$(30$ points$)$ The conversion of an irreversible first$-$order, liquid$-$phase reaction, taking place in

a plug flow reactor $($PFR$)$ of $500$ liter capacity is $50\%.$ In order to increase conversion, a $300$ liter

mixed flow reactor $($CSTR$)$ is installed upstream of $($before$)$ the PFR$.$ What is the exit

conversion in the new system?