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:

Options

A. 35.0 torr and 0.480
B. 38.0 torr and 0.589
C. 30.5 torr and 0.389
D. 35.8 torr and 0.280

Explanation

To solve the problem, we need to calculate the total vapor pressure of the solution and the mole fraction of benzene in equilibrium with it. Here’s a step-by-step solution:

### Step 1: Calculate the total number of moles in the solution.
The total number of moles (n_total) is the sum of the moles of benzene and toluene.

\[ n_{\text{total}} = n_{\text{benzene}} + n_{\text{toluene}} = 1.5 \, \text{mol} + 3.5 \, \text{mol} = 5.0 \, \text{mol} \]
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