A feed mixture composed of $42$ mole $\%$ heptanes and $58$ mole $\%$ ethyl benzene is to be fractionated at $760$ mm Hg to produce a distillate containing $97$mole $\%$ heptanes and a residue containing $1\%$ mole heptanes. Assuming feed to be saturated liquid.

Determine $($a$)$ The amounts of distillate and residue for a feed rate of $50$ kmol$/$hr$.$

$($b$)$ The number of theoretical stages for an operating reflux ratio of $2\mathrm{.}5.\backslash$table$[[$x$,0,0\mathrm{.}08,0\mathrm{.}2,0\mathrm{.}33,0\mathrm{.}5,0\mathrm{.}65,0\mathrm{.}8,0\mathrm{.}91,1],[$y$,0,0\mathrm{.}23,0\mathrm{.}42,0\mathrm{.}6,0\mathrm{.}72,0\mathrm{.}83,0\mathrm{.}9,0\mathrm{.}96,1],[$HL KJ$/$kmol$,592,570,552,536,526,517,516,512,510],[$HV KJ$/$kmol$,1452,1420,1392,1361,1345,1310,1290,1280,1270]]$