In this problem you will determine the conversion of a gas phase reaction with the following

stoichiometry: $A2B.$ This reaction is irreversible and first order in A with a reaction

rate constant of $k=0\mathrm{.}0035\frac{\text{m}\text{o}\text{l}\text{A}}{(sPakgcat)}.$ The reaction takes place in a $316$ stainless steel pipe.

The pipe is filled with catalyst with a bulk density of ${}_{\text{b}\text{u}\text{l}\text{k}}=1,100$kgca$\frac{t}{m^3}.$ The feed is

pure A with an initial flowrate of $5\mathrm{.}34\frac{m^3}{s}.$ The reactor operates at a pressure of $5\mathrm{.}2{10}^{5}Pa$

and the reactor pressure drop is negligible. Assume the reactor is isothermal at $400K.$ The

ideal gas law constant is $R=8\mathrm{.}314Pa\frac{m^3}{\text{m}\text{o}\text{l}\text{K}}$ You must show all your work. Do the

following:

a$)$ Sketch the reactor showing the control volume and all variables that you will use in the

derivation.

b$)$ State the assumption$($s$)$ that you will use in this derivation.

c$)$ Derive the unsteady state mole balance.

d$)$ Construct a stoichiometric table for this reaction based on the conversion of $A.$

e$)$ Determine the weight of catalyst required to reach a steady$-$state conversion of $A$ of $0\mathrm{.}8.$

Show all of your work including a sample calculation of any root finder that you use in your

calculator.