The variation of total vapour pressure ( P ) of an ideal solution of two volatile liquids P and Q with the mole fraction of component P ( X_P ) is a straight line. The line has a y-intercept of 150 torr at X_P = 0 and a y-intercept of 250 torr at X_P = 1 . If a solution is prepared by mixing P and Q in a 3 : 2 molar ratio, what is the total vapour pressure of this mixture?

Step-by-step solution

From the given boundary conditions of the graph: At X_P = 0 , the solution contains only liquid Q. Thus, the vapour pressure of pure Q is P_Q^ = 150 torr . At X_P = 1 , the solution contains only liquid P. Thus, the vapour pressure of pure P is P_P^ = 250 torr . The liquids P and Q are mixed in a molar ratio of 3 : 2 . Mole fraction of P, X_P = 3 3 + 2 = 3 5 = 0.6 Mole fraction of Q, X_Q = 2 3 + 2 = 2 5 = 0.4 According to Raoult's law, the total vapour pressure is: P_ total = X_P P_P^ + X_Q P_Q^ P_ total = (0.6 250