Consider the following elementary, first order, gaseous, reversible, exothermic reaction,

$A=B$

The rate constant for the forward and reverse reactions are given as below,

$k_1=0\mathrm{.}02$exp$(-\frac{29300}{RT}),s^{-1}$

$k_{-1}=0\mathrm{.}33$exp$(-\frac{46000}{RT}),s^{-1}$

I. At what optimized temperature profile will you carry out the reaction in a tubular reactor

that has a maximum allowable temperature of $1112F.$ The aim is to have a minimum

volume of the reactor. The feed rate is $F_A$ and the initial concentration is $C_{A0}.$ Discuss the

practicality of your solution.

II$.$ If a conversion of $0\mathrm{.}6$ is required, determine the value of $\frac{V}{F_A}$ in terms of $C_{A0}?$

III. If the reactor was to be operated isothermally at $1112F,$ determine $\frac{V}{F_A}$ for $0\mathrm{.}6$

conversion?

$($You may neglect the effect of temperature on concentration i$.$e$.$ assume constant density$)$