The liquid$-$phase reaction A $+3$B $->$C is carried in a CSTR$.$ The reaction rate is given by the equation r $=$ kc$\_$Ac$\_$B

with the rate constant equal to $0\mathrm{.}023$ Lmol$-1$min$-1$

$.$ The concentration of component A in the feed is $2$ molL$-1$

and component B is fed at $30\%$ excess.

a$)$ What will be the space time to obtain a conversion of $75\%?$

b$)$ What is the required reactor volume to achieve this conversion if the volumetric flow rate is $500$L$/$min$?$