Two parallel reactions:

A $+$ B $->$ P $($main reaction, reaction rate constant k$1)$

A $+$ B $->$ S $($side reaction, reaction rate constant k$2)$

rP $=$ k$1$cAcB$^0\mathrm{.}3$

rS $=$ k$2$cA$^0\mathrm{.}5$cB$^1\mathrm{.}8$

The following parameters are known: k$1=$ k$2=1($a$.$u$.)$; cA$0=$ cB$0=10$ mol$/$L; a PFR is used for the reaction; conversion of A is $90\%$ in the exit.

a$)$ Write down the instantaneous selectivity of P $()$ as a function of cA and cB$.$

b$)$ What is the overall selectivity for P $()$ after reaction?

$($c$)$ What is the overall yield of P after reaction?

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$).$