© 2013 Pearson Education, Inc. Chapter 7, Section 8 General, Organic, and Biological Chemistry Fourth Edition Karen Timberlake 7.8 The Ideal Gas Law Chapter 7 Gases © 2013 Pearson Education, Inc. Lectures

© 2013 Pearson Education, Inc. Chapter 7, Section 8 The four properties used in the measurement of a gas,  pressure (P),  volume (V),  temperature (T), and  amount (n), can be combined to give a single expression called the ideal gas law. PV = nRT Ideal Gas Law 2

© 2013 Pearson Education, Inc. Chapter 7, Section 8 Rearranging the ideal gas law equation shows that the four gas properties equal a constant, R. To calculate the value of R, we substitute the STP conditions for molar volume into the expression: R, Ideal Gas Constant 3

© 2013 Pearson Education, Inc. Chapter 7, Section 8 Another value for the universal gas constant, R, is obtained using mmHg for the STP pressure. What is the value of R when a pressure of 760 mmHg rather than 1.00 atm is used? Learning Check 4

© 2013 Pearson Education, Inc. Chapter 7, Section 8 Another value for the universal gas constant, R, is obtained using mmHg for the STP pressure. What is the value of R when a pressure of 760 mmHg rather than 1.00 atm is used? Solution 5

© 2013 Pearson Education, Inc. Chapter 7, Section 8 Unit Summary for R, the Ideal Gas Constant 6

© 2013 Pearson Education, Inc. Chapter 7, Section 8 Guide to Using the Ideal Gas Law 7

© 2013 Pearson Education, Inc. Chapter 7, Section 8 Dinitrogen oxide (N 2 O), laughing gas, is used by dentists as an anesthetic. If a 20.0 L tank of laughing gas contains 2.86 moles of N 2 O at 23  C, what is the pressure (mmHg) in the tank? Learning Check 8

© 2013 Pearson Education, Inc. Chapter 7, Section 8 If a 20.0 L tank of laughing gas contains 2.86 moles of N 2 O at 23 ˚C, what is the pressure (mmHg) in the tank? Step 1 State the given and needed quantities. Analyze the Problem. Solution 9

© 2013 Pearson Education, Inc. Chapter 7, Section 8 If a 20.0 L tank of laughing gas contains 2.86 moles of N 2 O at 23 ˚C, what is the pressure (mmHg) in the tank? Step 2 Rearrange the ideal gas law equation to solve for the needed quantity. Solution 10

© 2013 Pearson Education, Inc. Chapter 7, Section 8 If a 20.0 L tank of laughing gas contains 2.86 moles of N 2 O at 23 ˚C, what is the pressure (mmHg) in the tank? Step 3 Substitute the gas data into the equation and calculate the needed quantity. Solution 11

© 2013 Pearson Education, Inc. Chapter 7, Section 8 Ideal Gas Law and Molar Mass 12

© 2013 Pearson Education, Inc. Chapter 7, Section 8 Learning Check A cylinder contains 5.0 L of an unknown gas at 20.0 ˚C and 0.85 atm. If the mass of the gas in the cylinder is 5.8 g, what is the molar mass of the gas? 13

© 2013 Pearson Education, Inc. Chapter 7, Section 8 A cylinder contains 5.0 L of an unknown gas at 20.0 ˚C and 0.85 atm. If the mass of the gas in the cylinder is 5.8 g, what is the molar mass of the gas? Step 1 State the given and needed quantities. Analyze the Problem Solution 14

© 2013 Pearson Education, Inc. Chapter 7, Section 8 A cylinder contains 5.0 L of an unknown gas at 20.0 ˚C and 0.85 atm. If the mass of the gas in the cylinder is 5.8 g, what is the molar mass of the gas? Step 2 Rearrange the ideal gas law equation to solve for the number of moles. Step 3 Obtain the molar mass by dividing the given number of grams by the number of moles. Solution 15

© 2013 Pearson Education, Inc. Chapter 7, Section 8 Chemical Reactions and the Ideal Gas Law 16

© 2013 Pearson Education, Inc. Chapter 7, Section 8 Learning Check Nitrogen gas reacts with hydrogen gas to produce ammonia (NH 3 ) gas. How many liters of NH 3 can be produced at 0.93 atm and 24 ˚C from a 16.0-g sample of nitrogen gas and an excess of hydrogen gas? 17

© 2013 Pearson Education, Inc. Chapter 7, Section 8 Solution How many liters of NH 3 can be produced at 0.93 atm and 24 ˚C from a 16.0-g sample of nitrogen gas and an excess of hydrogen gas? Step 1 State the given and needed quantities. Analyze the Problem. 18

© 2013 Pearson Education, Inc. Chapter 7, Section 8 Solution How many liters of NH 3 can be produced at 0.93 atm and 24 ˚C from a 16.0-g sample of nitrogen gas and an excess of hydrogen gas? Step 2 Write a plan to convert the given quantity to the needed moles. grams molar moles mole−mole moles of N 2 mass of N 2 factor of NH 3 19

© 2013 Pearson Education, Inc. Chapter 7, Section 8 How many liters of NH 3 can be produced at 0.93 atm and 24 ˚C from a 16.0-g sample of nitrogen gas and an excess of hydrogen gas? Step 3 Write the equalities for molar mass and mole– mole factors. Solution 20

© 2013 Pearson Education, Inc. Chapter 7, Section 8 Solution How many liters of NH 3 can be produced at 0.93 atm and 24 ˚C from a 16.0-g sample of nitrogen gas and an excess of hydrogen gas? Step 4 Set up the problem to calculate moles of needed quantity. 21

© 2013 Pearson Education, Inc. Chapter 7, Section 8 Solution How many liters of NH 3 can be produced at 0.93 atm and 24 ˚C from a 16.0-g sample of nitrogen gas and an excess of hydrogen gas? Step 5 Convert the moles of needed to volume using the ideal gas law equation. 22