$1.(35$ 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 $200$ L$/$min and concentration $0\mathrm{.}02$ mol$/$L$,$ while the caustic soda

at $50$ L$/$min and $1$ mol$/$L$.$ The reaction rate constant of this irreversible second order reaction is $2$

L$/($mol min$).$ Three CSTR reactors in series are utilized; the volume of the first is unknown, the

second is $2200$ L and the third is $800$ L$.$ 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.