The liquid phase exothermic ionic catalytic reaction,

$A+$BharrP

follows the rate equation,

$r_A=[k_f{C}_A{C}_B-k_r{C}_C]C_{\text{c}\text{a}\text{t}\text{a}\text{l}\text{y}\text{s}\text{t}}$

where

$k_f=$exp$[7\mathrm{.}16-\frac{10100}{T}],m^6*mo{l}^{-1}*s^{-1}*mol{H}^{+}$

$k_r=$exp$[30\mathrm{.}4-\frac{16100}{T}],m^3*mol{H}^{+}*s^{-1}$

The effective catalyst concentration $(C_{\text{c}\text{a}\text{t}\text{a}\text{l}\text{y}\text{s}\text{t}})$ is $177mo{l}^{-3}.$ The

concentrations of $A,B,$ and $P$ in the feed are $5000,7000,$ and $0$

mol. $m^{-3},$ respectively. The feed volumetric flow rate is $0\mathrm{.}9m^3.h^{-1},$

and the conversion of the limiting reactant is $80\%.$ The concentrations of $A,B,$ and $P$ in the feed are $5000,7000,$

and $0$ mol. $m^{-3},$ respectively.

The effective catalyst concentration of $(C_{\text{c}\text{a}\text{t}\text{a}\text{l}\text{y}\text{s}\text{t}})$ is $177$ mol.m$-3.$

The feed volumetric flow rate is $0\mathrm{.}9m^3*h^{-1},$ and the conversion of

the limiting reactant is $80\%.$

$($a$)$ Determine the CSTR volume at the temperature that

maximizes the reaction rate.

$($b$)$ Determine the PFR volume at the temperature that

maximizes the reaction rate.