Consider the base hydrolysis of ethyl acetate in the liquid phase:

The reaction is second order overall, and the rate of reaction can be expressed as:

rate $of$ reaction $(\frac{molcsconsumsd}{L\text{m}\text{i}\text{n}})=k{C}_A{C}_B$

where A and $B$ refer to the ethyl acetate and sodium hydroxide reactants, respectively, $C_A$ and $C_B$ are the ethyl acetate and sodium hydroxide concentrations, respectively, in mol$/$L$,$ and $k$ is the reaction rate constant, which is $12\frac{1}{mo\frac{l}{m}in}$ at $25C.$

$1$

The reaction is carried out in a rigid batch reactor at $25C$ in which $100L$ of $0\mathrm{.}1mo\frac{l}{L}$ ethyl acetate is initially combined with $50L$ of $0\mathrm{.}2mo\frac{l}{L}$ of sodium hydroxide. Assume that the reactants are immediately mixed when combined, and the reaction mixture remains well$-$mixed over the course of the reaction.

$($a$)$ What can we say about the concentrations of A and $B$ at any time?

$($b$)$ Determine the fractional conversion of ethyl acetate $($defined as the ratio of the amount of ethyl acetate reacted to its initial amount$)$ at the end of $3h$ of reaction time.