PLEASE show ALL steps and WORK! 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 $20d\frac{m^3}{sec},$ at a pressure of $10$atm, and a temperature of $450K.$

Additional information:

$C_{PA}=40\frac{J}{m}ol*K,C_{PB}=25\frac{J}{m}ol*K,C_{PC}=15\frac{J}{m}ol*K$

$H_A=-70k\frac{J}{m}ol,H_B=-50k\frac{J}{m}ol,H_C=-40k\frac{J}{m}ol$

All heats of formation are referenced to $273K.$

$k=0\mathrm{.}133$exp$[\frac{E}{R}(\frac{1}{450}-\frac{1}{T})]\frac{d{m}^3}{(kg)-\text{c}\text{a}\text{t}*sec}$

With $E=31\mathrm{.}4k\frac{J}{m}ol$

a$)$ Plot and then analyze the conversion and temperature down the plug$-$flow reactor until and $80\%$ conversion $($if possible$)$ is reached. $($The maximum catalyst weight that can be packed into the $PFR$ is $50kg.)$ In other words plot $x$ and $T$ vs$.$ catalyst weight. Assume the $P=0\mathrm{.}0.$

b$)$ Now take the pressure drop into account in the PBR with ${}_b=1k\frac{g}{d}{m}^3.$ The reactor can be packed with two different particle sizes. With $D_1,=\frac{0\mathrm{.}019}{k}g-$cat and with $D_2,=\frac{0\mathrm{.}0075}{k}g-$cat. Plot the conversion and temperature for each catalyst diameter versus the catalyst weight.