A solution at 20°C is composed of 1.5 mol of benzene and 3.5 mol of toluene

A solution at 20°C is composed of 1.5 mol of benzene and 3.5 mol of toluene. If the vapour pressure of pure benzene and pure toluene at this temperature are 74.7 torr and 22.3 torr, respectively, then the total vapour pressure of the solution and the benzene mole fraction in equilibrium with it will be, respectively:

  1. 35.0 torr and 0.480
  2. 38.0 torr and 0.589
  3. 30.5 torr and 0.389
  4. 35.8 torr and 0.280

Solution

Here, the concept of Raoult’s Law is used which states that for a solution of volatile liquids, the partial vapour pressure of each liquid in the solution is directly proportional to its mole fraction.

Xbenzene  = 1.5/5 = 0.3

Xtoluene = 3.5/5 = = 0.7

PT = 74.7 x 0.3 + 0.7 x 22.3

= 22.41 + 15.61

= 38.02 torr

Ybenzene = 22.41/38.02 = 0.589

The correct option is B.