3.2 The International System of Units 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. Measuring with SI Units All measurements depend on units that serve as reference standards. The standards of measurement used in science are those of the metric system. The metric system is important because of its simplicity and ease of use. All metric units are based on multiples of 10. As a result, you can convert between units easily. The metric system was originally established in France in 1795. The International System of Units (abbreviated SI, after the French name, Le Système International d Unités) is a revised version of the metric system. The SI was adopted by international agreement in 1960. There are seven SI base units, which are listed in Table 3.1. From these base units, all other SI units of measurement can be derived. The five SI base units commonly used by chemists are the meter, the kilogram, the kelvin, the second, and the mole. All measured quantities can be reported in SI units. Sometimes, however, non-si units are preferred for convenience or for practical reasons. In this textbook you will learn about both SI and non-si units. Guide for Reading 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. 1 FOCUS Objectives 3.2.1 List SI units of measurement and common SI prefixes. 3.2.2 Distinguish between the mass and weight of an object. 3.2.3 Convert between the Celsius and Kelvin temperature scales. Guide for Reading Build Vocabulary Word Parts Have students predict the meanings of the SI prefixes deci, centi, and milli from their knowledge of the words decimal, century, and millennium. Reading Strategy Preview Have students look at Tables 3.1, 3.3., 3.4, and 3.5. Ask students to list any metric units with which they are already familiar. 2 INSTRUCT Table 3.1 SI Base Units Quantity SI base unit Symbol Length meter m Mass kilogram kg Temperature kelvin K Time second s Amount of substance mole mol Luminous intensity candela cd Electric current ampere A Section 3.2 The International System of Units 73 Have students study the photograph and read the text that opens the section. Ask, Do any of the signs list a measurement? (No. The signs show only numbers. A measurement contains both a number and a unit.) How can you determine what units are implied by the signs? (A library or Internet search will show that the names on the signs are towns in Australia, which adopted SI in 1970. The numbers on the signs represent distances in kilometers.) Section Resources Print Guided Reading and Study Workbook, Section 3.2 Core Teaching Resources, Section 3.2 Review, Interpreting Graphics Transparencies, T27 T30 Small-Scale Chemistry Lab Manual, Labs 3, 4, 5 Technology Interactive Textbook with ChemASAP, Problem-Solving 3.17, Assessment 3.2 Go Online, Section 3.2 Scientific Measurement 73
Section 3.2 (continued) Measuring with SI Units Discuss Explain that with the exception of those working in the sciences, the United States is the only country not using the metric system as a routine method of measurement. Ask, What are some examples of applications in which the metric system is used in the United States. (Acceptable answers include 35-mm film; meter distances in track and field; the dimensions of tools (wrenches) and hardware (bolts); power rating in watts of appliances, and road signs.) Units and Quantities Use Visuals Table 3.2 Discuss with students how SI prefixes are always in increments of ten and can be expressed using scientific notation. Ask, What does the prefix kilo mean? (The prefix kilo means 1000 times larger than the unit it precedes.) How is this prefix represented in scientific notation? (10 3 ) How much larger is the prefix centi compared to the prefix micro? Show students how to make this comparison by writing the following on the board: centi/micro = 10 2 /10 6 = 10 2 ( 6) =10 ( 2 + 6) =10 4 Remind students that in dividing numbers in scientific notation, the exponent of the denominator is subtracted from the exponent of the numerator. Explain that the prefix centi is 10 4, or 10, 000, times larger than the prefix micro. Length of 5 city blocks 1km 74 Chapter 3 Table 3.3 Table 3.2 Commonly Used Metric Prefixes Prefix Meaning Factor mega (M) 1 million times larger than the unit it precedes 10 6 kilo (k) 1000 times larger than the unit it precedes 10 3 deci (d) 10 times smaller than the unit it precedes 10 1 centi (c) 100 times smaller than the unit it precedes 10 2 milli (m) 1000 times smaller than the unit it precedes 10 3 micro (µ) 1 million times smaller than the unit it precedes 10 6 nano (n) 1000 million times smaller than the unit it precedes 10 9 pico (p) 1 trillion times smaller than the unit it precedes 10 12 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 millimeans 1/1000 (one-thousandth), so a millimeter (mm) is 1/1000 of a meter, or 0.001 m. A hyphen (-) measures about 1 mm. 