1. Gases

2. Characteristics of Gases
Uniformly fill any container
Easily compressed
Mix completely with any other gases
Exert pressure on their surroundings

4. Pressure
Created by collision of particles with each other and objects.
So, how do we measure gas pressure?

5. Barometer
Measures atmospheric pressure
Invented by Toricelli in 1643

6. Elevation and atmospheric pressure are INVERSELY proportional
The higher the elevation, the lower the pressure
Why?
Less air pushing down

7. Manometer
Device used for measuring the pressure of a gas in a container.

8. Equivalent Units of Pressure
760 mm Hg (millimeters Mercury)
760 Torr
1 atm (atmosphere)
101.3 kPa (kilopascals)
14.69 psi (pounds/square inch)

9. SI unit is the Pascal
1 atm = 101, 325 Pa
Too small to be useful in chemistry

10. Pressure Conversions Example
The pressure of air in a tire is measured to be 28 psi. Represent this pressure in
Atmospheres
torr
pascals.

11. Show your work:
28 psi 1 atm = psi 28 psi 760 torr = 28 psi 101, 325 Pa =

12. Answers:
a) 1.9 atm b) 1.5 x 103 torr c) 1.9 x 105 Pa

13. Kinetic Molecular Theory
The Kinetic Molecular Theory explains gas behavior

14. Kinetic Molecular Theory
Gas particles do not attract or repel each other (no I.M. forces).
Gas particles are much smaller than the space between them.
Gas particles are in constant, random motion.
Collisions between gas particles are elastic.

15. Ideal gases don’t really exist
Real gases behave most ideally at high temperatures and low pressures

16. TEMPERATURE Measures the Average Kinetic Energy of a gas.
Temperature and Average Kinetic Energy are directly proportional.
At the same temperature, all gases have the same average kinetic energy.

17. All gas temperatures are calculated using Kelvin
°C = K

18. Absolute Zero Temperature at which all molecular motion ceases.
Occurs at 0 K or -273 °C

19. and do homework

20. Gas Laws

21. Boyle’s Law
At a constant temperature, the volume of a gas is inversely related to its pressure

22. P1V1 = P2V2

23. Example
A sample of helium gas is compressed from 4.0 L to 250 mL at a constant temperature. If the original pressure of the gas is
210 kPa, what is the final pressure of the gas?

24. Show your work:
P1V 1 = P2V2 (210 kPa)(4.0 L) = (.250 L)(x) x 103 or 3400 kPa
Think about it:
The pressure ↓
So, the volume should ↑

25. Charles’ Law
At a constant pressure, the volume of a gas is directly proportional to the temperature
V1 = V2
T T2

26. Plot of Volume vs Temperature is linear

27. Example
At a pressure of 658 mm Hg, what is the volume of the air in a balloon that occupies L at 25.0 °C if the temperature is lowered to 0.00°C?

28. Show your work:
V1 = V2 T1 = T L = x 298 K 273 K .568 L

29. Gay-Lussac’s Law
At a constant volume, the pressure of a gas is directly proportional to the temperature (K)
P1 = P2
T T2

30. Example
The pressure in an automobile tire is 1.88 atm at 25.0 °C. What will the pressure be if the temperature increases to 37.0°C?

31. Show your work:
P1 = P2 T1 T atm = x 298 K 310. K 1.96 atm

32. Avogadro’s Law
If temperature and pressure are constant, the volume of a gas is directly proportional to the number of moles (n)
V1 = V2
n n2

33. Example
A 12.2 L sample containing 0.50 mole of oxygen gas, O2, at a pressure of 1.0 atm is converted to ozone, O3, at the same temperature and pressure. What is the volume of ozone produced?

34. Show your work:
V1 = V2 3O2 → 2O3 n1 n2 .50 mol O2 2 mol O3 = .33 mol O3 3 mol O L = x .50 mol O2 .33 mol O3
8.1 L

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36. The relationship between the volume, pressure, and temperature of a gas can be mathematically determined.

37. Combined Gas Law
P1V1 = P2V2
n1T n2T2

38. STP
Standard Temperature and Pressure
0 °C and 1 atm

39. Gas Law Calculations at STP
Example
A sample of gas has a volume of 2050 mL at 0.95 atm and 36°C. What will be the volume of the gas at STP?

