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

2. 3.2 Units of Measurement > 2 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 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. CHEMISTRY & YOU What’s the forecast for tomorrow — hot or cold?

3. 3.2 Units of Measurement > 3 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Using SI Units What makes metric or SI units easy to use? Using SI Units

4. 3.2 Units of Measurement > 4 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. All metric units are based on multiples of 10. As a result, you can convert between units easily. The standards of measurement used in science are those of the metric system or the SI system (International System of Units). Using SI Units

5. 3.2 Units of Measurement > 5 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 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 or modern version of the metric system. The SI was adopted by international agreement in 1960. Using SI Units

6. 3.2 Units of Measurement > 6 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 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. SI Base Units QuantitySI base unit Symbol Lengthmeterm Masskilogramkg TemperaturekelvinK Timeseconds Amount of substance molemol Luminous intensity candelacd Electric current ampereA

7. 3.2 Units of Measurement > 7 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Using SI Units The table below lists the prefixes in common use for very large and very small measurements. Units of Length Commonly Used Metric Prefixes PrefixSymbolMeaningFactor megaM1 million times larger than the unit it precedes10 6 kilok1000 times larger than the unit it precedes10 3 decid10 times smaller than the unit it precedes10 -1 centic100 times smaller than the unit it precedes10 -2 millim1000 times smaller than the unit it precedes10 -3 microμ1 million times smaller than the unit it precedes10 -6 nanon1 billion times smaller than the unit it precedes10 -9 picop1 trillion times smaller than the unit it precedes10 -12

8. 3.2 Units of Measurement > 8 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. In SI, the basic unit of length, or linear measure, is the meter (m). 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. For large distances, it is most appropriate to express measurements in kilometers (km). The prefix kilo- means 1000, so 1 km equals 1000 m. Units of Length Using SI Units

9. 3.2 Units of Measurement > 9 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. The space occupied by any sample of matter is called its volume. You calculate the volume of a rectangular solid by multiplying its length by its width by its height. The unit for volume is thus derived from the units of length. Units of Volume Using SI Units

10. 3.2 Units of Measurement > 10 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 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 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). Units of Volume Using SI Units

11. 3.2 Units of Measurement > 11 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. A smaller, unit of volume is the milliliter (mL). There are 1000 mL in 1 L. Because 1 L = 1000 cm 3, 1 mL and 1 cm 3 are the same volumes. The units milliliter and cubic centimeter are used interchangeably. Units of Volume Using SI Units

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

13. 3.2 Units of Measurement > 13 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. The volume of substances will change with temperature. Accurate volume-measuring devices are calibrated at a given temperature. Usually 20 degrees Celsius (20°C), which is about normal room temperature. Units of Volume Using SI Units

14. 3.2 Units of Measurement > 14 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Using SI Units The relationships among common metric units of volume are shown in the table below. Units of Volume Metric Units of Volume UnitSymbolRelationshipExample LiterLbase unitquart of milk ≈ 1 L MillilitermL10 3 mL = 1 L20 drops of water ≈ 1 mL Cubic centimetercm 3 1 cm 3 = 1 mLcube of sugar ≈ 1 cm 3 MicroliterμLμL10 6 μL = 1 Lcrystal of table salt ≈ 1 μL

15. 3.2 Units of Measurement > 15 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 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. Units of Mass Using SI Units

16. 3.2 Units of Measurement > 16 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Using SI Units The relationships among units of mass are shown in the table below. Units of Mass Metric Units of Mass UnitSymbolRelationshipExample Kilogram (base unit) kg1 kg = 10 3 gsmall textbook ≈ 1 kg Gramg1 g = 10 -3 kgdollar bill ≈ 1 g Milligrammg10 3 mg = 1 gten grains of salt ≈ 1 mg Microgramμgμg10 6 μg = 1 gparticle of baking powder ≈ 1 μg

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

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

19. 3.2 Units of Measurement > 19 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Density What determines the density of a substance? Density

20. 3.2 Units of Measurement > 20 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Density is an intensive property that depends only on the composition of a substance, not the size of the sample. Density

21. 3.2 Units of Measurement > 21 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. REMEMBER THAT: 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 Density =

22. 3.2 Units of Measurement > 22 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 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 ). Density

23. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. This figure compares the density of four substances: lithium, water, aluminum, and lead. Density Increasing density (mass per unit volume) 10 g 0.53 g/cm 3 19 cm 3 10 g 10 cm 3 10 g 3.7 cm 3 10 g 0.88 cm 3 1.0 g/cm 3 2.7 g/cm 3 11.36 g/cm 3

