$OR$

$4.$ A dilute aqueous solution of ethanol is to be concentrated from $20$ mass $\%$ to $85$ mass $\%$ alcohol in a tray tower at $1$atm pressure. The feed rate is $8000k\frac{g}{h}$ at its bubble point The bottom product must not contain more than $3\mathrm{.}5$ mass $\%$ ethanol.

Determine the minimum reflux ratio

$($a$)$ The number of ideal trays for a reflux ratio $1\mathrm{.}5$ times the minimum.

$($b$)$ The reboiler and condenser heat duties.

The enthalpy concentration $(k\frac{J}{k}$mol$)$; reference states: pure liquids at $0C)$ and the vapour liquid equilibrium data at the operating pressure of $1$atm are given bclow.

$\backslash$table$[[x,y,0,0\mathrm{.}417,0\mathrm{.}0891,0\mathrm{.}1436,0\mathrm{.}207,0\mathrm{.}281,0\mathrm{.}37,0\mathrm{.}477,0\mathrm{.}61,0\mathrm{.}779,1\mathrm{.}0],[H_L,7540,7125,6880,6915,7097,7397,7750,8105,8471,8945,9523],[H_{},48150,48250,48300,48328,48436,48450,48450,48631,48694,48950,]]$

$\backslash$table$[[x,0,0\mathrm{.}00792,0\mathrm{.}016,0\mathrm{.}0202,0\mathrm{.}0417,0\mathrm{.}0891,0\mathrm{.}1436,0\mathrm{.}281,0\mathrm{.}37,0\mathrm{.}477],[y,0,0\mathrm{.}0850,0\mathrm{.}1585,0\mathrm{.}191,0\mathrm{.}304,0\mathrm{.}427,0\mathrm{.}493,0\mathrm{.}568,0\mathrm{.}603,0\mathrm{.}644],[x,0\mathrm{.}61,0\mathrm{.}641,0\mathrm{.}706,0\mathrm{.}779,0\mathrm{.}86,0\mathrm{.}904,0\mathrm{.}95,1\mathrm{.}0,,],[y,0\mathrm{.}703,0\mathrm{.}72,0\mathrm{.}756,0\mathrm{.}802,0\mathrm{.}864,0\mathrm{.}902,0\mathrm{.}9456,1\mathrm{.}0,,]]$

Given : Enthalpy of the feed $=4790k\frac{J}{k}$mol