Only a few physical properties of gases depends on the identity of the gas.  Diffusion - The rate at which two gases mix.  Effusion - The rate at which a gas escapes through a pinhole into a vacuum.  Thomas Graham

Graham's Law of Diffusion

• The rate at which gases diffuse is inversely proportional to the square root of their densities.

• Since volumes of different gases contain the same number of particles (see Avogadro's Hypothesis), the number of moles per liter at a given T and P is constant.  Therefore, the density of a gas is directly proportional to its molar mass (MM).

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Graham's Law of Effusion

• The rate of effusion of a gas is inversely proportional to the square root of either the density or the molar mass of the gas.

The time required for 25-mL samples of different gasses to diffuse through a  pinhole into a vacuum.

The Kinetic Molecular Theory and Graham's Law

• Since KE_avg is dependent only upon T, two different gases at the same temperature must have the same KE_avg.

Simplify the equation by multiplying both sides by two:

Rearrange to give the following:

Take the square root of both sides to obtain the following relationship between the ratio of the velocities of the gases and the square root of the ratio of their molar masses:

This equation states that the velocity (rate) at which gas molecules move is inversely proportional to the square root of their molar masses.

 
Next:  "Deviation from Ideal Gas Behavior: Van der Waals Equation"