$1,4-$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 $760$ mm Hg and isothermally at $20\backslash$deg C 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 $1070$ mol$/$s$,$ how much liquid feed $($in mol$/$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 $\backslash$deg C and mm Hg$.$

Antoine$$s Constants

A B C

$1,4-$Dioxane $7\mathrm{.}431551554\mathrm{.}679240\mathrm{.}337$

Wilson Constants

$\backslash$Lambda DW $0\mathrm{.}2831$

$\backslash$Lambda WD $0\mathrm{.}3035$

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

b$)$ Provide your specifications used in Excel Solver

c$)$ What is the Lin flowrate $($mol$/$s$)?$

i$.$ Use an initial guess of L$=100$ mol$/$s