According to Roult's law, the partial pressure of each volatile components in the solution is directly. proportional to its mole fraction.

Let say -

x_{1} = mole fraction of solvent in solution.

x_{2 }= mole fraction of volatile solute in solution.

P_{1} = partial vapour pressure of solvent

P_{2} = partial vapour pressure of volatile solute.

∴ \(P_1 \propto x_1\)

\(P_1 = x_1 P^0_1\)

\(P^0_1 = \) Pure vapour pressure of solvent.

Similarly,

\(P_2 = x_2P^0_2\)

\(P^0_2 = \) Pure vapour pressure of volatile solute.

According to Dalton's Law of partial pressure -

\(P_{total} = P_1 + P_2\)

\(P_{total} = x_1P^0_1 + x_2P^0_2\)