$($a$)$ Consider the unimolecular type series reaction $A{k}_1{R}_{\text{d}\text{e}\text{s}\text{i}\text{r}\text{e}\text{d}}{k}_{2}S,k_1{k}_2$ in a Plug Flow Reactor and in a Mixed Flow Reactor.

$($i$)$ Write down the expression of $C_{R,\text{m}\text{a}\text{x}}$ and ${}_{op}$ for both the reactors considering $R$ as the desired product. Which reactor gives favourable product distribution? Justify your answer.

$($ii$)$ How will you plan for conversion of $A$ if $k_1>k_2$ and if Explain with the relevant plot.