(Solved): The reaction scheme for many organic syntheses process takes the following route: A2C1B ...

The reaction scheme for many organic syntheses process takes the following route: $\begin{array}{rl}\mathrm{A}& 1?\mathrm{B}\\ {?}^2& {?}^3\\ \mathrm{C}& ?\mathrm{D}\end{array}$ For one such process, the first order rate constants have been determined and provided below. $\begin{array}{l}{k}_1=0.010{\mathrm{h}}^{?1}\\ k_2=0.020{\mathrm{h}}^{?1}\\ k_3=0.018{\mathrm{h}}^{?1}\\ k_4=0.012{\mathrm{h}}^{?1}\end{array}$ a) Derive the expression for ${\mathrm{C}}_{\mathrm{A}},{\mathrm{C}}_{\mathrm{B}}$, and ${\mathrm{C}}_{\mathrm{C}}$ as a function of the reaction time in a batch reactor. b) Determine the optimal residence time leading to the maximum concentration of $B$ and $C$ in a plug flow reactor. Report specific values of concentration of $B$ and $C$ if the feed only consists of $A$ with an initial concentration of $1\mathrm{mol}/{\mathrm{dm}}^3$. c) What will be the optimum mean residence time if the same process takes place in a CSTR instead of PFR? Also calculate the maximum concentration of $B\&C$ for this case.