QUESTION $4[10$ MARKS$].$

$($a$)$ For an irreversible first$-$order liquid$-$phase reaction $($ CAO$=10mo\frac{l}{L})$ conversion is $90\%$ in a PFR$.$ If half of the stream leaving the reactor is recycled to the reactor entrance, and if the throughput to the whole reactor$-$recycle system is kept unchanged, what does this do to the concentration of reactant leaving the system?

$($b$)$ At present conversion is $\frac{2}{3}$ for our elementary second$-$order liquid reaction $2A$

$--->2$R when operating in an isothermal PFR with a recycle ratio of unity. What will be the conversion if the recycle stream is shut off?