Chapter 14 The Behavior of Gases 14.3 Ideal Gases 14.1 Properties of Gases 14.2 The Gas Laws 14.3 Ideal Gases 14.4 Gases: Mixtures and Movements Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

How can you blanket a stage with fog? CHEMISTRY & YOU How can you blanket a stage with fog? Solid carbon dioxide, or dry ice, can be used to make stage fog. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Ideal Gas Law Ideal Gas Law 1. How can you calculate the amount of a contained gas when the pressure, volume, and temperature are specified? Used the Ideal Gas Law Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Ideal Gas Law 2. Suppose you want to calculate the number of moles (n) of a gas in a fixed volume at a known temperature and pressure. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Ideal Gas Law Suppose you want to calculate the number of moles (n) of a gas in a fixed volume at a known temperature and pressure. The volume occupied by a gas at a specified temperature and pressure depends on the number of particles. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Ideal Gas Law Suppose you want to calculate the number of moles (n) of a gas in a fixed volume at a known temperature and pressure. The volume occupied by a gas at a specified temperature and pressure depends on the number of particles. The number of moles of gas is directly proportional to the number of particles. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Ideal Gas Law Suppose you want to calculate the number of moles (n) of a gas in a fixed volume at a known temperature and pressure. The volume occupied by a gas at a specified temperature and pressure depends on the number of particles. The number of moles of gas is directly proportional to the number of particles. Moles must be directly proportional to volume. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Ideal Gas Law You can introduce moles into the combined gas law by dividing each side of the equation by n. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Ideal Gas Law You can introduce moles into the combined gas law by dividing each side of the equation by n. This equation shows that (P  V)/(T  n) is a constant. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Ideal Gas Law You can introduce moles into the combined gas law by dividing each side of the equation by n. This equation shows that (P  V)/(T  n) is a constant. This constant holds for what are called ideal gases—gases that conform to the gas laws. P1  V1 P2  V2 T1  n1 T2  n2 = Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Ideal Gas Law 4. If you know the values for P, V, T, and n for one set of conditions, you can calculate a value for the ideal gas constant (R). P  V T  n R = Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Ideal Gas Law 4. If you know the values for P, V, T, and n for one set of conditions, you can calculate a value for the ideal gas constant (R). Recall that 1 mol of every gas occupies 22.4 L at STP (101.3 kPa and 273 K). P  V T  n R = Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Ideal Gas Law 4. If you know the values for P, V, T, and n for one set of conditions, you can calculate a value for the ideal gas constant (R). Recall that 1 mol of every gas occupies 22.4 L at STP (101.3 kPa and 273 K). Insert the values of P, V, T, and n into (P  V)/(T  n). P  V T  n R = = 101.3 kPa  22.4 L 273 K  1 mol Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Ideal Gas Law 4. If you know the values for P, V, T, and n for one set of conditions, you can calculate a value for the ideal gas constant (R). A. Recall that 1 mol of every gas occupies 22.4 L at STP (101.3 kPa and 273 K). B. Insert the values of P, V, T, and n into (P  V)/(T  n). P  V T  n R = = 101.3 kPa  22.4 L 273 K  1 mol R = 8.31 (L·kPa)/(K·mol) Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Ideal Gas Law 6. The gas law that includes all four variables—P, V, T, n—is called the ideal gas law. P  V = n  R  T PV = nRT or Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Ideal Gas Law 7. When the pressure, volume, and temperature of a contained gas are known, you can use the ideal gas law to calculate the number of moles of the gas. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Sample Problem 14.5 Using the Ideal Gas Law 8. At 34oC, the pressure inside a nitrogen-filled tennis ball with a volume of 0.148 L is 212 kPa. How many moles of nitrogen gas are in the tennis ball? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Analyze List the knowns and the unknown. Sample Problem 14.5 Analyze List the knowns and the unknown. 1 Use the ideal gas law (PV = nRT) to calculate the number of moles (n). KNOWNS UNKNOWN P = 212 kPa V = 0.148 L T = 34oC R = 8.31 (L·kPa)/(K·mol) n = ? mol N2 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Calculate Solve for the unknown. Sample Problem 14.5 Calculate Solve for the unknown. 2 Convert degrees Celsius to kelvins. T = 34oC + 273 = 307 K Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Calculate Solve for the unknown. Sample Problem 14.5 Calculate Solve for the unknown. 2 State the ideal gas law. P  V = n  R  T Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Calculate Solve for the unknown. Sample Problem 14.5 Calculate Solve for the unknown. 2 Rearrange the equation to isolate n. P  V = n  R  T Isolate n by dividing both sides by (R  T): = R  T n  R  T P  V n = R  T P  V Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Calculate Solve for the unknown. Sample Problem 14.5 Calculate Solve for the unknown. 2 Substitute the known values for P, V, R, and T into the equation and solve. n = R  T P  V n = 8.31 (L·kPa) / (K·mol)  307 K 212 kPa  0.148 L n = 1.23  10–2 mol N2 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

