$150$kmo$\frac{l}{h}r$ of feed containing equal moles of styrene and ethylbenzene is separated using fractional distillation to obtain a top product containing $98$mol$\%$ ethylbenzene and a bottom product containing $96$mol$\%$ styrene. $($ styrene $=3\mathrm{.}63x{10}^5\frac{J}{k}g$; $$ethylbenzene $=3\mathrm{.}35{10}^5\frac{J}{k}gMW$ styrene $=104$

$\frac{g}{m}ol,$ MWethylbenzene $=106\frac{g}{m}ol)$ Determine $($a$)$ amount of distillate and bottoms produced $($b$)$ the minimum number of ideal trays required $($c$)$ the number of ideal trays and the feed tray location if the actual reflux ratio is $1\mathrm{.}5$ times the minimum and the feed is $($i$)$ saturated liquid $($ii$)$ saturated vapor $($iii$)\frac{1}{3}$ liquid, $\frac{2}{3}$ vapor $($d$)$ the amount of water needed in the condenser for the different feed types $($i$),($ii$),($iii$)$ if it enters at $20$degC and exits at $50$degC $($e$)$ the amount of steam $($Latent heat of vaporization $=522ca\frac{l}{g})$ needed in the reboiler for the different feed types $($i$),($ii$),($iii$).$ The column operated at $20mmHg$ pressure and the equilibrium data at this pressure are given below $(x,y$ are in mole fraction of ethylbenzene$)(45$ PTS$)$

Ethylbenzene$-$Styrene