3.2 Units of Measurement > Chapter 3 Scientific Measurement. 3.2 Units of Measurement. 3.1 Using and Expressing Measurements

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1 Chapter 3 Scientific Measurement 3.1 Using and Expressing Measurements 3.2 Units of Measurement 3.3 Solving Conversion Problems 1 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

2 CHEMISTRY & YOU What s the forecast for tomorrow hot or cold? Will the high temperature tomorrow be 28 C, which is very warm? Or 28 F, which is very cold? Without the correct units, you can t be sure. 2 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

3 Using SI Units Using SI Units What makes metric units easy to use? 3 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

4 Using SI Units The standards of measurement used in science are those of the metric system. All metric units are based on multiples of 10. As a result, you can convert between units easily. 4 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

5 Using SI Units The metric system was originally established in France in 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 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

6 Using SI Units There are seven SI base units. From these base units, all other SI units of measurement can be derived. Derived units are used for measurements such as volume, density, and pressure. Quantity SI Base Units SI base unit Symbol Length meter m Mass kilogram kg Temperature kelvin K Time second s Amount of substance Luminous intensity Electric current mole candela ampere mol cd A 6 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

7 Using SI Units Units of Length In SI, the basic unit of length, or linear measure, is the meter (m). All measurements of length can be expressed in meters. For very large and very small lengths, however, it may be more convenient to use a unit of length that has a prefix. 7 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

8 Using SI Units Units of Length The table below lists the prefixes in common use. Commonly Used Metric Prefixes Prefix Symbol 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 1 billion times smaller than the unit it precedes 10-9 pico p 1 trillion times smaller than the unit it precedes Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

9 Using SI Units Units of Length For example, the prefix milli- means 1/1000 (one-thousandth), so a millimeter (mm) is 1/1000 of a meter, or m. A hyphen (-) measures about 1 mm. For large distances, it is most appropriate to express measurements in kilometers (km). The prefix kilo- means 1000, so 1 km equals 1000 m. 9 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

10 Using SI Units 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 the units of length. 10 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

11 Using SI Units Units of Volume 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 ). 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 x 10 cm x 10 cm = 1000 cm 3 = 1 L). 11 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

12 Using SI Units Units of Volume 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. 12 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

13 Using SI Units Units of Volume These figures give you some idea of the relative sizes of a liter and a milliliter. 1 L 1 ml 13 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

14 Using SI Units Units of Volume There are many devices for measuring liquid volumes, including graduated cylinders, pipets, burets, volumetric flasks, and syringes. The volume of substances will change with temperature, so accurate volume-measuring devices are calibrated at a given temperature usually 20 degrees Celsius (20 C), which is about normal room temperature. 14 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

15 Using SI Units Units of Volume The relationships among common metric units of volume are shown in the table below. Metric Units of Volume Unit Symbol 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 3 μl = 1 L crystal of table salt 1 μl 15 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

16 Using SI Units 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. 16 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

17 Using SI Units Units of Mass The relationships among units of mass are shown in the table below. Metric Units of Mass Unit Symbol Relationship Example Kilogram (base unit) kg 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 17 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

18 Using SI Units Units of Mass 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. The weight of an object can change with its location. An astronaut in orbit is weightless, but not massless. 18 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

19 Using SI Units Units of Energy The capacity to do work or to produce heat is called energy. The SI unit of energy is the joule (J), named after the English physicist James Prescott Joule ( ). A common non-si unit of energy is the calorie. One calorie (cal) is the quantity of heat that raises the temperature of 1 g of pure water by 1 C. 19 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

20 Using SI Units Units of Energy Conversions between joules and calories can be carried out using the following relationships. 1 J = cal 1 cal = J A kilojoule is 1000 joules; a kilocalorie is 1000 calories. 20 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

21 What is the SI unit of volume? 21 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

22 What is the SI unit of volume? The SI unit of volume is the cubic meter (m 3 ). A liter (L) can be converted to the SI unit of volume, because a liter is defined as 1000 cm Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

23 Temperature Scales Temperature Scales What temperature units do scientists commonly use? 23 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

24 Temperature Scales 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. 24 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

25 Temperature Scales 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 bulb thermometer. 25 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

26 Temperature Scales The liquid in a thermometer expands and contracts more than the volume of the glass, producing changes in the column height of liquid. 26 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

27 Temperature Scales Scientists commonly use two equivalent units of temperature, the degree Celsius and the kelvin. 27 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

28 Temperature Scales 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). 28 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

29 Temperature Scales Another temperature scale used in the physical sciences is the Kelvin, or absolute, scale. This scale is named for Lord Kelvin ( ), a Scottish physicist. On the Kelvin scale, the freezing point of water is kelvins (K), and the boiling point is (K). Note that with the Kelvin scale, the degree sign is not used. 29 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

30 Temperature Scales The figure below compares the Celsius and Kelvin scales. The zero point on the Kelvin scale, 0 K, or absolute zero, is equal to C. Celsius Kelvin 0 C Freezing point of water K 100 divisions 100 divisions 100 C Boiling point of water K 30 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

31 Temperature Scales 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 C = K Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

32 CHEMISTRY & YOU In a few countries, such as the United States, metric units are not commonly used in everyday measurements. What temperature units are used for a typical weather forecast in the United States? What about for a country that uses the metric system, such as Australia or Japan? 32 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

33 CHEMISTRY & YOU In a few countries, such as the United States, metric units are not commonly used in everyday measurements. What temperature units are used for a typical weather forecast in the United States? What about for a country that uses the metric system, such as Australia or Japan? In the United States, temperatures are usually given in degrees Fahrenheit. Countries that use the metric system forecast the weather in degrees Celsius. 33 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

