Please solve using Polymath

A microreactor $($very small PBR$)$ is used for the gas$-$phase reaction:

$CO+C{l}_{2}COC{l}_2$

$A+BC$

At the entering point, the molar flow rate of both $CO$ and $C{l}_2$ is $2{10}^{-5}mo\frac{l}{s}.$ The partial

pressure of $CO$ is $230$kPa, and the volumetric flow rate is $2\mathrm{.}83{10}^{-7}\frac{m^3}{s}.$ The

microreactor has $3\mathrm{.}5{10}^{-6}kg$ catalyst, and is kept at a constant $T=120C.$ The rate law

of the reaction on this catalyst follows elementary rate law, with $.$

$k{g}_{\text{c}\text{a}\text{t}})$ at $120C.$ The pressure drop parameter has been measured as $3\mathrm{.}55{10}^{5}kgca{t}^{-1}.$

a$.$ Plot the conversion $x,$ pressure ratio $p,$ and volumetric flow rate as a function of

catalyst weight in the bed until $3\mathrm{.}5{10}^{-6}kg.$

b$.$ If the reaction were reversible with $K_c=0\mathrm{.}1d\frac{m^3}{m}ol,$ which step of the reaction

design algorithm should we change? Re$-$do part a$)$ in this scenario.

c$.$ If the catalyst weight remains the same but particle diameter is cut in half, what is

the new pressure drop parameter, assuming that the flow is $100\%$ laminar flow?

Re$-$do part a$)$ in this scenario, explain why you encounter a problem.