Problem $1(5$ points$)$

The elementary reversible liquid phase reaction: $A+$Bharr$2C$ occurs in an isothermal mixed flow reactor operated at $400K.$ The feed is equal molar in A and $B$ with the total flow rate of $510$mol$\frac{e}{m}in$ and the initial concentration of A equal to $3$ mole$/$liter$.$ Calculate the reactor volume needed to achieve $90\%$ of the equilibrium conversion.

Additional information for the problem:

$k_{+}=0\mathrm{.}59$ liter$/($mole$*($:min