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. Metric Units of Length Unit Relationship Example Kilometer (km) 1 km 10 3 m length of about five city blocks 1 km Meter (m) base unit height of doorknob from the floor 1 m Decimeter (dm) 10 1 dm 1 m diameter of large orange 1 dm Centimeter (cm) 10 2 cm 1 m width of shirt button 1 cm Millimeter (mm) 10 3 mm 1 m thickness of dime 1 mm Micrometer (µm) 10 6 µm 1 m diameter of bacterial cell 1 µm Nanometer (nm) 10 9 nm 1 m thickness of RNA molecule 1 nm 74 Chapter 3
a b c 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 (m 3 ). An automatic dishwasher has a volume of about 1 m 3. A more convenient unit of volume for everyday use is the liter, a non-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 cm 3 1 L). A decimeter (dm) is equal to 10 cm, so 1 L is also equal to 1 cubic decimeter (dm 3 ). 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 cm 3, 1 ml and 1 cm 3 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. There are 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. Checkpoint Table 3.4 What is the SI unit of volume? Metric Units of Volume Unit Relationship Example Liter (L) base unit quart of milk 1 L Milliliter (ml) 10 3 ml 1 L 20 drops of water 1 ml Cubic centimeter (cm 3 ) 1 cm 3 1 ml cube of sugar 1 cm 3 Microliter (µl) 10 6 µl 1 L crystal of table salt 1 µl Facts and Figures SI Units of Distance and Time In 1790, with the establishment of the metric system, the French became the first to adopt measurement standards that were close to being precise. The meter was defined as one ten-millionth of the distance from the equator to the North Pole along the meridian that passes through Paris. The second was defined as 1/86,400 of the average day. 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 med icine dropper is approximately 1 ml. b A sugar cube is 1 cm on each edge and has a volume of 1 cm 3. Note that 1 ml is the same as 1 cm 3. 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? Section 3.2 The International System of Units 75 The definitions of these and other base units have since become more precise. The meter is now defined as thedistance traveled by light in a vacuum in1/299,792,458 of a second. The second is now defined in terms of the number of cycles of radiation given off by a specific isotope of the element cesium. Discuss Point out that data can be reported accurately in various related units (mm, cm, m), but it is best to choose the unit closest in scale to the object being measured. The unit of mass most often used by chemists is the gram not the kilogram. Kilograms of chemicals are too large for laboratory experiments. The density of most gases is measured in grams per liter; the densities of most solids and liquids are measured in grams per cubic centimeter. The milliliter is the most common unit of volume used by chemists. The cubic meter is much too large a volume for most laboratory experiments. TEACHER Demo Volume Measurements Purpose To introduce students to laboratory equipment used to measure volume Materials sets of Erlenmeyer flasks, buret, graduated cylinder, beaker, and volumetric flask; water; food coloring Safety Have students wear goggles to emphasize safety in the laboratory. Procedure Before the demonstration, fill the glassware with water and add a few drops of food coloring. Place the sets at various stations around the classroom. Assign groups of students to each station. As students inspect the glassware, explain that beakers, Erlenmeyer flasks, and graduated cylinders are used to measure approximate volumes. Volumetric flasks and burets allow measurements that are more precise. Ask, What is the appropriate instrument to use to measure a large volume, such as a 1 L, accurately? (Students should choose the volumetric flask.) Expected Outcome Students should be able to select the appropriate glassware when presented with the volumetric parameters for an experiment. Answers to... Figure 3.6 2000 cm 3 Checkpoint cubic meter (m 3 ) Scientific Measurement 75
