double bond is formed as an HX or an HOH molecule is removed. There are other functional groups that contain O atoms. Before we introduce them, we define the carbonyl group, which is formed when an O atom and a C atom are joined by a double bond: The other two bonds on the C atom are attached to other atoms. It is the identities of these other atoms that define what specific type of compound an organic molecule is. If one bond of the carbonyl group is made to an H atom, then the molecule is classified as an aldehyde. (If there are two H atoms, there is only 1 C atom.) When naming aldehydes, the main chain of C atoms must include the carbon in the carbonyl group, which is numbered as position 1 in the carbon chain. The parent name of the hydrocarbon is used, but the suffix -al is appended. (Do not confuse -al with -ol, which is the suffix used for alcohols.) So we have Methanal has a common name with which you may be familiar: formaldehyde. The main thing to note about aldehydes is that the carbonyl group is at the end of a carbon chain. A carbonyl group in the middle of a carbon chain implies that both remaining bonds of the carbonyl group are made to C atoms. This type of molecule is called a ketone. Despite the fact that aldehydes and ketones have the same carbonyl group, they have different chemical and physical properties and are properly grouped as two different types of compounds. The smallest ketone has three C atoms in it. When naming a ketone, we take the name of the parent hydrocarbon and change the suffix to -one: The common name for propanone is acetone. With larger ketones, we must use a number to indicate the position of the carbonyl group, much like a number is used with alkenes and alkynes: There is another way to name ketones: name the alkyl groups that are attached to the carbonyl group and add the word ketone to the name. So propanone can also be called dimethyl ketone, while 2-butanone is called methyl ethyl ketone. The combination of a carbonyl functional group and an OH group makes the carboxyl group. Molecules with a carboxyl group are called carboxylic acids. As with aldehydes, the functional group in carboxylic acids is at the end of a carbon chain. Also as with aldehydes, the C atom in the functional group is counted as one of the C atoms that defines the parent hydrocarbon name. To name carboxylic acids, the parent name of the hydrocarbon is used, but the suffix -oic acid is added: Methanoic acid and ethanoic acid are also called formic acid and acetic acid, respectively. Formic acid is the compound that makes certain ant bites sting, while acetic acid is the active substance in vinegar. How acidic are carboxylic acids? It turns out that they are not very acidic. No carboxylic acid is on the list of strong acids (Table 12.2 "Strong Acids and Bases"). (For more information about strong acids, see Chapter 12 "Acids and Bases", Section 12.4 "Strong and Weak Acids and Bases and Their Salts".) This means that all carboxylic acids are weak acids. A 1 M solution of formic acid is only about 1.3% dissociated into H+ ions and formate ions, while a similar solution of acetic acid is ionized by about only 0.4%. Some carboxylic acids are stronger—for example, trichloroacetic acid is about 45% dissociated in aqueous solution. But no carboxylic acid approaches the 100% dissociation amount required by the definition of a strong acid. As their name suggests, however, carboxylic acids do act like acids in the presence of bases. The H atom in the carboxyl group comes off as the H+ ion, leaving a carboxylate anion: Carboxylate ions are named from the acid name: the -oic acid is replaced with -oate to name the ion. One reaction to consider is that of a carboxylic acid and an alcohol. When combined under the proper conditions, a water molecule will be removed, and the remaining pieces will combine to form a new functional group—the ester functional group: Note how the acid molecule contributes one alkyl side (represented by R), while the alcohol contributes the other side (represented by R′). Esters are named using the alkyl group name from the alcohol plus the carboxylate name from the acid—for example, the molecule is called methyl propanoate. Finally, the ether functional group is an O atom that is bonded to two organic groups: R—O—R′ The two R groups may be the same or different. Naming ethers is like the alternate way of naming ketones. In this case, the R groups are named sequentially, and the word ether is appended. The molecule CH3OCH3 is dimethyl ether, while CH3OCH2CH3 is methyl ethyl ether. Diethyl ether, another ether, was once used as an anesthetic, but its flammability and toxicity caused it to fall out of favor. Smaller ether molecules that are liquids at room temperature are common solvents for organic chemical reactions. KEY TAKEAWAY - Aldehydes, ketones, carboxylic acids, esters, and ethers have oxygen-containing functional groups. There are some common—and important—functional groups that contain elements other than oxygen. In this section, we will consider three of them. An amine is an organic derivative of ammonia (NH3). In amines, one or more of the H atoms in NH3 is substituted with an organic group. A primary amine has one H atom substituted with an R group: A secondary amine has two H atoms substituted with R groups: A tertiary amine has all three H atoms substituted with R group: Naming simple amines is straightforward: name the R groups as substituents and then add the suffix -amine, using numerical suffixes on the substituent names as necessary. This amine is diethylamine (the H atoms on the C atoms are omitted for clarity), while this amine is ethyldipropylamine. As with NH3, the N