QUESTION $1[25$ Marks$]$

Ethyl acetate is an extensively used solvent and can be formed by the vapor$-$phase esterification of

acetic acid and ethanol.

$C{H}_3\frac{C}{O}OH+C_2{H}_{6}O{C}_4{H}_8{O}_2+H_{2}O$

The reaction was studied using a microporous resin as a catalyst in a packed bed reactor isothermally

at $223C$ and $10$atm. The reaction is second order in acetic acid $(CH3\frac{C}{O}OH)$ and zero$-$order in ethanol

$(C2H6O).$ The total volumetric feed rate is $25d\frac{m^3}{m}in,$ the initial pressure is $10$atm, and the pressure$-$

drop parameter, $,$ equals $0\mathrm{.}01k{g}^{-1}.$ For an equal molar feed rate of acetic acid and ethanol, the

specific reaction rate is about $1\mathrm{.}3d\frac{m^3}{k}g-$cat$-$min.

Calculate the maximum weight of catalyst that one could use to maintain an exit pressure of $1$atm.

Write out the CRE algorithm $($steps$)$ and then solve these equations analytically to determine the

catalyst weight necessary to achieve $20\%$ conversion.