QUESTION $4$

Question #$4$: $(25$ pts$)$For the elementary reversible liquid$-$phase reaction $(AharrB)$ :

$($a$)$ Determine the adiabatic equilibrium temperature and conversion when pure $A$ is fed to the reactor at a temperature of $300K.$

Additional Information:

$H_A(298K)=-40,000ca\frac{l}{m}ol,H_B(298K),=-60,000ca\frac{l}{m}ol$

$C{P}_A,=50ca\frac{l}{\text{m}\text{o}\text{l}*K},C{P}_{P_B}=50ca\frac{l}{\text{m}\text{o}\text{l}*K}$

$100,000at298K,k={10}^{-3}$exp$(\frac{E}{R}(\frac{1}{298}-\frac{1}{T})mi{n}^{-1})$ with $E=10,000ca\frac{l}{m}ol$

$K_c=100,000$ at $298K,k={10}^{-3}$exp$(\frac{E}{R}(\frac{1}{298}-\frac{1}{T})mi{n}^{-1})$ with $E=10,000ca\frac{l}{m}ol$

Conversion vs$.$ Temperature $-$ Finding the Adiabatic Equilibrium

$($b$)$ What is the CSTR volume to achieve $90\%$ of the adiabatic equilibrium conversion for $v_0=5d\frac{m^3}{m}in?$

$($c$)$ What is the PFR volume to achieve $90\%$ of the adiabatic equilibrium conversion for $v_0=5d\frac{m^3}{m}in?$

$($d$)$ If the reaction is to be carried out adiabatically in a batch reactor $($BR$),$ what should be the volume of the $BR$ to achieve $90\%$ of the adiabatic equilibrium conversion for $N_{AO}=46\mathrm{.}5$mol of A fed to the reactor. Assume tbatch $=3\mathrm{.}5$mins and $C_{A0}=2\mathrm{.}5mo\frac{l}{L}.$