atom in amines can accept a proton onto the lone electron pair on the N atom. That is, amines act as Brønsted-Lowry bases (i.e., proton acceptors): (For more information on Brønsted-Lowry bases, see Chapter 12 "Acids and Bases", Section 12.2 "Brønsted-Lowry Acids and Bases".) The amine becomes an ion, the organic counterpart of the ammonium (NH4+) ion. Because no amine is presented in Table 12.2 "Strong Acids and Bases", all amines are weak bases. The weakness of amines is about as the same as that for carboxylic acids. N-containing organic compounds are very common in nature, and they all act as weak bases. Some of these compounds have rather complicated structures. Figure 16.4 "Some Naturally Occurring N-Containing Compounds" shows some N-containing substances that you may recognize. An amide functional group is a combination of an amine group and a carbonyl group: Amides are actually formed by bringing together an amine-containing molecule and a carboxylic acid-containing molecule. A molecule of H2O is lost, much like when an ester forms: The bond between the N of the amine group and the C of the carbonyl group is called an amide bond. Amide bonds are particularly important in biological molecules called proteins, which are composed of strings of amino acids—molecules that have an amine group and a carboxylic acid group in them. The amine group on one amino acid reacts with the carboxylic acid group of another amino acid, making a chain held together by amide bonds. We will consider proteins later in this chapter. Sulfur is below oxygen on the periodic table, and it occasionally shows some similar chemistry. One similarity is that an S atom can take the place of an O atom in an alcohol, to make a molecule that looks like this: R–SH The sulfur analog of an alcohol is called a thiol. The formal way of naming a thiol is similar to that of alcohols, except that instead of using the suffix -ol, you use -thiol as the suffix. The following illustrates thiol nomenclature: An older system uses the word mercaptan in naming simple thiols, much like the word alcohol is used with small alcohols. These thiols can also be named like this: Many thiols have strong, objectionable odors; indeed, the spray from skunks is composed of thiols and is detectable by the human nose at concentrations less than 10 ppb. Because natural gas is odorless, thiols are intentionally added to natural gas—at very low levels, of course—so that gas leaks can be more easily detected. Not all thiols have objectionable odors; this thiol is responsible for the odor of grapefruit: One amino acid that is a thiol is cysteine: Cysteine plays an important role in protein structure. If two cysteine amino acids in a protein chain approach each other, they can be oxidized, and a S–S bond (also known as a disulfide bond) is formed: R–SH + HS–R → R–S–S–R where the R group is the rest of the cysteine molecule. The disulfide bond is strong enough to fix the position of the two cysteine groups, thus imposing a structure on the protein. Hair is composed of about 5% cysteine, and the breaking and remaking of disulfide bonds between cysteine units is the primary mechanism behind straightening and curling hair (hair “perms”). KEY TAKEAWAY - Other functional groups include amine, amide, and thiol functional groups. Among other applications, organic chemistry has had a huge impact on the development of modern materials called polymers. Many objects in daily life are composed of polymers; curiously, so are several important biological materials. Consider a molecule with a double bond, such as ethylene: Imagine the bond between the carbons opening up and attacking another ethylene molecule: Now imagine further that the second ethylene molecule’s double bond opens up and attacks a third ethylene molecule, which also opens up its double bond and attacks a fourth ethylene molecule, and so forth. The end result is long, virtually endless molecule: This long, almost nonstop molecule is called a polymer (from the Greek meaning “many parts”). The original part—ethylene—is called the monomer (meaning “one part”). The process of making a polymer is called polymerization. A polymer is an example of a macromolecule, the name given to a large molecule. Simple polymers are named after their monomers; the ethylene polymer is formally called poly(ethylene), although in common use, the names are used without parentheses: polyethylene. Because adding one monomer to another forms this polymer, polyethylene is an example of a type of polymer called addition polymers. Figure 16.5 "Some Monomers and Their Addition Polymers" lists some addition polymers and their monomers. One of them, poly(ethylene oxide), results not from the opening of a double bond but the opening of a ring in the monomer; the concept of bonding with other monomers, however, is the same. Another type of polymer is the condensation polymer, which is a polymer made when two different monomers react together and release some other small molecule as a product. We have already seen an example of this, in the formation of an amide bond: Here, H2O is released when the ends of the molecules react to form a polymer. Related to condensation polymers are the copolymers, polymers made from more than one type of monomer. For example, ethylene and propylene can be combined into a polymer that is a mixture of the two monomers. A common form of synthetic rubber called styrene butadiene rubber (SBR) is made from two monomers: styrene and butadiene: The physical and chemical properties of polymers vary widely, based on their monomers, structures, and additives. Among the other properties that can be modified based on these factors include solubility