40. Show your work:
P1V1 = P2V2 T1 T2 (.95 atm)(2.05 L) = (1 atm) (x) 309 K 273 K 1.7 L

41. Ideal Gas Law
Ideal gases follow all gas laws under all conditions of temperature and pressure.

42. PV = nRT Where P = pressure V = volume (Liters) n = number of moles
R = ideal gas constant
T = temperature (Kelvin)

43. Universal Gas Constant
R = L ∙atm
mol·K

44. Example
Calculate the number of moles of gas contained in a 3.0 L vessel at 33°C and a pressure of 1.50 atm.

45. Show your work:
PV = nRT
(1.5 atm)(3.0 L) = (n)( L∙atm/mol∙K)(306 K)
n = mol

46. Example
Determine the Celsius temperature of 2.49 mol of gas contained in a L vessel at a pressure of 143 kPa.

47. Show your work:
1) Convert pressure to atm 143 kPa 1 atm = 1.41 atm kPa 2) Solve for Temp (K) using PV = nRT (1.41 atm)(.750 L) = (2.49 mol)(.08206)(x) x = 5.18 K 3) Convert from K to oC = -268 oC

48. Molar Mass of a Gas
PV = nRT therefore n = PV RT n = m (given mass) M (Molar Mass)

49. Example
Calculate the grams of N2 present in a L sample kept at 765 mmHg and a temperature of 22.0 °C.

50. Show your work:
m = PV M RT = x (1.01 atm)(.600 L N2) 28.0 g N2 (.08206)(295 K) g N2

51. Gas Density
PV = nRT and d = m therefore: V Molar Mass (M) = dRT P

52. Example
What is the density of NO2 at
681 Torr and 23.0 °C?

53. Show your work:
M = dRT P 46.0 = (x)(.08206)(296) .896 d = 1.70 g/L

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55. Dalton’s Law of Partial Pressure
The total pressure of a mixture of gases is equal to the sum of the partial pressures of each component gas.

56. Ptotal = P1 + P2 + P3…

57. Example
A scuba tank contains a mixture of gases including 0.42 atm N2,
205 torr O2 and kPa CO2.
What is the total pressure inside the tank, in atmospheres?

58. Show your work:
Ptotal = P1 + P2 + P3 = .42 atm atm atm = 1.04 = 1.0 atm

59. Example
What is the partial pressure of He gas in a mixture of He, Ar, and Ne if the total pressure of the mixture is 5.8 atm, and the partial pressure of Ne is 1.2 atm and Ar is 0.9 atm?

60. Show your work:
Ptotal = P1 + P2 + P3 5.8 = x PNe = 3.7 atm

61. Collecting a Gas Over Water
Total pressure is the pressure of the gas + the vapor pressure of the water.

62. Subtract the vapor pressure of the water from the total pressure to get the pressure of the gas

63. Ptotal = Pdry gas + Pwater vapor
This is still a partial pressure calculation

64. Example
A sample of oxygen gas was collected over water at 20.0°C and a barometric pressure of 731 mmHg. What is the pressure of the dry gas?

65. Show your work:
Ptotal = Pdry gas + Pwater vapor 731 torr = x torr 713 mm Hg

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67. Remember Avogadro? Gas Stoichiometry
Equal volumes of gases at the same temperature and pressure contain equal numbers of particles

68. Molar Volume of a Gas
1 mole of any gas at STP = 22.4 L

69. Remember…. 1 Mole = ___ grams (molar mass)
6.022 x 1023 atoms, mlc, fmu
22.4 liters (gas at STP)

70. Example
What size container, in liters, would be needed to hold moles of N2 gas at STP?

71. Show your work:
.0459 moles N L = 1.03 L 1 mol N2

72. Example
What mass of carbon dioxide gas is in a 2.5 L flask at STP?

73. Show your work:
2.5 L 1 mol CO g CO2 = 4.9 g CO L 1 mol CO2

74. Example
How many atoms of He are present in a 1.75 L balloon?

75. Show your work:
1.75 L He 1 mol He x 1023 atoms He
22.4 L He mol He
4.70 x 1022 atoms

76. Example
If 25 Liters of butane combusts in an excess amount of air, how many liters of carbon dioxide gas are produced?

77. Show your work: Write the balanced equation:
2C4H O2 → 8CO2 + 10H2O
Calculate the volume of CO2 gas produced
25 L C4H mol C4H mol CO L CO2
22.4 L C4H mol C4H mol CO2
1.0 x 102 L C4H10

78. Example
When ethane combusts, carbon dioxide and water are produced. If 6.50 grams of ethane is reacted with excess oxygen, and the carbon dioxide gas is collected over water at 18.0 °C and 725 Torr, what volume of gas, in mL, can be collected? The vapor pressure of water at 18.0 °C is 15.5 Torr.

79. Show your work: Write the balanced equation: 2C2H6 + 7O2 → 4CO2 + 6H2O
1) Determine moles of CO2 produced
6.5 g C2H mol C2H mol CO = mol CO2
30.0 g C2H mol C2H6

80. 2) Calculate pressure of dry gas: Ptotal = Pdry gas + PH2O vapor 725 torr = PC2H torr PC2H6 = torr 709.5/760 = atm

81. 3) Solve for VCO2 in mL PV = nRT (. 9335)(V) = (. 4333)(
3) Solve for VCO2 in mL PV = nRT (.9335)(V) = (.4333)(.08206)(291) V = 11.1 L x 1000 mL/L = 11, 100 mL CO2

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