According to Roult's law, the partial pressure of each volatile components in the solution is directly. proportional to its mole fraction.
Let say -
x1 = mole fraction of solvent in solution.
x2 = mole fraction of volatile solute in solution.
P1 = partial vapour pressure of solvent
P2 = 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 -
\(P_{total} = P_1 + P_2\)
\(P_{total} = x_1P^0_1 + x_2P^0_2\)