A solution at 20 o C is composed of 1.5 mol of benzene and 3.5 mol of toluene. If the vapour pressure of…

${\mathrm{X}}_{\mathrm{B}\mathrm{e}\mathrm{n}\mathrm{z}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{ }}=\frac{1.5}{5}=0.3$

${\mathrm{X}}_{\mathrm{T}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{e}\mathrm{n}\mathrm{e}}=\frac{3.5}{5}=0.7$
According to Raoult's Law

$\mathrm{P}={\mathrm{x}}_{\mathrm{A}}\mathrm{P}{°}_{\mathrm{A}} +{\mathrm{x}}_{\mathrm{B}}\mathrm{P}{°}_{\mathrm{B}}$

${\mathrm{P}}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}=0.3\times 74.7+0.7\times 22.3$

$=22.41+15.61=38.02$

$\approx 38\mathrm{ }\mathrm{T}\mathrm{o}\mathrm{r}\mathrm{r}$

By Dalton's law to vapour phase

$\text{Mole fraction of a gas in a mixture of gas}=\frac{\text{Partial pressure of gas}\left({\text{P}}_1\right)}{\text{Total no.moles in the mixture}}$

${\mathrm{X}}_{\mathrm{B}\mathrm{e}\mathrm{n}\mathrm{z}\mathrm{e}\mathrm{n}\mathrm{e}}^{\mathrm{\prime }}\left(\mathrm{V}\mathrm{a}\mathrm{p}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{ }\mathrm{p}\mathrm{h}\mathrm{a}\mathrm{s}\mathrm{e}\right)=\frac{0.3\times 74.7}{38}=\frac{22.41}{38}$

$=0.589$