Chapter 1 Chemistry, Matter, and Measurement

Physical and Chemical Properties

The properties that chemists use to describe matter fall into two general categories. Physical propertiesA charactristic that describes matter, such as size, shape, and color. are characteristics that describe matter. They include characteristics such as size, shape, color, and mass. Chemical propertiesA characteristic that describes how matter changes its chemical structure or composition. are characteristics that describe how matter changes its chemical structure or composition. An example of a chemical property is flammability—a material’s ability to burn—because burning (also known as combustion) changes the chemical composition of a material.

Elements and Compounds

Any sample of matter that has the same physical and chemical properties throughout the sample is called a substanceAny sample of matter that has the same physical and chemical properties throughout the sample.. There are two types of substances. A substance that cannot be broken down into chemically simpler components is an elementA substance that cannot be broken down into chemically simpler components.. Aluminum, which is used in soda cans, is an element. A substance that can be broken down into chemically simpler components (because it has more than one element) is a compoundA substance that can be broken down into chemically simpler components. (Figure 1.2 "The General Steps of the Scientific Method"). Water is a compound composed of the elements hydrogen and oxygen. Today, there are about 118 elements in the known universe. In contrast, scientists have identified tens of millions of different compounds to date.

The smallest part of an element that maintains the identity of that element is called an atomThe smallest part of an element that maintains the identity of that element.. Atoms are extremely tiny; to make a line 1 inch long, you would need 217 million iron atoms. The smallest part of a compound that maintains the identity of that compound is called a moleculeThe smallest part of a compound that maintains the identity of that compound.. Molecules are composed of atoms that are attached together and behave as a unit. Scientists usually work with millions and millions of atoms and molecules at a time. When a scientist is working with large numbers of atoms or molecules at a time, the scientist is studying the macroscopicA view of the universe in which one is working with large numbers of atoms or molecules at a time. view of the universe. However, scientists can also describe chemical events on the level of individual atoms or molecules, which is referred to as the microscopicA view of the universe in which one is working with a few atoms or molecules at a time. viewpoint. We will see examples of both macroscopic and microscopic viewpoints throughout this book (Figure 1.3 "How Many Particles Are Needed for a Period in a Sentence?").

Mixtures

A material composed of two or more substances is a mixtureA sample composed of two or more substances.. In a mixture, the individual substances maintain their chemical identities. Many mixtures are obvious combinations of two or more substances, such as a mixture of sand and water. Such mixtures are called heterogeneous mixturesA mixture that is a combination of two or more substances.. In some mixtures, the components are so intimately combined that they act like a single substance (even though they are not). Mixtures with a consistent composition throughout are called homogeneous mixtures (or solutions)A mixture that acts as a single substance so that it is not obvious that two or more substances are present.. Sugar dissolved in water is an example of a solution. A metal alloy, such as steel, is an example of a solid solution. Air, a mixture of mainly nitrogen and oxygen, is a gaseous solution.

Phases

Another way to classify matter is to describe it as a solid, a liquid, or a gas, which was done in the examples of solutions. These three descriptions, each implying that the matter has certain physical properties, represent the three phasesA certain form of matter that includes a specific set of physical properties. of matter. A solid has a definite shape and a definite volume. Liquids ordinarily have a definite volume but not a definite shape; they take the shape of their containers. Gases have neither a definite shape nor a definite volume, and they expand to fill their containers. We encounter matter in each phase every day; in fact, we regularly encounter water in all three phases: ice (solid), water (liquid), and steam (gas).

We know from our experience with water that substances can change from one phase to another if the conditions are right. Typically, varying the temperature of a substance (and, less commonly, the pressure exerted on it) can cause a phase changeA physical process in which a substance goes from one phase to another., a physical process in which a substance goes from one phase to another (Figure 1.4 "Boiling Water"). Phase changes have particular names depending on what phases are involved, as summarized in Table 1.1 "Phase Changes".

Figure 1.5 "The Classification of Matter" illustrates the relationships between the different ways matter can be classified.

Combining Numbers

It is important to be aware of significant figures when you are mathematically manipulating numbers. For example, dividing 125 by 307 on a calculator gives 0.4071661238… to an infinite number of digits. But do the digits in this answer have any practical meaning, especially when you are starting with numbers that have only three significant figures each? When performing mathematical operations, there are two rules for limiting the number of significant figures in an answer—one rule is for addition and subtraction, and one rule is for multiplication and division.

