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

acid and ethanol.

$C{H}_3-C^O\frac{-}{O}OH+C{H}_{3}C{H}_{2}OHlongrightarrowC{H}_3-C^O-OC{H}_{2}C{H}_3+H_{2}O$

The reaction was studied using a microporous resin as a catalyst in a packed$-$bed microreactor $[$Ind$.$ Eng.

Chem. Res., $26(2),198(1987)].$ The reaction is first order in ethanol and pseudo zeroth order in acetic

acid $(-r_A=k{C}_A).$ The total volumetric feed rate is $25d\frac{m^3}{m}in,$ the initial pressure is $10$atm, the

temperature is $223C,$ and the pressure drop parameter, $,$ is $0\mathrm{.}01k{g}^{-1}.$ For an equimolar feed rate of

acetic acid and ethanol, the specific reaction rate is roughly $1\mathrm{.}3d\frac{m^3}{k{g}_{\text{c}\text{a}\text{t}}*min}.$

a$.$ Calculate the maximum weight of catalyst that one could use and maintain an exit pressure

above $1$atm.

b$.$ Write out the CRE algorithm and then solve these equations analytically to determine the catalyst

weight necessary to achieve $90\%$ conversion.

c$.$ Write a python program to plot and analyze conversion $(x),$ pressure ratio $(p=\frac{P}{P_0}),$ and

volumetric flowrates $(\frac{v}{v_0})$ as a function of catalyst weight down the packed$-$bed reactor.

d$.$ Neglecting pressure drop, re$-$analyze $x$ as a function of catalyst weight down the packed$-$bed

reactor. How does this result compare with part c$.?$

e$.$ How would the conversion from part $c.$ be affected if we pack the catalyst with the same density

and total weight in a longer reactor with half the pipe diameter?