The following reactions, all of which follow elementary rate laws, occur in the liquid phase

in a plug$-$flow reactor that operates isothermally,

$\frac{1}{2}A2C,E_{\text{a}\text{c}\text{t}\text{,}2}=50kJmo{l}^{-1}$

$CD,E_{\text{a}\text{c}\text{t}\text{,}3}=80kJmo{l}^{-1}$

Pure $A$ is fed to the PFR at a concentration of CA$,0.$

Express the species balance equations in terms of species concentrations and rate

coefficients, using residence time $()$ as the independent variable.

Write an equation for the instantaneous selectivity of species $B$ relative to species $C$ and

$D(S_{\frac{B}{C},D})$ in terms of species concentrations and rate coefficients. For this part of the problem $($and

part $3),$ you can treat the first reaction as irreversible.

Based on the solution to part $(2),$ comment on whether a PFR or CSTR will be optimal

for maximizing the selectivity to species B$.$ How would your answer change if you could not consider

Step $1$ irreversible?

Would increasing or decreasing the temperature increase or decrease the selectivity to

species B $($assume for this part that Step $1$ is irreversible$).$