The reaction $AB$ is carried out isothermally in liquid phase in a flow reactor. The entering volumetric flow rate is $10\frac{d{m}^3}{hr}.$ The inlet concentration, $C_{A0},$ is $0\mathrm{.}5mo\frac{l}{d}{m}^3.$ Calculate the volume necessary for both a PFR and a CSTR necessary to achieve $99\%$ conversion of species A when the reaction rate is given by:

a$.-r_A=k$ with $k=0\mathrm{.}05\frac{\text{m}\text{o}\text{l}}{d{m}^3*hr}$

b$.-r_A=k{C}_A$ with $k=0\mathrm{.}0001s^{-1}$

c$.$ Extend the work of parts a$.$ and b$.$ to calculate the time to achieve $99\%$ conversion of species $A$ in a batch reactor of $1000d{m}^3$ with the same initial concentration.