Simple batch distillation: A charge of $100$kmol of a mixture of benzene and chlorobenzene having $50$mol$\%$ of the less volatile component is to be batch$-$distilled.

a$)$ If $40$kmol of the solution are vaporized and condensed as the distillate, calculate the composition of the produced distillate. $(3\mathrm{.}5$ marks, A&A $1\mathrm{.}5)$

b$)$ If the concentration of the accumulated product is found to be $76$mol$\%$ benzene, calculate its amount in kmol. $(3\mathrm{.}5$ marks, A&A $1\mathrm{.}5)$

The relative volatility of benzene in the mixture is $4\mathrm{.}15.$