$2.$An autocatalytic $(($iquid$)$ phase reaction is to be carried out in aqueous solution in a mixedflow reactor connected to a plug$-$flow reactor in series. The first mixed flow reactor will operate at the maximum reaction rate. The reaction stoichiometry and rate expression are given betow.

If the system is to operate at $50C$ under isothermal conditions, determine the minimum reactor volume $(V_{MFR}+V_{PFR})$ to achieve $80\%$ total conversion? The feed rate of $A$ to the first reactor is $0\mathrm{.}3$mol$\frac{e}{sec}$ and the initial concentration of $A$ in the feed stream is $2$kmo$\frac{l}{m^3}.$