Graham's law of diffusion and its applications

Gases have the tendency to spontaneously intermix and form a homogenous mixture without the help of external agency. This is due to the presence of large amount of empty space between the gas molecules that makes their movement rapid into each other. The gases move from a region of higher concentration to a region of lower concentration until the mixture attains uniform concentration.

Graham studied the rate of diffusion of various gases and gave this law. It states that under similar conditions of temperature and pressure, the rates of diffusion of gases are inversely proportional to the square roots of their densities.

If r1 and r2 are the rates of diffusion of two gases 'A' and 'B' and r1 and r2 are their densities, then

Molecular mass is twice the vapour density, substituting this in the above equation, we have

where M1 and M2 are the molecular masses of the two gases. Thus, the rate of diffusion of gases are inversely proportional to the square root of their molecular masses.

Rate of diffusion is also equal to the volume of the gas, which diffused per unit time,

If V1 and V2 are the volumes of the gases diffusing in time t1 and t2 respectively, then

Therefore,

If the volume diffused is the same, (V1 = V2)

Then,

From kinetic theory,

Since the rate of diffusion of a gas is determined by the molecular speed,

The rate of diffusion of a gas depends inversely on the square root of its density. This is Graham's law of diffusion.

Graham's law is useful in:

• Separation of gases having different densities by diffusion.
• Determining the densities and molecular masses of unknown gases by comparing their rates of diffusion with known gases.
• Separating the isotopes of some of the elements.