The elementary liquid$-$phase series reaction

is carried out in an isothermal, constant$-$volume CSTR$,$ where $k_1=0\mathrm{.}5mi{n}^{-1}$ and $k_2=0\mathrm{.}2mi{n}^{-1}.$ If the feed to the reactor consists of pure $A,$ determine the optimum residence time $({}_{\text{o}\text{p}\text{t}})$ required to maximize the concentration of species $B$ under steady conditions. The inlet concentration of species $A$ is $C_{AO}=2M.$

A$.{}_{\text{o}\text{p}\text{t}}=2\mathrm{.}16$min

B$.{}_{\text{o}\text{p}\text{t}}=0\mathrm{.}16$min

C$.{}_{\text{o}\text{p}\text{t}}=1\mathrm{.}16$min

D$.{}_{\text{o}\text{p}\text{t}}=3\mathrm{.}16$min

E$.{}_{\text{o}\text{p}\text{t}}=5\mathrm{.}16$min