$7.$ Consider the autocatalytic reaction:

$2$A $->$ B $+$ C

where $-$rA$=$k$1$ C A$2+$k$2$ C ACB

with k $1=1\mathrm{.}0$x$10-6$ L$/($mol$$s$)$ and k$2=75\mathrm{.}0$x$10-6$ L$/($mol$$s$).$

We want to use two reactors $($a PFR and a CSTR$)$ connected in series to convert $95\%$ of A

into B$.$ We also want to minimize the total reactor volume we will use. The reaction will be

carried out isothermally with an initial feed to the first reactor of pure A at a rate of $10$

mol$/$s$.$ Use the Levenspiel diagram to determine the volume and the arrangement of the

reactors in order to minimize the total reactor volum