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 ingredient stays 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 $3$ bar 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 a 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 $K.$

$A,B,C$

THF $4\mathrm{.}121181202\mathrm{.}942-46\mathrm{.}818$

$1-$IBA $4\mathrm{.}400621260\mathrm{.}453-92\mathrm{.}588$

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 $1)$