In a two stage process shown in Figure $1,$ acetic acid $($A$)$ is extracted from water $($W$)$ into hexanol $(H)$ in a liquid$-$liquid extraction vessel and the extract is subsequently separated by distillation column. Assume that water is completely insoluble in hexanol. A mixture of $18wt\%$ acetic acid and the balance water is fed to a liquid$-$liquid extraction vessel. Pure hexanol is fed to the vessel to extract the acetic acid. The water$-$rich stream leaving the vessel is containing $99\mathrm{.}5wt\%$ water and the balance is acetic acid. The hexanol$-$rich extract is fed to a distillation column. The composition of the distillate is $96wt\%$ acetic acid and the balance is hexanol. The bottom stream contains $97\mathrm{.}2wt\%$ hexanol and recovers $95\%$ of the hexanol fed to the liquid$-$liquid extraction vessel.

$($a$)$ Draw and completely label the process flowchart.

$[6$ Marks$]$

$($b$)$ Perform degree of freedom analysis on each unit process and overall system.

$[10$ Marks$]$

$($c$)$ If the amount of pure hexanol fed to the extraction vessel is $100k\frac{g}{h},$ calculate

i$)$ the flowrate for each stream,

ii$)$ the composition of hexanol$-$rich stream, and

iii$)$ percentage of acetic acid in the process that is recovered in the distillate stream.

$[14$ Marks$]$