Propylene oxide $($A$)$ is hydrolysed to propylene glycol according to the equation $.$The reaction is carried out in a batch reactor charged with $8$ gallons of the reaction mixture. If the reactor is operated adiabatically, find the necessary time and the final reaction temperature for $95\%$ conversion. The following data can be used:

$-$ra$=5$x$10\backslash$deg Exp $[-16,000$T$]$ Ca Ibmol $/$ft$^3$ s

$-$deltaHr $=36,400$ Btu$/$lbmol A

Cao $=0\mathrm{.}02$ Ibmol$/$ft$^3$

To $=77$ F$,$ Cp $=0\mathrm{.}9$ Btu$/$lb F

p $=601$b$/$ft$^3$