Using Carothers' Equation

a$.$ Given a reaction mixture of $50$ mols of ethylene glycol, $50$ mols terephthalic acid, and $1\mathrm{.}5$mol benzoic acid $($a monofunctional impurity added to control molecular weight$),$ what value of $x_N$ would be expected if complete conversion $)=(1\mathrm{.}0$ of the limiting reactant is achieved?

b$.$ Draw the monomers and resultant polymer repeat unit structure. What is the MW of the repeat unit?

c$.$ What type of polymer is this? $($i$.$e$.,$ polyamide, polyester, polycarbonate, etc.$)$

d$.$ Using a linear or semi$-$log plot, illustrate the MW increase this polymer vs$.$ conversion of the limiting reactant. Using a linear plot, plot PDI vs$.$ conversion as well.

Please do the first three at least