Soap consists of sodium and potassium salts of various fatty acids, such as oleic, stearic, palmitic, lauric, and myristic acids. The saponification for the formation of soap from aqueous caustic soda and glyceryl stearate is$,$

$3$NaOH$(aq)+(C_{17}{H}_{35}\frac{C}{O}O{)}_3{C}_3{H}_{5}3C_{17}{H}_{35}\frac{C}{O}ONa+C_3{H}_5(OH{)}_3$

a$)$ Letting $x$ represent the conversion of sodium hydroxide $($the moles of sodium hydroxide reacted per mole of sodium hydroxide initially present$),$ prepare a stoichiometric table for this liquid$-$phase batch reaction by expressing the concentration of each species in terms of its initial concentration and the conversion.

b$)$ Using the stoichiometric table set up in part a$),$ what are the concentrations of glycerol stearate $($B$)$ and of glycerin $($D$),$ when the conversion of sodium hydroxide $($A$)$ is $20\%$ and $90\%.$ Assume the initial mixture consists of sodium hydroxide $($A$)$ at a concentration of $10mo\frac{l}{L}$ and glyceryl stearate $($B$)$ at a concentration of $2mo\frac{l}{L}.$

c$)$ What is the limiting reactant? Why?