It is desired to separate a mixture of benzene $(50$mol$\%)$ and toluene $(50$mol$\%)$ into a top product containing $95$mol$\%$ of benzene and a bottom product containing $95$mol$\%$ of toluene. The distillation is to be carried out at $1$atm, and feed is $1000$kgmo$\frac{l}{h}$ in saturated vapor.

$25\%$

$($i$)$ calculate the moles of overhead and bottom products per hour;

$($ii$)$ calculate minimum reflux ratio and minimum stages;

$($iii$)$ determine the number of ideal stages as $R=1\mathrm{.}25R_{\text{m}\text{i}\text{n}}$

$($iv$)$ estimate condenser and reboiler duty, using the following information benzene$-$ heat capacity $33$kca$\frac{l}{k}$molK; latent heat: $7360$kca$\frac{l}{k}$mol toluene$-$ heat capacity $40$kca$\frac{l}{k}$molK; latent heat: $7960$kca$\frac{l}{k}$mol