The total condenser produces a stream of $96\%$mol benzene, and the thermosyphon reboiler produces a liquid $($bootom$)$ stream with $5$mol$\%$benzene. The quilibirum curve for the benzene follows the equation: y$=$x$(2\mathrm{.}05-$x$)$

$($a$)$ At what reflux ratio is the column operating?

$($b$)$ Determine the distillate and bottoms flow rates.

$($c$)$ Determine the number of theoretical stages needed and feed plate location.

$($d$)$ What is the ratio of reflux ratio $($under operating conditions$)$ to that under minimum reflux condition.

In other words what is $\frac{R}{R_m}?$

$($e$)$ Estimate the condenser heat duty.