1. Chapter 11 Gas Laws

2. The Gas Phase Gases have no distinct volume or shape. Gases expand to fill the volume of their container. Gas particles are miscible with each other. Evidence for gas particles being far apart :  We can see through gases  We can walk through gases  Gases are compressible  Gases have low densities

3. Composition of Earth’s Atmosphere Compound%(Volume)Mole Fraction a Nitrogen78.080.7808 Oxygen20.950.2095 Argon0.9340.00934 Carbon dioxide0.0330.00033 Methane2 x 10 -4 2 x 10 -6 Hydrogen5 x 10 -5 5 x 10 -7 a. mole fraction = mol component/total mol in mixture. The Air We Breathe

4. Kinetic Theory of Gases Kinetic Theory Postulates: Gas particles are sizeless relative to the volume of the gas Gas particles are in constant rapid motion Gas particles have elastic collisions; means no kinetic energy is lost on impact. The absolute temperature is directly proportional to the kinetic energy of a gas. Gas particles have no attraction to each other; i.e. no inter particle froces.

5. Parameters Affecting Gases Pressure (P); atm, mmHg, torr, lbs/in 2 Volume (V); L, mL Temperature (T); K (only) Number of Moles (n)

6. Pressure Pressure is equal to force/unit area (P =F/A) lbs/in 2 Force is a push which comes from gas particles striking a container wall

7. Pressure Units SI units = Newton/meter 2 = 1 Pascal (Pa) 1 standard atmosphere (atm) = 101,325 Pa  1 atm = 760 mm Hg  1 atm = 760 torr (torr is abbreviation of mmHg)  1 atm = 14.7 lbs/in 2  1 atm = 1.013 barr  Barr = 100 kPa

8. Measurement of Pressure What is above mercury?

9. Measurement of Pressure

10. Elevation and Atmospheric Pressure

11. Units for Expressing Pressure UnitValue Atmosphere1 atm Pascal (Pa)1 atm = 1.01325 x 10 5 Pa Kilopascal (kPa)1 atm = 101.325 kPa mmHg1 atm = 760 mmHg Torr1 atm = 760 torr Bar1 atm = 1.01325 bar mbar1 atm = 1013.25 mbar psi1 atm = 14.7 psi

12. Pressure Measurement Open Tube Manometer Is the atmosphere or the gas in the canister pushing harder? = 15 mm

13. Pressure Measurement Open Tube Manometer Is the atmosphere or the gas in the canister pushing harder? Gas in the canister If the atmospheric pressure is 766 mm, then what is the pressure of the canister? = 15 mm

14. Pressure Measurement Open Tube Manometer Is the atmosphere or the gas in the canister pushing harder? Gas in the canister If the atmospheric pressure is 766 mm, then what is the pressure of the canister? P = 766 + 15 = 781 mm (torr) = 15 mm gas

15. Pressure Measurement Open Tube Manometer Is the atmosphere or the gas in the canister pushing harder? gas

16. Pressure Measurement Open Tube Manometer Is the atmosphere or the gas in the canister pushing harder? The atmosphere What is the pressure of the gas if the atmosphere is 766 mm? = 13 mm gas

17. Pressure Measurement Open Tube Manometer Is the atmosphere or the gas in the canister pushing harder? The atmosphere What is the pressure of the gas if the atmosphere is 766 mm? 753 mm = 13 mm gas

18. Pressure Measurement Open Tube Manometer gas Now what is pushing harder, the gas or the atomosphere?

19. Pressure Measurement Open Tube Manometer gas Now what is pushing harder, the gas or the atmosphere? Neither, both the same.

20. Pressure Measurement Open Tube Manometer gas Now what is pushing harder, the gas or the atmosphere? Neither, both the same. Is the gas canister empty?

21. Pressure Measurement Open Tube Manometer gas Now what is pushing harder, the gas or the atmosphere? Neither, both the same. Is the gas canister empty? No, completely full of gas!