For addition or subtraction, the rule is to stack all the numbers with their decimal points aligned and then limit the answer’s significant figures to the rightmost column for which all the numbers have significant figures. Consider the following:

The arrow points to the rightmost column in which all the numbers have significant figures—in this case, the tenths place. Therefore, we will limit our final answer to the tenths place. Is our final answer therefore 1,459.0? No, because when we drop digits from the end of a number, we also have to roundThe process of assessing the final significant figure of a quantity to determine if it should be kept or moved higher. the number. Notice that the second dropped digit, in the hundredths place, is 8. This suggests that the answer is actually closer to 1,459.1 than it is to 1,459.0, so we need to round up to 1,459.1. The rules in rounding are simple: If the first dropped digit is 5 or higher, round up. If the first dropped digit is lower than 5, do not round up.

For multiplication or division, the rule is to count the number of significant figures in each number being multiplied or divided and then limit the significant figures in the answer to the lowest count. An example is as follows:

The final answer, limited to four significant figures, is 4,094. The first digit dropped is 1, so we do not round up.

Scientific notation provides a way of communicating significant figures without ambiguity. You simply include all the significant figures in the leading number. For example, the number 450 has two significant figures and would be written in scientific notation as 4.5 × 10², whereas 450.0 has four significant figures and would be written as 4.500 × 10². In scientific notation, all significant figures are listed explicitly.

Remember that calculators do not understand significant figures. You are the one who must apply the rules of significant figures to a result from your calculator.

Base SI Units

Base (or basic) unitsA fundamental unit of SI., are the fundamental units of SI. There are seven base units, which are listed in Table 1.2 "The Seven Base SI Units". Chemistry uses five of the base units: the mole for amount, the kilogram for mass, the meter for length, the second for time, and the kelvin for temperature. The degree Celsius (°C) is also commonly used for temperature. The numerical relationship between kelvins and degrees Celsius is as follows:

K = °C + 273

The size of each base unit is defined by international convention. For example, the kilogram is defined as the quantity of mass of a special metal cylinder kept in a vault in France (Figure 1.8 "The Kilogram"). The other base units have similar definitions. The sizes of the base units are not always convenient for all measurements. For example, a meter is a rather large unit for describing the width of something as narrow as human hair. Instead of reporting the diameter of hair as 0.00012 m or even 1.2 × 10⁻⁴ m, SI also provides a series of prefixes that can be attached to the units, creating units that are larger or smaller by powers of 10.

Common prefixes and their multiplicative factors are listed in Table 1.3 "Prefixes Used with SI Units". (Perhaps you have already noticed that the base unit kilogram is a combination of a prefix, kilo- meaning 1,000 ×, and a unit of mass, the gram.) Some prefixes create a multiple of the original unit: 1 kilogram equals 1,000 grams, and 1 megameter equals 1,000,000 meters. Other prefixes create a fraction of the original unit. Thus, 1 centimeter equals 1/100 of a meter, 1 millimeter equals 1/1,000 of a meter, 1 microgram equals 1/1,000,000 of a gram, and so forth.

Both SI units and prefixes have abbreviations, and the combination of a prefix abbreviation with a base unit abbreviation gives the abbreviation for the modified unit. For example, kg is the abbreviation for kilogram. We will be using these abbreviations throughout this book.

Derived SI Units

Derived unitsA combinations of the SI base units. are combinations of SI base units. Units can be multiplied and divided, just as numbers can be multiplied and divided. For example, the area of a square having a side of 2 cm is 2 cm × 2 cm, or 4 cm² (read as “four centimeters squared” or “four square centimeters”). Notice that we have squared a length unit, the centimeter, to get a derived unit for area, the square centimeter.

Volume is an important quantity that uses a derived unit. VolumeThe amount of space that a given substance occupies. is the amount of space that a given substance occupies and is defined geometrically as length × width × height. Each distance can be expressed using the meter unit, so volume has the derived unit m × m × m, or m³ (read as “meters cubed” or “cubic meters”). A cubic meter is a rather large volume, so scientists typically express volumes in terms of 1/1,000 of a cubic meter. This unit has its own name—the liter (L). A liter is a little larger than 1 US quart in volume. (Table 1.4 "Approximate Equivalents to Some SI Units" gives approximate equivalents for some of the units used in chemistry.) As shown in Figure 1.9 "The Liter", a liter is also 1,000 cm³. By definition, there are 1,000 mL in 1 L, so 1 milliliter and 1 cubic centimeter represent the same volume.

