Q$3)$

$x=0\mathrm{.}60$

$[35$ marks$]$

An isothermal plug flow reactor is designed to give $60\%$ conversion of monomer A for a second order liquid phase emulsion reaction $AB.$ Pure monomer $A$ at concentration $2$kmo$\frac{l}{m^3}$ is fed to the reactor at a flow rate of $2\mathrm{.}5m^{3}hr.$ The rate constant for the reaction at a specified operating temperature is $0\mathrm{.}25\frac{m^3}{k}$mol. hr$.$ When the reactor is actually operated on this design, it was found that $30\%$ of the initial reactor behaved as a well$-$mixed reactor while the remaining behaved as a plug flow reactor. Calculate the conversion obtained in such a reactor.