GASES – Part II
Ideal Gas Law: An equation of state for a gas. “state” is the condition of the gas at a given time.
PV = nRT
Ideal Gases fit all 3 assumptions of the Kinetic Molecular Theory (KT):
1.
Molecules are infinitely far apart.
2.
Zero attractive forces exist between the molecules.
3.
Molecules are infinitely small--zero molecular volume (“point masses”).
What is an example of an ideal gas?
Real Gases:
1.
Molecules are relatively far apart compared to their size.
2.
Very small attractive forces exist between molecules.
3.
The volume of the molecule is small compared to the distance between molecules.
What is an example of a real gas?
PV = nRT
R = proportionality constant = 0.08206 L atm K -1 mol -1
P = pressure in atm
V = volume in Liters
n = moles
T = temperature in Kelvin
Holds closely at P < 1 atm
Example Problems #7-8: Ideal Gas Law Calculations
7. A 1.5 mol sample of radon gas has a volume of 21.0 L at 33 ° C. What is the pressure of the gas?

8. A sample of hydrogen gas, H
2
, has a volume of 8.56 L at a temperature of O
⁰
C and a pressure of
1.5 atm. Calculate the number of moles of hydrogen present.
Standard Temperature and Pressure:
P = 1 atmosphere
T = 0°C = 273.15 K
GAS STOICHIOMETRY 
1.
Mass-Volume
2.
Volume-Volume
Derivation of Molar Volume from Ideal Gas Law:
Example Problem #9: Gas Stoichiometry (not at STP)
P= 1.00 atm
V = ? n = 1.28 x 10 -1 mol
T = 25 ° C (room temperature) = 298 K
R = .0821 L · atm
mol · K

Example Problems #10-12: Gas Stoichiometry (at STP)
10. A sample of nitrogen gas has a volume of 1.75 L at STP. How many moles of N
2 are present?
11. Quicklime, CaO, is produced by heating calcium carbonate, CaCO
3
. Calculate the volume of CO
2 produced at STP from the decomposition of 152 g of CaCO
3.
CaCO
3 (s)
 CaO
2 (s)
+ CO
2 (g)
Volume – Volume
12. If 25.0 L of hydrogen reacts with an excess of nitrogen gas, how much ammonia gas will be produced? All gases are measured at the same temperature and pressure.
MOLAR MASS OF A GAS 𝑚
𝑀 n = number of moles m = mass
M = molar mass
P = mRT
VM or P =
DRT
M
therefore M =
DRT
P

Example #13: Molar Mass Calculations
M = ? T = 27 ° C = 300. K D = 1.95 g/L P = 1.50 atm
M =
DRT
P
Dalton’s Law of Partial Pressures:
For a mixture of gases in a container,
P = P + P + P + . . .
Total 1 2 3
Example #14: Dalton’s Law of Partial Pressure Calculations
A mixture of nitrogen gas at a pressure of 1.25 atm, oxygen at 2.55 atm, and carbon dioxide at .33 atm would have what total pressure?
Example #15: Water Vapor Pressure Calculations
When a sample of potassium chlorate is decomposed and the oxygen produced collected by water displacement, the oxygen has a volume of 0.650 L at a temperature of 22 ° C. The combined pressure of the oxygen and water vapor is 754 torr (water vapor pressure at
22 °C is 21 torr). How many moles of oxygen are produced?
?
2KClO
3 (s)
→ 2KCl
(s)
+ 3O
2 (g)

Mole Fraction: the ratio of the number of moles of a given component in a mixture to the total number of moles of the mixture.

1
= n
1
n total

1
=
V
1
V total

1
=
P
1
P total
(volume & temperature constant)
Kinetic Molecular Theory (KMT or KT): recall the assumptions: (only ideal gases follow these assumptions perfectly)
1.
Volume of individual particles is
≈
zero (“point masses”)
2.
Collisions of particles with container walls cause pressure exerted by a gas
3.
Particles exert no force on each other (intermolecular forces = 0)
4.
Average kinetic energy
∝
Kelvin temperature of a gas
05_58
0 4 x 10 2 8 x10 2
Molecular velocity (m/s)
Plot of relative number of oxygen molecules with a given velocity at STP (Boltzmann Distribution).

05_59
273 K
(KE) avg
1273 K

3
2
RT
2273 K
0 1000 2000 3000
Velocity (m/s)
Plot of relative number of nitrogen molecules with a given velocity at three different temperatures.
The Meaning of Temperature:
(KE) avg
=
3
RT
2
Kelvin temperature is an index of the random motions of gas particles (higher T means greater motion.)
 rms

3 RT
M
Diffusion: describes the mixing of gases. The rate of diffusion is the rate of gas mixing.
Effusion: describes the passage of gas into an evacuated chamber
05_60
Pinhole
Gas
Vacuum

Effusion:
Diffusion:
What is the name of the above gas law?
Real Gases:
Must correct ideal gas behavior when at
 high pressure (smaller volume) and
 low temperature (attractive forces become important)
05_62
CH
4
N
2
2.0
H
2
PV nRT
1.0
CO
2
Ideal gas
0
0 200 400 600 800 1000
[
Plots of
P (atm)
𝑃𝑉 𝑛𝑅𝑇
vs. P for several gases at 200 K. - Note the significant deviation from ideal behavior.
Correction:
P obs
 a n
2
( ) ]
V
 
V
 nb
  nRT

05_68
0.5
Molecules of unburned fuel (petroleum)
0.4
0.3
0.2
0.1
0
NO
NO
2
O
3
Other pollutants
Time of day
Concentration for some smog components vs. time of day
NO
2(g)
= NO
(g)
+ O
(g)
O
(g)
+ O
2(g)
= O
3(g)
NO
(g)
+
1
2
O
2(g)
= NO
2(g)
3
2
O
2(g)
= O
3(g)
What substances represent intermediates?
Which substance represents the catalyst?