The following elementary liquid$-$phase reaction occurs in a PFR:

$A+2$BlongrightarrowC$+D$

If the inlet flowrates of the reactants are $F_{A_0}=2mo\frac{l}{s},F_{B_0}=6mo\frac{l}{s},$ with an inlet volumetric flowrate of $v_0=0\mathrm{.}5d\frac{m^3}{s}.$ Determine the following:

$($a$)$ The limiting reactant.

$($b$)$ Set up a stoichiometric table by expressing the concentrations of reactants, products, and inerts.

$($c$)$ If this reaction has a rate constant of $k=0\mathrm{.}15d\frac{m^6}{m}o{l}^{2}s,$ determine the required PFR volume for $60\%$ conversion of the limiting reactant.