$[70]$ The elementary gas reaction $2AB+C$ is taking place at constant temperature and pressure in a

PFR reactor. Pure A enters the reactor with $C_{A_0}=2\frac{\text{m}\text{o}\text{l}}{L}.$ Rate constant $k_A=5(\frac{L}{\text{m}\text{o}\text{l}*s}).$ The volumetric

flowrate is kept constant $v_0=267(\frac{L}{s})$

Determine the volume of the reactor in order to achieve $80\%$ conversion of A$.($Follow $5$ steps: mole

balance, rate law, stoichiometry, combine and solve$)$