14.3 Ideal Gases > Chapter 14 The Behavior of Gases Ideal Gases Properties of Gases The Gas Laws Gases: Mixtures and Movements

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1 Chapter 14 The Behavior of Gases 14.1 Properties of Gases 14.2 The Gas Laws 14.3 Ideal Gases 14.4 Gases: Mixtures and Movements 1 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

2 CHEMISTRY & YOU How can you blanket a stage with fog? Solid carbon dioxide, or dry ice, can be used to make stage fog. 2 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

3 Ideal Gas Law Ideal Gas Law How can you calculate the amount of a contained gas when the pressure, volume, and temperature are specified? 3 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

4 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. 4 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

5 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. 5 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

6 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. 6 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

7 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. 7 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

8 Ideal Gas Law You can introduce moles into the combined gas law by dividing each side of the equation by n. 8 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

9 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. 9 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

10 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. P 1 V 1 P 2 V 2 = T 1 n 1 T 2 n 2 10 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

11 Ideal Gas Law 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). R = P V T n 11 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

12 Ideal Gas Law 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). R = P V T n 12 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

13 Ideal Gas Law 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). R = P V T n = kpa 22.4 L 273 K 1 mol 13 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

14 Ideal Gas Law 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). R = P V T n = kpa 22.4 L 273 K 1 mol R = 8.31 (L kpa)/(k mol) 14 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

15 Ideal Gas Law The gas law that includes all four variables P, V, T, n is called the ideal gas law. P V = n R T or PV = nrt 15 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

16 Ideal Gas Law 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. 16 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

17 Sample Problem 14.5 Using the Ideal Gas Law At 34 o C, the pressure inside a nitrogen-filled tennis ball with a volume of L is 212 kpa. How many moles of nitrogen gas are in the tennis ball? 17 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

18 Sample Problem Analyze List the knowns and the unknown. Use the ideal gas law (PV = nrt) to calculate the number of moles (n). KNOWNS P = 212 kpa V = L T = 34 o C UNKNOWN n =? mol N 2 R = 8.31 (L kpa)/(k mol) 18 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

19 Sample Problem Calculate Solve for the unknown. Convert degrees Celsius to kelvins. T = 34 o C = 307 K 19 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

20 Sample Problem Calculate Solve for the unknown. State the ideal gas law. P V = n R T 20 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

21 Sample Problem Calculate Solve for the unknown. Rearrange the equation to isolate n. P V = n R T P V n = R T Isolate n by dividing both sides by (R T): P V R T = n R T R T 21 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

22 Sample Problem Calculate Solve for the unknown. Substitute the known values for P, V, R, and T into the equation and solve. P V n = R T 212 kpa L n = 8.31 (L kpa) / (K mol) 307 K n = mol N 2 22 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

23 Sample Problem Evaluate Does the result make sense? A tennis ball has a small volume and is not under great pressure. It is reasonable that the ball contains a small amount of nitrogen. 23 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

24 Sample Problem 14.6 Using the Ideal Gas Law A deep underground cavern contains 2.24 x 10 6 L of methane gas (CH 4 ) at a pressure of 1.50 x 10 3 kpa and a temperature of 315 K. How many kilograms of CH 4 does the cavern contain? 24 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

25 Sample Problem Analyze List the knowns and the unknown. 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 P = kpa V = L T = 315 K UNKNOWN m =? kg CH 4 R = 8.31 (L kpa)/(k mol) molar mass CH4 = 16.0 g 25 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

26 Sample Problem Calculate Solve for the unknown. State the ideal gas law. P V = n R T Rearrange the equation to isolate n. P V n = R T 26 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

27 Sample Problem Calculate Solve for the unknown. Substitute the known quantities into the equation and find the number of moles of methane. n = ( kpa) ( L) 8.31 (L kpa)/(k mol) 315 K n = mol CH 4 27 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

28 Sample Problem Calculate Solve for the unknown. Do a mole-mass conversion mol CH g CH 4 1 mol CH 4 = g CH 4 = g CH 4 28 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

29 Sample Problem Calculate Solve for the unknown. Convert from grams to kilograms g CH 4 1 kg 10 3 g = kg CH 4 29 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

30 Sample Problem Evaluate Does the result make sense? Although the methane is compressed, its volume is still very large. So it is reasonable that the cavern contains a large amount of methane. 30 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

31 How would you rearrange the ideal gas law to isolate the temperature, T? A. T = nr PV C. T = PV nr B. T = nv PR D. T = np RV 31 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

32 How would you rearrange the ideal gas law to isolate the temperature, T? A. T = nr PV C. T = PV nr B. T = nv PR D. T = np RV 32 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

33 Ideal Gases and Real Gases Ideal Gases and Real Gases Under what conditions are real gases most likely to differ from ideal gases? 33 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

34 Ideal Gases and Real Gases An ideal gas is one that follows the gas laws at all conditions of pressure and temperature. 34 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

35 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. 35 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

36 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. There could be no attraction between particles in the gas. 36 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

37 Ideal Gases and Real Gases There is no gas for which these assumptions are true. So, an ideal gas does not exist. 37 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

38 Ideal Gases and Real Gases At many conditions of temperature and pressure, a real gas behaves very much like an ideal gas. 38 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

39 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. 39 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

40 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. 40 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

41 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. Because of these attractions, a gas can condense, or even solidify, when it is compressed or cooled. 41 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

42 Ideal Gases and Real Gases Real gases differ most from an ideal gas at low temperatures and high pressures. 42 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

43 Interpret Graphs This graph shows how real gases deviate from the ideal gas law at high pressures. 43 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

44 What are the characteristics of an ideal gas? 44 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

45 What are the characteristics of an ideal gas? The particles of an ideal gas have no volume, and there is no attraction between them. 45 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

46 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? 46 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

47 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. 47 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

48 Key Concepts and Key Equation 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. Real gases differ most from an ideal gas at low temperatures and high pressures. Key Equation: ideal gas law P V = n R T or PV = nrt 48 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

49 Glossary Terms ideal gas constant: the constant in the ideal gas law with the symbol R and the value 8.31 (L kpa)/(k mol) ideal gas law: the relationship PV = nrt, which describes the behavior of an ideal gas 49 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

50 BIG IDEA Kinetic Theory Ideal gases conform to the assumptions of kinetic theory. The behavior of ideal gases can be predicted by the gas laws. 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. Although an ideal gas does not exist, real gases behave ideally under a variety of temperature and pressure conditions. 50 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

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