Two parallel reactions:

$A+BP($main reaction, reaction rate constant $k_1)$

$A+BS($side reaction, reaction rate constant $k_2)$

$r_P=k_1{c}_A{c}_B^{0\mathrm{.}3}$

$r_S=k_2{c}_A^{0\mathrm{.}5}{c}_B^{1\mathrm{.}8}$

The following parameters are known: $k_1=k_2=1($a$.$u$.)$; $c_{A0}=c_{B0}=10mo\frac{l}{L}$; a PFR is used for the reaction; conversion of $A$ is $90\%$ in the exit.

a$)$ Write down the instantaneous selectivity of $P({}_{\frac{P}{A}})$ as a function of $c_A$ and $c_B.$

b$)$ What is the overall selectivity for P $({}_{\frac{P}{A}})$ after reaction? $(0\mathrm{.}189)$

c$)$ What is the overall yield of $P$ after reaction? $(0\mathrm{.}17)$

d$)$ What are the desirable concentrations of $cA$ and $cB$ in the reactor $($high or low$)$ to obtain high selectivity towards P$?$

e$)$ Sketch two types of flow reactor design that can satisfy concentration requirement you found in d$).$