General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc.1 Chapter 7 Gases 7.5 Temperature and Pressure (Gay-Lussac’s Law)

General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc.2 Gay-Lussac’s Law: P and T In Gay-Lussac’s law,  the pressure exerted by a gas is directly related to the Kelvin temperature  V and n are constant P 1 = P 2 T 1 T 2

General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc.3 Learning Check Solve Gay-Lussac’s law for P 2. P 1 = P 2 T 1 T 2

General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc.4 Solution Solve Gay-Lussac’s law for P 2. P 1 = P 2 T 1 T 2 Multiply both sides by T 2 and cancel: P 1 x T 2 = P 2 x T 2 T 1 T 2 P 2 = P 1 x T 2 T 1

General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc.5 A gas has a pressure at 2.0 atm at 18 °C. What is the new pressure when the temperature is 62 °C? (V and n constant) STEP 1 Set up a data table: Conditions 1 Conditions 2 Know Predict P 1 = 2.0 atm P 2 = ? P increases T 1 = 18 °C T 2 = 62 °C T increases = 291 K = 335 K Calculation with Gay-Lussac’s Law

General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc.6 Calculation with Gay-Lussac’s Law (continued) STEP 2 Solve Gay-Lussac’s Law for P 2 : P 1 = P 2 T 1 T 2 P 2 = P 1 x T 2 T 1 STEP 3 Substitute values to solve for unknown: P 2 = 2.0 atm x 335 K = 2.3 atm 291 K Temperature ratio increases pressure

General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc.7 Learning Check A gas has a pressure of 645 mmHg at 128 °C. What is the temperature in Celsius if the pressure increases to 824 mmHg (n and V remain constant)?

General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc.8 Solution A gas has a pressure of 645 mmHg at 128 °C. What is the temperature in Celsius if the pressure increases to 1.50 atm (n and V remain constant)? P 2 = 1.50 atm x 760 mmHg = 1140 mmHg 1 atm STEP 1 Set up a data table: Conditions 1 Conditions 2 Know Predict P 1 = 645 mmHg P 2 = 1140 mmHg P increases T 1 = 128 °C T 2 = K – 273 T increases = 401 K = ? °C

General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc.9 Solution (continued) STEP 2 Solve Gay-Lussac’s Law for T 2 : P 1 = P 2 T 1 T 2 T 2 = T 1 x P 2 P 1 STEP 3 Substitute values to solve for unknown: T 2 = 401 K x 1140 mmHg = 709 K – 273 = 436 °C 645 mmHg Pressure ratio increases temperature

General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc. Vapor Pressure The vapor pressure of water  is the pressure above water at equilibrium in a closed container  at the boiling point is equal to the external (atmospheric) pressure 10

General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc.11 Vapor Pressure and Boiling Point Vapor pressure  is the pressure of gas molecules above the surface of a liquid  at the boiling point, becomes equal to the external pressure

General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc.12 Boiling Point of Water The boiling point of water  depends on the vapor pressure  is lower at higher altitudes  is increased by using an autoclave to increase external pressure

General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc. Learning Check In which pair of temperatures for water will boiling occur? Atmospheric pressure Vapor Pressure A. 760 mmHg 760 mmHg B. 960 mmHg 760 mmHg C. 520 mmHg 620 mmHg 13

General, Organic, and Biological Chemistry Copyright © 2010 Pearson Education, Inc. Solution In which pair of temperatures for water will boiling occur? Atmospheric Vapor Boiling PressurePressure Occurs? A. 760 mmHg760 mmHg yes B. 960 mmHg760 mmHg no C. 520 mmHg620 mmHg yes 14