1.1 Some Basic Definitions

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.

MatterAnything that has mass and takes up space. 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 propertiesA characteristic that describes matter as it exists. 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 ).

Chemical propertiesA characteristic that describes how matter changes form in the presence of other matter. 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 (). 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 changeA change that occurs when a sample of matter changes one or more of its physical properties. occurs when a sample of matter changes one or more of its physical properties. For example, a solid may melt (), 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 changeThe process of demonstrating a chemical property. is the process of demonstrating a chemical property, such as the burning match in . 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 substanceMatter that has the same physical and chemical properties throughout.. 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 elementA substance that cannot be broken down into simpler chemical substances by ordinary chemical means. 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 .) Each element has its own unique set of physical and chemical properties. Examples of elements include iron, carbon, and gold.

A compoundA combination of more than one element. 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 mixturesA physical combination of more than one substance.. There are two types of mixtures. A heterogeneous mixtureA mixture composed of two or more substances. 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 mixtureA combination of two or more substances that is so intimately mixed that the mixture behaves as a single substance. 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 solutionAnother name for a homogeneous mixture.. 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 ().

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 metalAn element that conducts electricity and heat well and is shiny, silvery, solid, ductile, and malleable. 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 nonmetalAn element that exists in various colors and phases, is brittle, and does not conduct electricity or heat well. 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 (). 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)An element that has properties of both metals and nonmetals.. We will see later how these descriptions can be assigned rather easily to various elements.

is a flowchart of the relationships among the different ways of describing matter.

1.2 Chemistry as a Science

Chemistry is a branch of science. Although science itself is difficult to define exactly, the following definition can serve as starting point. ScienceThe process of knowing about the natural universe through observation and experiment. 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 hypothesisAn educated guess about how the natural universe works.. 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. ExperimentsA test of the natural universe to see if a guess (hypothesis) is correct. 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 theoryA general statement that explains a large number of observations. 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 lawA specific statement that is thought to be never violated by the entire natural universe.. 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 .)

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 .) 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.

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. QualitativeA description of the quality of an object. 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 quantitativeA description of a specific amount of something. 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.

2.1 Expressing Numbers

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 notationA straightforward expression of a number. 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 notationAn expression of a number using powers of 10. 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 exponentThe raised number to the right of a 10 indicating the number of factors of 10 in the original number.. (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 coefficientThe part of a number in scientific notation that is multiplied by a power of 10.. 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 × 10⁴

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:

$$\begin{array}{cc}5\underset{4}{\underset{\nwarrow }{6}},\underset{3}{\underset{\nwarrow }{9}}\underset{2}{\underset{\nwarrow }{0}}\underset{1}{\underset{\nwarrow }{0}}=5.69\times {10}^4& 0.\underset{1}{\underset{\nearrow }{0}}\underset{2}{\underset{\nearrow }{0}}\underset{3}{\underset{\nearrow }{0}}\underset{4}{\underset{\nearrow }{0}}\underset{5}{\underset{\nearrow }{2}}8=2.8\times {10}^{-5}\end{array}$$

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".)

2.2 Expressing Units

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 unitsOne of the seven basic units of SI used in science. 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 ). 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 prefixesA prefix used with a unit that refers to a multiple or fraction of a fundamental unit to make a more conveniently sized unit for a specific quantity. that refer to multiples or fractions of a fundamental unit to make a unit more conveniently sized for a specific quantity. 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 unitsA unit that is a product or a quotient of a fundamental unit. 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 ). 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 (). 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.

2.3 Significant Figures

If you use a calculator to evaluate the expression 337/217, you will get the following:

$$\frac{337}{217}=\mathrm{1.55299539171...}$$

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 . 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 figuresThe limit of the number of places a measurement can be properly expressed with.. 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. (See for another example.)

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):

$$\frac{23}{448}=\mathrm{0.051339286...}=0.051$$

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.

2.4 Converting Units

In , 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

$$\frac{1}{2}\text{ yd}=\frac{3}{2}\text{ ft}$$

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):

$$\frac{\text{1 yd}}{\text{1 yd}}=\frac{\text{3 ft}}{\text{1 yd}}$$

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:

$$\frac{\cancel{\text{1}}\cancel{\text{ yd}}}{\cancel{\text{1}}\cancel{\text{ yd}}}=\frac{\text{3 ft}}{\text{1 yd}}$$

When everything cancels in a fraction, the fraction reduces to 1:

$$1=\frac{\text{3 ft}}{\text{1 yd}}$$

We have an expression, $\frac{\text{3 ft}}{\text{1 yd}}$, 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 $\frac{\text{3 ft}}{\text{1 yd}}$ is called a conversion factorA fraction that can be used to convert a quantity from one unit to another., 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 $\frac{\text{3 ft}}{\text{1 yd}}$:

$$\text{4 yd}\times \frac{\text{3 ft}}{\text{1 yd}}$$

The 4 yd term can be thought of as $\frac{\text{4 yd}}{1}$; 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:

$$\text{4}\cancel{\text{ yd}}\times \frac{\text{3 ft}}{\text{1}\cancel{\text{ yd}}}$$

