1. Gas Laws Part 3: Ideal Gas Law

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

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

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

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

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

7. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. You can introduce moles into the combined gas law by dividing each side of the equation by n. P 1  V 1 P 2  V 2 T1  n1T1  n1 T2  n2T2  n2 = 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. Ideal Gas Law

8. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 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  VP  V T  nT  n R = Ideal Gas Law

9. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 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  VP  V T  nT  n R = Ideal Gas Law

10. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 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  VP  V T  nT  n R == 101.3 kPa  22.4 L 273 K  1 mol Ideal Gas Law

11. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 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  VP  V T  nT  n R == 101.3 kPa  22.4 L 273 K  1 mol R = 8.31 (L·kPa)/(K·mol) Ideal Gas Law

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

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

14. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. At 34 o C, 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? Sample Problem 14.5 Using the Ideal Gas Law

15. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Use the ideal gas law (PV = nRT) to calculate the number of moles (n). KNOWNS P = 212 kPa V = 0.148 L T = 34 o C R = 8.31 (L · kPa)/(K · mol) UNKNOWN n = ? mol N 2 Analyze List the knowns and the unknown. 1 Sample Problem 14.5

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

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

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

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

20. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 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. Evaluate Does the result make sense? 3 Sample Problem 14.5

21. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 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? Sample Problem 14.6 Using the Ideal Gas Law

22. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 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 = 1.50  10 3 kPa V = 2.24  10 3 L T = 315 K R = 8.31 (L · kPa)/(K · mol) molar mass CH 4 = 16.0 g UNKNOWN m = ? kg CH 4 AnalyzeList the knowns and the unknown. 1 Sample Problem 14.6

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

24. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Substitute the known quantities into the equation and find the number of moles of methane. Calculate Solve for the unknown. 2 n =n = 8.31 (L·kPa)/(K·mol)  315 K (1.50  10 6 kPa)  (2.24  10 6 L) n = 1.28  10 6 mol CH 4 Sample Problem 14.6

25. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Do a mole-mass conversion. Calculate Solve for the unknown. 2 1.28  10 6 mol CH 4  16.0 g CH 4 1 mol CH 4 = 20.5  10 6 g CH 4 = 2.05  10 7 g CH 4 Sample Problem 14.6

26. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Convert from grams to kilograms. Calculate Solve for the unknown. 2 2.05  10 6 g CH 4  1 kg 10 3 g = 2.05  10 4 kg CH 4 Sample Problem 14.6

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

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

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

30. 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?

31. 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.

32. 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.

33. 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. There could be no attraction between particles in the gas.

34. 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.

35. 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.

36. 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.

37. 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.

38. 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. Because of these attractions, a gas can condense, or even solidify, when it is compressed or cooled.

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

40. 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.

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

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

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

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

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

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

47. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Kinetic Theory BIG IDEA 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.