Graham’s Law of Diffusion of Gases

Graham’s Law of Diffusion

Graham's Law may be stated as under similar conditions of temperature and pressure, the rate of diffusion or effusion of gas is inversely proportional to the square root of its density.

If 'r' is the rate of diffusion of a gas and its density be 'd' then according to Grahm's law,
r ∝ 1/√d
Therefore, lighter gas diffuses at faster rate.
Since, r = V/t
so, V/t = 1//√d
If 't' is constant then,
V ∝ 1/√d
And If 'V' is constant then,
t ∝ √d

If d₁ be the density of a gas A and d₂ be the density of gas B then under similar conditions of temperature and pressure, their rate of diffusion or effusion r₁ and r₂ are related as,

If under similar conditions 'd' be the density of hydrogen then,
where, D₁ and D₂ are vapour densities of gaases A and B respectively.

Also,
Since, molecular weight of a gas = 2 x vapour density.
i.e. M = 2D

Hence, under similar conditions of temperature and pressure, the rate of diffusion or effusion of gasses are inversly proportional to square root of their molecular mass or vapour density.

Applications of Diffusion or Effusion

Graham's law of diffusion is used as followes:

1. It is used in the determination of vapour density of a gas using equation: 2.
2. It is used in the determination of molecular weight of a gas by using the equation: 3
3. It is used for the separation of isotopes. This process is called atmolysis.
4. It is used to measure the rate of diffusion of a gas.
5. It is used for the construction of Ansell's Marsh Gas Indicator for the detection of Marsh gas in coal mines.