Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Chapter 6 Gases 6.5 Temperature and Pressure Gay-Lussac’s Law 1

Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Gay-Lussac’s Law 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 2

Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Learning Check Solve Gay-Lussac’s law for P 2. P 1 = P 2 T 1 T 2 3

Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. 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  T 2 = P 2  T 2 T 1 T 2 P 2 = P 1  T 2 T 1 4

Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Calculations Using Gay-Lussac’s Law 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 Organize the data into a table of initial and final conditions. Conditions Initial Final P 1 = 2.0 atm P 2 = ? T 1 = 18  C T 2 = 62  C = 291 K = 335 K Be sure to use the Kelvin (K) temperature in gas calculations. 5

Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Calculations Using Gay-Lussac’s Law Step 2Rearrange to solve for unknown quantity: P 2 Solve Gay-Lussac’s law for P 2 : P 1 = P 2 P 2 = P 1  T 2 T 1 T 2 T 1 Step 3Substitute the values into the gas law equation and calculate. P 2 = 2.0 atm  335 K = 2.3 atm 291 K Temperature ratio increases pressure 6

Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Learning Check A gas has a pressure of 645 torr at 128  C. What is the temperature in Celsius if the pressure increases to 824 torr (n and V remain constant)? 7

Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution A gas has a pressure of 645 torr at 128  C. What is the temperature in Celsius if the pressure increases to 824 torr (n and V remain constant)? Step 1 Organize the data into a table of initial and final conditions. Conditions Initial Final P 1 = 645 torr P 2 = 824 torr T 1 = 128  C T 2 = K – 273 = ?  C = 401 K 8

Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution A gas has a pressure of 645 torr at 128  C. What is the temperature in Celsius if the pressure increases to 824 torr (n and V remain constant)? Step 2 Rearrange the gas law equation to solve for the unknown quantity. Solve Gay-Lussac’s law for T 2 : P 1 = P 2 T 2 = T 1  P 2 T 1 T 2 P 1 9

Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution A gas has a pressure of 645 torr at 128  C. What is the temperature in Celsius if the pressure increases to 824 torr (n and V remain constant)? Step 3 Substitute values into the gas law equation and calculate. T 2 = 401 K  824 torr = 512 K − 273 = 239  C 645 torr Pressure ratio increases temperature 10

Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Vapor Pressure and Boiling Point Vapor pressure is the pressure that accumulates when molecules of a liquid collect over the surface of a liquid in a closed container is specific for a given temperature increases when the temperature increases When the vapor pressure of a liquid equals the external pressure, the liquid reaches its boiling point. 11

Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Temperature and Vapor Pressure of Water 12

Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Pressure and Boiling Point of Water People who live at high altitudes often use pressure cookers to obtain higher temperatures when preparing food. In a pressure cooker, water is heated in a closed container so that pressures above 1 atm are obtained, raising the boiling point of water. 13

Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Learning Check Explain why water boils at a lower temperature in the mountains than at sea level. 14

Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution Explain why water boils at a lower temperature in the mountains than at sea level. Atmospheric pressure in the mountains is less than at sea level. The vapor pressure of the water reaches the atmospheric pressure at a lower temperature. 15