1. CHAPTER 10
GASES 1 1 1 1 1 1 1

2. Characteristics of Gases
There are three phases for all substances: solid, liquid and gases.
Gases are highly compressible and occupy the full volume of their containers.
When a gas is subjected to pressure, its volume decreases.
Gases always form homogeneous mixtures with other gases.
Gases only occupy about 0.1 % of the volume of their containers.

3. Pressure Pressure is the force acting on an object per unit area:
Units: psi pounds per square inch

4. Pressure SI Units: 1 N = 1 kg.m/s2; 1 Pa = 1 N/m2.
Atmospheric pressure is measured with a barometer.
If a tube is inserted into a container of mercury open to the atmosphere, the mercury will rise 760 mm up the tube.
Standard atmospheric pressure is the pressure required to support 760 mm of Hg in a column.

5. Pressure force per unit area standard pressure
76 cm Hg
760 mm Hg
760 torr
1 atmosphere
101.3 kPa
Units: 1 atm = 760 mmHg = 760 torr =  105 Pa = kPa.
density = 13.6 g/mL 3 3 2 3 3 3 3

6. Pressure
The pressures of gases not open to the atmosphere are measured in manometers.
A manometer consists of a bulb of gas attached to a U-tube containing Hg.

7. Pressure

8. Pressure
If the U-tube is closed, then the pressure of the gas is the difference in height of the liquid (usually Hg).
If the U-tube is open to the atmosphere, a correction term needs to be added:
If Pgas < Patm then Pgas + Ph2 = Patm.
If Pgas > Patm then Pgas = Patm + Ph2.

9. The Gas Laws
Weather balloons are used as a practical consequence to the relationship between pressure and volume of a gas.
As the weather balloon ascends, the volume decreases.
As the weather balloon gets further from the earth’s surface, the atmospheric pressure decreases.
Boyle’s Law: the volume of a fixed quantity of gas is inversely proportional to its pressure.

10. Boyle’s Laws Mathematically: A plot of V versus P is a hyperbola.
Similarly, a plot of V versus 1/P must be a straight line passing through the origin.

11. Boyle’s Laws

12. Boyle’s Law Vµ 1/P V= k (1/P) or PV = k P1V1 = k1 P2V2 = k2
k1 = k2 (for same sample of same T)
P1V1 = P2V2 Boyle’s Law (math form)
think in terms of balloons!!! 4 3 4 4 4 4 4

13. Boyle’s Law
Example At 250C a sample of He has a volume of 400 mL under a pressure of 760 torr. What volume would it occupy under a pressure of 2.00 atm at the same T? 5 4 5 5 5 5 5

14. Boyle’s Law
Example At 250C a sample of He has a volume of 400 mL under a pressure of 760 torr. What volume would it occupy under a pressure of 2.00 atm at the same T? 6 5 6 6 6 6 6

15. Boyle’s Law
Example At 250C a sample of He has a volume of 400 mL under a pressure of 760 torr. What volume would it occupy under a pressure of 2.00 atm at the same T? 7 6 7 7 7 7 7

16. The Gas Laws
We know that hot air balloons expand when they are heated.
Charles’ Law: the volume of a fixed quantity of gas at constant pressure increases as the temperature increases.
Mathematically:

17. Charles’ Law A plot of V versus T is a straight line.
When T is measured in C, the intercept on the temperature axis is C.
We define absolute zero, 0 K = C.
Note the value of the constant reflects the assumptions: amount of gas and pressure.

18. Charles’ Law

19. Charles’ Law
volume of a gas is directly proportional to the absolute temperature at constant pressure 9 8 9 9 9 9 9

20. Charles’ Law
volume of a gas is directly proportional to the absolute temperature at constant pressure 9 8 9 9 9 9 9

21. Charles’ Law
volume of a gas is directly proportional to the absolute temperature at constant pressure 9 8 9 9 9 9 9

22. Charles’ Law
Example A sample of hydrogen, H2, occupies 100 mL at 250C and 1.00 atm. What volume would it occupy at 500C under the same pressure?
T1 = = 298
T2 = = 323

23. Charles’ Law
Example A sample of hydrogen, H2, occupies 100 mL at 250C and 1.00 atm. What volume would it occupy at 500C under the same pressure?

