b
Total \(V.P.\) of solution \(=\,P^o_Ax_A\,+\,P^o_Bx_B\)

Given, \(P^o_A\,=\,74.7\,torr\), \(P^o_B\,=\,22.3\,torr\)

\(n_{benzene}\,=\,1.5\,mol\), \(n_{toluene}\,=\,3.5\,mol\)

\(n_{solution}\,=\,1.5+3.5=5\,mol\)

\(X_A\,=\,\frac {n_{benzene}}{n_{solution}}\,=\,\frac {1.5}{5}\)

Total \(V.P.\) of solution

\( = \left( {\frac{{1.5}}{5}\, \times \,74.7\, + \,\frac{{3.5}}{5}\, \times \,22.3} \right)\,torr\)

\(=\,(15.6+22.4)\,torr\,\,=\,38\,torr\)

Mole fraction of benzene in vapour form

\(=\,\frac {22.4}{38}\,=\,0.589\)