Graham's Law of Diffusion

If you open a bottle of perfume in one corner of a room or burn an incense stick you can feel the smell of the perfume or the incense stick all over the room also. The smell of perfume or incense stick spreads from one point of the room to the other by mixing with air. This free intermingling of gases when placed in contact with each other is known as diffusion.

Diffusion occurs in liquids as well as in gases. Effusion is the escape of a gas through a small hole, as in case of a puncture in a tyre.

At constant temperature and pressure, the rate of diffusion of a gas is inversely proportional to the square root of its density. Graham’s law is applicable to both diffusion and effusion.

If the time for a given volume of gas A to escape is t_A, while the time for the same volume of gas B to escape is t_B,

t_A/t_B = (rate)_B/(rate)_A = √(ρ_A/ρ_B)

The ratio of the densities of the molecules is the same as the ratio of the molecular masses of the gases at the same temperature and pressure.

ρ_A/ρ_B = √(M_A/M_B)