24. Standard Temperature & Pressure
STP
P = atm or kPa
T = 273 K or 00C 14 10 14 14 14 14 14

25. The Gas Laws
Avogadro’s Hypothesis: equal volumes of gas at the same temperature and pressure will contain the same number of molecules.
Avogadro’s Law: the volume of gas at a given temperature and pressure is directly proportional to the number of moles of gas.

26. Avogadro’s Law Mathematically: V = constant  n.
We can show that 22.4 L of any gas at 0C contain 6.02  1023 gas molecules.

27. The Ideal Gas Equation Summarizing the Gas Laws Boyle: (constant n, T)
Charles: V  T (constant n, P)
Avogadro: V  n (constant P, T).
Combined:
Ideal gas equation:

28. The Ideal Gas Equation Ideal gas equation: PV = nRT.
R = gas constant = L•atm/mol-K.
We define STP (standard temperature and pressure) = 0C, K, 1 atm.
Volume of 1 mol of gas at STP is 22.4 L.

29. Ideal Gas Law R has several values depending upon the choice of units
R = J/mol K
R = kg m2/s2 K mol
R = dm3 kPa/K mol
R = cal/K mol 20 16 21 26 26 26 26

30. Ideal Gas Law
Example: What volume would 50.0 g of ethane, C2H6, occupy at 140oC under a pressure of torr? 21 17 22 27 27 27 27

31. Ideal Gas Law
Example: What volume would 50.0 g of ethane, C2H6, occupy at 140oC under a pressure of torr?
T = = 413 K
P = 1820 torr (1 atm/760 torr) = 2.39 atm
50 g (1 mol/30 g) = 1.67 mol 21 17 22 27 27 27 27

32. Ideal Gas Law 28 28

33. Ideal Gas Law 30 30

34. Ideal Gas Law
Example: Calculate the number of moles in, and the mass of, an 8.96 L sample of methane, CH4, measured at standard conditions. 22 18 23 31 31 31 28

35. Ideal Gas Law 32 32

36. Ideal Gas Law
Example: Calculate the pressure exerted by 50.0 g of ethane, C2H6, in a 25.0 L container at 25oC. 22 18 23 31 33 33 28

37. Ideal Gas Law 34 34

38. The Ideal Gas Law
If PV = nRT and n and T are constant, then PV = constant and we have Boyle’s law.
Other laws can be generated similarly.
In general, if we have a gas under two sets of conditions, then

39. Ideal Gas Law
Example: A sample of nitrogen gas, N2, occupies 750 mL at 750C under a pressure of 810 torr. What volume would it occupy at standard conditions? 17 17 17 17

40. Example: A sample of nitrogen gas, N2, occupies 750 mL at 750C under a pressure of 810 torr. What volume would it occupy at standard conditions? 18 18 18 18

41. Ideal Gas Laws
A sample of methane, CH4, occupies 260 mL at 32oC under a pressure of atm. At what temperature would it occupy 500 mL under a pressure of 1200 torr? 16 12 17 19 19 19 19

42. Ideal Gas Laws 20 20 20

43. Molar Mass and Density Density has units of mass over volume.
Rearranging the ideal-gas equation with M as molar mass we get

44. Molar Mass and Density Volumes of Gases in Chemical Reactions
The molar mass of a gas can be determined as follows:
Volumes of Gases in Chemical Reactions
The ideal-gas equation relates P, V, and T to number of moles of gas.
The n can then be used in stoichiometric calculations.