10. Evaluate Does the result make sense? Sample Problem 14.5 10. Evaluate Does the result make sense? 3 A. A tennis ball has a small volume and is not under great pressure. B. It is reasonable that the ball contains a small amount of nitrogen. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Sample Problem 14.6 Using the Ideal Gas Law 11. A deep underground cavern contains 2.24 x 106 L of methane gas (CH4) at a pressure of 1.50 x 103 kPa and a temperature of 315 K. How many kilograms of CH4 does the cavern contain? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Analyze List the knowns and the unknown. Sample Problem 14.6 Analyze List the knowns and the unknown. 1 Calculate the number of moles (n) using the ideal gas law. Use the molar mass of methane to convert moles to grams. Then convert grams to kilograms. KNOWNS UNKNOWN P = 1.50  103 kPa V = 2.24  103 L T = 315 K R = 8.31 (L·kPa)/(K·mol) molar massCH4 = 16.0 g m = ? kg CH4 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Calculate Solve for the unknown. Sample Problem 14.6 Calculate Solve for the unknown. 2 State the ideal gas law. P  V = n  R  T Rearrange the equation to isolate n. n = R  T P  V Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Calculate Solve for the unknown. Sample Problem 14.6 Calculate Solve for the unknown. 2 Substitute the known quantities into the equation and find the number of moles of methane. n = 8.31 (L·kPa)/(K·mol)  315 K (1.50  106 kPa)  (2.24  106 L) n = 1.28  106 mol CH4 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Calculate Solve for the unknown. Sample Problem 14.6 Calculate Solve for the unknown. 2 Do a mole-mass conversion. 1.28  106 mol CH4  16.0 g CH4 1 mol CH4 = 20.5  106 g CH4 = 2.05  107 g CH4 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Calculate Solve for the unknown. Sample Problem 14.6 Calculate Solve for the unknown. 2 Convert from grams to kilograms. 2.05  106 g CH4  1 kg 103 g = 2.05  104 kg CH4 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Evaluate Does the result make sense? Sample Problem 14.6 Evaluate Does the result make sense? 3 Although the methane is compressed, its volume is still very large. So it is reasonable that the cavern contains a large amount of methane. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

How would you rearrange the ideal gas law to isolate the temperature, T? PV nR T = A. nR PV T = C. PR nV T = B. RV nP T = D. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

How would you rearrange the ideal gas law to isolate the temperature, T? PV nR T = A. nR PV T = C. PR nV T = B. RV nP T = D. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Ideal Gases and Real Gases Under what conditions are real gases most likely to differ from ideal gases? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Ideal Gases and Real Gases 15. An ideal gas is one that follows the gas laws at all conditions of pressure and temperature. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Ideal Gases and Real Gases An ideal gas is one that follows the gas laws at all conditions of pressure and temperature. Its particles could have no volume. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Ideal Gases and Real Gases 15. An ideal gas is one that follows the gas laws at all conditions of pressure and temperature. A. Its particles could have no volume. B. There could be no attraction between particles in the gas. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Ideal Gases and Real Gases There is no gas for which these assumptions are true. So, an ideal gas does not exist. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Ideal Gases and Real Gases At many conditions of temperature and pressure, a real gas behaves very much like an ideal gas. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Ideal Gases and Real Gases At many conditions of temperature and pressure, a real gas behaves very much like an ideal gas. The particles in a real gas have volume. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Ideal Gases and Real Gases At many conditions of temperature and pressure, a real gas behaves very much like an ideal gas. The particles in a real gas have volume. There are attractions between the particles. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Ideal Gases and Real Gases 17. At many conditions of temperature and pressure, a real gas behaves very much like an ideal gas. The particles in a real gas have volume. There are attractions between the particles. Because of these attractions, a gas can condense, or even solidify, when it is compressed or cooled. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Ideal Gases and Real Gases 18. Real gases differ most from an ideal gas at low temperatures and high pressures. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Interpret Graphs This graph shows how real gases deviate from the ideal gas law at high pressures. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

What are the characteristics of an ideal gas? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

What are the characteristics of an ideal gas? 20. The particles of an ideal gas have no volume, and there is no attraction between them. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

CHEMISTRY & YOU Certain types of fog machines use dry ice and water to create stage fog. What phase changes occur when stage fog is made? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

CHEMISTRY & YOU Certain types of fog machines use dry ice and water to create stage fog. What phase changes occur when stage fog is made? Dry ice doesn’t melt—it sublimes. As solid carbon dioxide changes to gas, water vapor in the air condenses and forms a white fog. Dry ice can exist because gases don’t obey the assumptions of kinetic theory at all conditions. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Key Concepts and Key Equation 21. When the pressure, volume, and temperature of a contained gas are known, you can use the ideal gas law to calculate the number of moles of the gas. 22. Real gases differ most from an ideal gas at low temperatures and high pressures. 23. Key Equation: ideal gas law P  V = n  R  T or PV = nRT Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Glossary Terms 24. ideal gas constant: the constant in the ideal gas law with the symbol R and the value 8.31 (L·kPa)/(K·mol) 25. ideal gas law: the relationship PV = nRT, which describes the behavior of an ideal gas Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

BIG IDEA Kinetic Theory 26. Ideal gases conform to the assumptions of kinetic theory. 27. The behavior of ideal gases can be predicted by the gas laws. 28. With the ideal gas law, the number of moles of a gas in a fixed volume at a known temperature and pressure can be calculated. 29. Although an ideal gas does not exist, real gases behave ideally under a variety of temperature and pressure conditions. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

END OF 14.3 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.