SHOW POLYMATH CODE!! Ethyl acetate $($C$)$ is extensively used as a solvent and can be formed by the vapor$-$phase esterification of acetic acid $($A$)$ and ethanol $($B$)$

$A(g)+B(g)C(g)+H_{2}O(l)$

The reaction was studied using a micro$-$porous resin as a catalyst in a packed bed reactor. The reaction is firstorder in ethanol and pseudo$-$zero$-$order in acetic acid. The total molar feed rate is $10mo\frac{l}{m}in,$ the initial pressure is $10$atm, the temperature is $118C,$ and the pressure drop parameter, $,$ is $0\mathrm{.}01g^{-1}.$ For an equimolar feed of acetic acid and ethanol, the specific reaction rate is about cat $*min.$

a$)$ Assuming that the liquid water product does not contribute to the gas pressure, gas$-$phase reaction, gas concentration, or other gas$-$phase conditions in this PBR$,$ determine the catalyst weight necessary to achieve $90\%$ conversion. Use Polymath to evaluate. Plot $x,y,$ and $f=\frac{v}{v_0}$ as functions of catalyst weight down the packed$-$bed reactor.

b$)$ Calculate the maximum weight of catalyst that one could use and maintain an exit pressure above $1$atm.