$6\mathrm{.}13$b$.$ Difterential distillation of a mixture of isopropenol in water

A mixture of $40$mol$\%$ isopropanol in water is to be differentially distilled at

$1$atm until $70$mol$\%$ of the charge has been vaporized. Calculate the composition

of the liquid residue in the still pot, and the average composition of the collected

distillate. VLE data for this system, in mol fraction of isopropanol, at $1$ atm are

$($Seader and Henley, $1998)$:

Composition of the azeotrope is $x=y=0\mathrm{.}685$; boiling point of the azeotrope $=$

$353\mathrm{.}2K.$

Answer: $y_{D,av}=0\mathrm{.}543$