Molecular Compostion
of Gases
Effusion and Diffusion
Objectives
1. State graham’s law of
effusion
2. Determine the relative
rate of effusion of two
gases of known molar
masses.
Effusion and Diffusion
Diffusion – mixing of
particles as a result of
random motion.
Effusion – process by
which gas particles pass
through a tiny opening.
Graham’s Law of Effusion
• The rates of diffusion and effusion depend on the
velocity of gas particles.
• Velocity of gas particles varies inversely with mass
For two different gas samples at the same temperature,
particles of each gas have the same average kinetic
energy. Therefore:
1
2
m Av
2
A

1
2
2
mBvB
Graham’s Law of Effusion
Multiplying both sides by two and considering that mass
is proportional to Molar mass….
M Av
or…
 M Bv
2
A
2
vA
2

vB
vA
vB

M
B
M
A
M
B
M
A
2
B
Graham’s Law of Effusion
• The rates of effusion of gases at the same temperature
and pressure are inversely proportional to the square
roots of their molar masses.
Graham's Law Demonstration - Animated - YouTube
Because the rate of effusion is directly proportional to
molecular velocities:
rate of effusion of A

rate of effusion of B
Also:
rate of effusion of A
rate of effusion of B

M
B
M
A

M
B
M
A
density
B
density
A
Sample Problems
1. At 25oC, the average velocity of oxygen molecules
is 420 m/s. What is the average velocity of helium
atoms at the same temperature?
2. At a certain temperature, hydrogen molecules move
at an average velocity of 1.84 x 103 m/s. Estimate
the molar mass of a gas whose molecules have an
average velocity of 312 m/s.
Sample Problems
3. Nitrogen effuses through a pinhole 1.7 times as fast
as another gaseous element at the same conditions.
Estimate the other element’s molar mass, and
determine its probable identity.
4. Determine the molecular mass ratio of two gases
whose rates of diffusion have a ratio of 16:1.
Review Questions
1. When a cylinder of oxygen is left standing in the sun,
the temperature of the gas reaches 42oC. The cylinder
has a volume of 10.0 L and contains 128 g of oxygen.
What is the pressure in atmospheres inside the
cylinder? 10.3 atm
2. Sulfur dioxide has a density of 2.927 g/L at STP. What
is its density at a pressure of 108 kPa and 50.0oC?
2.65 g/L
3. What would be the density of 1.0 L of hydrogen at STP?
What would be the density of 1.0 L of oxygen at STP?
0.089 g/L and 1.4 g/L
4. An unknown gas effuses at 0.850 times the effusion
rate of nitrogen dioxide. Estimate the molar mass of the
unknown gas. 64 g/mol
Review Questions
5. A gas sample that has a mass of 0.993 g occupies
0.570 L. Given that the temperature is 281 K and the
pressure is 1.44 atm, what is the molar mass of the
gas? 27.9 g/mol
6. The density of a gas is 3.07 g/L at STP. Calculate the
gas’s molar mass. 68.8 g/mol
7. Compare the rates of diffusion of carbon monoxide and
sulfur trioxide. CO is 1.7 times faster than SO3