Many properties of matter are quantitative; that is, they are associated with numbers. When a number represents a measured quantity, the units of that quantity must always be specified. To say that the length of a pencil is 17.5 is meaningless. To say that it is 17.5 centimeters (cm) properly specifies the length. The units used for scientific measurements are those of the metric system.

The metric system, which was first developed in France during the late eighteenth century, is used as the system of measurement in most countries throughout the world. The United States has traditionally used the English system, although use of the metric system has become more common in recent years. For example, the contents of most canned goods and soft drinks in grocery stores are now given in metric as well as in English units as shown in Figure 1.16.

SI Units

In 1960 an international agreement was reached specifying a particular choice of metric units for use in scientific measurements. These preferred units are called SI units, after the French Système International d'Unités. The SI system has seven base units from which all other units are derived. Table 1.4 lists these base units and their symbols. In this chapter we will consider the base units for length, mass, and temperature.

Prefixes are used to indicate decimal fractions or multiples of various units. For example, the prefix milli- represents a fraction of a unit: A milligram (mg) is gram (g), a millimeter (mm) is meter (m), and so forth. Table 1.5 presents the prefixes commonly encountered in chemistry. In using the SI system and in working problems throughout this text, you must be comfortable using exponential notation. If you are unfamiliar with exponential notation or want to review it, refer to Appendix A.1.

Although non-SI units are being phased out, there are still some that are commonly used by scientists. Whenever we first encounter a non-SI unit in the text, the proper SI unit will also be given.

Length and Mass

The SI base unit of length is the meter (m), a distance only slightly longer than a yard. The relations between the English and metric system units that we will use most frequently in this text appear on the back inside cover. We will discuss how to convert English units into metric units, and vice versa, in Section 1.6.

Mass* is a measure of the amount of material in an object. The SI base unit of mass is the kilogram (kg), which is equal to about 2.2 pounds (lb). This base unit is unusual because it uses a prefix, kilo-, instead of the word gram alone. We obtain other units for mass by adding prefixes to the word gram.

Temperature

We sense temperature as a measure of the hotness or coldness of an object. Indeed, temperature determines the direction of heat flow. Heat always flows spontaneously from a substance at higher temperature to one at lower temperature. Thus, we feel the influx of energy when we touch a hot object, and we know that the object is at a higher temperature than our hand.

The temperature scales commonly employed in scientific studies are the Celsius and Kelvin scales. The Celsius scale is also the everyday scale of temperature in most countries (Figure 1.17). It was originally based on the assignment of 0°C to the freezing point of water and 100°C to its boiling point at sea level (Figure 1.18).

The Kelvin scale is the SI temperature scale, and the SI unit of temperature is the kelvin (K). Historically, the Kelvin scale was based on the properties of gases; its origins will be considered in Chapter 10. Zero on this scale is the lowest attainable temperature, a temperature referred to as absolute zero. Both the Celsius and Kelvin scales have equal-sized units—that is, a kelvin is the same size as a degree Celsius. Thus, the Kelvin and Celsius scales are related as follows:

[1.1]

The freezing point of water, is 273.15 K (Figure 1.18). Notice that we do not use a degree sign (°) with temperatures on the Kelvin scale.

The common temperature scale in the United States is the Fahrenheit scale, which is not generally used in scientific studies. On the Fahrenheit scale water freezes at and boils at

The Fahrenheit and Celsius scales are related as follows:

[1.2]

Derived SI Units

The SI base units in Table 1.4 are used to derive the units of other quantities. To do so, we use the defining equation for the quantity, substituting the appropriate base units. For example, speed is defined as the ratio of distance to elapsed time. Thus, the SI unit for speed is the SI unit for distance (length) divided by the SI unit for time, which we read as "meters per second." We will encounter many derived units, such as those for force, pressure, and energy, later in this text. In this chapter we examine the derived units for volume and density.

Volume

The volume of a cube is given by its length cubed, (length)³. Thus, the basic SI unit of volume is the cubic meter, or m³, the volume of a cube that is 1 m on each edge. Smaller units, such as cubic centimeters, cm³ (sometimes written as cc), are frequently used in chemistry. Another unit of volume commonly used in chemistry is the liter (L), which equals a cubic decimeter, dm³, and is slightly larger than a quart. The liter is the first metric unit we have encountered that is not an SI unit. There are 1000 milliliters (mL) in a liter (Figure 1.19), and each milliliter is the same volume as a cubic centimeter: 1 mL

The terms milliliter and cubic centimeter are used interchangeably in expressing volume.

The devices used most frequently in chemistry to measure volume are illustrated in Figure 1.20. Syringes, burets, and pipets deliver liquids with more accuracy than graduated cylinders. Volumetric flasks are used to contain specific volumes of liquid.

Density

Density is widely used to characterize substances. It is defined as the amount of mass in a unit volume of the substance:

[1.3]

The densities of solids and liquids are commonly expressed in units of grams per cubic centimeter () or grams per milliliter (). The densities of some common substances are listed in Table 1.6. It is no coincidence that the density of water is the gram was originally defined as the mass of 1 mL of water at a specific temperature. Because most substances change volume when heated or cooled, densities are temperature dependent. When reporting densities, the temperature should be specified. We usually assume that the temperature is close to normal room temperature, if no temperature is reported.

The terms density and weight are sometimes confused. A person who says that iron weighs more than air generally means that iron has a higher density than air; 1 kg of air has the same mass as 1 kg of iron, but the iron occupies a smaller volume, thereby giving it a higher density. If we combine two liquids that do not mix, the less dense one will float on the more dense one.