$($a$)$ What are the different factors that effects the rate of reaction when a porous catalyst particle is immersed$/$cover completely by reactant?

$($b$)$ Draw a plot between the effectiveness factor and the Thiele modulus or $($:$M_T\}.$

$($c$)$ The results of the kinetic runs on the reaction $AR$ made in an experimental packed bed reactor using a fixed feed rate $F_{Ao}=10$kmo$\frac{l}{h}$ are as follows:

$\backslash$table$[[$W$,$ kg catalyst,$1,2,3,4,5,6,7],[x_A,0\mathrm{.}12,0\mathrm{.}20,0\mathrm{.}27,0\mathrm{.}33,0\mathrm{.}37,0\mathrm{.}41,0\mathrm{.}44]]$

$($i$)$ Find the reaction rate at $40\%$ conversion.

$($ii$)$ For a feed rate of $400$kmo$\frac{l}{h}$ to large scale packed bed reactor, find the amount of catalyst needed for $40\%$ conversion.

$($iii$)$ Find the amount of catalyst that would be required in part $($ii$)$ if the reactor employed a very large recycle of product stream.