1 Chapter 6Gases 6.3 Pressure and Volume (Boyle’s Law) Copyright © 2009 by Pearson Education, Inc.

2 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. if volume decreases, the pressure increases. Copyright © 2009 by Pearson Education, Inc.

3 In Boyle’s law, the product P x V is constant as long as T and n do not change. P 1 V 1 = 8.0 atm x 2.0 L = 16 atm L P 2 V 2 = 4.0 atm x 4.0 L = 16 atm L P 3 V 3 = 2.0 atm x 8.0 L = 16 atm L Boyle’s law can be stated as P 1 V 1 = P 2 V 2 (T, n constant) PV Constant in Boyle’s Law

4 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 xP 1 = V 2 P 2

5 Boyles’ Law and Breathing During an inhalation, the lungs expand. the pressure in the lungs decreases. air flows towards the lower pressure in the lungs. Copyright © 2009 by Pearson Education, Inc.

6 Boyles’ 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. Copyright © 2009 by Pearson Education, Inc.

7 Calculations with Boyle’s Law Copyright © 2009 by Pearson Education, Inc.

8 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? 1. Set up a data table: Conditions 1Conditions 2 P 1 = 550 mmHgP 2 = 2200 mmHg V 1 = 8.0 LV 2 = Calculation with Boyle’s Law ?

9 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 x P 1 P 2 V 2 = 8.0 L x 550 mmHg = 2.0 L 2200 mmHg pressure ratio decreases volume Calculation with Boyle’s Law (continued)

10 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 Copyright © 2009 by Pearson Education, Inc.

11 Solution 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 B 2) pressure increases A Copyright © 2009 by Pearson Education, Inc.

12 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? 1) 60 mL 2) 120 mL3) 240 mL

13 3) 240 mL P 1 = 850 mmHgP 2 = 425 mmHg V 1 = 120 mLV 2 = ?? V 2 = V 1 x P 1 = 120 mL x 850 mmHg = 240 mL P mmHg Pressure ratio increases volume Solution

14 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? Copyright © 2009 by Pearson Education, Inc.

15 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. Copyright © 2009 by Pearson Education, Inc.

16 If the sample of helium gas has a volume of 6.4 L at a pressure of 0.70 atm, what is the new volume when the pressure is increased to 1.40 atm (T constant)? A) 3.2 LB) 6.4 LC) 12.8 L Learning Check

17 Solution If the sample of helium gas has a volume of 6.4 L at a pressure of 0.70 atm, what is the new volume when the pressure is increased to 1.40 atm (T constant)? A) 3.2 L V 2 = V 1 x P 1 P 2 V 2 = 6.4 L x 0.70 atm = 3.2 L 1.40 atm Volume decreases when there is an increase in the pressure (temperature is constant.)

18 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). 1) 200. mmHg 2) 400. mmHg 3) 1200 mmHg Copyright © 2009 by Pearson Education, Inc.

19 Solution 1) 200. mmHg Data Table Conditions 1Conditions 2 P 1 = 600. mmHgP 2 = ??? V 1 = 12.0 LV 2 = 36.0 L P 2 = P 1 x V 1 V mmHg x 12.0 L = 200. mmHg 36.0 L

20 If the sample of nitrogen (gas) has a volume of 360 mL at a pressure of 720 mmHg, what is the new volume when the pressure is increased to 1.20 atm (T constant)? A) 284 mLB) 456 mLC) 2160 mL Learning Check

21 Solution We need to make the units for initial and final pressure the same: 1.20 atm x 760 mmHg = 912 mmHg 1 atm V 2 = V 1 x P 1 P 2 V 2 = 360 mL x 720 mmHg = 284 mL (A) 912 mmHg Volume decreases when there is an increase in the pressure (temperature is constant.)