Methylamine converts to dimethylamine using a silica$-$alumina catalyst. This is a reversible reaction. $2C{H}_{3}N{H}_2+(C{H}_3{)}_{2}NH{N}_2{H}_4$

The molar flow rate into a packed$-$bed reactor is $23\mathrm{.}6mo\frac{l}{s}$ and the entering pressure is $18$atm. Assume there is no pressure drop or temperature change in the reactor. The reaction rate follows an elementary rate law in terms of partial pressure.

Questions:

$($a$)$ How many kilograms of catalyst is needed to load in a PBR to obtain a conversion of $0\mathrm{.}9$X$?$

$($b$)$ What conversion would be achieved in a $100kg$ PBR with pressure drop and alpha$=0\mathrm{.}0098k{g}^{-1}?$