$11\mathrm{.}6-3.$ Minimum Reflux and Theoretical Number of Trays. A feed of ethanol$-$water containing $60wt\%$ ethanol is to be distilled at $101\mathrm{.}32$kPa pressure to give a distillate containing $85wt\%$ ethanol and a bottoms containing $2wt\%$ ethanol. The feed rate is $10000k\frac{g}{h}$ and its enthalpy is $116\mathrm{.}3k\frac{J}{k}g(50bt\frac{u}{l}bm).$ Use consistent units of $k\frac{g}{h},$ weight fraction, and $k\frac{J}{k}g.$

$($a$)$ Calculate the amount of distillate and bottoms.

$($b$)$ Determine the minimum reflux ratio using enthalpy$-$concentration data from Appendix A$.3.$

$($c$)$ Using $2\mathrm{.}0$ times the minimum reflux ratio, determine the theoretical number of trays needed.

$($d$)$ Calculate the condenser and reboiler heat loads.

$($e$)$ Determine the minimum number of theoretical plates at total reflux.

Ans. $($b$)R_m=0\mathrm{.}373$

$($c$)4\mathrm{.}4$ theoretical trays plus reboiler

$($d$)q_c=3634kW,q_R=4096kW$

$($e$)2\mathrm{.}8$ theoretical trays plus reboiler