$(35$ points$)$ Ester is hydrolyzed with an excess of caustic soda $($see below$).$ The ester solution is

fed to the first reactor at a rate of $200\frac{L}{m}in$ and concentration $0\mathrm{.}02mo\frac{l}{L},$ while the caustic soda

at $50\frac{L}{m}in$ and $1mo\frac{l}{L}.$ The reaction rate constant of this irreversible second order reaction is $2$

$\frac{L}{\text{m}\text{o}\text{l}\text{m}\text{i}\text{n}}.$ Three CSTR reactors in series are utilized; the volume of the first is unknown, the

second is $2200L$ and the third is $800L.$ Calculate the volume of the first reactor and the conversion

at the outlet of each reactor. Assume final conversion of $95\%$ and use the analytical method.