45. Molar Mass and Density
Example: One mole of a gas occupies 36.5 L and its density is 1.36 g/L at a given T & P.
(a) What is its molar mass?
(b) What is its density at STP? 18 14 19 22 22 22 22

46. Molar Mass and Density
Example: One mole of a gas occupies 36.5 L and its density is 1.36 g/L at a given T & P.
(a) What is its molar mass?
(b) What is its density at STP? 18 14 19 23 23 23 23

47. Molar Mass and Density
Example: One mole of a gas occupies 36.5 L and its density is 1.36 g/L at a given T & P.
(a) What is its molar mass?
(b) What is its density at STP? 18 14 19 24 24 24 24

48. Determination of Molar Mass & Formulas of Gaseous Compounds
Example: A compound that contains only carbon & hydrogen is 80.0% C and 20.0% H by mass. At STP 546 mL of the gas has a mass of g . What is the molecular (true) formula for the compound?
100 g of compound contains:
80 g of C & 20 g of H 23 19 24 32 35 35 29

49. Determination of Molar Mass & Formulas of Gaseous Compounds36 36

50. Determination of Molar Mass & Formulas of Gaseous Compounds37 37

51. Determination of Molar Mass & Formulas of Gaseous Compounds38 38

52. Determination of Molar Mass & Formulas of Gaseous Compounds
Example: A 1.74 g sample of a compound that contains only carbon & hydrogen contains 1.44 g of C and g of H. At STP 101 mL of the gas has a mass of gram. What is its molecular (true) formula? 25 21 26 34 39 39 31

53. Determination of Molar Mass & Formulas of Gaseous Compounds40 40

54. Determination of Molar Mass & Formulas of Gaseous Compounds41 41

55. Determination of Molar Mass & Formulas of Gaseous Compounds
Example: A 250 mL flask contains g of vapor at 1000C and 746 torr. What is molar mass of compound? 26 22 27 35 42 42 32

56. Determination of Molar Mass & Formulas of Gaseous Compounds
Example: A 250 mL flask contains g of vapor at 1000C and 746 torr. What is molar mass of compound? 26 22 27 35 43 43 32

57. Gas Mixtures and Partial Pressures
Since gas molecules are so far apart, we can assume they behave independently.
Dalton’s Law: in a gas mixture the total pressure is given by the sum of partial pressures of each component:
Pt = P1 + P2 + P3 + …

58. Gas Mixtures and Partial Pressures
Each gas obeys the ideal gas equation:
Combining equations:

59. Mole Fractions
Let ni be the number of moles of gas i exerting a partial pressure Pi, then
Pi = iPt
where i is the mole fraction (ni/nt).

60. Collecting Gases over water
It is common to synthesize gases and collect them by displacing a volume of water.
To calculate the amount of gas produced, we need to correct for the partial pressure of the water:
Ptotal = Pgas + Pwater

61. Collecting Gases over water

62. Dalton’s Law of Partial Pressures
Example: If 100 mL of hydrogen, measured at 250C & 3.00 atm pressure, and 100 mL of oxygen, measured at 250C & 2.00 atm pressure, were forced into one of the containers at 250C, what would be the pressure of the mixture of gases? 27 23 28 36 45 45 33

63. Dalton’s Law of Partial Pressures
Example: If 100 mL of hydrogen, measured at 250C & 3.00 atm pressure, and 100 mL of oxygen, measured at 250C & 2.00 atm pressure, were forced into one of the containers at 250C, what would be the pressure of the mixture of gases? 27 23 28 36 45 45 33

64. Vapor Pressure Pressure exerted by gas over the liquid at equilibrium.28 24 29 37 46 46 34

65. Vapor Pressure
Example: A sample of hydrogen was collected by displacement of water at 250C. The atmospheric pressure was 748 torr. What pressure would the dry hydrogen exert in the same container? 29 25 30 38 47 47 35

66. Vapor Pressure
Example: A sample of hydrogen was collected by displacement of water at 250C. The atmospheric pressure was 748 torr. What pressure would the dry hydrogen exert in the same container? 29 25 30 38 47 47 35

67. Vapor Pressure
Example: A sample of oxygen was collected by displacement of water. The oxygen occupied 742 mL at 27oC. The barometric pressure was 753 torr. What volume would the dry oxygen occupy at STP? 29 25 30 38 48 48 35

68. Vapor Pressure 49

69. Kinetic-Molecular Theory
Theory developed to explain gas behavior.
Theory of moving molecules.
Assumptions:
Gases consist of a large number of molecules in constant random motion.
Volume of individual molecules negligible compared to volume of container.
Intermolecular forces (forces between gas molecules) negligible.
Energy can be transferred between molecules, but total kinetic energy is constant at constant temperature.
Average kinetic energy of molecules is proportional to temperature.

