1. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 1 Gases Chapter 5 Become familiar with the definition and measurement of gas pressure. Learn the gas law and ideal gas equation. Understand the concept of the partial pressures. Study the kinetic molecular theory and gas Effusion/Diffusion Main differences between ideal and real gases.

2. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 2 Elements that exist as gases at 25 0 C and 1 atmosphere

3. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 3 Gases assume the volume and shape of their containers. Gases are the most compressible state of matter. Gases will mix evenly and completely when confined to the same container. Gases have much lower densities than liquids and solids. Exerts pressure on its surroundings. Physical Characteristics of Gases

4. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 4 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.

5. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 5 Figure 5.01b: As the can cools, the water vapor condenses, lowering the gas pressure inside the can. This causes the can to crumple.

6. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 6 Units of Pressure 1 pascal (Pa) = 1 N/m 2 1 atm = 760 mmHg = 760 torr 1 atm = 101,325 Pa Pressure = Force Area

7. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 7 Sea level1 atm 4 miles0.5 atm 10 miles0.2 atm

8. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 8

9. 9 As P (h) increasesV decreases

10. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 10 Boyle’s Law

11. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 11 P  1/V P x V = constant P 1 x V 1 = P 2 x V 2 Boyle’s Law Constant temperature Constant amount of gas

12. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 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.)

13. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 13 As pressure increases, the volume of SO 2 decrease

14. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 14 A gas that strictly obeys Boyle’s Law is called an ideal gas.

15. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 15 A sample of chlorine gas occupies a volume of 946 mL at a pressure of 726 mmHg. What is the pressure of the gas (in mmHg) if the volume is reduced at constant temperature to 154 mL? P 1 x V 1 = P 2 x V 2 P 1 = 726 mmHg V 1 = 946 mL P 2 = ? V 2 = 154 mL P 2 = P 1 x V 1 V2V2 726 mmHg x 946 mL 154 mL = = 4460 mmHg

16. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 16 As T increasesV increases Volume-Temperature Relationship

17. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 17 Charles's Law Figure 5.9: Plots of V versus T as in Fig. 5.8 except here the Kelvin scale is used for temperature.

18. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 18 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

19. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 19 Charles’s Law

20. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 20 A sample of carbon monoxide gas occupies 3.20 L at 125 0 C. At what temperature will the gas occupy a volume of 1.54 L if the pressure remains constant? V 1 = 3.20 L T 1 = 398.15 K V 2 = 1.54 L T 2 = ? T 2 = V 2 x T 1 V1V1 1.54 L x 398.15 K 3.20 L = = 192 K V 1 /T 1 = V 2 /T 2

21. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 21 Avogadro’s Law V  number of moles (n) V = constant x n V 1 /n 1 = V 2 /n 2 Constant temperature Constant pressure

22. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 22 Figure 5.18: The effects of increasing the number of moles of gas particles at constant temperature and pressure.

23. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 23 Ideal Gas Equation Charles’ law: V  T  (at constant n and P) Avogadro’s law: V  n  (at constant P and T) Boyle’s law: V  (at constant n and T) 1 P V V  nT P V = constant x = R nT P P R is the gas constant PV = nRT

24. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 24 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 Holds closely at P < 1 atm

25. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 25 The conditions 0 0 C and 1 atm are called standard temperature and pressure (STP). PV = nRT R = PV nT = (1 atm)(22.42L) (1 mol)(273.15 K) R = 0.082067 L atm / (mol K) Experiments show that at STP, 1 mole of an ideal gas occupies 22.42 L.

26. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 26

27. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 27 What is the volume (in liters) occupied by 49.8 g of HCl at STP? PV = nRT V = nRT P T = 0 0 C = 273.15 K P = 1 atm n = 49.8 g x 1 mol HCl 36.45 g HCl = 1.37 mol V = 1 atm 1.37 mol x 0.0821 x 273.15 K Latm molK V = 30.6 L

28. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 28 Argon is an inert gas used in lightbulbs to retard the vaporization of the filament. A certain lightbulb containing argon at 1.20 atm and 18 0 C is heated to 85 0 C at constant volume. What is the final pressure of argon in the lightbulb (in atm)? PV = nRT n, V and R are constant nR V = P T = constant P1P1 T1T1 P2P2 T2T2 = P 1 = 1.20 atm T 1 = 291 K P 2 = ? T 2 = 358 K P 2 = P 1 x T2T2 T1T1 = 1.20 atm x 358 K 291 K = 1.48 atm

29. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 29 Ex 9 P 1 = 345 torrP 2 = 468 torr T 1 = -15 o CT 2 = 36 o C V 1 = 3.48 LV 2 = ?

30. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 30 Ex 10 n 1 = 0.35n 2 = 0.35 P 1 = 568 torrP 2 = 1.18 atm T 1 = 13 o C = 286 KT 2 = 56 o C =329

31. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 31 Gas Stoichiometry What is the volume of CO 2 produced at 37 0 C and 1.00 atm when 5.60 g of glucose are used up in the reaction: C 6 H 12 O 6 (s) + 6O 2 (g) 6CO 2 (g) + 6H 2 O (l) g C 6 H 12 O 6 mol C 6 H 12 O 6 mol CO 2 V CO 2 5.60 g C 6 H 12 O 6 1 mol C 6 H 12 O 6 180 g C 6 H 12 O 6 x 6 mol CO 2 1 mol C 6 H 12 O 6 x = 0.187 mol CO 2 V = nRT P 0.187 mol x 0.0821 x 310.15 K Latm molK 1.00 atm = = 4.76 L 5.5

32. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 32 S.Ex 5.13 CH 4 + O 2 → CO 2 + H 2 O 2.80 L 35.0 L V? 25 o C 31 o C125 o C 1.65 atm 1.25 atm2.50 atm 0.189 mol 1.75 mol? Balance eq. CH 4 + 2 O 2 → CO 2 + 2 H 2 O CH 4 is limiting ! Mol of CO 2 = 0.189 > V = 0.189 x 0.0821 x398 2.50 atm = 2.47 L

33. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 33 Density (d) Calculations d = m V = PMPM RT m is the mass of the gas in g M is the molar mass of the gas Molar Mass ( M ) of a Gaseous Substance dRT P M = d is the density of the gas in g/L

34. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 34 S. Ex 5.14 P = 1.50 atm;27 o C ; d = 1.95 g/L; MM=? MM = dRT = 1.95 g/Lx0.0821L.atm/(K.mol)x300K P1.50 atm = 32.0 g/mole

35. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 35 Dalton’s Law of Partial Pressures For a mixture of gases in a container, the total pressure exerted is the sum of the pressures that each gas would exert if it were alone P Total = P 1 + P 2 + P 3 +...

36. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 36 Dalton’s Law of Partial Pressures V and T are constant P1P1 P2P2 P total = P 1 + P 2

37. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 37 S.Ex 5.15 At 25 o C He 46L, 1 atm + O 2 12L, 1 atm He+O 2 5.0L, P = ? ↓ P 1 V 1 = P 2 V 2 P He = 46Lx1atm/5.0L = 9.2 atm P O2 = 12Lx1 atm/5.0L =2.4 atm P T = 9.2atm + 2.4 atm =11.7 atm

38. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 38 Mole Fraction – Χ The ratio of the number of moles of a given component in a mixture to the total number of moles in the mixture. Χ i = n i = ____ n i ______ n total n 1 + n 2 +n 3 + …

39. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 39 Consider a case in which two gases, A and B, are in a container of volume V. P A = n A RT V P B = n B RT V n A is the number of moles of A n B is the number of moles of B P T = P A + P B X A = nAnA n A + n B X B = nBnB n A + n B P A = X A P T P B = X B P T P i = X i P T

40. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 40 S.E. 5.16 The partial pressure of oxygen is 156 torr in air with a total atmospheric pressure of 743 torr. Calculate the mole fraction of oxygen in air. Χ O2 = P O2 = 156 torr = 0.210 P total 743 torr

41. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 41 S.Ex 5.17 The mole fraction of nitrogen in air is 0.7808. Calculate the partial pressure of nitrogen in air when the atm pressure is 760 torr. P N2 = Χ N2 x P total = 0.7808x760 torr = 593 torr

42. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 42 A sample of natural gas contains 8.24 moles of CH 4, 0.421 moles of C 2 H 6, and 0.116 moles of C 3 H 8. If the total pressure of the gases is 1.37 atm, what is the partial pressure of propane (C 3 H 8 )? P i = X i P T X propane = 0.116 8.24 + 0.421 + 0.116 P T = 1.37 atm = 0.0132 P propane = 0.0132 x 1.37 atm= 0.0181 atm

43. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 43 2KClO 3 (s) 2KCl (s) + 3O 2 (g) Bottle full of oxygen gas and water vapor P T = P O + P H O 22

44. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 44 S.Ex 5.18 2KClO 3 (s) → 2KCl (s) + 3O 2 (g) O 2 collected at 22 o C, at P total = 754 torr; V=0.650 L ; v.p. of water at 22 o C = 21 torr P total = P O2 + P H2O = P O2 + 21 torr Thus, P O2 = 754 torr – 21 torr = 733 torr Ideal gas eq. to find moles of O 2 Moles O 2 → moles KClO 3 → g KClO 3

45. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 45 Kinetic Molecular Theory of Gases 1.A gas is composed of molecules that are separated from each other by distances far greater than their own dimensions. The molecules can be considered to be points that is, they possess mass but have negligible volume (V  zero). 2.Gas molecules are in constant motion in random directions. Collisions among molecules are perfectly elastic. The collision of particles with the wall of the container are the cause of the pressure exerted by the gas 3.Gas molecules exert neither attractive nor repulsive forces on one another. 4.The average kinetic energy of the molecules is proportional to the temperature of the gas in kelvins. Any two gases at the same temperature will have the same average kinetic energy

46. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 46 Kinetic theory of gases and … Compressibility of Gases Boyle’s Law P  collision rate with wall Collision rate  number density Number density  1/V P  1/V Charles’ Law P  collision rate with wall Collision rate  average kinetic energy of gas molecules Average kinetic energy  T P  TP  T

47. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 47 Kinetic theory of gases and … Avogadro’s Law P  collision rate with wall Collision rate  number density Number density  n P  nP  n Dalton’s Law of Partial Pressures Molecules do not attract or repel one another P exerted by one type of molecule is unaffected by the presence of another gas P total =  P i

48. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 48 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: The concept of Average Speed

49. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 49 The Meaning of Temperature Kelvin temperature is an index of the random motions of gas particles (higher T means greater motion.)

50. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 50 Root Mean Square Velocity

51. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 51 The distribution of speeds for nitrogen gas molecules at three different temperatures The distribution of speeds of three different gases at the same temperature u rms = 3RT M 

52. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 52 S.Ex. 5.19 Calculate the root mean square velocity for the atoms in a sample of He gas at 25 o C. MM = 4.00 g/mol x1kg/1000g =4.00x10 -3 kg/mol

53. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 53 Diffusion: describes the mixing of gases. The rate of diffusion is the rate of gas mixing.

54. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 54 Gas diffusion is the gradual mixing of molecules of one gas with molecules of another by virtue of their kinetic properties. NH 3 17 g/mol HCl 36 g/mol NH 4 Cl

55. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 55 Effusion: describes the passage of gas into an evacuated chamber.

56. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 56 Effusion: Diffusion:

57. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 57 S.Ex. 5.20 Calculate the ratio of the effusion rates of H 2 gas and UF 6

58. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 58

59. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 59 Real Gases Must correct ideal gas behavior when at high pressure (smaller volume) and low temperature (attractive forces become important).

60. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 60 Figure 5.25: Plots of PV/nRT versus P for several gases (200 K).

61. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 61 Figure 5.26: Plots of PV/nRT versus P for nitrogen gas at three temperatures.

62. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 62 Real gases tend to behave like ideal gases, when P is low (large volume of container relative to volume of molecule ) T is high ( at high T attractive and repulsive forces are negligible, relative to the high speed of molecules)

63. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 63 Figure 5.27: (a) Gas at low concentration— relatively few interactions between particles. (b) Gas at high concentration—many more interactions between particles.

64. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 64 Real Gases corrected pressure corrected volume P ideal V ideal

65. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 65