A solution at 20$$^\circ$$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:

To find the total vapour pressure and the benzene mole fraction in the vapour phase, we use Raoult's law. First, calculate the total moles in the solution.

Total moles = moles of benzene + moles of toluene = 1.5 mol + 3.5 mol = 5.0 mol.

Next, determine the mole fractions in the liquid phase. Mole fraction of benzene, $$X_{\text{benzene}} = \frac{\text{moles of benzene}}{\text{total moles}} = \frac{1.5}{5.0} = 0.3$$.

Mole fraction of toluene, $$X_{\text{toluene}} = \frac{\text{moles of toluene}}{\text{total moles}} = \frac{3.5}{5.0} = 0.7$$.

According to Raoult's law, the partial vapour pressure of benzene is given by $$P_{\text{benzene}} = X_{\text{benzene}} \times P^{\circ}_{\text{benzene}}$$, where $$P^{\circ}_{\text{benzene}} = 74.7$$ torr. So, $$P_{\text{benzene}} = 0.3 \times 74.7 = 22.41$$ torr.

Similarly, the partial vapour pressure of toluene is $$P_{\text{toluene}} = X_{\text{toluene}} \times P^{\circ}_{\text{toluene}}$$, where $$P^{\circ}_{\text{toluene}} = 22.3$$ torr. So, $$P_{\text{toluene}} = 0.7 \times 22.3 = 15.61$$ torr.

The total vapour pressure of the solution is the sum of the partial pressures: $$P_{\text{total}} = P_{\text{benzene}} + P_{\text{toluene}} = 22.41 + 15.61 = 38.02$$ torr. Rounding to one decimal place as per the options, we get 38.0 torr.

Now, to find the mole fraction of benzene in the vapour phase (denoted as $$Y_{\text{benzene}}$$), we use Dalton's law of partial pressures. The mole fraction in the vapour phase is the ratio of the partial pressure of benzene to the total vapour pressure: $$Y_{\text{benzene}} = \frac{P_{\text{benzene}}}{P_{\text{total}}} = \frac{22.41}{38.02}$$.

Calculating this: $$\frac{22.41}{38.02} \approx 0.5893$$. Rounding to three decimal places, we get 0.589.

Therefore, the total vapour pressure is 38.0 torr and the benzene mole fraction in the vapour phase is 0.589.

Comparing with the options:
A. 30.5 torr and 0.389
B. 35.0 torr and 0.480
C. 38.0 torr and 0.589
D. 35.8 torr and 0.280

Our calculated values match option C.

Hence, the correct answer is Option C.