$($a$)$ Explain cataly'st deactivation by 'sintering'. Derive an equation for conversion as a function of time for the first order reaction $AB$ which is carried out isothermally in a batch reactor on a catalyst which is decaying as a result of sintering$.$

$)=(5$

$($b$)$ "The most appropriate reactor $($or reactor systems$)$ for obtaining best product distribution can be found from $$ versus $C_A$ curve" $-$ How?