Section 3.2 (continued) Table 3.5 Metric Units of Mass CLASS Activity Mass of a Penny Purpose To provide practice in weighing groups of objects Materials balance with a precision of at least 0.01 g, sets of 10 pennies each separated according to minting dates between 1970 and the present. (Be sure that sets include pre- and post- 1982 minting dates.) Safety Have student wear goggles when weighing the pennies. Procedure Have students weigh three five-penny samples from each set of pennies and record their data. Have students calculate the average mass of a penny and plot the average mass versus the year it was minted. Expected Outcome Students should observe slight variations in mass from year to year due to chance error, and a dramatic decrease in mass between 1982 and 1983. (Pennies minted before 1982 are mostly copper. Pennies minted after 1982 are mostly zinc, which is less dense than copper.) Ask students to propose a hypothesis for their findings. (Acceptable answers include a change in the composition of the penny.) Have students maintain their graph, results, and hypothesis for future reference in Section 3.4. Use Visuals Figure 3.8 Have students inspect the three thermometers shown. Ask, Which thermometer is the most precise? (liquid-in-glass thermometer) Which is the least precise? (bimetallic strip thermometer) Which probably measures the greatest range of temperatures? (bimetallic strip thermometer) Unit Relationship Example Kilogram (kg) (base unit) 1 kg 10 3 g small textbook 1 kg Gram (g) 1 g 10 3 kg dollar bill 1 g Milligram (mg) 10 3 mg 1 g ten grains of salt 1 mg Microgram (µg) 10 6 µg 1 g particle of baking powder 1 µg 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? 76 Chapter 3 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 cm 3 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. 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. Checkpoint How does weight differ from mass? Differentiated Instruction Less Proficient Readers Have students search magazines and newspapers for examples of SI units. Have them report seasonal day/night temperature ranges for their countries of origin. Gifted and Talented L3 Have students research the efforts to make the metric system standard in the United States. Who has promoted the change? What progress has been made? What obstacles remain? 76 Chapter 3
a 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. 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 Kelvin scale, 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. K C 273 C K 273 b c 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. For: Links on Temperature Scales Visit: www.scilinks.org Web Code: cdn-1032 Discuss Have students compare the freezing point of water on the Celsius and Kelvin temperature scales (0 C and 273.15 K) Ask, What temperature scale has its zero point at absolute zero? (the Kelvin scale) Why do you think scientists use more than one temperature scale? (Acceptable answers include that one scale may be more convenient than the other depending on what is being measured; for example, extremely low temperatures are all negative numbers when expressed in degrees Celsius but positive when expressed in kelvins.) Download a worksheet on Temperature Scales for students to complete, and find additional support for NSTA SciLinks. Section 3.2 The International System of Units 77 Facts and Figures Near Absolute-Zero Temperatures The coldest temperature achieved so far in a laboratory is one-half nanokelvin, that is 0.000 000 000 5 K above absolute zero. Compare this temperature to the cold temperature of outer space, which is about 2.7 K. Answers to... Figure 3.7 The astronaut s mass is the same both on Earth and in space. Checkpoint Weight is a force that measures the pull on a given mass by gravity. The weight of an object can change with its location. Its mass remains constant regardless of its location. Scientific Measurement 77