34 Sample Problem 3.7 Converting Between Temperature Scales Normal human body temperature is 37 C. What is this temperature in kelvins? 34 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

35 Sample Problem Analyze List the known and the unknown. Use the known value and the equation K = C to calculate the temperature in kelvins. KNOWN Temperature in C = 37 C UNKNOWN Temperature in K =? K 35 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

36 Sample Problem Calculate Solve for the unknown. Substitute the known value for the Celsius temperature into the equation and solve. K = C = = 310 K 36 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

37 Sample Problem 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. 37 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

38 Is the change of one degree on the Celsius scale equivalent to one kelvin on the Kelvin scale? 38 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

39 Is the change of one degree on the Celsius scale equivalent to one kelvin on the Kelvin scale? Yes, a change of one degree on the Celsius scale is equivalent to a change of one kelvin on the Kelvin scale. 39 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

40 Density Density What determines the density of a substance? 40 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

41 Density The relationship between an object s mass and its volume tells you whether it will float or sink. This relationship is called density. Density is the ratio of the mass of an object to its volume. Density = mass volume 41 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

42 Density When mass is measured in grams, and volume in cubic centimeters, density has units of grams per cubic centimeter (g/cm 3 ). The SI unit of density is kilograms per cubic meter (kg/m 3 ). 42 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

43 Density This figure compares the density of four substances: lithium, water, aluminum, and lead. Increasing density (mass per unit volume) 10 g 10 g 10 g 10 g 19 cm 3 10 cm cm cm g/cm g/cm g/cm g/cm 3 43 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

44 Density Density is an intensive property that depends only on the composition of a substance, not the size of the sample. 44 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

45 Density Because of differences in density, liquids separate into layers. As shown at right, corn oil floats on top of water because it is less dense. Corn syrup sinks below water because it is more dense. Corn oil Water Corn syrup 45 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

46 Interpret Data Densities of Some Common Materials Solids and Liquids Material Density at 20 C (g/cm 3 ) Material Gases Density at 20 C (g/l) Gold 19.3 Chlorine 2.95 Mercury 13.6 Carbon dioxide 1.83 Lead 11.3 Argon 1.66 Aluminum 2.70 Oxygen 1.33 Table sugar 1.59 Air 1.20 Corn syrup Nitrogen 1.17 Water (4 C) Neon 0.84 Corn oil Ammonia Ice (0 C) Methane Ethanol Helium Gasoline Hydrogen Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

47 Density What happens to the density of a substance as its temperature increases? The volume of most substances increases as the temperature increases, while the mass remains the same. Since density is the ratio of an object s mass to its volume, the density of a substance generally decreases as its temperature increases. Water is an important exception. 47 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

48 Sample Problem 3.8 Calculating Density A copper penny has a mass of 3.1 g and a volume of 0.35 cm 3. What is the density of copper? 48 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

49 Sample Problem Analyze List the knowns and the unknown. Use the known values and the equation for density to solve the problem. KNOWNS mass = 3.1 g volume = 0.35 cm 3 UKNOWN density =? g/cm 3 49 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

50 Sample Problem Calculate Solve for the unknown. Start with the equation for density. Density = mass volume 50 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

51 Sample Problem Calculate Solve for the unknown. Substitute the known values for mass and volume and then calculate. Density = 31 g 0.35 cm 3 = g/cm3 = 8.9 g/cm 3 The calculated answer must be rounded to two significant figures. 51 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

52 Sample Problem Evaluate Does the result make sense? A piece of copper with a volume of about 0.3 cm 3 has a mass of about 3 grams. About three times that volume of copper, 1 cm 3, should have a mass three times larger, about 9 grams. This estimate is close to the calculated result. 52 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

53 Can you assume that something with a low weight will float in water? 53 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

54 Can you assume that something with a low weight will float in water? No, it is the relationship between an object s mass and its volume, its density, that tells you whether it will float or sink. 54 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

55 Key Concepts All metric units are based on multiples of 10. As a result, you can convert between units easily. Scientists commonly use two equivalent units of temperature, the degree Celsius and the kelvin. Density is an intensive property that depends only on the composition of a substance. 55 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

56 Key Equations K = C C = K 273 Density = mass volume 56 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

57 Glossary Terms International System of Units (SI): the revised version of the metric system, adopted by international agreement in 1960 meter (m): the base unit of length in SI liter (L): the volume of a cube measuring 10 centimeters on each edge (1000 cm 3 ); it is the common unprefixed unit of volume in the metric system kilogram (kg): the mass of 1 L of water at 4 C; it is the base unit of mass in SI gram (g): a metric mass unit equal to the mass of 1 cm 3 of water at 4 C 57 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

58 Glossary Terms weight: a force that measures the pull of gravity on a given mass energy: the capacity for doing work or producing heat Joule (J): the SI unit of energy; J equals one calorie calorie (cal): the quantity of heat needed to raise the temperature of 1 g of pure water 1 C temperature: a measure of the average kinetic energy of particles in matter; temperature determines the direction of heat transfer 58 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

59 Glossary Terms Celsius scale: the temperature scale in which the freezing point of water is 0 C and the boiling point is 100 C Kelvin scale: the temperature scale in which the freezing point of water is 273 K and the boiling point is 373 K; 0 K is absolute zero absolute zero: the zero point on the Kelvin temperature scale, equivalent to C density: the ratio of the mass of an object to its volume 59 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

60 END OF Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.