That is all that we can cancel. Now, multiply and divide all the numbers to get the final answer:

$$\frac{4\times 3\text{ ft}}{1}=\frac{\text{12 ft}}{1}=12\text{ ft}$$

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:

$$\frac{\mathrm{1,000}\text{ mm}}{\mathrm{1,000}\text{ mm}}=\frac{1\text{ m}}{\mathrm{1,000}\text{ mm}}\text{or}\frac{\mathrm{1,000}\text{ mm}}{1\text{ m}}=\frac{1\text{ m}}{1\text{ m}}$$ $$1=\frac{1\text{ m}}{\mathrm{1,000}\text{ mm}}\text{or}\frac{\mathrm{1,000}\text{ mm}}{1\text{ m}}=1$$

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

$$\text{14}.\text{66}\cancel{\text{ m}}\times \frac{\mathrm{1,000}\text{ mm}}{1\cancel{\text{ m}}}=\mathrm{14,660}\text{ mm}$$

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:

$$17.6{\text{ m}}^2=17.6\left(\cancel{\text{ m}}\times \cancel{\text{ m}}\right)\times \frac{100\text{ cm}}{1\cancel{\text{ m}}}\times \frac{100\text{ cm}}{1\cancel{\text{ m}}}=\mathrm{176,000}\text{ cm}\times \text{cm}=1.76\times {10}^5{\text{ cm}}^2$$

Suppose the unit you want to convert is in the denominator of a derived unit; what then? Then, in the conversion factor, the unit you want to remove must be in the numerator. This will cancel with the original unit in the denominator and introduce a new unit in the denominator. The following example illustrates this situation.

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:

$$\begin{array}{ll}2.77\cancel{\text{ kg}}\times \frac{\text{1,000 g}}{1\cancel{\text{ kg}}}=\mathrm{2,770}\text{ g}\hfill & \left(\text{convert to the base unit of grams}\right)\hfill \end{array}$$ $$\begin{array}{ll}\mathrm{2,770}\cancel{\text{ g}}\times \frac{\text{1,000 mg}}{\text{1}\cancel{\text{ g}}}=\mathrm{2,770,000}\text{ mg}=\text{2}\text{.77}\times {\text{10}}^6\text{ mg}\hfill & \left(\text{convert to desired unit}\right)\hfill \end{array}$$

Alternatively, it can be done in a single multistep process:

$$2.77\cancel{\text{ kg}}\times \frac{\text{1,000}\cancel{\text{ g}}}{\text{1}\cancel{\text{ kg}}}\times \frac{\text{1,000 mg}}{\text{1}\cancel{\text{ g}}}=\mathrm{2,770,000}\text{ mg}=\text{2}\text{.77}\times {\text{10}}^6\text{ mg}$$

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 numberA number from a defined relationship that technically has an infinite number of significant figures.. 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

$$\frac{\mathrm{1,000}\text{ g}}{1\text{ kg}}$$

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

$$\frac{\mathrm{1,000.0000000000}\dots \text{ g}}{1.0000000000\dots \text{ kg}}$$

The other numbers in the calculation will determine the number of significant figures in the final answer.

2.5 Other Units: Temperature and Density

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. TemperatureA measure of the average amount of kinetic energy a system contains. 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 degreesThe unit of temperature scales., 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:

$$\begin{array}{c}\text{°C}=\left(\text{°F}–\text{32}\right)\times \frac{5}{9}\\ \text{°F}=\left(\text{°C}\times \frac{9}{5}\right)+\text{32}\end{array}$$

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 kelvinThe fundamental unit of temperature in SI. (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 zeroThe minimum possible temperature, labeled 0 K (zero kelvins).. 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.)

DensityA physical property defined as a substance’s mass divided by its volume. is a physical property that is defined as a substance’s mass divided by its volume:

$$\text{density}= \frac{\text{mass}}{\text{volume}} \text{or }d=\frac{m}{V}$$

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:

$$\text{7}.\text{88 }\cancel{{\text{cm}}^{\text{3}}}\times \frac{2.7\text{ g}}{\cancel{{\text{cm}}^3}}=\text{21 g of aluminum}$$

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:

$$d=\text{19}.\text{3 g/mL}=\frac{19.3\text{ g}}{\text{mL}}$$

Although this was not previously pointed out, it can be assumed that there is a 1 in the denominator:

$$d=\text{19}.\text{3 g/mL}=\frac{19.3\text{ g}}{1\text{ mL}}$$

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:

$$\frac{1}{d}=\frac{1\text{ mL}}{19.3\text{ g}}$$

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:

$$\text{45}.\text{9}\cancel{\text{ g}}\times \frac{1\text{ mL}}{19.3\cancel{\text{ g}}} =\text{2}.\text{38 mL}$$

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.

