$(26$ pts$)1,4-$Dioxane has historically been used to stabilize chlorinated solvents and more recently has been found to contaminant numerous consumer and food products. Based on this experimental evidence, the U$.$S$.$ Environmental Protection Agency $($EPA$)$ has listed $1,4-$dioxane as a high priority chemical and classified it as a probable human carcinogen. You are tasked with analyzing a $5-$stage stripping column that operates isobarically at $760mmHg$ and isothermally at $20C$ and is used to purify water contaminated with $1,4-$dioxane. The entering liquid stream contains $2\mathrm{.}5$ mol$\%1,4-$dioxane $[$D$]$ and the balance water $[$W$].$ If the amount of pure nitrogen $[$N$]$ available is $1070mo\frac{l}{s},$ how much liquid feed $($in $mo\frac{l}{s})$ can this column treat if the EPA requires the column to produce a liquid stream containing $0\mathrm{.}05$mol$\%1,4-$dioxane in water. Assume solute free flow rates are constant, meaning water is nonvolatile and nitrogen does not dissolve in water. Use the Wilson equation to describe the $1,4-$dioxane and water equilibrium. The Wilson constants for $1,4-$dioxane $($D$)$ and water $($W$)$ are given below and the Antione's Constants for $1,4-$dioxane are given below in terms of $C$ and $mmHg.$

$\backslash$table$[[,$Antoine's Constants$],[,$A$,$B$,$C$],[1,4-$Dioxane,$7\mathrm{.}43155,1554\mathrm{.}679,240\mathrm{.}337]]$

$\backslash$table$[[$Wilson Constants$],[{}_{DW},0\mathrm{.}2831],[{}_{WD},0\mathrm{.}3035]]$

a$)$ Draw a PFD and label using solute free flowrates and mole ratios $(4$ pts$)$

b$)$ Provide your specifications used in Excel Solver $(7$ pts$)$

c$)$ What is the $L_{in}$ flowrate $(mo\frac{l}{s})?(15pts)$

i$.$ Use an initial guess of $L^{\text{'}}=100mo\frac{l}{s}$