Graham's Law

Graham's law, known as Graham's law of effusion, was formulated by Scottish physical chemist Thomas Graham in 1846. Graham found experimentally that the rate of effusion of a gas is inversely proportional to the square root of the mass of its particles. This formula can be written as:

where:

Rate₁ is the rate of effusion of the first gas (volume or number of moles per unit time).

Rate₂ is the rate of effusion for the second gas.

M₁ is the molar mass of gas 1

M₂ is the molar mass of gas 2.

Graham's law states that the rate of effusion of a gas is inversely proportional to the square root of its molecular weight. Thus, if the molecular weight of one gas is four times that of another, it would diffuse through a porous plug or escape through a small pinhole in a vessel at half the rate of the other. A complete theoretical explanation of Graham's law was provided years later by the kinetic theory of gases. Graham's law provides a basis for separating isotopes by diffusion — a method that came to play a crucial role in the development of the atomic bomb.

Graham's law is most accurate for molecular effusion which involves the movement of one gas at a time through a hole. It is only approximate for diffusion of one gas in another or in air, as these processes involve the movement of more than one gas.