Two volatile liquids A and B form an ideal solution. The vapour pressure of pure A is 200 torr and that of pure B is 800 torr . If the mole fraction of component A in the vapour phase is 0.2 , then the total vapour pressure of the solution (in torr) is _______.

Step-by-step solution

Let P_T be the total vapour pressure of the solution. According to Dalton's law of partial pressures and Raoult's law, the relationship between total pressure and vapour phase composition is: 1 P_T = Y_A P_A^ + Y_B P_B^ Given: P_A^ = 200 torr P_B^ = 800 torr Y_A = 0.2 Therefore, Y_B = 1 - 0.2 = 0.8 Substituting the values into the equation: 1 P_T = 0.2 200 + 0.8 800 1 P_T = 1 1000 + 1 1000 1 P_T = 2 1000 = 1 500 P_T = 500 torr Answer: 500