Question $3[12$ marks$]$

Distillation is the process of separating the components or substances from a liquid mixture by using selective boiling and condensation. Distillation may result in essentially complete separation $($nearly pure components$),$ or it may be a partial separation that increases the concentration of selected components in the mixture. In either case, the process exploits differences in the volatility of the mixture's components. In Chemical Engineering, distillation is a unit operation of practically universal importance. Assume that you are a newly employed Chemical Engineer who has been requested by your Process Manager to conduct some investigations pertaining to a distillation process as follows. You carried out an experiment in which a mixture of components A and $B$ with $0\mathrm{.}6$ mole fraction of $B$ is to be differentially distilled. Determine the average composition of the collected distillate and the composition of the remaining liquid residue at the end of operation using the vapour liquid equilibrium of A given in the table if $70$mole$\%$ of the initial mixture has been vaporized.

$1$

Table $1.$ Vapour liquid equilibrium of component $A$ in mole fractions at $1$atm pressure

$\backslash$table$[[$Temp K$,366,357,355\mathrm{.}1,354\mathrm{.}3,353\mathrm{.}6,353\mathrm{.}2,353\mathrm{.}3,354\mathrm{.}5],[x,0\mathrm{.}012,0\mathrm{.}084,0\mathrm{.}198,0\mathrm{.}350,0\mathrm{.}453,0\mathrm{.}679,0\mathrm{.}769,0\mathrm{.}944],[y,0\mathrm{.}220,0\mathrm{.}462,0\mathrm{.}524,0\mathrm{.}569,0\mathrm{.}593,0\mathrm{.}682,0\mathrm{.}742,0\mathrm{.}916]]$