A micro$-$reactor is used for the following reaction:

$A+$BlongrightarrowC

With a rate law of

$-r_A^{\text{'}}=k_A{C}_A{C}_B$

The microreactor is $20mm$ long, $500$ um in diameter, and packed with catalyst particles $35$ um in diameter. The entering pressure is $830$kPa, and the entering flow to each microreactor is equimolar. Assume you have unrealistically large values, where the molar flow rate of $A$ is $2mo\frac{l}{s}$ and the volumetric flow is $2\mathrm{.}83\frac{m^3}{s}.$ The weight of catalyst in one microreactor: $W=40kg.$ The reactor is kept isothermal at $120C$ with a rate constant of $4\frac{m^6}{m}ol.s.kg$ catalyst. The alpha value is $0\mathrm{.}00355k{g}^{-1}$ catalyst.

a$)$ Plot the molar flow rates $F_A,F_B,$ and $F_C,$ the conversion $x,$ and the pressure drop along the length $($i$.$e$.,$ catalyst weight, $W)$ of the reactor $(25$ marks$).$

b$)$ Repeat part a for the case when the catalyst weight remains the same but the particle diameter is doubled. How are they different? Why? $(10$ marks$).$