A liquid mixture containing $30$ mole $\%$ benzene, $25$ mole $\%$ toluene and

the balance xylene is fed to a distillation column. The bottom product

contains $98$ mole $\%$ xylene and no benzene, and $96\mathrm{.}0\%$ of the xylene in

the feed is recovered in this stream. The overhead product is fed to a

second column. The overhead product from the second column contains $97$

$\%$ of the benzene in the feed to this column. The composition of this

stream is $94$ mole $\%$ benzene and the balance toluene.

$($a$)$ Draw and label a flowchart of the process

$($b$)$ Perform the degree$-$of$-$freedom analysis and list all mass balance

equations for the unknowns

$($c$)$ Calculate all the unknown variables for each stream