1. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Chapter 1 Chemistry and Measurements 1.9 Problem Solving 1

2. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Given and Needed Units To solve a problem, identify the given unit identify the needed unit Example: A person has a height of 2.0 meters. What is that height in inches? The given unit is the initial unit of height. given unit = meters (m) The needed unit is the unit for the answer. needed unit = inches (in.) 2

3. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Study Tip: Problem Solving Using GPS The steps in the Guide to Problem Solving (GPS) are useful in setting up a problem with conversion factors. 3

4. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Setting Up a Problem How many minutes are in 2.5 hours? Solution: Step 1 State the given and needed quantities. Given unit: 2.5 hours Needed unit: min Step 2 Write a unit plan. Plan:hours min 4

5. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solving a Problem How many minutes are in 2.5 hours? Step 3 State equalities and conversion factors to cancel units. 60 min= 1 h60 min and 1 h 1 h 60 min Step 4 Set up problem to cancel units. Given Conversion Needed unit unit factor 2.5 h x 60 min = 150 min (2 SF) 1 h 5

6. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Learning Check A rattlesnake is 2.44 m long. How many centimeters long is the snake? 6

7. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution A rattlesnake is 2.44 m long. How many centimeters long is the snake? Step 1 State the given and needed quantities. Given unit: 2.44 m Needed unit: cm Step 2 Write a unit plan. Plan:meters centimeters 7

8. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution A rattlesnake is 2.44 m long. How many centimeters long is the snake? Step 3 State equalities and conversion factors to cancel units. 1 m = 10 2 cm10 2 cm and 1 m 1 m 10 2 cm Step 4 Set up problem to cancel units. Given Conversion Needed unit unit factor 2.44 m x 10 2 cm = 244 cm (3 SF) 1 m 8

9. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Learning Check How many minutes are in 1.4 days? 9

10. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution How many minutes are in 1.4 days? Step 1 State the given and needed quantities. Given unit: 1.4 days Needed unit: minutes Step 2 Write a unit plan. Factor 1 Factor 2 Plan: days h min 10

11. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution How many minutes are in 1.4 days? Step 3 State equalities and conversion factors to cancel units. 1 day = 24 hours24 hours and 1 day 1 day 24 hours 1 hour = 60 minutes 60 min and 1 h 1 h 60 min 11

12. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution How many minutes are in 1.4 days? Step 4 Set up problem to cancel units. Given Conversion Conversion Needed unit unit factor factor 1.4 days x 24 h x 60 min = 2.0 x 10 3 min 1 day 1 h (rounded) 2 SF Exact Exact = 2 SF 12

13. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Study Tip: Check Unit Cancellation Be sure to check the unit cancellation in the setup. The units in the conversion factors must cancel to give the correct unit for the answer. What is wrong with the following setup? 1.4 day x 1 day x 1 h 24 h 60 min = day 2 /min is not the unit needed. Units don’t cancel properly. 13

14. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Learning Check 14 If your pace on a treadmill is 65 meters per minute, how many minutes will it take for you to walk a distance of 7.5 kilometers?

15. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution 15 If your pace on a treadmill is 65 meters per minute, how many minutes will it take for you to walk a distance of 7.5 kilometers? Step 1 State the given and needed quantities. Given units: 7.5 km, 65 meters per minute Needed unit: minutes Step 2 Write a unit plan. Factor 1 Factor 2 Plan: kilometers meters min

16. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution 16 If your pace on a treadmill is 65 meters per minute, how many minutes will it take for you to walk a distance of 7.5 kilometers? Step 3 State equalities and conversion factors to cancel units. 1 kilometer = 10 3 meters 10 3 meters and 1 kilometer 1 kilometer 10 3 meters 65 meters = 1 minute 65 meters and 1 minute 1 minute 65 meters

17. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution 17 If your pace on a treadmill is 65 meters per minute, how many minutes will it take for you to walk a distance of 7.5 kilometers? Step 4 Set up problem to cancel units. Given Conversion Conversion Needed unit unit factor factor 7.5 kilometers x 10 3 meters x 1 minute = 120 minutes 1 kilometer 65 meters (rounded) 2 SF Exact 2 SF = 2 SF

18. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Percent Factor in a Problem If the thickness of the skin fold at the waist indicates 11% body fat, how much fat is in a person with a mass of 86 kg? Percent factor: 11 kg fat 100 kg mass percent factor 86 kg mass x 11 kg fat 100 kg mass = 9.5 kg of fat 18

19. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Learning Check How many pounds of sugar are in 120 g of candy if the candy is 25% (by mass) sugar? 19

20. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution How many pounds of sugar are in 120 g of candy if the candy is 25% (by mass) sugar? Step 1 State the given and needed quantities. Given units: 120 g of candy 25% by mass sugar Needed unit: pounds sugar Step 2 Write a unit plan. ConversionPercent factor factor Plan: grams pounds candy pounds sugar 20

21. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution How many pounds of sugar are in 120 g of candy if the candy is 25% (by mass) sugar? Step 3 State equalities and conversion factors to cancel units. 1 pound = 454 grams 454 g and 1 lb 1 lb 454 g 25 pounds of sugar = 100 pounds of candy 25 lb sugar and 100 lb candy 100 lb candy 25 lb sugar 21

22. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution How many pounds of sugar are in 120 g of candy if the candy is 25% (by mass) sugar? Step 4 Set up problem to cancel units. Given Conversion Percent unit factor factor 120 g candy x 1 lb candy x 25 lb sugar 454 g candy 100 lb candy = 0.066 lb of sugar 22