1. 5–15–1 Chapter 5: GASES

2. 5–25–2 Figure 5.1a: The pressure exerted by the gases in the atmosphere can be demonstrated by boiling water in a large metal can (a) and then turning off the heat and sealing the can.

3. 5–35–3 Figure 5.01b: As the can cools, the water vapor condenses, lowering the gas pressure inside the can. This causes the can to crumple (b). (cont’d)

4. 5–45–4 A Gas 4 Uniformly fills any container. 4 Mixes completely with any other gas 4 Exerts pressure on its surroundings.

5. 5–55–5 Figure 5.2: A torricellian barometer. The tube, completely filled with mercury, is inverted in a dish of mercury.

6. 5–65–6 Figure 5.3: A simple manometer.

7. 5–75–7 Pressure 4 is equal to force/unit area 4 SI units = Newton/meter 2 = 1 Pascal (Pa) 4 1 standard atmosphere = 101,325 Pa 4 1 standard atmosphere = 1 atm = 760 mm Hg = 760 torr mm Hg = torr

8. 5–85–8 Figure 5.4: A J-tube similar to the one used by Boyle.

9. 5–95–9 VxP=kVxP=k

10. 5–10 Figure 5.5: Plotting Boyle's data from Table 5.1. (a) A plot of P versus V shows that the volume doubles as the pressure is halved. (b) A plot of V versus 1/P gives a straight line. The slope of this line equals the value of the constant k.

11. 5–11 Figure 5.6: A plot of PV versus P for several gases at pressures below 1 atm.

12. 5–12 Boyle ’ s Law * Pressure  Volume = Constant (T = constant) P 1 V 1 = P 2 V 2 (T = constant) V  1/P (T = constant) ( * Holds precisely only at very low pressures.) A gas that strictly obeys Boyle ’ s Law is called an ideal gas.

13. 5–13 Ex. 5.2 As pressure increases, the volume of SO 2 decreases.

14. 5–14 Ex. 5.3 Figure 5.7: A plot of PV versus P for 1 mol of ammonia. The dashed line shows the extrapolation of the data to zero pressure to give the "ideal" value of PV of 22.41 L atm.

15. 5–15 Figure 5.8: Plots of V versus T (ºC) for several gases.

16. 5–16 Figure 5.9: Plots of V versus T as in Fig. 5.8 except here the Kelvin scale is used for temperature.

17. 5–17 Charles ’ s Law The volume of a gas is directly proportional to temperature, and extrapolates to zero at zero Kelvin. V = bT (P = constant) b = a proportionality constant

18. 5–18 Charles ’ s Law

19. 5–19 Avogadro ’ s Law For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas (at low pressures). V = an a = proportionality constant V = volume of the gas n = number of moles of gas

20. 5–20 Figure 5.10: These balloons each hold 1.0L of gas at 25ºC and 1 atm. Each balloon contains 0.041 mol of gas, or 2.5 x 10 22 molecules.

21. 5–21 Ideal Gas Law We can bring all of these laws together into one comprehensive law: Boyle ’ s law: V = k/P (at const T and n) Charle ’ s law:V = bT(at const P and n) Avogardro ’ s law: V = an(at const T and P) ⇒ V = or PV = nRT

22. 5–22 Ideal Gas Law PV = nRT R = proportionality constant = 0.08206 L atm   mol  P = pressure in atm V = volume in liters n = moles T = temperature in Kelvins

23. 5–23 As pressure increases, the volume decreases.

24. 5–24 Gas stoichiometry V = = 22.42 L (molar volume) Standard Temperature and Pressure “STP” P = 1 atmosphere T =  C The molar volume of an ideal gas is 22.42 liters at STP

25. 5–25

26. 5–26 Molar Mass of a Gas n = = = m/V = d Or

27. 5–27 Dalton ’ s Law of Partial Pressures For a mixture of gases in a container, P Total = P 1 + P 2 + P 3 +... P Total = n total (RT/V)

28. 5–28 Figure 5.12: The partial pressure of each gas in a mixture of gases in a container depends on the number of moles of that gas.

29. 5–29 Kinetic Molecular Theory 1.Volume of individual particles is  zero. 2.Collisions of particles with container walls cause pressure exerted by gas. 3.Particles exert no forces on each other. 4.Average kinetic energy  Kelvin temperature of a gas.

