Reading Chapter Three: 3.2

Connecting to Your World “Are we there yet?” You may have asked this question during a long road trip with family or friends. To find out how much farther you have to go, you can read the roadside signs that list destinations and their distances. In the signs shown here, however, the distances are listed as numbers with no units attached. Is Carrieton 44 kilometers or 44 miles away? Without the units, you can’t be sure. When you make a measurement, you must assign the correct units to the numerical value. Without the units, it is impossible to communicate the measurement clearly to others.



Key Concepts

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Which five SI base units do chemists commonly use?
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What metric units are commonly used to measure length, volume, mass, temperature, and energy?

Vocabulary

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International System of Units (SI)
*

meter (m)
*

liter (L)
*

kilogram (kg)
*

gram (g)
*

weight
*

temperature
*

Celsius scale
*

Kelvin scale
*

absolute zero
*

energy
*

joule (J)
*

calorie (cal)

Reading Strategy

Summarizing As you read about SI units, summarize the main ideas in the text that follows the red and blue headings.

Connecting to Your World “Are we there yet?” You may have asked this question during a long road trip with family or friends. To find out how much farther you have to go, you can read the roadside signs that list destinations and their distances. In the signs shown here, however, the distances are listed as numbers with no units attached. Is Carrieton 44 kilometers or 44 miles away? Without the units, you can’t be sure. When you make a measurement, you must assign the correct units to the numerical value. Without the units, it is impossible to communicate the measurement clearly to others.



Key Concepts

*

Which five SI base units do chemists commonly use?
*

What metric units are commonly used to measure length, volume, mass, temperature, and energy?

Vocabulary

*

International System of Units (SI)
*

meter (m)
*

liter (L)
*

kilogram (kg)
*

gram (g)
*

weight
*

temperature
*

Celsius scale
*

Kelvin scale
*

absolute zero
*

energy
*

joule (J)
*

calorie (cal)

Reading Strategy

Summarizing As you read about SI units, summarize the main ideas in the text that follows the red and blue headings.

Units and Quantities

As you already know, you don’t measure length in kilograms or mass in centimeters. Different quantities require different units. Before you make a measurement, you must be familiar with the units corresponding to the quantity that you are trying to measure.
Units of Length

Size is an important property of matter. In SI, the basic unit of length, or linear measure, is the meter (m). All measurements of length can be expressed in meters. (The length of a page in this book is about one-fourth of a meter.) For very large and very small lengths, however, it may be more convenient to use a unit of length that has a prefix. Table 3.2 lists the prefixes in common use. For example, the prefix milli- means 1/1000 (one-thousandth), so a millimeter (mm) is 1/1000 of a meter, or 0.001 m. A hyphen (-) measures about 1 mm.

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Table 3.2: Commonly Used Metric Prefixes

For large distances, it is usually most appropriate to express measurements in kilometers (km). The prefix kilo- means 1000, so 1 km equals 1000 m. A standard marathon distance race of about 42,000 m is more conveniently expressed as 42 km (42 × 1000 m). Common metric units of length include the centimeter, meter, and kilometer. Table 3.3 summarizes the relationships among metric units of length.

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Table 3.3: Metric Units of Length

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Length of 5 city blocks ≈ 1 km
Units of Volume

The space occupied by any sample of matter is called its volume. You calculate the volume of any cubic or rectangular solid by multiplying its length by its width by its height. The unit for volume is thus derived from units of length. The SI unit of volume is the amount of space occupied by a cube that is 1 m along each edge. This volume is a cubic meter (m3). An automatic dishwasher has a volume of about 1 m3.

A more convenient unit of volume for everyday use is the liter, anon-SI unit. A liter (L) is the volume of a cube that is 10 centimeters (10 cm) along each edge (10 cm × 10 cm × 10 cm = 1000 cm3 = 1 L). A decimeter (dm) is equal to 10 cm, so 1 L is also equal to 1 cubic decimeter (dm3). A smaller non-SI unit of volume is the milliliter (mL); 1 mL is 1/1000 of a liter. Thus there are 1000 mL in 1 L. Because 1 L is defined as 1000 cm3, 1 mL and 1 cm3 are the same volume. The units milliliter and cubic centimeter are thus used interchangeably. Common metric units of volume include the liter, milliliter, cubic centimeter, and microliter. Table 3.4 summarizes the relationships among these units of volume.

Figure 3.6 These photographs above give you some idea of the relative sizes of some different units of volume. a The volume of 20 drops of liquid from a medicine dropper is approximately 1 mL. b A sugar cube is 1 cm on each edge and has a volume of 1 cm3. Note that 1 mL is the same as 1 cm3. c A gallon of milk has about twice the volume of a 2-L bottle of soda. Calculating How many cubic centimeters are in 2 liters?

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Table 3.4: Metric Units of Volume

There're many devices for measuring liquid volumes, including graduated cylinders, pipets, burets, volumetric flasks, and syringes. Note that the volume of any solid, liquid, or gas will change with temperature (although the change is much more dramatic for gases). Consequently, accurate -volume-measuring devices are calibrated at a given temperature—usually 20 degrees Celsius (20°C), which is about normal room temperature.