22. Dalton’s Law of Partial Pressures For a mixture of gases in a container P Total = P 1 + P 2 + P 3 +...

23. Boyles Law Atm ● ● ● ● Consider a gas in a closed system containing a movable plunger. If the plunger is not moving up or down, what can be said about the pressure of the gas relative to the atmospheric pressure?

24. Boyles Law Atm ● ● ● ● Suppose we add some red gas to the container, what would happen to the collisions of gas particles with container walls. Would they increase, decrease or stay the same? ● ● ●

25. Boyles Law Atm ● ● ● ● Suppose we add some red gas to the container, what would happen to the collisions of gas particles with container walls. Would they increase, decrease or stay the same? More particles, more collisions, and more pressure. What happens to the plunger? ● ● ●

26. Boyles Law Atm ● ● ● ● Suppose we add some red gas to the container, what would happen to the collisions of gas particles with container walls. Would they increase, decrease or stay the same? More particles, more collisions, and more pressure. What happens to the plunger? ● ● ●

27. Boyles Law ● ● ● ● ● ● ● ● ● ● The number of particles remain the same, but the surface area they have to strike increases, thus the number of collisions per square inch decrease as the plunger goes up exposing more surface area causing a decrease in pressure.

28. Boyle’s Law P  1/V (T and n fixed) P  V = Constant P 1 V 1 = P 2 V 2 Pressure and volume are inversely proportional.

29. Charles’s Law The volume of a gas is directly proportional to Kelvin temperature, and extrapolates to zero at zero Kelvin. V  T (P & n are constant) V 1 = V 2 T 1 T 2

30. Combined Gas Law Combining the gas laws the relationship P  T(n/V) can be obtained. If n (number of moles) is held constant, then PV/T = constant. Volume: L, mL, cm 3, … Pressure: Atm, mmHg, Torr, PSI, KPa Temperature, K (only)

31. Example A balloon is filled with hydrogen to a pressure of 1.35 atm and has a volume of 2.54 L. If the temperature remains constant, what will the volume be when the pressure is increased to 2.50 atm? A balloon is filled with hydrogen to a pressure of 1.35 atm and has a volume of 2.54 L. If the temperature remains constant, what will the volume be when the pressure is increased to 2.50 atm? (1.35 atm) (2.54 L) T1T1 = (2.50atm)V 2 T1T1 Constant Temp. means T 1 =T 2 (1.35 atm ) (2.54 L ) (2.50atm) V 2 = V 2 = 1.37 L

32. Example A sample of oxygen gas is at 0.500 atm and occupies a volume of 11.2 L at 0 0 C, what volume will the gas occupy at 6.00 atm at room temperature (25 0 C)?

33. Ideal Gas Law PV = nRT R = universal gas constant = 0.08206 L atm K -1 mol -1 P = pressure in atm V = volume in liters n = moles T = temperature in Kelvin

34. STP “STP” means standard temperature and standard pressure  P = 1 atmosphere  T = 0  C  The molar volume of an ideal gas is 22.42 liters at STP (put 1 mole, 1 atm, R, and 273 K in the ideal gas law and calculate V)

35. Example Calculate the pressure of a 1.2 mol sample of methane gas in a 3.3 L container at 25°C. Calculate the pressure of a 1.2 mol sample of methane gas in a 3.3 L container at 25°C.

36. Example Calculate the pressure of a 1.2 mol sample of methane gas in a 3.3 L container at 25°C. Calculate the pressure of a 1.2 mol sample of methane gas in a 3.3 L container at 25°C. 0.0821 L-atm Mole-K

37. Example Calculate the pressure of a 1.2 mol sample of methane gas in a 3.3 L container at 25°C. Calculate the pressure of a 1.2 mol sample of methane gas in a 3.3 L container at 25°C. 0.0821 L-atm Mole-K 3.3 L

38. Example Calculate the pressure of a 1.2 mol sample of methane gas in a 3.3 L container at 25°C. Calculate the pressure of a 1.2 mol sample of methane gas in a 3.3 L container at 25°C. 0.0821 L-atm Mole-K 3.3 L 298 K

39. Example Calculate the pressure of a 1.2 mol sample of methane gas in a 3.3 L container at 25°C. Calculate the pressure of a 1.2 mol sample of methane gas in a 3.3 L container at 25°C. 0.0821 L-atm Mole-K 3.3 L 298 K 1.2 mole

40. Example Calculate the pressure of a 1.2 mol sample of methane gas in a 3.3 L container at 25°C. Calculate the pressure of a 1.2 mol sample of methane gas in a 3.3 L container at 25°C. 0.0821 L-atm Mole-K 3.3 L 298 K 1.2 mole = 8.9 atm

41. Example An experiment shows that a 0.495 g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas. An experiment shows that a 0.495 g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas.

