Graham's Law of Diffusion

Graham's Law of Diffusion

When two gases are placed in contact, they mix spontaneously. This is due to the movement of molecule of one gas into the other gas. This process of mixing of gases by random motion of the molecules is called as diffusion.

In 1829, Graham formulated what is now known as Graham's law of diffusion. It states that,

"Under the same conditions of temperature and pressure, the rates of diffusion of different gases are inversely proportional to the square roots of their molecular masses". Mathematically the law can be expressed as

r1/r2 = root of (  ^M1/ ^M2 )

where r1 and r2 are the rates of diffusion of gases 1 and 2, while M1 and M2 are their molecular masses respectively.

When a gas escapes through a pin-hole into a region of low pressure or vacuum, the process is called Effusion. The rate of diffusion of a gas also depends on the molecular mass of the gas. Dalton's law when applied to effusion of a gas is called the Dalton's law of Effusion. It may be expressed mathematically as

Effusion rate of Gas 1/ Effusion rate of Gas 2 =  root of (^M2/ ^M1)

The determination of rate of effusion is much easier compared to the rate of diffusion. Therefore Dalton's law of effusion is often used to find the molecular mass of a given gas.

Self Test

75ml of gas A effuses through a pin hole in 73 seconds. The same volume of SO2 under identical conditions effuses in 75 seconds. Calculate the molecular mass of A.

(Ans = 60.6)

Self Test

If a gas diffuses at the rate of one quarter as fast as N₂. Find the molecular mass.

[Ans = 448]