Section 3.2 (continued) Use Visuals Figure 3.9 Ask, Can the 10-K temperature change from 30 K to 40 K be read on either of these thermometers? (no) Figure 3.9 These thermometers show a comparison of the Celsius and Kelvin temperature scales. Note that a 1 C change on the Celsius scale is equal to a 1 K change on the Kelvin scale. Interpreting Diagrams What is a change of 10 K equivalent to on the Celsius scale? Celsius 0 C Freezing point of water 273.15 K 100 divisions 100 C Boiling point of water 373.15 K Sample Problem 3.4 Answers 16. 196 C 17. melting point: 1234 K; boiling point: 2485 K Practice Problems Plus The boiling point of water on top of Mount Everest is 343 K, while at the bottom of Death Valley, California, water boils at 373.3 K. Express these temperatures in degrees Celsius. (Mount Everest: 7.0 10 1 C; Death Valley: 1.00 10 2 C) Math For a math refresher and practice, direct students to algebraic equations, page R69. Math For help with algebraic equations, go to page R69. Kelvin SAMPLE PROBLEM 3.4 100 divisions Converting Between Temperature Scales Normal human body temperature is 37 C. What is that temperature in kelvins? Analyze List the known and the unknown. Known Temperature in C 37 C Unknown Temperature in K? K Use the known value and the equation K C 273 to calculate the temperature in kelvins. Calculate Solve for the unknown. Substitute the known value for the Celsius temperature into the equation and solve. K C 273 37 273 310 K Evaluate Does the result make sense? You should expect a temperature in this range, since the freezing point of water is 273 K and the boiling point of water is 373 K; normal body temperature is between these two values. Practice Problems Problem-Solving 3.17 Solve Problem 17 with the help of an interactive guided tutorial. withchemasap 16. Liquid nitrogen boils at 77.2 K. What is this temperature in degrees Celsius? 17. The element silver melts at 960.8 C and boils at 2212 C. Express these temperatures in kelvins. 78 Chapter 3 78 Chapter 3
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. 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. 1 J 0.2390 cal 1 cal 4.184 J 3.2 Section Assessment 18. Key Concept Which five SI base units are commonly used in chemistry? 19. Key Concept Which metric units are commonly used to measure length, volume, mass, temperature, and energy? 20. Name the quantity measured by each of the seven SI base units and give the SI symbol of the unit. 21. What is the symbol and meaning of each prefix? a. milli- b. nanoc. deci- d. centi- 22. List the following units in order from largest to smallest: m 3, ml, cl, µl, L, dl. 23. What is the volume of a paperback book 21 cm tall, 12 cm wide, and 3.5 cm thick? 24. State the difference between mass and weight. 25. State the relationship between degrees Celsius and kelvins. 18. m, kg, K, s, mol 19. length: cm, m, km; volume: L, ml, cm 3, µl; mass: kg, g, mg, µm; temperature: C, K; energy: J, cal 20. length (m), mass (kg), temperature (K), time (s), amount of substance (mol), luminous intensity (cd), electric current (A) 21. a. m; 10 3 of the unit b. n; 10 9 of the unit c. d; 10 1 of the unit d. c; 10 2 of the unit Assessment 3.2 Test yourself on the concepts in Section 3.2. withchemasap Section 3.2 Assessment Figure 3.10 Photoelectric panels convert solar energy into electricity. 26. Surgical instruments may be sterilized by heating at 170 C for 1.5 hr. Convert 170 C to kelvins. 27. State the relationship between joules and calories. Boiling Points Look up the boiling points of the first four elements in Group 7A on page R32. Convert these temperatures into kelvins. Section 3.2 The International System of Units 79 22. m 3, L, dl, cl, ml, µl 23. 8.8 10 2 cm 3 24. Mass is a measure of the amount of matter in an object. Weight is a measure of the force of gravity on an object. 25. C = K 273 26. 443 K 27. 1 J = 0.2390 cal 3 ASSESS Evaluate Understanding Write the following chart on the board. Student s Magnitude SI Unit age 1.6 K body temp. 6.2 10 1 kg height 3.1 10 2 m mass 4.8 10 8 s Have students match the appropriate magnitude and SI unit in columns II and III, with the item in column I. (4.8 10 8 s, 3.1 10 2 K, 1.6 m, 6.2 10 1 kg) Reteach Review Tables 3.3, 3.4, and 3.5 with students. Display each on an overhead projector and review the SI base unit listed in each table, pronunciations of the derived units, and the use of the prefixes to determine the numerical relationships between the base unit and the derived units. Elements Group 7A Element Fluorine (F) Chlorine (Cl) Bromine (Br) Iodine (I) with ChemASAP Boiling Point (K) 85 K 238 K 332 K 457 K If your class subscribes to the Interactive Textbook, use it to review key concepts in Section 3.2. Answers to... Figure 3.9 10 C Scientific Measurement 79