1. AP Notes Chapter 11
Properties Of Gases

2. Temperature
An indirect measure of the average kinetic energy of a collection of particles
KEavg = kT
Boltzman Plot

4. Pressure
Measure of the number of collisions between gas particles and a unit area of the wall of the container Pressure = force / unit area

5. Force/area English system: pounds/in2 (psi) Metric system:
Newton/m2 (pascal)

6. Torricelli Barometer
h = 760 mm Hg
1 atmosphere
pressure

7. 1 atm = 760 torr (mm Hg)
= kPa
= bar
=14.70 psi

9. Patm
Manometer h
Pgas

10. Patm
Manometer h
Pgas

11. Volume
Total space of a container that gases occupy due to the free random motion of the gas molecules

12. Relationship between Volume & Pressure of Gases
P-V

13. V
P (at constant T)

14. Slope = k V
1/P (at constant T)

15. In mathematical terms:
y = mx + b
Boyle’s Law

16. Relationship between Volume & Temperature of Gases
V-T

17. In mathematical terms:
y = mx + b
V = mT + b
Charles’ Law

18. Where T must be in Kelvin (K) temperature
K = 0C + 273

20. Relationship between Pressure & Temperature of Gases
P-T

21. In mathematical terms:
y = mx + b
P = mT + b
Gay-Lussac’s Law

22. Relationship between Volume & Moles
of Gases
V-n

23. In mathematical terms:
y = mx + b
V = mn + b
Avogadro’s Law

24. Avogadro’s Hypothesis
At constant temperature and pressure, equal volumes of gases contain equal number of particles

25. 3. Hydrogen gas [8. 3 liters] reacts in the presence of 2
3. Hydrogen gas [8.3 liters] reacts in the presence of 2.5 liters of nitrogen gas at 370C and 100 kPa. What volume of ammonia is produced at these same conditions?

26. Combined Gas Law

27. Ideal & Real
Gasses

28. Kinetic Molecular Theory
1. Gases consist of small particles that are far apart in comparison to their own size. These particles are considered to be tiny points occupying a negligible volume compared to that of their container.

29. Kinetic Molecular Theory
2. Molecules are in rapid and random straight-line motion. This motion can be described by well-defined and established laws of motion.

30. Kinetic Molecular Theory
3. The collisions of molecules with the walls of a container or with other molecules are perfectly elastic. That is, no loss of energy occurs.

31. Kinetic Molecular Theory
4. There are no attractive forces between molecules or between molecules and the walls with which they collide.

32. Kinetic Molecular Theory
5. At any particular instant, the molecules in a given sample of gas do not all possess the same amount of energy.

33. PARTICLE
IN THE
BOX
Have 1 particle,
with mass m,
with velocity 

34. Consider the P exerted:

35. But:
f = ?

36. But:
f = ma
where

37. 

38.  

39.  
Change in velocity =
(

41. Thus, the pressure exerted by one particle on a wall is:

42. But,

43. But,
and, the distance a particle travels between collisions with the same wall is ?

45. Substituting
into
we get:

46. Simplifying:

47. but,

48. This represents the pressure (P) that one particle exerts striking opposite walls in the box.

49. Now assume the box contains N particles
Now assume the box contains N particles. Then, N/3 particles are traveling between opposite walls.

50. the total pressure on opposite walls is:
Thus,
the total pressure on opposite walls is:

51. Substitute & rearrange

53. From classical physics
where k is the
Boltzman constant

54. R = universal gas constant
where
R = universal gas constant
N0 = Avogadro’s number

56. Ideal Gas Equation

58. Note that
is similar to the
Combined Gas Law
derived earlier.

59. Variations on
Ideal Gas Equation

60. 4. What is the molar
mass of methylamine
if g of the gas
occupies 125 mL with
a pressure of 99.5 kPa
at 220C?

61. Variations on Ideal Gas Equation
Bromine
Variations on
Ideal Gas Equation

62. 5. Calculate the density of fluorine gas at:
300C and 725 torr.
STP

63. Real Gas
Behavior

64. Ideal Gas
Equation
P V = n R T

65. N2
2.0
CH4 H2 PV
nRT
1.0
Ideal
gas
CO2
P (atm)

66. “correct” for volume of molecules
(V - b)

67. attractive forces between molecules
also “correct” for
attractive forces between molecules

68. van der Waals’ Equation
for 1 mole

69. van der Waals’ Equation
for n moles

70. from CRC Handbook
a* b* He Ne
*when P(atm) & V(L)

71. from CRC Handbook
a* b* NH
H2O
*when P(atm) & V(L)

72. from CRC Handbook
a* b*
CCl
C5H
*when P(atm) & V(L)

73. Cl2 gas has a = 6.49, b =
For 8.0 mol Cl2 in a 4.0 L tank at 27oC.
P (ideal) = nRT/V = 49.3 atm
P (van der Waals) = 29.5 atm

74. T & P conditions
where a real gas
approximates
an ideal gas?

75. N2 gas PV nRT 203 K 293 K 1.8 1.4 673 K Ideal 1.0 gas 0.6
P (atm)

76. T & P conditions
where a real gas
approximates
an ideal gas?
high temperature
low pressure

77. Gaseous
Molecular
Movement

78. pressure exerted by each component in a mixture of gases
Partial Pressure
pressure exerted by each component in a mixture of gases

79. this assumes that
NO interactions
occurs between
the molecules of gas

80. must conclude 1. each gas acts as if it is in container alone
2. each gas collides with the container wall as an “event”

81. where n = # components or
PT = P1 + P2 + P

82. Pi V = ni R T or

83. thus:

84. or

85. therefore:
nT =  ni
and PT  sum of mols
of gas

86. Mole Fraction

88. Since:
and

89. Then

90. and
Pi = Xi PT

92. diffusion is the gradual mixing of molecules of different gases.
effusion is the movement of molecules through a small hole into an empty container.

93. rate of  average
effusion speed

95. But ...
where

96. thus
then
RMS speed

99. substituting:

100. simplifying
Graham’s Law
NH3-HCl

102. if “d” is constant

103. if “t” is constant

104. GAS LAW
STOICHIOMETRY

105. 1. Ethanol, C2H5OH, is
often prepared by
fermentation of sugars
such as glucose,
C6H12O6, with carbon
dioxide as the other
product.

106. [A] What volume of CO2 is produced from 125 g of glucose if the reaction is 97.5% efficient?

107. [B] Ethanol can also be made from ethylene, C2H4 according to the following chemical system:

108. 3 C2H4(g) + 2 H2SO4 
C2H5HSO4 + (C2H5)2SO4
then
C2H5HSO4 + (C2H5)2SO4 + 3H2O
 3C2H5OH H2SO4

109. What volume (mL) of 95% ethanol is produced from 142. 5 dm3 of C2H4
What volume (mL) of 95% ethanol is produced from dm3 of C2H4? The density of 95% ethanol is g/mL.

110. 2. What is the final pressure
[kPa] if g uranium
reacts with sufficient
fluorine gas to produce
gaseous uranium
hexafluoride at 32oC in a
300. L container?

111. 3. What mass of sodium
metal is needed to
produce 250 mL of
hydrogen gas at 24oC
and 740 Torr?