24. 3.2 Units of Measurement > 24 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Interpret Data Densities of Some Common Materials Solids and LiquidsGases Material Density at 20°C (g/cm 3 ) Material Density at 20°C (g/L) Gold19.3Chlorine2.95 Mercury13.6Carbon dioxide1.83 Lead11.3Argon1.66 Aluminum2.70Oxygen1.33 Table sugar1.59Air1.20 Corn syrup 1.35 – 1.38 Nitrogen1.17 Water (4°C)1.000Neon0.84 Corn oil0.922Ammonia0.718 Ice (0°C)0.917Methane0.665 Ethanol0.789Helium0.166 Gasoline 0.66 – 0.69 Hydrogen0.084

25. 3.2 Units of Measurement > 25 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 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. Density

26. 3.2 Units of Measurement > 26 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Sample Problem Calculating Density A copper coin has a mass of 8.2 g and a volume of 0.93 cm 3. What is the density of copper?

27. 3.2 Units of Measurement > 27 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Sample Problem Analyze List the knowns and the unknown. Use the known values and the equation for density to solve the problem. KNOWNS mass = 8.2 g volume = 0.93 cm 3 UKNOWN density = ? g/cm 3 1

28. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Sample Problem Density = mass volume Calculate Solve for the unknown. Start with the equation for density. 2

29. 3.2 Units of Measurement > 29 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Calculate Solve for the unknown. Substitute the known values for mass and volume and then calculate. Sample Problem 2 Density = 8.2 g 0.93 cm 3 The calculated answer must be rounded to two significant figures. = 8.8172 g/cm 3 = 8.8 g/cm 3

30. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 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. 3

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

32. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 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.

33. 3.2 Units of Measurement > 33 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Weight is the force of gravity pulling on the mass of an object. 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. Units of Mass Using SI Units

34. 3.2 Units of Measurement > 34 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 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 (1818–1889). A common 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. Units of Energy Using SI Units

35. 3.2 Units of Measurement > 35 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Conversions between joules and calories can be carried out using the following relationships. 1 J = 0.2390 cal 1 cal = 4.184 J A kilojoule is 1000 joules; a kilocalorie is 1000 calories. Units of Energy Using SI Units

36. 3.2 Units of Measurement > 36 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Temperature Scales What temperature units do scientists commonly use? Temperature Scales

37. 3.2 Units of Measurement > 37 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Scientists commonly use two equivalent units of temperature, the degree Celsius and the kelvin. Temperature Scales

38. 3.2 Units of Measurement > 38 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 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. Temperature Scales

39. 3.2 Units of Measurement > 39 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 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 thermometer. Temperature Scales

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

41. 3.2 Units of Measurement > 41 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 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). Temperature Scales

42. 3.2 Units of Measurement > 42 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 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. On the Kelvin scale, the freezing point of water is 273.15 kelvins (K), and the boiling point is 373.15 (K). Note that with the Kelvin scale, the degree sign is not used. Temperature Scales

43. 3.2 Units of Measurement > 43 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. The figure below compares the Celsius and Kelvin scales. The zero point on the Kelvin scale, 0 K, or absolute zero, is equal to –273.15°C. Temperature Scales Celsius Kelvin 100 divisions 100 divisions 100°C Boiling point of water 373.15 K 0°C Freezing point of water 273.15 K

44. 3.2 Units of Measurement > 44 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Because one degree on the Celsius scale is equivalent to one kelvin on the Kelvin scale, converting from one temperature to another is easy. To convert from one scale to another simply add or subtract 273, as shown in the following equations. Temperature Scales K = °C + 273 °C = K – 273

45. 3.2 Units of Measurement > 45 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Sample Problem Converting Between Temperature Scales Normal room temperature is 20°C. What is this temperature in kelvins?

46. 3.2 Units of Measurement > 46 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Sample Problem Analyze List the known and the unknown. Use the known value and the equation K = °C + 273 to calculate the temperature in kelvins. KNOWN Temperature in °C = 20°C UNKNOWN Temperature in K = ? K 1

47. 3.2 Units of Measurement > 47 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Sample Problem Calculate Solve for the unknown. Substitute the known value for the Celsius temperature into the equation and solve. K = °C + 273 = 20 + 273 = 293 K 2

48. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 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 room temperature is between these two values. 3

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

50. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 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.

51. 3.2 Units of Measurement > 51 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. All metric units are based on multiples of 10. As a result, you can convert between units easily. Density is an intensive property that depends only on the composition of a substance. Scientists commonly use two equivalent units of temperature, the degree Celsius and the kelvin. Key Concepts

52. 3.2 Units of Measurement > 52 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. K = °C + 273 °C = K – 273 Key Equations Density = mass volume

53. 3.2 Units of Measurement > 53 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. END OF 3.2