The elementary, irreversible gas$-$phase reaction $AB+C,$ is carried out adiabatically in a PFR

packed with a catalyst. Pure A enters the reactor at a volumetric flow rate of $20d\frac{m^3}{s},$ at a

pressure of $10$atm, and a temperature of $450K.$

Additional Information $($all heats of formation are referenced to $T_{\text{r}\text{e}\text{f}}=273K)$:

$C_{P,A}=40\frac{J}{mo{l}^{**}(K)}$

$C_{P,B}=25\frac{J}{mo{l}^{**}(K)}$

$C_{P,C}=15\frac{J}{mo{l}^{**}(K)}$

$H_A^0=-70k\frac{J}{m}ol$

$H_B^0=-50k\frac{J}{m}ol$

$H_C^0=-40k\frac{J}{m}ol$

$k={0\mathrm{.}133}^{**}$exp$(\frac{E}{R}(\frac{1}{450}-\frac{1}{T}))\frac{d{m}^3}{kg-ca{t}^{**}s}$ where $E=31\mathrm{.}4k\frac{J}{m}ol$

a$)$ Plot and then analyze the conversion and temperature down the plug$-$flow reactor until an

$80\%$ conversion $($if possible$)$ is reached. $($The maximum catalyst weight that can be

packed into the PFR is $50kg).$ Assume $P=0.$

b$)$ Vary the inlet temperature and describe its effect on conversion.

c$)$ Plot the heat that must be removed along the reactor $(Q$ vs$.$ W$)$ to maintain isothermal

operation.

d$)$ Now take pressure drop into account in the PBR with ${}_b=1k\frac{g}{d}{m}^3.$ The reactor can be

packed with one of the two particles. Show the conversion and pressure drop along the

length of the reactor for both $($similar to part a$).$ Which one minimizes the pressure drop?

i$)=\frac{0\mathrm{.}019}{k}g-$ cat for particle diameter $D_1$

ii$),=\frac{0\mathrm{.}0075}{k}g-$ cat for particle diameter $D_2$

e$)$ Plot and then analyze the temperature, conversion, and the pressure along the length of

the reactor. Vary the parameters $$ and $P_0$ and describe how this affects the system.

PLEASE HELP WITH C$-$E