For an ideal binary solution containing components A and B, the partial vapour pressures according to Raoult's law are: $P_A = x_A p_A$ $P_B = x_B p_B$ According to Dalton's law of partial pressures, the total pressure of the solution ($P_{\text{total}}$) is the sum of the partial pressures: $P_{\text{total}} = P_A + P_B = x_A p_A + x_B p_B$ We know that the sum of mole fractions of all components in a solution is unity, i.e., $x_A + x_B = 1$, which gives $x_B = 1 - x_A$. Substituting this into the total pressure equation: $P_{\text{total}} = x_A p_A + (1 - x_A) p_B$ $P_{\text{total}} = x_A p_A + p_B - x_A p_B$ $P_{\text{total}} = p_B + x_A(p_A - p_B)$