Derive the relationship between relative lowering of vapour pressure and molar mass of the solute.

The vapour pressure of a mixture of vapours is reduced when one of the components is non-volatile in nature. This implicates the lowering of vapour pressure is significant for knowing the properties of a vapour-liquid mixture.

The relative lowering of vapour pressure is the ratio of vapour pressure lowering of solvent from solution to the vapour pressure of pure solvent.

And we know that, according to Raoult’s law, the partial pressure of any volatile component is the product of vapour pressure of the pure component and its mole fraction in the solution.

For a mixture of two components

By Daltons law for partial pressure,

Now for a non-volatile component-2 in the mixture,

Thus we get from given equations that,

The molar fraction of a component is given by,

For a non-volatile solute n₁ ≫ n₂. Hence n₂ is neglected to get: