Saponification of ethyl acetate to produce sodium acetate and ethanol is a well$-$known and well$-$

characterized reaction. Its kinetics are known to be overall second order, with the following

elementary reaction:

$C{H}_3\frac{C}{O}O{C}_2{H}_5+$NaOH$C{H}_3\frac{C}{O}ONa+C_2{H}_{5}OH$

The following data was collected using conductivity measurements by Das and colleagues $($Das$,$

et al$,$ International Journal of Chemical Kinetics, $2011).$

The data were collected using a differential batch reaction with a constant temperature water bath

and continuous stirring.

Your goal is to use this data to design a continuous process that produces $25mo\frac{l}{s}$ ethanol. Your

feed stream is at $298K.$ The inlet molar flow rate is $90mo\frac{l}{s}$ and is equimolar in water, ethyl

acetate, and sodium hydroxide. The volumetric flow rate is $3\mathrm{.}25d\frac{m^3}{s}.$ Calculate the minimum

PFR volume needed for this design specification assuming isothermal operation at $310K.$

Note: you may need to look up thermodynamic properties in a reference book to answer

this question.