$($a$)$ Justify the statement "The rate of reaction in the absence of pore diffusion resistance is the maximum rate of reaction".

$($b$)$ What are the different parameters to be considered when the results of a single pore to be applied for porous catalyst particles of various shapes.

$($c$)$ The second order reaction $AR$ is studied in an experimental recycle reactor with very large recycle ratio.

The data recorded are as follows:

Void volume of reactor $=11$

Amount of catalyst used $=3g$

Feed to the reactor: $v_o=\frac{11}{h}$ with $C_{Ao}=2mo\frac{l}{l}$

Concentration of $A$ in the exit stream from the recycle system $(C_{\text{A}\text{o}\text{u}\text{t}})=0\mathrm{.}5mo\frac{l}{1}$

$($i$)$ Find the rate constant for this reaction.

$($ii$)$ Calculate the amount of catalyst needed in a packed bed reactor to achieve $80\%$ conversion for feed to the reactor: $v_o=1000\frac{l}{h}$ and $C_{Ao}=1mo\frac{l}{l}$

$($iii$)$ Repeat part $($ii$)$ if the reactor is packed with $1$ part catalyst to $3$ parts inert solid.