42. Example An experiment shows that a 0.495 g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas. An experiment shows that a 0.495 g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas. mole-K 0.0821 L-atm

43. Example An experiment shows that a 0.495 g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas. An experiment shows that a 0.495 g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas. mole-K 0.0821 L-atm0.495 g

44. Example An experiment shows that a 0.495 g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas. An experiment shows that a 0.495 g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas. mole-K 0.0821 L-atm0.495 g 10 -3 L mL

45. Example An experiment shows that a 0.495 g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas. An experiment shows that a 0.495 g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas. mole-K 0.0821 L-atm0.495 g 10 -3 L mL 127 mL

46. Example An experiment shows that a 0.495 g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas. An experiment shows that a 0.495 g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas. mole-K 0.0821 L-atm0.495 g 10 -3 L mL 127 mL 760 torr atm

47. Example An experiment shows that a 0.495 g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas. An experiment shows that a 0.495 g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas. mole-K 0.0821 L-atm0.495 g 10 -3 L mL 127 mL 760 torr atm 754 torr

48. Example An experiment shows that a 0.495 g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas. An experiment shows that a 0.495 g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas. mole-K 0.0821 L-atm0.495 g 10 -3 L mL 127 mL 760 torr atm 754 torr 371 K

49. Example An experiment shows that a 0.495 g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas. An experiment shows that a 0.495 g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas. mole-K 0.0821 L-atm0.495 g 10 -3 L mL 127 mL 760 torr atm 754 torr 371 K = 120 g/mole

50. Collecting a Gas Over Water

51. A sample of KClO 3 is heated and decomposes to produce O 2 gas. The gas is collected by water displacement at 25°C. The total volume of the collected gas is 229 mL at a pressure of 755 torr. How many moles of oxygen formed? Hint: The gas collected is a mixture so use Dalton’s Law to calculate the pressure of oxygen then the ideal gas law to find the number of moles oxygen. Hint: The gas collected is a mixture so use Dalton’s Law to calculate the pressure of oxygen then the ideal gas law to find the number of moles oxygen. P T = P + P Practice O2O2 H2OH2O

52. Vapor Pressure of Water

53. A sample of KClO 3 is heated and decomposes to produce O 2 gas. The gas is collected by water displacement at 25°C. The total volume of the collected gas is 229 mL at a pressure of 755 torr. How many moles of oxygen formed? Hint: The gas collected is a mixture so use Dalton’s Law to calculate the pressure of oxygen then the ideal gas law to find the number of moles oxygen. Hint: The gas collected is a mixture so use Dalton’s Law to calculate the pressure of oxygen then the ideal gas law to find the number of moles oxygen. P T = P + P Practice O2O2 H2OH2O 755 torr = P O2O2 + 23.8 torr P = 755 – 23.8 = 731 torr O2O2

54. Practice A sample of KClO 3 is heated and decomposes to produce O 2 gas. The gas is collected by water displacement at 25°C. The total volume of the collected gas is 229 mL at a pressure of 755 torr. How many moles of oxygen formed? mole-K 0.0821 L-atm

55. Practice A sample of KClO 3 is heated and decomposes to produce O 2 gas. The gas is collected by water displacement at 25°C. The total volume of the collected gas is 229 mL at a pressure of 755 torr. How many moles of oxygen formed? mole-K 0.0821 L-atm atm 760 torr

56. Practice A sample of KClO 3 is heated and decomposes to produce O 2 gas. The gas is collected by water displacement at 25°C. The total volume of the collected gas is 229 mL at a pressure of 755 torr. How many moles of oxygen formed? mole-K 0.0821 L-atm atm 760 torr 731 torr