30. 5–30 Figure 5.14: (a) One mole of N 2 (l) has a volume of approximately 35 mL and density of 0.81 g/mL. B) One mole of N 2 (g) has a volume of 22.4 L (STP) and a density of 1.2 x 10 -3 g/mL. Thus the ratio of the volumes of gaseous N 2 and liquid N 2 is 22.4/0.035 = 640 and the spacing of the molecules is 9 times farther apart in N 2 (g).

31. 5–31 Figure 5.15: The effects of decreasing the volume of a sample of gas at constant temperature.

32. 5–32 Figure 5.16: The effects of increasing the temperature of a sample of gas at constant volume.

33. 5–33 Figure 5.17: The effects of increasing the temperature of a sample of gas at constant pressure.

34. 5–34 Figure 5.18: The effects of increasing the number of moles of gas particles at constant temperature and pressure.

35. 5–35 P is the pressure of the gas, n is the number of molecules of the gas, N A is the Avogadero’s number, m is the mass of each particles, is the average of the square of the velocities of the particles, and V is the volume of the gas. or

36. 5–36 ∵ (KE) avg  T or Fromexperiment,

37. 5–37 The Meaning of Temperature Kelvin temperature is an index of the random motions of gas particles (higher T means greater motion.)

38. 5–38 Room mean square velocity : average of the squares of the particles velocity Room mean square velocity  rms = and (KE) avg = (2/3)RT R = 0.08206L.atm.K -1.mol -1 = 8.314 l K -1.mol -1

39. 5–39 Figure 5.19: Path of one particle in a gas. Any given particle will continuously change its course as a result of collisions with other particles, as well as with the walls of the container. Mean free path : average distance between collisions O 2 at STP: 1 x 10 -7 m

40. 5–40 Figure 5.20: A plot of the relative number of O 2 molecules that have a given velocity at STP.

41. 5–41 Figure 5.21: A plot of the relative number of N 2 molecules that have a given velocity at three temperatures.

42. 5–42 Effusion: describes the passage of gas into an evacuated chamber. Diffusion: describes the mixing of gases. The rate of diffusion is the rate of gas mixing.

43. 5–43 Figure 5.22: The effusion of a gas into an evacuated chamber.

44. 5–44 Effusion:

45. 5–45 Figure 5.23: Relative molecular speed distribution of H 2 and UF 6.

46. 5–46 Diffusion:

47. 5–47 Figure 5.24: (top) When HCl(g) and NH 3 (g) meet in the tube, a white ring of NH 4 Cl(s) forms. (bottom) A demonstration of the relative diffusion rates of NH 3 and HCl molecules through air.

48. 5–48 Figure 5.25: Plots of PV/nRT versus P for several gases (200 K).

49. 5–49 Figure 5.26: Plots of PV/nRT versus P for nitrogen gas at three temperatures.

50. Real Gases Must correct ideal gas behavior when at high pressure (smaller volume) and low temperature (attractive forces become important). Ideal gas behavior: Low pressure and/or high temperature

51. 5–51 Idea gas: Modification with volume P obs = (P ’ -correction factor) = P obs = P ’ -a(n/V) 2

52. 5–52 Figure 5.27: (a) Gas at low concentration— relatively few interactions between particles. (b) Gas at high concentration—many more interactions between particles.

53. 5–53 Figure 5.28: Illustration of pairwise interactions among gas particles.

54. 5–54 Real Gases corrected pressure corrected volume P ideal V ideal ↑↑↑ Van der Waals equation:

55. 5–55

56. 5–56 Figure 5.29: The volume taken up by the gas particles themselves is less important at (a) large container volume (low pressure) than at (b) small container volume (high pressure).

57. 5–57

58. 5–58 Figure 5.30: The variation of temperature (blue) and pressure (dashed lines) with attitude. Note that the pressure steadily decreases with altitude, but the temperature increases and decreases.

59. 5–59 Figure 5.31: Concentration (in molecules per million molecules of "air") for some smog components versus time of day.

60. 5–60 Figure 5.33: A schematic diagram of the process for scrubbing sulfur dioxide from stack gases in power plants.