II$)$ The following reversible gas$-$phase reaction is carried out isothermally in a plug$-$flow reactor $)=(1\mathrm{.}00ctm.$

$A2B$

This is an elementary reaction and the forward reaction rate constant $(k_A)$ at $400K$ is $3\mathrm{.}00{10}^{-3}(s^{-1}).$ The equilibrium constant $(K_s)$ at $400K$ is $1\mathrm{.}00{10}^2\frac{\text{m}\text{o}\text{l}}{m^3}.$ The feed is solely composed of A and $B$ and the molar flow rates of A and $B$ are $5\mathrm{.}00\frac{\text{m}\text{o}\text{l}}{s}$ and $1\mathrm{.}00\frac{\text{m}\text{o}\text{l}}{s},$ respectively. The equation of state for the ideal gas can be applied. $($The gas constant $(R)=8\mathrm{.}314\frac{J}{\text{m}\text{o}\text{l}*K})$

calculate the volume of PFR to achieve the conversion of $80\%$ of the equilibrium conversion