Two volatile liquids A and B are mixed to form an ideal solution. The vapour pressures of pure A and pure B are 120 Torr and 30 Torr , respectively. If the vapour phase in equilibrium with the solution is found to be equimolar, the mole fraction of liquid A in the mixture is _______ 10⁻² .

Step-by-step solution

Let the mole fractions of A and B in the liquid phase be X_A and X_B , respectively. According to Raoult's Law, the partial vapour pressures are: P_A = P_A^ X_A = 120 X_A P_B = P_B^ X_B = 30 X_B Since the vapour phase is equimolar, the mole fractions of A and B in the vapour phase are equal ( Y_A = Y_B = 0.5 ). This implies that their partial pressures in the vapour phase must be equal: P_A = P_B 120 X_A = 30 X_B 4 X_A = X_B We know that X_A + X_B = 1 . Substituting X_B into this equation: X_A + 4 X_A = 1 5 X_A = 1