# Graham’s law of Diffusion

## Graham’s law of Diffusion

Diffusion in the ability of a gas to spread and occupy the whole available volume irrespective of other gases present in the container. Thomas Graham in 1831 proposed the law of gaseous diffusion. The law 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.

Mathematically:

r α 1/√ρ

Where,

r = Rate of diffusion,

ρ = Density of the gas.

When two gases at the same pressure and temperature are allowed to diffuse into each other, the rate of diffusion of each gas is inversely proportional to the square root of the density of the gas. This is known as Graham’s law of diffusion.

It is reasonable to assume that the rate of diffusion is proportional to the rms speed of the molecules of the gas. Then, if r₁ and r₂ be the rates of diffusion of the two gases.

$$\frac{{{r}_{1}}}{{{r}_{2}}}=\frac{{{v}_{1,\,rms}}}{{{v}_{2,\,rms}}}$$ … (1)

From kinetic theory of gases, we have:

$${{v}_{rms}}=\sqrt{\frac{3P}{\rho }}$$.

If the pressure of the two gases are the same,

$$\frac{{{v}_{1,\,rms}}}{{{v}_{2,\,rms}}}=\sqrt{\frac{{{\rho }_{2}}}{{{\rho }_{1}}}}$$.

So that from equation (1):

$$\frac{{{r}_{1}}}{{{r}_{2}}}=\sqrt{\frac{{{\rho }_{2}}}{{{\rho }_{1}}}}$$.

Which is Graham’s Law.