Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Chapter 1 Chemistry and Measurements 1.8 Writing Conversion Factors 1

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Equalities use two different units to describe the same measured amount are written for relationships between units of the metric system, U.S. units, or between metric and U.S. units For example, 1 m = 1000 mm 1 lb = 16 oz 2.20 lb = 1 kg 2

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Exact and Measured Numbers in Equalities Equalities between units in the same system of measurement are definitions that use exact numbers different systems of measurement (metric and U.S.) use measured numbers that have significant figures Exception: The equality 1 in. = 2.54 cm has been defined as an exact relationship and therefore 2.54 is an exact number. 3

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Some Common Equalities 4

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Equalities on Food Labels The contents of packaged foods in the U.S. are listed in both metric and U.S. units indicate the same amount of a substance in two different units 5

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Conversion Factors A conversion factor is obtained from an equality and written in the form of a fraction with a numerator and denominator Equality: 1 in. = 2.54 cm inverted to give two conversion factors for every equality 1 in. and 2.54 cm 2.54 cm 1 in. 6

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Learning Check Write conversion factors from the equality for each of the following: A. L and mL B. hours and minutes C. meters and kilometers 7

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution Write conversion factors from the equality for each of the following: A. 1 L = 1000 mL 1 L and 1000 mL 1000 mL 1 L B. 1 h = 60 min 1 h and 60 min 60 min 1 h C. 1 km = 1000 m 1 km and 1000 m 1000 m 1 km 8

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Conversion Factors in a Problem A conversion factor may be obtained from information in a word problem is written for that problem only Example 1: The price of one pound (1 lb) of red peppers is $ lb red peppers and $2.39 $ lb red peppers Example 2: The cost of one gallon (1 gal) of gas is $ gal gas and $2.89 $ gal gas 9

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Percent as a Conversion Factor A percent factor gives the ratio of the parts to the whole % = parts x 100 whole uses the same unit in the numerator and denominator uses the value of 100 can be written as two factors Example: A food contains 30% (by mass) fat: 30 g fatand 100 g food 100 g food 30 g fat 10

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Percent Factor in a Problem The thickness of the skin fold at the waist indicates 11% body fat. What factors can be written for percent body fat (in kg)? Percent factors using kg: 11 kg fat and 100 kg mass 100 kg mass 11 kg fat 11

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Smaller Percents: ppm and ppb Small percents are given as ppm and ppb. Parts per million (ppm) = mg part kg whole Example: The EPA allows 15 ppm cadmium in food colors. 15 mg of cadmium = 1 kg of food color Parts per billion (ppb) = μg part kg whole Example: The EPA allows 10 ppb arsenic in public water. 10 μg of arsenic = 1 kg of water 12

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Learning Check Write the conversion factors for 10 ppb arsenic in public water from the equality. 10 μg of arsenic = 1 kg of water 13

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution Write the conversion factors for 10 ppb arsenic in public water from the equality. 10 μg of arsenic = 1 kg of water Conversion Factors 10 μg arsenic and 1 kg wate r 1 kg water 10 μg arsenic 14

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Study Tip: Conversion Factors An equality is written as a fraction (ratio) provides two conversion factors that are the inverse of each other 15

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Learning Check Write the equality and conversion factors for each of the following. A. meters and centimeters B. jewelry that contains 18% gold C. one gallon of gas is $

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution A. meters and centimeters: 1 m = 100 cm 1m and 100 cm 100 cm 1m B. jewelry that contains 18% gold: 100 g of jewelry = 18 g of gold 18 g gold and 100 g jewelry 100 g jewelry 18 g gold C. one gallon of gas is $3.40: 1 gal gas = $ gal gas and $3.40 $ gal gas 17

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Risk-Benefit Assessment A measurement of toxicity is LD 50 or “lethal dose” the concentration of the substance that causes death in 50% of the test animals in milligrams per kilogram (mg/kg or ppm) of body mass in micrograms per kilogram (  g/kg or ppb) of body mass 18

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Learning Check The LD 50 for aspirin is 1100 ppm. How many grams of aspirin would be lethal in 50% of persons with a body mass of 85 kg? A. 9.4 g B. 94 g C g 19

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution The LD 50 for aspirin is 1100 ppm. How many grams of aspirin would be lethal in 50% of persons with a body mass of 85 kg? 85 kg x 1100 mg x 1 g = 94 g of aspirin 1 kg 1000 mg 20