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Question:

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

35.0 torr and 0.480

30.5 torr and 0.389

38.0 torr and 0.589

35.8 torr and 0.280

Solution:

The mole fraction of benzene is χB = 1.5/(1.5 + 3.5) = 0.3
The partial pressure of benzene is PB = 0.3 × 74.7 = 22.4 torr
The partial pressure of toluene is χT = 0.7 × 22.3 = 15.6 torr
The total pressure is PT = 22.4 + 15.6 = 38.0 torr
The mole fraction of benzene in vapor is Y = 22.4/38.0 = 0.589.
Hence, the correct option is C