70. Kinetic Molecular Theory
Postulate 1
gases are discrete molecules that are far apart
have few intermolecular attractions
molecular volume small compared to gas’s volume
Proof - Gases are easily compressible. 30 26 31 39 50 50 36

71. Kinetic Molecular Theory
Postulate 2
molecules are in constant straight line motion
varying velocities
molecules have elastic collisions
Proof - A sealed, confined gas exhibits no pressure drop over time. 31 27 32 40 51 51 37

72. Kinetic Molecular Theory
Postulate 3
kinetic energy is proportional to absolute T
average kinetic energies of molecules of different gases are equal at a given T
Proof - Motion increases as temperature increases. 32 28 33 41 52 52 38

73. Kinetic Molecular Theory
Boyle’s & Dalton’s Law
P µ 1/V as V increases collisions decrease so P drops
Ptotal = PA + PB + PC because few intermolecular attractions
Charles’ Law
V µ T increased T raises molecular velocities, V increases to keep P constant 33 29 34 42 53 53 39

74. Kinetic-Molecular Theory
Kinetic molecular theory gives us an understanding of pressure and temperature on the molecular level.
Pressure of a gas results from the number of collisions per unit time on the walls of container.

75. Kinetic-Molecular Theory
Magnitude of pressure given by how often and how hard the molecules strike.
Gas molecules have an average kinetic energy.
Each molecule has a different energy.
There is a spread of individual energies of gas molecules in any sample of gas.
As the temperature increases, the average kinetic energy of the gas molecules increases.

76. Kinetic-Molecular Theory

77. Kinetic-Molecular Theory
As kinetic energy increases, the velocity of the gas molecules increases.
Root mean square speed, u, is the speed of a gas molecule having average kinetic energy.
Average kinetic energy, , is related to root mean square speed:
 = ½mu2

78. Kinetic-Molecular Theory
As volume increases at constant temperature, the average kinetic energy of the gas remains constant. Therefore, u is constant. However, volume increases so the gas molecules have to travel further to hit the walls of the container. Therefore, pressure decreases.
If temperature increases at constant volume, the average kinetic energy of the gas molecules increases. Therefore, there are more collisions with the container walls and the pressure increases.

79. Effusion & Diffusion diffusion - intermingling of gases
effusion - gases pass through porous containers
rates are inversely proportional to square roots of molecular weights or densities 34 30 35 43 54 54 40

80. Effusion & Diffusion effusion - gases pass through porous containers
Effusion is the escape of a gas through a tiny hole (a balloon will deflate over time due to effusion).
rates are inversely proportional to square roots of molecular weights or densities 34 30 35 43 54 54 40

81. Effusion & Diffusion
Diffusion of a gas is the spread of the gas through space.
Diffusion is faster for light gas molecules.
Diffusion is significantly slower than rms speed (consider someone opening a perfume bottle: it takes while to detect the odor but rms speed at 25C is about 1150 mi/hr).
Diffusion is slowed by gas molecules colliding with each other.
Average distance of a gas molecule between collisions is called mean free path.