57. Practice A sample of KClO 3 is heated and decomposes to produce O 2 gas. The gas is collected by water displacement at 25°C. The total volume of the collected gas is 229 mL at a pressure of 755 torr. How many moles of oxygen formed? mole-K 0.0821 L-atm atm 760 torr 731 torr 298 K

58. Practice A sample of KClO 3 is heated and decomposes to produce O 2 gas. The gas is collected by water displacement at 25°C. The total volume of the collected gas is 229 mL at a pressure of 755 torr. How many moles of oxygen formed? mole-K 0.0821 L-atm atm 760 torr 731 torr 298 KmL 10 -3 L

59. Practice A sample of KClO 3 is heated and decomposes to produce O 2 gas. The gas is collected by water displacement at 25°C. The total volume of the collected gas is 229 mL at a pressure of 755 torr. How many moles of oxygen formed? mole-K 0.0821 L-atm atm 760 torr 731 torr 298 KmL 10 -3 L 229 mL = 9.00 X 10 -3 mole

60. Stoichiometry and Gases Calculate the volume of hydrogen gas at 25°C and 766 torr from 13.4 g of zinc and an excess of hydrochloric acid. Zn (s) + 2 HCl (aq) ZnCl 2 (aq) + H 2 (g) 13.4 g Zn

61. Stoichiometry and Gases Calculate the volume of hydrogen gas at 25°C and 766 torr from 13.4 g of zinc and an excess of hydrochloric acid. Zn (s) + 2 HCl (aq) ZnCl 2 (aq) + H 2 (g) 13.4 g Zn 65.39 g Zn mole Zn

62. Stoichiometry and Gases Calculate the volume of hydrogen gas at 25°C and 766 torr from 13.4 g of zinc and an excess of hydrochloric acid. Zn (s) + 2 HCl (aq) ZnCl 2 (aq) + H 2 (g) 13.4 g Zn 65.39 g Zn mole Zn mole H 2

63. Stoichiometry and Gases Calculate the volume of hydrogen gas at 25°C and 766 torr from 13.4 g of zinc and an excess of hydrochloric acid. Zn (s) + 2 HCl (aq) ZnCl 2 (aq) + H 2 (g) 13.4 g Zn 65.39 g Zn mole Zn mole H 2 0.08206 L-atm mole H 2 -K

64. Stoichiometry and Gases Calculate the volume of hydrogen gas at 25°C and 766 torr from 13.4 g of zinc and an excess of hydrochloric acid. Zn (s) + 2 HCl (aq) ZnCl 2 (aq) + H 2 (g) 13.4 g Zn 65.39 g Zn mole Zn mole H 2 0.08206 L-atm mole H 2 -K 298.15 K

65. Stoichiometry and Gases Calculate the volume of hydrogen gas at 25°C and 766 torr from 13.4 g of zinc and an excess of hydrochloric acid. Zn (s) + 2 HCl (aq) ZnCl 2 (aq) + H 2 (g) 13.4 g Zn 65.39 g Zn mole Zn mole H 2 0.08206 L-atm mole H 2 -K 298.15 K 760 torr

66. Stoichiometry and Gases Calculate the volume of hydrogen gas at 25°C and 766 torr from 13.4 g of zinc and an excess of hydrochloric acid. Zn (s) + 2 HCl (aq) ZnCl 2 (aq) + H 2 (g) 13.4 g Zn 65.39 g Zn mole Zn mole H 2 0.08206 L-atm mole H 2 -K 298.15 K 760 torr atm 766 torr

67. Stoichiometry and Gases Calculate the volume of hydrogen gas at 25°C and 766 torr from 13.4 g of zinc and an excess of hydrochloric acid. Zn (s) + 2 HCl (aq) ZnCl 2 (aq) + H 2 (g) 13.4 g Zn 65.39 g Zn mole Zn mole H 2 0.08206 L-atm mole H 2 -K 298.15 K 760 torr atm 766 torr = 4.97 L

68. The End