The liquid phase reaction A $+$ B $->2$C at $70$C takes place in a stirred tank flow reactor $($RATB$)$ where the conversion to A is $65\%.($RATB$)$ where the conversion to A is $65\%.$ The reaction proceeds in a pseudo$-$first$-$order with kA $=0\mathrm{.}257/$hour$.$ The reactor feed concentration was $1\mathrm{.}5$ kmol$/$m$3.$

a$.$ Determine the reactor volume required for a production capacity of $1140$ kg$/$hr$,$ if compound A reacts $75\%($Note: for safety reasons liquid only fulfills $80\%$ of the reactor capacity$).$

Known BM C $=30$ kg$/$kmol

b$.$ Assuming the reactor is cylindrical, determine the diameter and height of the react or $($use theratio of diameter to height $1$: $2)$