Prove that the relative lowering of vapour pressure is equal to the mole fraction of non-volatile solute in the solution.

If the non volatile solute is present in the solution, the vapour pressure of the solution depends only upon the solvent. If the vapour pressure of the solution is P and the partial vapour pressure of solvent is P_A then P = P_A
(Because solute has no partial vapour pressure due to non-volatile nature)
or          
where P⁰_A is the vapour pressure of pure solvent and x_A and x_B are the mole fractions of solvent and solute respectively.