$(10$ points$)$ Problem $2.$ Example $8-1$ in the textbook

Maximizing the Selectivity for the Famous Trambouze Reactions

Reactant A decomposes by three simultaneous reactions to form three products, one that is desired, B$,$ and two that are undesired, $x$ and $Y.$ These gas$-$phase reactions, along with the appropriate rate laws, are called the Trambouze reactions $($AIChE J$.,5,384).$

$A{A}_{1}x,-r_{1A}=r_x=k_1=0\mathrm{.}0001\frac{\text{m}\text{o}\text{l}}{d{m}^3*s}($zero order$)$

$A{k}_{2}B,-r_{2A}=r_B=k_2{C}_A=(0\mathrm{.}0015s^{-1})C_A,($first order$)$

$A{t}_{3}Y,-r_A=r_Y=k_3{C}_A^2=(0\mathrm{.}008\frac{d{m}^3}{(mol)*s})C_A^2,($second order$)$

The specific reaction rates are given at $300K$ and the activation energies for reactions $(1),(2),$ and $(3)$ are $E_1=10,000$kca$\frac{l}{m}$ole,$E_2=15,000$kca$\frac{l}{m}$ole, and $E_3=20,000$kca$\frac{l}{m}$ole.

$($a$)$ What would have been the selectivity $S_{\frac{B}{x}Y}$ and conversion, $x,$ if the reaction had been carried out in a single PFR with the same volume as the CSTR$?($Encourage you to plot the CA$,C_B,C{x}_x,C_Y$ and $S_{\frac{B}{x}Y}$ versus space time $)$

$($b$)$ How would your answers change if the pressure were increased by a factor of $100$ in a CSTR with respect to Example $8-1$ in the textbook?