Consider a reactor with 80% conversion and a separator with 95% efficiency of separation, with the following modifications: - The reaction A + B C has a side reaction A + B D, where the overall single-pass conversion is X and the yield to C is Y (that is, the fraction of the reaction going to C is Y). - D is a product that separates easily from C but not from A and B. Thus, the separation will have two outlets: a stream that is mostly C, and then a stream that contains unreacted A and B, along with most of the D. - The separation efficiency is still defined by a factor S for all components, where S is the fraction of a component that goes to the stream it is meant to (A, B, and D to the recycle stream, and C to the product stream). The feed is 10 kmol/hr each of A and B. The process is to be run at steady state.

a) Determine whether this process is possible as specified. If it is possible, determine criteria for X, Y, and S so that we can achieve an overall conversion to C of Xoverall in terms of X, Y, and S. (Overall conversion to C means the fraction of A that is converted to C in the final product stream). If it is not possible, explain why.

b) A purge is to be implemented for the recycle stream with P as the fraction of the stream to be purged out of the system. Repeat the question in part a), now with the purge stream in place, and P is another variable to be included. If it is possible, determine the combination(s) of S and P that would allow 95% overall conversion to C.