Graham's Law of Diffusion and Effusion

What You Need To Know About Graham's Law

Chemist Thomas Graham
Thomas Graham. Wikipedia/Public Domain

Graham's law expresses the relationship between the rate of effusion or diffusion and the molar mass of the gas. Diffusion describes the spreading of a gas throughout a volume or a second gas, while effusion describes movement of a gas through a tiny hole into an open chamber.

In 1829, Scottish physical chemist Thomas Graham experimentally determined the rate of effusion of a gas is inversely proportional to the square root of the gas particle mass and to its density.

In 1848, he showed the rate of effusion is also inversely proportional to the square root of the molar mass of the gas. So, there are various ways of stating Graham's Law. One important point about the law is that it shows the kinetic energies of gases are equal at the same temperature.

Graham's Law Formula

Graham's law of diffusion and effusion states the rate of diffusion or effusion for a gas is inversely proportional to the square root of the molar mass of the gas.

r ∝ 1/(M)½

or

r(M)½ = constant

where
r = rate of diffusion or effusion
M = molar mass

Generally, this law is used to compare the difference in rates between between two different gases: Gas A and Gas B.  The law assumes temperature and pressure are the same for the two gases. This formula is:

rGas A/rGas B = (MGas B)½/(MGas A)½

Graham's Law Chemistry Problems

One way to apply Graham's law is to determine whether one gas will effuse more quickly or slowly than another and to quantify the difference in rate.

For example, if you want to compare the rate of effusion of hydrogen gas (H2) and oxygen gas (O2), you use the molar mass of the gases (2 for hydrogen and 32 for oxygen, which is the atomic mass multiplied by 2 because each molecule contains two atoms) and relate them inversely:

rate H2/rate O2 = 321/2 / 21/2 = 161/2 / 11/2 = 4/1

So, hydrogen gas molecules effuse four times more quickly than oxygen molecules.

Another type of Graham's law problem may ask you to find the molecular weight of a gas if you know the identity of one gas and the ratio between the rates of effusion of two gases is known.

M2 = M1Rate12 / Rate22

A practical application of Graham's law is uranium enrichment. Natural uranium consists of a mixture of isotopes, which have slightly different masses. In gaseous diffusion, uranium from its ore is made into uranium hexafluoride gas, which is repeatedly diffused through a porous substance. Each time, the material that passes through the pores becomes more concentrated in U-235 versus U-238. This is because the lighter isotope diffuses at a faster rate than the heavier one.