A liquid$-$phase reaction takes place in a CSTR of volume $V_R$ in the presence of a large excess of reactant B$.$ Assume the reactor achieves $50\%$ conversion of A at steady$-$state.

$A+BC$;$,r=k{C}_A^2{C}_B$

a$)$ What is the steady$-$state conversion if the original reactor is replaced by two CSTR$\text{'}$s of volume $\frac{V_R}{2}$ in series?

b$)$ What is the steady$-$state conversion if the original reactor is replaced by three CSTR$\text{'}$s of volume $\frac{V_R}{3}$ in series?

c$)$ What is the conversion achieved if the original reactor is replaced by a plug$-$flow reactor of volume $V_R?$