P$11-4$ The elementary, irreversible, organic liquid$-$phase reaction

$A+BC$

is carried out adiabatically in a flow reactor. An equal molar feed in A and $B$ enters at $27C,$ and the volumetric flow rate is $2d\frac{m^3}{s}$ and $C_{A0}=0\mathrm{.}1$kmo$\frac{l}{m^3}.$

Additional information:

$H_A(273K)=-20$kca$\frac{l}{m}ol,H_B(273K)=-15$kca$\frac{l}{m}ol$

$H_C(273K)=-41$kca$\frac{l}{m}ol$

$C_{P_A}=C_{P_B}=15ca\frac{l}{m}ol*K,C_{P_C}=30ca\frac{l}{m}ol*K$

$k=0\mathrm{.}01\frac{d{m}^3}{(mol)*s}at300K,E=10,000ca\frac{l}{m}ol$

PFR

$($a$)$ Plot and then analyze the conversion and temperature as a function of PFR volume up to where $x=0\mathrm{.}85.$ Describe the trends.

$($b$)$ What is the maximum inlet temperature one could have so that the boiling point of the liquid $(550K)$ would not be exceeded even for complete conversion?

$($c$)$ Plot the heat that must be removed along the reactor $(Q^{}$ vs$.V)$ to maintain isothermal operation.

$($d$)$ Plot and then analyze the conversion and temperature profiles up to a PFR reactor volume of $10d{m}^3$ for the case when the reaction is reversible with $K_C=10\frac{m^3}{k}$mol at $450K.$ Plot the equilibrium conversion profile. How are the trends different than part $($a$)?($Ans$.$: When $V=10d{m}^3$ then $($:$x=0\mathrm{.}0051,x_{eq}=0517$