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Units and measurement

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- 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 units easy to use? Using SI Units
- 4. 3.2 Units of Measurement > 4 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. • 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. 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 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 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
- 7. 3.2 Units of Measurement > 7 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. • 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. Units of Length Using SI Units
- 8. 3.2 Units of Measurement > 8 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Using SI Units The table below lists the prefixes in common use. Units of Length Commonly Used Metric Prefixes Prefix Symbol Meaning Factor mega M 1 million times larger than the unit it precedes 106 kilo k 1000 times larger than the unit it precedes 103 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 10-12
- 9. 3.2 Units of Measurement > 9 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. • 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
- 10. 3.2 Units of Measurement > 10 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 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. Units of Volume Using SI Units
- 11. 3.2 Units of Measurement > 11 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 (m3). • 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 cm3 = 1 L). Units of Volume Using SI Units
- 12. 3.2 Units of Measurement > 12 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. • 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. Units of Volume Using SI Units
- 13. 3.2 Units of Measurement > 13 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
- 14. 3.2 Units of Measurement > 14 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. • 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. Units of Volume Using SI Units
- 15. 3.2 Units of Measurement > 15 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 Unit Symbol Relationship Example Liter L base unit quart of milk ≈ 1 L Milliliter mL 103 mL = 1 L 20 drops of water ≈ 1 mL Cubic centimeter cm3 1 cm3 = 1 mL cube of sugar ≈ 1 cm3 Microliter μL 103 μL = 1 L crystal of table salt ≈ 1 μL
- 16. 3.2 Units of Measurement > 16 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 cm3 of water at 4°C is 1 g. Units of Mass Using SI Units
- 17. 3.2 Units of Measurement > 17 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 Unit Symbol Relationship Example Kilogram (base unit) kg 1 kg = 103 g small textbook ≈ 1 kg Gram g 1 g = 10-3 kg dollar bill ≈ 1 g Milligram mg 103 mg = 1 g ten grains of salt ≈ 1 mg Microgram μg 106 μg = 1 g particle of baking powder ≈ 1 μg
- 18. 3.2 Units of Measurement > 18 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. • 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. Units of Mass Using SI Units
- 19. 3.2 Units of Measurement > 19 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 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. Units of Energy Using SI Units
- 20. 3.2 Units of Measurement > 20 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
- 21. 3.2 Units of Measurement > 21 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. What is the SI unit of volume?
- 22. 3.2 Units of Measurement > 22 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 (m3). A liter (L) can be converted to the SI unit of volume, because a liter is defined as 1000 cm3.
- 23. 3.2 Units of Measurement > 23 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Temperature Scales What temperature units do scientists commonly use? Temperature Scales
- 24. 3.2 Units of Measurement > 24 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
- 25. 3.2 Units of Measurement > 25 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 bulb thermometer. Temperature Scales
- 26. 3.2 Units of Measurement > 26 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
- 27. 3.2 Units of Measurement > 27 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
- 28. 3.2 Units of Measurement > 28 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
- 29. 3.2 Units of Measurement > 29 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
- 30. 3.2 Units of Measurement > 30 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
- 31. 3.2 Units of Measurement > 31 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. • You simply add or subtract 273, as shown in the following equations. Temperature Scales K = °C + 273 °C = K – 273
- 32. 3.2 Units of Measurement > 32 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 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? CHEMISTRY & YOU
- 33. 3.2 Units of Measurement > 33 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 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? CHEMISTRY & YOU In the United States, temperatures are usually given in degrees Fahrenheit. Countries that use the metric system forecast the weather in degrees Celsius.
- 34. 3.2 Units of Measurement > 34 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Sample Problem 3.7 Converting Between Temperature Scales Normal human body temperature is 37°C. What is this temperature in kelvins?
- 35. 3.2 Units of Measurement > 35 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Sample Problem 3.7 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 = 37°C UNKNOWN Temperature in K = ? K 1
- 36. 3.2 Units of Measurement > 36 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Sample Problem 3.7 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 2
- 37. 3.2 Units of Measurement > 37 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Sample Problem 3.7 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. 3
- 38. 3.2 Units of Measurement > 38 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?
- 39. 3.2 Units of Measurement > 39 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.
- 40. 3.2 Units of Measurement > 40 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Density What determines the density of a substance? Density
- 41. 3.2 Units of Measurement > 41 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. • 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 =
- 42. 3.2 Units of Measurement > 42 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/cm3). • The SI unit of density is kilograms per cubic meter (kg/m3). Density
- 43. 3.2 Units of Measurement > 43 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/cm3 19 cm3 10 g 10 cm3 10 g 3.7 cm3 10 g 0.88 cm3 1.0 g/cm3 2.7 g/cm3 0.88 g/cm3
- 44. 3.2 Units of Measurement > 44 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
- 45. 3.2 Units of Measurement > 45 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. • 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. Density Corn oil Water Corn syrup
- 46. 3.2 Units of Measurement > 46 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Interpret Data Densities of Some Common Materials Solids and Liquids Gases Material Density at 20°C (g/cm3) Material 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 1.35–1.38 Nitrogen 1.17 Water (4°C) 1.000 Neon 0.84 Corn oil 0.922 Ammonia 0.718 Ice (0°C) 0.917 Methane 0.665 Ethanol 0.789 Helium 0.166 Gasoline 0.66–0.69 Hydrogen 0.084
- 47. 3.2 Units of Measurement > 47 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
- 48. 3.2 Units of Measurement > 48 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Sample Problem 3.8 Calculating Density A copper penny has a mass of 3.1 g and a volume of 0.35 cm3. What is the density of copper?
- 49. 3.2 Units of Measurement > 49 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Sample Problem 3.8 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 cm3 UKNOWN density = ? g/cm3 1
- 50. 3.2 Units of Measurement > 50 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Sample Problem 3.8 Density = mass volume Calculate Solve for the unknown. Start with the equation for density. 2
- 51. 3.2 Units of Measurement > 51 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 3.8 2 Density = 31 g 0.35 cm3 = 8.8571 g/cm3 = 8.9 g/cm3 The calculated answer must be rounded to two significant figures.
- 52. 3.2 Units of Measurement > 52 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Sample Problem 3.8 Evaluate Does the result make sense? A piece of copper with a volume of about 0.3 cm3 has a mass of about 3 grams. About three times that volume of copper, 1 cm3, should have a mass three times larger, about 9 grams. This estimate is close to the calculated result. 3
- 53. 3.2 Units of Measurement > 53 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Can you assume that something with a low weight will float in water?
- 54. 3.2 Units of Measurement > 54 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.
- 55. 3.2 Units of Measurement > 55 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. 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. Key Concepts
- 56. 3.2 Units of Measurement > 56 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. K = °C + 273 °C = K – 273 Key Equations Density = mass volume
- 57. 3.2 Units of Measurement > 57 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. • 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 cm3); 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 cm3 of water at 4°C Glossary Terms
- 58. 3.2 Units of Measurement > 58 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. • 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; 4.184 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 Glossary Terms
- 59. 3.2 Units of Measurement > 59 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. • 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 –273.15°C • density: the ratio of the mass of an object to its volume Glossary Terms
- 60. 3.2 Units of Measurement > 60 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. END OF 3.2