Consider the liquid phase, irreversible cis$-$trans isomerization of $2-$butene with $1^{st}$ order reaction kinetics as shown below.

$1^{st}$ order reaction kinetics $r_A=-k{C}_A,k=0\mathrm{.}23$min$-1=0\mathrm{.}003833s^{-1}$

a$)$ Assuming steady state, calculate the volume of a CSTR necessary to reduce the exiting concentration to $10\%$ of the entering concentration. The volumetric flow rate is $10d\frac{m^3}{m}in.$

b$)$ Calculate the volume of a PFR for the conditions used in part $($a$).$

c$)$ Calculate the time necessary to reduce the number of moles of $A$ to $1\%$ of its initial value in a constant$-$volume batch reactor for the same reaction.