1 mL = 1 cm³

EnergyThe ability to perform work., another important quantity in chemistry, is the ability to perform work, such as moving a box of books from one side of a room to the other side. It has a derived unit of kg·m²/s². (The dot between the kg and m units implies the units are multiplied together.) Because this combination is cumbersome, this collection of units is redefined as a jouleThe SI unit of energy. (J). An older unit of energy, the calorie (cal), is also widely used. There are 4.184 J in 1 cal. All chemical processes occur with a simultaneous change in energy. (For more information on energy changes, see Chapter 7 "Energy and Chemical Processes".)

DensityThe mass of an object divided by its volume. is defined as the mass of an object divided by its volume; it describes the amount of matter contained in a given amount of space.

$$\text{density}=\frac{\text{mass}}{\text{volume}}$$

Thus, the units of density are the units of mass divided by the units of volume: g/cm³ or g/mL (for solids and liquids), g/L (for gases), kg/m³, and so forth. For example, the density of water is about 1.00 g/cm³, while the density of mercury is 13.6 g/mL. (Remember that 1 mL equals 1 cm³.) Mercury is over 13 times as dense as water, meaning that it contains over 13 times the amount of matter in the same amount of space. The density of air at room temperature is about 1.3 g/L.

Conversion Factors

If you learned the SI units and prefixes described in Section 1.6 "The International System of Units", then you know that 1 cm is 1/100th of a meter.

$$1\text{ cm = }\frac{\text{1}}{\text{100}}\text{ m}$$ or 100 cm = 1 m

Suppose we divide both sides of the equation by 1 m (both the number and the unit):

$$\frac{\text{100 cm}}{1\text{m}}=\frac{1\text{m}}{1\text{m}}$$

As long as we perform the same operation on both sides of the equals sign, the expression remains an equality. Look at the right side of the equation; it now has the same quantity in the numerator (the top) as it has in the denominator (the bottom). Any fraction that has the same quantity in the numerator and the denominator has a value of 1:

We know that 100 cm is 1 m, so we have the same quantity on the top and the bottom of our fraction, although it is expressed in different units. A fraction that has equivalent quantities in the numerator and the denominator but expressed in different units is called a conversion factorA fraction that has equivalent quantities in the numerator and the denominator but expressed in different units..

Here is a simple example. How many centimeters are there in 3.55 m? Perhaps you can determine the answer in your head. If there are 100 cm in every meter, then 3.55 m equals 355 cm. To solve the problem more formally with a conversion factor, we first write the quantity we are given, 3.55 m. Then we multiply this quantity by a conversion factor, which is the same as multiplying it by 1. We can write 1 as $\frac{100\text{ cm}}{\text{1 m}}$ and multiply:

$$3.55\text{ m}\times \frac{\text{100 cm}}{\text{1 m}}$$

The 3.55 m can be thought of as a fraction with a 1 in the denominator. Because m, the abbreviation for meters, occurs in both the numerator and the denominator of our expression, they cancel out:

$$\frac{3.55\cancel{\text{ m}}}{\text{1}}\times \frac{\text{100 cm}}{\text{1}\cancel{\text{ m}}}$$

The final step is to perform the calculation that remains once the units have been canceled:

$$\frac{3.55}{1}\times \frac{100\text{ cm}}{\text{1}}=355\text{ cm}$$

In the final answer, we omit the 1 in the denominator. Thus, by a more formal procedure, we find that 3.55 m equals 355 cm. A generalized description of this process is as follows:

quantity (in old units) × conversion factor = quantity (in new units)

You may be wondering why we use a seemingly complicated procedure for a straightforward conversion. In later studies, the conversion problems you will encounter will not always be so simple. If you can master the technique of applying conversion factors, you will be able to solve a large variety of problems.

