An ideal binary solution is prepared by mixing two volatile liquids, A and B. The vapour pressure of pure liquid A is 150 torr and that of pure liquid B is 300 torr at a certain temperature. If the total vapour pressure of the solution at the same temperature is 210 torr , what is the mole fraction of component A in the liquid mixture?

Step-by-step solution

According to Raoult's Law, the total vapour pressure of an ideal binary solution is given by: P_ total = X_ A P_ A ^ + X_ B P_ B ^ Since X_ A + X_ B = 1 , we can write this in terms of X_ A : P_ total = X_ A P_ A ^ + (1 - X_ A )P_ B ^ Substituting the given values: 210 = X_ A (150) + (1 - X_ A )(300) 210 = 150X_ A + 300 - 300X_ A 210 = 300 - 150X_ A 150X_ A = 90 X_ A = 90 150 = 0.6 A common mistake is solving for the mole fraction of B ( 0.4 ) instead of A. Answer: 0.6