1. Ch. 14 The Behavior of Gases

2. 14.1 PROPERTIES OF GASES

3. Compressibility Compressibility: a measure of how much the volume of matter decreases under pressure Gases are easily compressed because of the spaces between gas particles

4. Factors Affecting Gas Pressure Amount of gas (moles) n Volume (liters) V Temperature (Kelvins) T Pressure (kilopascals) P

5. Amount of Gas

6. Volume

7. Temperature

8. 14.2 THE GAS LAWS

9. Boyle’s Law For a given mass of gas at constant temperature, the volume of the gas varies inversely with pressure P 1 x V 1 = P 2 x V 2

10. Sample Problems Nitrous oxide (N 2 O) is used as an anesthetic. The pressure on 2.50 L of N 2 O changes from 105 kPa to 40.5 kPa. If the temperature does not change, what will the new volume be? A gas with a volume of 4.00 L at a pressure of 205 kPa is allowed to expand to a volume of 12.0 L. What is the pressure in the container if the temperature remains constant?

11. Charles’ Law The volume of a fixed mass of gas is directly proportional to its Kelvin temperature if the pressure is kept constant V 1 /T 1 = V 2 /T 2

12. Sample Problems If a sample of gas occupies 6.80 L at 325 ⁰C, what will its volume be at 25⁰C if the pressure does not change? ⁰C + 273 = K Exactly 5.00 L of air at -50.0⁰C is warmed to 100.0⁰C. What is the new volume if the pressure remains constant?

13. Gay-Lussac’s Law The pressure of a gas is directly proportional to the Kelvin temperature if the volume remains constant P 1 /T 1 = P 2 /T 2

14. Sample Problems The pressure in a sealed plastic container is 108 kPa at 41 ⁰C. What is the pressure when the temperature drops to 22 ⁰C? Assume that the volume has not changed. The pressure in a car tire is 198 kPa at 27 ⁰C. After a long drive, the pressure is 225 kPa. What is the temperature of the air in the tire? Assume that the volume is constant.

15. The Combined Gas Law

16. Sample Problems A gas at 155 kPa and 25 ⁰C has an initial volume of 1.00 L. The pressure of the gas increases to 605 kPa as the temperature is raised to 125⁰C. What is the new volume? A 5.00 L air sample has a pressure of 107 kPa at a temperature of -50.0 ⁰C. If the temperature is raised to 102 ⁰C and the volume expands to 7.00 L, what will the new pressure be?

17. 14.3 IDEAL GASES

18. Ideal Gas Law Combining all four factors P 1 x V 1 / T 1 x n 1 = P 2 x V 2 / T 2 x n 2 If you know the values for P, V, T, and n for one set of conditions, you can calculate a value for a constant 1 mol of gas occupies 22.4 L at STP (101.3 kPa and 273 K) Plugging in these values, R=P x V/T x n = 8.31 (L  kPa)/(K  mol)

19. Ideal Gas Law R is the ideal gas constant ◦ 8.31 (L  kPa)/(K  mol) Ideal gas law is written P x V = n x R x T ◦ PV=nRT ◦ If the gas behaves ideally, this equation can be used to calculate any 1 of the four factors (R is a constant)

20. Sample Problems At 34°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?

21. Sample Problems When the temperature of a rigid hollow sphere containing 685 L of helium gas is held to 621 K, the pressure of the gas is 1.89 x 10 3 kPa. How many moles of helium does the sphere contain?

22. Sample Problems What pressure will be exerted by 0.450 mol of gas at 25°C if it is contained in a 0.650-L vessel? A helium-filled balloon contains 0.16 mol He at 101 kPa and a temperature of 23°C. What is the volume of gas in the balloon?

23. Sample Problems 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. Sample Problems A child’s lungs can hold 2.20 L. How many grams of air do her lungs hold at a pressure of 102 kPa and a body temperature of 37°C? Use a molar mass of 29 g for air, which is about 20% O 2 (32 g/mol) and 80% N 2 (28 g/mol).

25. Sample Problems What volume will 12.0 g of oxygen gas (O 2 ) occupy at 25°C and a pressure of 52.7 kPa? When the temperature of a rigid cylinder containing 235 L of argon gas is held to 365 K, the pressure of the gas is 768 kPa. How many moles of argon does the cylinder contain?

26. Ideal Gases and Real Gases Ideal gases do not exist ◦ But, at many conditions real gases do behave similarly to ideal gases Real gases differ most from an ideal gas at low temperatures and high pressures

27. 14.4 GASES: MIXTURES AND MOVEMENTS

28. Dalton’s Law In a mixture of gases, the total pressure is the sum of the partial pressures of the gases. P total = P 1 + P 2 + P 3 + … Partial pressure: pressure exerted by one gas in a mixture If the % composition of the mixture does not change, then the fraction of pressure does not change as the total pressure changes

29. Sample Problems Air contains oxygen, nitrogen, carbon dioxide, and trace amounts of other gases. What is the partial pressure of oxygen at 101.30 kPa of total pressure if the partial pressures of nitrogen, carbon dioxide, and other gases are 79.10 kPa, 0.040 kPa, and 0.94 kPa, respectively?

30. Sample Problems A gas mixture containing oxygen, nitrogen, and carbon dioxide has a total pressure of 32.9 kPa. If P O2 =6.6 kPa and P N2 =23.0 kPa, what is P CO2 ? Determine the total pressure of a gas mixture that contains oxygen, nitrogen, and helium. The partial pressures are P O2 =20.0 kPa, P N2 =46.7 kPa, and P He =26.7 kPa.

31. Graham’s Law Diffusion: the tendency of molecules to move toward areas of lower concentration until the concentration is uniform throughout Effusion: gas escapes through a tiny hole in a container Gases of lower molar mass diffuse and effuse faster than gases of higher molar mass

32. Graham’s Law

33. Sample Problems How much faster does helium (He) effuse than nitrogen (N 2 ) at the same temperature? Calculate the ratio of the velocity of hydrogen molecules to the velocity of carbon dioxide molecules at the same temperature.