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

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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.

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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

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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

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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.

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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.

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

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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 ?

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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)

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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.

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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.

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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

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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 2 425 mmHg Pressure ratio increases volume Solution

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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.

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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.

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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

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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.)

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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.

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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 2 600. mmHg x 12.0 L = 200. mmHg 36.0 L

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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

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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.)

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