Q$2.$ A liquid stream contains $60\mathrm{.}0wt\%$ ethanol $($E$),5\mathrm{.}0wt\%$ of a dissolved $S,$ and the balance water. The second liquid stream in the feed rate of $200k\frac{g}{s}$ contains $20\mathrm{.}0wt\%$ of a dissolved $T$ and balanced with water. These two streams are fed to a continuous distillation column operating at a steady state. Product streams emerge at the top and bottom of the column. The column design calls for the product streams in a ratio of $1($top$)$ to $5($bottom$),$ for the top stream to contain $60\mathrm{.}0wt\%$ ethanol and no $S$ nor $T,$ and for the bottom stream to contain $10\mathrm{.}0wt\%T.$

$($a$)$ Get a basis of calculation, and draw a fully labelled process block flow diagram.

$($b$)$ Perform the degree$-$of$-$freedom analysis to check if there is information to calculate all unknown stream flows and compositions.

$($c$)$ Calculate the mass fraction of $S$ in the bottom stream and

$($d$)$ Calculate the fraction of the ethanol in the feed that leaves in the bottom product stream $($i$.$e$.,$ the amount of $E$ in the bottom stream over the amount of $E$ in the feed$)$ if the process operates as designed.