An elemental isomerization $AB$ is being carried out in a real reactor with the following RTD function.

At $350K,$ the conversion predicted by the tanks$-$in$-$series model was $60\%.$

$($a$)$ How many tanks in$-$series have been used to model this reactor?

$($b$)$ What will be the conversion, if the reaction is carried out isothermally at $370k.$ From the literature, we know the activation energy for this reaction is $25$kca$\frac{l}{m}ol.$ We also assume the temperature will not affect the RTD pattern of the reactor.