Develop equations to determine plug flow reactor size for 50% conversion of reactant A. The reaction is gas-phase, in an isothermal PFR, and is at 5.0 atm pressure and 55°C. The volumetric flow rate of the feed is 50 L/min.

A + 2B → 2D r_{A} = -2.5C_{A}^{0.5}C_{B} mol L^{-1} min^{-1}

Feed mole fractions: y_{A} = 0.2, y_{B} = 0.5, y_{C} = 0.3 (C is an inert.)