Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Chapter 6 Gases 6.3 Pressure and Volume Boyle’s Law 1

Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Boyle’s Law Boyle’s law states that the pressure of a gas is inversely related to its volume when T and n are constant the product P  V is constant when temperature and moles are held constant if volume decreases, the pressure increases P 1 V 1 = P 2 V 2 2

Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Boyle’s Law: PV = Constant P 1 V 1 = 8.0 atm  2.0 L = 16 atm L P 2 V 2 = 4.0 atm  4.0 L = 16 atm L P 3 V 3 = 2.0 atm  8.0 L = 16 atm L Boyle’s law can be stated as P 1 V 1 = P 2 V 2 (T, n constant) 3

Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Boyle’s Law and Breathing During an inhalation, the lungs expand the pressure in the lungs decreases air flows toward the lower pressure in the lungs 4

Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Boyle’s Law and Breathing During an exhalation, lung volume decreases pressure within the lungs increases air flows from the higher pressure in the lungs to the outside 5

Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solving for a Gas Law Factor The equation for Boyle’s law can be rearranged to solve for any factor. P 1 V 1 = P 2 V 2 Boyle’s law To solve for V 2, divide both sides by P 2. P 1 V 1 = P 2 V 2 P 2 P 2 V 1 x P 1 = V 2 P 2 6

Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Barometer Measures Pressure A barometer measures the pressure exerted by the gases in the atmosphere indicates atmospheric pressure as the height in mm of the mercury column 760 mmHg = 1 atm 7

Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Atmospheric Pressure Atmospheric pressure is the pressure exerted by a column of air from the top of the atmosphere to the surface of Earth decreases as altitude increases is 1 atm at sea level is higher on a rainy day 8

Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Guide to Using Gas Laws 9

Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Calculations Using Boyle’s Law Freon-12, CCl 2 F 2, is used in refrigeration systems. What is the new volume (L) of a 8.0-L sample of Freon gas initially at 550 mmHg after its pressure is changed to 2200 mmHg at constant T and n? Step 1 Organize the data in a table of initial and final conditions. Conditions Initial Final P 1 = 550 mmHg P 2 = 2200 mmHg V 1 = 8.0 L V 2 = ? 10

Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution Step 2 When pressure increases, volume decreases. Solve Boyle’s law for V 2 : P 1 V 1 = P 2 V 2 V 2 = V 1  P 1 P 2 Step 3 Substitute values into the gas law equation and calculate. V 2 = 8.0 L  550 mmHg = 2.0 L 2200 mmHg pressure ratio decreases volume 11

Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Learning Check A sample of oxygen gas has a volume of 12.0 L at 600. mmHg. What is the new pressure when the volume changes to 36.0 L (T and n constant)? A mmHg B mmHg C mmHg 12

Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution A sample of oxygen gas has a volume of 12.0 L at 600. mmHg. What is the new pressure when the volume changes to 36.0 L (T and n constant)? Step 1 Organize the data in a table of initial and final conditions. Data Table Conditions 1Conditions 2 P 1 = 600. mmHgP 2 = ? V 1 = 12.0 LV 2 = 36.0 L 13

Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution A sample of oxygen gas has a volume of 12.0 L at 600. mmHg. What is the new pressure when the volume changes to 36.0 L (T and n constant)? Step 2 Rearrange the gas law equation to solve for the unknown quantity. P 2 = P 1  V 1 V 2 Step mmHg  12.0 L = 200. mmHg The answer is A L The answer is A, 200. mmHg. 14

Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Learning Check For a cylinder containing helium gas, indicate if cylinder A or cylinder B represents the new volume for the following changes (n and T are constant). 1. pressure decreases 2. pressure increases 15

Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Learning Check For a cylinder containing helium gas, indicate if cylinder A or cylinder B represents the new volume for the following changes (n and T are constant). 1. pressure decreases cylinder B 2. pressure increases cylinder A 16

Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Learning Check If a sample of helium gas has a volume of 120 mL and a pressure of 850 mmHg, what is the new volume if the pressure is changed to 425 mmHg? A. 60 mL B. 120 mLC. 240 mL 17

Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution If a sample of helium gas has a volume of 120 mL and a pressure of 850 mmHg, what is the new volume if the pressure is changed to 425 mmHg? Step 1Organize the data in a table of initial and final conditions. Data Table Conditions 1 Conditions 2 P 1 = 850 mmHgP 2 = 425 mm Hg V 1 = 120 mLV 2 = ? Step 2Rearrange the gas law equation to solve for the unknown quantity. V 2 = V 1  P 1 P 2 18

Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution If a sample of helium gas has a volume of 120 mL and a pressure of 850 mmHg, what is the new volume if the pressure is changed to 425 mmHg? Step 3 Substitute values into the gas law equation and calculate. V 2 = V 1  P 1 = 120 mL  850 mmHg = 240 mL P mmHg Pressure ratio increases volume The answer is C, 240 mL. 19

Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Learning Check A sample of helium gas in a balloon has a volume of 6.4 L at a pressure of 0.70 atm. At 1.40 atm (T is constant), is the new volume represented by A, B, or C? 20

Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution A sample of helium gas in a balloon has a volume of 6.4 L at a pressure of 0.70 atm. At a higher pressure (T constant), the new volume is represented by the smaller balloon A. 21