82. Effusion & Diffusion
At sea level, mean free path is about 6  10-6 cm.

83. Effusion & Diffusion
Calculate the ratio of the rate of effusion of He to that of sulfur dioxide, SO2, at the same T & P. 35 31 36 44 55 55 41

84. Effusion & Diffusion
Calculate the ratio of the rate of effusion of He to that of sulfur dioxide, SO2, at the same T & P. 35 31 36 44 55 55 41

85. Effusion & Diffusion
Example: A sample of hydrogen, H2, was found to effuse through a pinhole 5.2 times as rapidly as the same volume of unkown gas ( at the same T & P). What is the molecular weight of the unknown gas? 35 31 36 44 56 56 41

86. Effusion & Diffusion 57

87. Average Speed
As kinetic energy increases, the velocity of the gas molecules increases.
Average kinetic energy of a gas is related to its mass:
 = ½mu2

88. Average Speed
Consider two gases at the same temperature: the lighter gas has a higher rms than the heavier gas.
Mathematically:
The lower the molar mass, M, the higher the rms for that gas at a constant temperature.

89. Average Speed

90. Real Gases real gases behave ideally at ordinary T’s & P’s
at low T and high P - large deviations
molecules are on top of one another
molecular interactions become important 38 34 39 47 62 62 44

91. Real Gases
As the pressure on a gas increases, the molecules are forced closer together.
As the molecules get closer together, the volume of the container gets smaller.
The smaller the container, the more space the gas molecules begin to occupy.
Therefore, the higher the pressure, the less the gas resembles an ideal gas.
As the gas molecules get closer together, the smaller the intermolecular distance.

92. Real Gases

93. Real Gases

94. Real Gases
The smaller the distance between gas molecules, the more likely attractive forces will develop between the molecules.
Therefore, the less the gas resembles and ideal gas.
As temperature increases, the gas molecules move faster and further apart.
Also, higher temperatures mean more energy available to break intermolecular forces.
Therefore, the higher the temperature, the more ideal the gas.

95. Real Gases

96. Real Gases van der Waals’s equation a & b are van der Waal’s constants
different values for each gas 38 34 39 47 62 62 44

97. Real Gases van der Waals’s equation
a accounts for intermolecular attractions
b accounts for volume of gas molecules
large V’s a & b reduce to small quantities
van der Waal’s equation reduces to ideal gas law at high temperatures and low pressures 39 35 40 48 63 63 45

98. Real Gases attractive forces in nonpolar gases
London Forces
noble gases- instantaneous induced dipole moments
Chapter 9
attractive forces in polar gases
dipole-dipole or H-bonds
water molecules can H-bond
why ice floats - Chapter 9 40 36 41 49 64 64 46

99. Real Gases

100. Real Gases
Example: Calculate the pressure exerted by 84.0 g of ammonia, NH3, in a 5.00 L at 2000C using the ideal gas law. 41 37 42 50 65 65 47

101. Real Gases 41 37 42 50 66 66 47

102. Real Gases
Example: Solve previous example using the van der Waal’s equation. 42 38 43 51 68 68 48

103. Real Gases
Example: Solve previous example using the van der Waal’s equation. 42 38 43 51 67 67 48

104. Real Gases 42 38 43 51 68 68 48

105. We can’t forget about moles!
Example: What volume of oxygen measured at STP, can be produced by the thermal decomposition of 120 g of KClO3? 44 40 45 53 70 70 50

106. Mass-Volume Relationships in Reactions Involving Gases
2 mol mol mol
2(122.6g) (74.6g) (32g)
3 moles of oxygen
equal to 3(22.4L) or
67.2 L at STP 43 39 44 52 69 69 49

107. Mass-Volume Relationships in Reactions Involving Gases71

108. Synthesis Question
The lethal dose for hydrogen sulfide is 6 ppm. In other words, if in 1 million molecules of air there are six hydrogen sulfide molecules then that air would be deadly to breathe. How many hydrogen sulfide molecules would be required to reach the lethal dose in a room that is 77 feet long, 62 feet wide and 50 feet tall at 1.0 atm and 25.0o C?

109. Synthesis Question

110. Synthesis Question

111. Group Question
Tires on a car are typically filled to a pressure of 35 psi at 300K. A tire is 16 inches in radius and 8.0 inches in thickness. The wheel that the tire is mounted on is 6.0 inches in radius. What is the mass of the air in a tire?