Molecular Compostion of Gases

Effusion and Diffusion

Objectives1. State graham’s law of

effusion2. Determine the relative

rate of effusion of two gases of known molar masses.

Effusion and DiffusionDiffusion – 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:

22

21

21

BBAA vmvm

Graham’s Law of EffusionMultiplying both sides by two and considering that

mass is proportional to Molar mass….

or…

22BBAA vMvM

A

B

B

A

MM

vv

2

2

A

B

B

A

M

Mvv

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 - YouTubeBecause the rate of effusion is directly proportional to

molecular velocities:

Also:

A

B

M

MBofeffusionofrateAofeffusionofrate

A

B

A

B

density

density

M

MBofeffusionofrateAofeffusionofrate

Sample Problems1. 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 Problems3. 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 Questions1. 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/L4. 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