3.1 Atomic Theory

The smallest piece of an element that maintains the identity of that element is called an atomThe smallest piece of an element that maintains the identity of that element.. 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 theoryThe concept that atoms play a fundamental role in chemistry., 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 electronA tiny subatomic particle with a negative charge., 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 protonA subatomic particle with a positive charge. is a more massive (but still tiny) subatomic particle with a positive charge, represented as p⁺. The neutronA subatomic particle with no charge. 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. 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 modelThe model of an atom that has the protons and neutrons in a central nucleus with the electrons in orbit about the nucleus. of the atom. The relatively massive protons and neutrons are collected in the center of an atom, in a region called the nucleusThe center of an atom that contains protons and neutrons. of the atom (plural nuclei). The electrons are outside the nucleus and spend their time orbiting in space about the nucleus. (See .)

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 numberThe number of protons in an atom. 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 isotopesAtoms of the same element that have different numbers of neutrons.. 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 numberThe sum of the number of protons and neutrons in a nucleus. 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 symbolA one- or two-letter representation of the name of an element. 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.) lists some common elements and their symbols. You should memorize the symbols in , as this is how we will be representing elements throughout chemistry.

The elements are grouped together in a special chart called the periodic tableA chart of all the elements.. A simple periodic table is shown in , while a more extensive one is presented in . 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 ). 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

$${}_Z{}^A\text{X}$$

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

$${}_{\text{6}}{}^{\text{12}}\text{C}$$

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.

3.2 Molecules and Chemical Nomenclature

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 moleculesThe smallest part of a substance that has the physical and chemical properties of that substance.. 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 moleculesA molecule with only two atoms. (see ). As with any molecule, these elements are labeled with a molecular formulaA formal listing of what and how many atoms are in a molecule., 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 ). 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.

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 bondThe connection between two atoms in a molecule.. In , 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 .) 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 nomenclatureA very specific system for naming compounds, in which unique substances get unique names.. 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 .

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 . Do not use the prefix mono- if there is only one atom of the first element.

   Table 3.4 Numerical Prefixes Used in Naming Molecular Compounds

   The Number of Atoms of an Element	Prefix
   1	mono-
   2	di-
   3	tri-
   4	tetra-
   5	penta-
   6	hexa-
   7	hepta-
   8	octa-
   9	nona-
   10	deca-

3. Name the second element by using three pieces:

   1. a numerical prefix indicating the number of atoms of the second element, plus
   2. the stem of the element name (e.g., ox for oxygen, chlor for chlorine, etc.), plus
   3. 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 ) 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.

3.3 Masses of Atoms and Molecules

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 unitOne-twelfth of the mass of a carbon-12 atom. (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 massThe weighted average of the masses of the isotopes that compose an element. 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 massThe sum of the masses of the atoms in a molecule. 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.

3.4 Ions and Ionic Compounds

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 ionsA species with an overall electric charge.. Species with overall positive charges are termed cationsA species with an overall positive charge., while species with overall negative charges are called anionsA species with an overall negative charge.. 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 compoundsA compound formed from positive and negative ions..

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 formulasThe chemical formula for an ionic compound.. 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 ionsAn ion that contains more than one atom.. 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.

3.5 Acids

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 acidAn ionic compound of the ${\text{H}}^{+}$ cation dissolved in water. 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.

4.1 The Chemical Equation

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 equationA concise way of representing a chemical reaction., which is a concise way of representing a chemical reaction. The initial substances are called reactantsAn initial substance in a chemical equation., and the final substances are called productsA final substance in a chemical equation..

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 coefficientA number in a chemical equation indicating more than one molecule of the substance.. 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 balancedA condition when the reactants and products of a chemical equation have the same number of atoms of all elements present.. 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,

$${\text{2NaHCO}}_{\text{3}}\text{(s)} \stackrel{\text{200}\text{°C}}{\to } {\text{Na}}_{\text{2}}{\text{CO}}_{\text{3}}\text{(s)}+{\text{CO}}_{\text{2}}\text{(g)}+{\text{H}}_{\text{2}}\text{O}(\ell )$$

4.2 Types of Chemical Reactions: Single- and Double-Displacement Reactions

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 reactionA chemical reaction in which one element is substituted for another element in a compound. 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 seriesA list of elements that will replace elements below them in single-replacement reactions. 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 reactionA chemical reaction in which parts of two ionic compounds are exchanged. 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 reactionA chemical reaction in which two ionic compounds are dissolved in water and form a new ionic compound that does not dissolve. 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 precipitateA solid that falls out of solution in a precipitation reaction.. 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 rulesGeneral statements that predict which ionic compounds dissolve and which do not., 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 (Figure 4.2 "Double-Replacement Reactions").