Ethylacetate $(C{H}_{3}C{O}_{2}C{H}_{2}C{H}_3)$ is produced via an esterification reaction between acetic acid $(C{H}_3\frac{C}{O}OH)$ and ethanol $(C{H}_{3}C{H}_{2}OH)$ in gas phase. A packed back reactor is used for this purpose. The reaction follows the elementary rate law while an excess amount of ethanol is used.

$C{H}_3\frac{C}{O}OH+C{H}_{3}C{H}_{2}OHC{H}_{3}C{O}_{2}C{H}_{2}C{H}_3$

If the reaction rate constant is $1\mathrm{.}2\frac{l}{g}$cat.min, the molar feed rate is $10mo\frac{l}{m}in,$ the initial pressure of acetic acid is $10$atm, temperature is $118C,$ and the pressure drop parameter is $0\mathrm{.}01g-1$ then

a$.$ Calculate the conversion of the catalyst if the weight of the catalyst is $80g.$

b$.$ Calculate the conversion if the diameter of the catalyst is increased by twice.

c$.$ Calculate the weight of the the catalyst amount if the conversion is increased to the same conversion as that in problem $b$ but the catalyst size is kept the same size as the original size.