Reading Checkpoint
Units of Mass

The mass of an object is measured in comparison to a standard mass of 1 kilogram (kg), which is the basic SI unit of mass. A kilogram was originally defined as the mass of 1 L of liquid water at 4°C. A cube of water at 4°C measuring 10 cm on each edge would have a volume of 1 L and a mass of 1000 grams (g), or 1 kg. A gram (g) is 1/1000 of a kilogram; the mass of 1 cm3 of water at 4°C is 1 g. Common metric units of mass include the kilogram, gram, milligram, and microgram. The relationships among units of mass are shown in Table 3.5.

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Table 3.5: Metric Units of Mass

You can use a platform balance to measure the mass of an object. The object is placed on one side of the balance, and standard masses are added to the other side until the balance beam is level. The unknown mass is equal to the sum of the standard masses. Laboratory balances range from very sensitive instruments with a maximum capacity of only a few milligrams to devices for measuring quantities in kilograms. An analytical balance is used to measure objects of less than 100 g and can determine mass to the nearest 0.0001 g (0.1 mg).

The astronaut shown on the surface of the moon in Figure 3.7 weighs one sixth of what he weighs on Earth. The reason for this difference is that the force of gravity on Earth is about six times what it is on the moon. Weight is a force that measures the pull on a given mass by gravity. Weight, a measure of force, is different from mass, which is a measure of the quantity of matter. Although the weight of an object can change with its location, its mass remains constant regardless of its location. Objects can thus become weightless, but they can never become massless.

Figure 3.7 An astronaut’s weight on the moon is one sixth as much as it is on Earth. Earth exerts six times the force of gravity as the moon. Inferring How does the astronaut’s mass on the moon compare to his mass on Earth?

Reading Checkpoint
Units of Temperature

When you hold a glass of hot water, the glass feels hot because heat transfers from the glass to your hand. When you hold an ice cube, it feels cold because heat transfers from your hand to the ice cube. Temperature is a measure of how hot or cold an object is. An object’s temperature determines the direction of heat transfer. When two objects at different temperatures are in contact, heat moves from the object at the higher temperature to the object at the lower temperature.

Almost all substances expand with an increase in temperature and contract as the temperature decreases. (A very important exception is water.) These properties are the basis for the common liquid-in-glass thermometer. The liquid in the thermometer expands and contracts more than the volume of the glass, producing changes in the column height of liquid. Figure 3.8 shows a few different types of thermometers.

Figure 3.8 Thermometers are used to measure temperature. a A liquid-in-glass thermometer contains alcohol or mineral spirits. b A dial thermometer contains a coiled bimetallic strip. c A Galileo thermometer contains several glass bulbs that are calibrated to sink or float depending on the temperature. The Galileo thermometer shown uses the Fahrenheit scale, which sets the freezing point of water at 32°F and the boiling point of water at 212°F.

Several temperature scales with different units have been devised. Scientists commonly use two equivalent units of temperature, the degree Celsius and the kelvin. The Celsius scale of the metric system is named after the Swedish astronomer Anders Celsius (1701–1744). It uses two readily determined temperatures as reference temperature values: the freezing point and the boiling point of water. The Celsius scale sets the freezing point of water at 0°C and the boiling point of water at 100°C. The distance between these two fixed points is divided into 100 equal intervals, or degrees Celsius (°C).

Another temperature scale used in the physical sciences is the Kelvin, or absolute, scale. This scale is named for Lord Kelvin (1824–1907), a Scottish physicist and mathematician. On the Kelvin scale, the freezing point of water is 273.15 kelvins (K), and the boiling point is 373.15 K. Notice that with the Kelvin scale, the degree sign is not used. Figure 3.9 on the next page compares the Celsius and Kelvin scales. A change of one degree on the Celsius scale is equivalent to one kelvin on the Kelvin scale. The zero point on the Kelvinscale, 0 K, or absolute zero, is equal to −273.15°C. For problems in this text, you can round −273.15°C to −273°C. Because one degree on the Celsius scale is equivalent to one kelvin on the Kelvin scale, converting from one temperature to another is easy. You simply add or subtract 273, as shown in the following equations.

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Figure 3.9

K = °C + 273

°C = K − 273

Go Online
For: Links on Temperature Scales
Visit: www.SciLinks.org
Web Code: cdn-1032

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3.4 Converting Between Temperature Scales

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Problem-Solving 3.17 Solve Problem 17 with the help of an interactive guided tutorial.
Units of Energy

Figure 3.10 shows a house equipped with solar panels. The solar panels convert the radiant energy from the sun into electrical energy that can be used to heat water and power appliances. Energy is the capacity to do work or to produce heat.

Figure 3.10 Photoelectric panels convert solar energy into electricity.

Like any other quantity, energy can be measured.The joule and the calorie are common units of energy. The joule (J) is the SI unit of energy. It is named after the English physicist James Prescott Joule (1818–1889). One calorie (cal) is the quantity of heat that raises the temperature of 1 g of pure water by 1°C. Conversions between joules and calories can be carried out using the following relationships.

1J = 0.2390 cal 1 cal = 4.184 J