A co$-$polymer $A{B}_2$ is to be made from its constituent monomers A and $B$ according to the equation

$A+2B+ClongrightarrowA{B}_2+C$

where $C$ is a catalyst required for the reaction. It is known that the reaction also generates an impurity I at a rate of $0\mathrm{.}001$ moles of $\frac{\text{I}}{?}$ mole of $A{B}_2$ generated. A manufacturing process is set up in such a way that a feed stream containing pure A and B are sent to the reactor along with another stream of catalyst C which contains $400$ ppm of I. It is known that a $5\%$ excess of B has been charged into the reactor. The exit stream from the reactor is sent to a separator which generates a product

stream containing $A{B}_2$ and any unreacted reactants and a catalyst stream containing the recovered catalyst and any impurities.

Assuming a basis of $45$ moles$/$h of product $A{B}_2$ and steady state,

$($a$)$ Without performing any calculations, identify the limiting reagent in this reaction.

$($b$)$ Calculate the composition of the feed stream.

$($c$)$ How much of the catalyst mixture $(C+I)$ is required for the assumed basis?

$($d$)$ Calculate the composition of the catalyst stream leaving the separator

$($e$)$ In order to reduce the cost of the catalyst, it is suggested that all the recovered catalyst be recycled completely back into the reactor. Is there any issue with this set up$?$ If there are any issues, how can they be rectified?

$($f$)$ A modified recycle stream is shown in Figure $3.$ It is desired to maintain the impurity concentration at $400ppm$ at the inlet to the reactor. How much of the fresh Catalyst of I$)$ must be charged to the reactor to maintain this constraint?

$($g$)$ How much of the recovered catalyst is purged?

$($h$)$ If pure catalyst costs $$\frac{125}{?}$ mole and the impure catalyst $(400$ ppm$)$ costs $$\frac{85}{?}$ mole, compute if including the recycle stream is cost effective.

Figure $3$: rolymer syntnesis witn recycie