Pure butanol is to be fed into a semibatch reactor containing pure ethyl acetate to produce butyl acetate and ethanol. The reaction

$C{H}_3\frac{C}{O}O{C}_2{H}_5+C_4{H}_{9}OHharrC{H}_3\frac{C}{O}O{C}_4{H}_9+C_2{H}_{5}OH$

is elementary and reversible. The reaction is carried out isothermally at $300K.$ At this temperature, the equilibrium constant is $1\mathrm{.}08$ and the specific reaction rate is $9{10}^{-5}d{m}^3/$mol$.$s $($mol$.$s$).$ Initially, there is $200d{m}^3$ of ethyl acetate in the vat, and butanol is fed at a volumetric flow rate of $0\mathrm{.}05d\frac{m^3}{s}.$ The feed and initial concentrations of butanol and ethyl acetate are $10\mathrm{.}93mo\frac{l}{d}{m}^3$ and $7\mathrm{.}72mo\frac{l}{d}{m}^3,$ respectively.

$($a$)$ Plot and analyze the equilibrium conversion ethyl acetate as a function of time.

$($b$)$ Plot and analyze the conversion of ethyl acetate, the rate of reaction, and the concentration of butanol as a function of time.