The liquid phase reaction

$2$A $->$P

was found to follow the rate law $($at $70$ oC$)$:

$-$r$1=0\mathrm{.}002$ CA

$2$

$($mol of A $/$ L$.$ s$)$

It is thought that the activation energy of this reaction is $176$ J$/$mol $($of A$).$ The feed is

$10\%($molar fraction$)$ of A in a solvent S$,$ a solution with total concentration $44\mathrm{.}2$ mol$/$L;

the solvent is inert and the feed is at room temperature, $25$ oC$.$

a$.$ A CSTR of $1,000$ L is available for the reaction. If the flow rate is such that

whatever the temperature of the reactor we ensure a conversion of $85\%$ of A$,$

what will be the temperature of operation in adiabatic mode?

$[60$ Marks$]$

b$.$ And what flow rate gives us the conversion of $85\%$ at that temperature?

$[40$ Marks$]$

Data:

Specific heats:

A: $377$ J$/$mol

S: $47$ J$/$mol

P: $215$ J$/$mol

Heats of formation at $25$ oC:

A: $17$ kJ$/$mol

P: $-20$ kJ$/$mol