A solution at 20 °C is composed of I .5 mol of benzene and 3.5 mol of toluene. If the vapour pressure of pure benzene and pure toluene at this tempei'ature 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:

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38.0 torr and 0.589

30.5 torr and 0.389

30.5 torr and 0.480

35.8 torr and 0.280

answer is B.

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Detailed Solution

Total V.P. of solution = $P_{A}^{\circ} x_{A} + P_{B}^{\circ} x_{B}$
$Given, P_{A}^{\circ} = 74 .7 torr, P_{B}^{\circ} = 22 .3 torr$
$n_{benzene} = 1 .5 mol, n_{toluene} = 3 .5 mol$
$n_{solution} = 1.5 + 3.5 = 5 mol$
$x_{A} = \frac{n_{benzene}}{n_{solution}} = \frac{1.5}{5}$
Total V.P. of solution
$\begin{array}{l} = (\frac{1 .5}{5} \times 74 .7 + \frac{3 .5}{5} \times 22 .3) torr \\ = (15 .6 + 22 .4) torr = 38 torr \end{array}$
Mole fraction of benzene in vapour form
$= \frac{22.4}{38} = 0.589$