in H2O and other solvents, melting point, flammability, color, hardness, transparency, film thickness, wetability, surface friction, moldability, and particle size—the list goes on. The uses of polymers are almost too numerous to consider. Anything that you might describe as “plastic” is likely a polymer. Polymers are used to make everything from toothbrushes to computer cases to automobile parts. Many epoxy-based adhesives are condensation polymers that adhere strongly to other surfaces. Polyurethane paints and coatings are polymers, as are the polyester fabrics used to make clothing. Nylon, Dacron, and Mylar are polymers (in fact, both Dacron and Mylar are forms of polyethylene terephthalate [PET]). The product known as Saran Wrap was originally constructed from Saran, a name for poly(vinylidene chloride), which was relatively impervious to oxygen and could be used as a barrier to help keep food fresh. (It has since been replaced with polyethylene, which is not as impervious to atmospheric oxygen.) Poly(vinyl chloride) is the third-most produced polymer [after poly(ethylene) and poly(propylene)] and is used to make everything from plastic tubing to automobile engine parts, water pipes to toys, flooring to waterbeds and pools. All the polymers we have considered so far are based on a backbone of (largely) carbon. There is another class of polymers based on a backbone of Si and O atoms; these polymers are called silicones. The Si atoms have organic groups attached to them, so these polymers are still organic. One example of a silicone is as follows: Silicones are used to make oils and lubricants; they are used as sealants for glass objects (such as aquariums) and films for waterproofing objects. Solid silicones are heat resistant and rubbery and are used to make cookware and electrical insulation. Some very important biological materials are polymers. Of the three major food groups, polymers are represented in two: proteins and carbohydrates. Proteins are polymers of amino acids, which are monomers that have an amine functional group and a carboxylic acid functional group. These two groups react to make a condensation polymer, forming an amide bond: Proteins are formed when hundreds or even thousands of amino acids form amide bonds to make polymers. Proteins play a crucial role in living organisms. A carbohydrate is a compound that has the general formula Cn(H2O)n. Many carbohydrates are relatively small molecules, such as glucose: Linking hundreds of glucose molecules together makes a relatively common material known as starch: Starch is an important source of energy in the human diet. Note how individual glucose units are joined together. They can also be joined together in another way, like this: This polymer is known as cellulose. Cellulose is a major component in the cell walls of plants. Curiously, despite the similarity in the building blocks, some animals (such as humans) cannot digest cellulose; those animals that can digest cellulose typically rely on symbiotic bacteria in the digestive tract for the actual digestion. Animals do not have the proper enzymes to break apart the glucose units in cellulose, so it passes through the digestive tract and is considered dietary fiber. Deoxyribonucleic acid (DNA) and ribonucleic acid (RNA) are also polymers, composed of long, three-part chains consisting of phosphate groups, sugars with 5 C atoms (ribose or deoxyribose), and N-containing rings referred to as bases. Each combination of the three parts is called a nucleotide; DNA and RNA are essentially polymers of nucleotides that have rather complicated but intriguing structures (Figure 16.6 "Nucleotides"). DNA is the fundamental material in chromosomes and is directly responsible for heredity, while RNA is an essential substance in protein synthesis. KEY TAKEAWAYS - Polymers are long molecules composed of chains of units called monomers. - Several important biological polymers include proteins, starch, cellulose, and DNA. In this chapter, we present some data on the chemical elements. The periodic table, introduced in Chapter 3 "Atoms, Molecules, and Ions", lists all the known chemical elements, arranged by atomic number (that is, the number of protons in the nucleus). The periodic table is arguably the best tool in all of science; no other branch of science can summarize its fundamental constituents in such a concise and useful way. Many of the physical and chemical properties of the elements are either known or understood based on their positions on the periodic table. Periodic tables are available with a variety of chemical and physical properties listed in each element’s box. What follows here is a more complex version of the periodic table than what was presented in Chapter 3 "Atoms, Molecules, and Ions". The Internet is a great place to find periodic tables that contain additional information. One item on most periodic tables is the atomic mass of each element. For many applications, only one or two decimal places are necessary for the atomic mass. However, some applications (especially nuclear chemistry; see Chapter 15 "Nuclear Chemistry") require more decimal places. The atomic masses in Table 17.1 "The Basics of the Elements of the Periodic Table" represent the number of decimal places recognized by the International Union of Pure and Applied Chemistry, the worldwide body that develops standards for chemistry. The atomic masses of some elements are known very precisely, to a large number of decimal places. The atomic masses of other elements, especially radioactive elements, are not known as precisely. Some elements, such as lithium, can have varying atomic masses depending on how their isotopes are isolated.