$12-10$ The Diels$-$Alder liquid$-$phase reaction between $1,4-$benzoquinone $(A,C_6{H}_4{O}_2)$ and cyclopentadiene $(B,C_5{H}_6)$ to form the adduct $C_{11}{H}_{10}{O}_2$ is second$-$order with a rate constant $k_A=9\mathrm{.}92{10}^{-6}{m}^{3}mo{l}^{-1}{s}^{-1}$ at $25C($Wassermann$,1936).$ Calculate the size $(m^3)$ of a batch reactor required to produce adduct at the rate of $125mol{h}^{-1},$ if $c_{Ao}=c_{Bo}=100mol{m}^{-3},$ the reactants are $90\%$ converted at the end of each batch $($cycle$),$ the reactor operates isothermally at $25C,$ and the reactor down$-$time $($for discharging, cleaning, charging$)$ between batches is $30\%$ of the total batch $($cycle$)$ time.