Two volatile liquids A and B form an ideal solution. At a certain temperature, the vapour pressures of pure A and pure B are 300 Torr and 800 Torr , respectively. If the mole fraction of component A in the vapour phase is 0.6 , the total vapour pressure of the liquid mixture is ________ Torr.

Step-by-step solution

Let the total vapour pressure be P_ total . The mole fraction of A in the vapour phase is y_ A = 0.6 . The mole fraction of B in the vapour phase is y_ B = 1 - 0.6 = 0.4 . Using the relation between total pressure and vapour-phase mole fractions: 1 P_ total = y_ A P_ A ^ + y_ B P_ B ^ Substitute the given values: 1 P_ total = 0.6 300 + 0.4 800 1 P_ total = 2 1000 + 0.5 1000 = 2.5 1000 1 P_ total = 1 400 P_ total = 400 Torr Answer: 400