In the previous example, we used the fraction $\frac{\text{100 cm}}{\text{1 m}}$ as a conversion factor. Does the conversion factor $\frac{\text{1 m}}{\text{100 cm}}$ also equal 1? Yes, it does; it has the same quantity in the numerator as in the denominator (except that they are expressed in different units). Why did we not use that conversion factor? If we had used the second conversion factor, the original unit would not have canceled, and the result would have been meaningless. Here is what we would have gotten:

$$3.55\text{ m}\times \frac{\text{1 m}}{\text{100 cm}}=0.0355\frac{{\text{m}}^2}{\text{cm}}$$

For the answer to be meaningful, we have to construct the conversion factor in a form that causes the original unit to cancel out. Figure 1.10 "A Concept Map for Conversions" shows a concept map for constructing a proper conversion. The steps for doing a unit conversion problem are summarized in the margin.

Significant Figures in Conversions

How do conversion factors affect the determination of significant figures? Numbers in conversion factors based on prefix changes, such as kilograms to grams, are not considered in the determination of significant figures in a calculation because the numbers in such conversion factors are exact. Exact numbersA number that is defined or counted. are defined or counted numbers, not measured numbers, and can be considered as having an infinite number of significant figures. (In other words, 1 kg is exactly 1,000 g, by the definition of kilo-.) Counted numbers are also exact. If there are 16 students in a classroom, the number 16 is exact. In contrast, conversion factors that come from measurements (such as density, as we will see shortly) or are approximations have a limited number of significant figures and should be considered in determining the significant figures of the final answer.

Conversion factors can also be constructed for converting between different kinds of units. For example, density can be used to convert between the mass and the volume of a substance. Consider mercury, which is a liquid at room temperature and has a density of 13.6 g/mL. The density tells us that 13.6 g of mercury have a volume of 1 mL. We can write that relationship as follows:

13.6 g mercury = 1 mL mercury

This relationship can be used to construct two conversion factors:

$$\frac{13.6\text{ g}}{\text{1 mL}}\text{ and }\frac{\text{1 mL}}{\text{13}\text{.6 g}}$$

Which one do we use? It depends, as usual, on the units we need to cancel and introduce. For example, suppose we want to know the mass of 16 mL of mercury. We would use the conversion factor that has milliliters on the bottom (so that the milliliter unit cancels) and grams on top so that our final answer has a unit of mass:

$$16\cancel{\text{ mL}}\times \frac{\text{13}\text{.6 g}}{\text{1}\cancel{\text{ mL}}}=217.6\text{ g}=\text{220 g}$$

In the last step, we limit our final answer to two significant figures because the volume quantity has only two significant figures; the 1 in the volume unit is considered an exact number, so it does not affect the number of significant figures. The other conversion factor would be useful if we were given a mass and asked to find volume, as the following example illustrates.

Sometimes you will have to perform more than one conversion to obtain the desired unit. For example, suppose you want to convert 54.7 km into millimeters. You can either memorize the relationship between kilometers and millimeters, or you can do the conversion in steps. Most people prefer to convert in steps.

To do a stepwise conversion, we first convert the given amount to the base unit. In this example, the base unit is meters. We know that there are 1,000 m in 1 km:

$$\text{54}\text{.7}\cancel{\text{ km}}\times \frac{\text{1,000 m}}{\text{1}\cancel{\text{ km}}}=\mathrm{54,700}\text{ m}$$

Then we take the result (54,700 m) and convert it to millimeters, remembering that there are 1,000 mm for every 1 m:

$$\mathrm{54,700}\cancel{\text{ m}}\times \frac{\text{1,000 mm}}{\text{1}\cancel{\text{ m}}}=\mathrm{54,700,000}\text{ mm}=5.47\times {10}^7\text{mm}$$

We have expressed the final answer in scientific notation.

As a shortcut, both steps in the conversion can be combined into a single, multistep expression:

$$54.7\cancel{\text{ km}}\times \frac{\text{1,000 }\cancel{\text{ m}}}{\text{1}\cancel{\text{ km}}}\times \frac{\text{1,000 mm}}{\text{1}\cancel{\text{ m}}}=\mathrm{54,700,000}\text{ mm}=5.47\times {10}^7\text{mm}$$

Either method—one step at a time or all the steps together—is acceptable. If you do all the steps together, the restriction for the proper number of significant figures should be done after the last step. As long as the math is performed correctly, you should get the same answer no matter which method you use.