The elementary liquid$-$phase reaction A $+$ B $->$ C is carried out at $300$ K$.$ The volumetric flow rate of the feed is $10$ L$/$min with concentrations of A and B being $1$ M$,$ each. The rate constant at $300$ K is $0\mathrm{.}07$ L$/($mol$$min$).$

a$)$ The reaction is carried in a $200-$L CSTR and $44\%$ conversion is achieved. A $800-$L PFR is placed in series after the CSTR$.$ What is the conversion at the exit of the PFR$?$

b$)$ Assume that the $200-$L CSTR and the $800-$L PFR are connected in parallel instead of in series. If the feed is split evenly to each reactor, what is the conversion achieved in the overall system?