Consider two flow reactors that are connected in series and operating at steady state. Both reactors have the same volume $V$ as shown:

The reaction kinetics is given by

$A$ products, with $-r_A=k{C}_A^2(i.e.$ a second order reaction$)$

$($a$)$ What should the units of the rate constant $k$ be if

$[r_A]=\frac{mo\frac{l}{s}}{m^3}$ and $[C_A]=\frac{\text{m}\text{o}\text{l}}{m^3}?$

The reaction is liquid phase, which means the volumetric flow rate $Q$ remains the same throughout. For this problem, suppose

$F_{A0}=1mo\frac{l}{s}$

$k\frac{V}{Q^2}=2\frac{s}{m}ol($even though we do not know the individual values of $k,V$ or $Q)$

We now need to determine the overall conversion of $A,$ which is given by

$x_A=1-\frac{F_{A2}}{F_{A0}}$

$($b$)$ What is $x_A$ if Reactor $1$ was a CSTR and Reactor $2$ a PFR$?$

$($c$)$ What is $x_A$ if Reactor $1$ was a PFR and Reactor $2$ a CSTR$?$

$($d$)$ Comment on your answers to parts $($b$)$ and $($c$)$ in the context of the discussions in Section $3\mathrm{.}2\mathrm{.}2.$ Use no more than $30$ words.