In the pharmaceutical industry, distillation is utilized to exchange solvents in preparation

for isolation of an active ingredient or intermediate. You are tasked with solvent swapping

an active ingredient from $1-$Isobutanol $(1-$IBA$)$ to Tetrahydrofuran $($THF$).$ All of the active

ingredients stay in the vapor phase and thus can be ignored in your analysis. Prior to

entering the distillation column, $325mo\frac{l}{h}$ of $1-$IBA and the active ingredient in the vapor

phase is mixed with $175mo\frac{l}{h}$ of THF vapor to create a vapor feed of $500mo\frac{l}{h}$ of a $35$

mol$\%THF$ and $65$mol$\%1-$IBA at $\frac{3}{b}ar$ and $410K.$ This is fed to the $5$ th tray of an $8-$tray

distillation column equipped with a total condenser and a partial reboiler at $3$ bar. The total

condenser produces saturated liquid. The bottoms fraction $(\frac{B}{F})$ is $0\mathrm{.}70$ and the reflux ratio

$(\frac{L_0}{D})$ is $7\mathrm{.}0.$ EMO can be assumed. Assume this mixture behaves ideally. Antoine's

Constants are given for $lo{g}_{10}$ in bar and $K.$

a$.$ Draw a process flow diagram.

b$.$ Use a guess of $x_{DTHF}=0\mathrm{.}94,$ solve for all unknowns for the Total Condenser and

Stage $1($Include a degree of freedom analysis for Total Condenser and Stage $1)$