Q$1.$ A gas mixture consisting of $50$mole$\%$ of A and $50$mole$\%$ inert at $10$ atmosphere enter the reactor with a flow rate of $6li\frac{t}{s}$ at $144C$

The laboratory measurement of the rate as a function of conversion at $144C$ and $10$ atmospheres are:

$\backslash$table$[[x_A,0,0\mathrm{.}1,0\mathrm{.}2,0\mathrm{.}3,0\mathrm{.}4,0\mathrm{.}5,0\mathrm{.}6,0\mathrm{.}7,0\mathrm{.}8,0\mathrm{.}85],[-r_A,0\mathrm{.}0053,0\mathrm{.}0052,0\mathrm{.}005,0\mathrm{.}0045,0\mathrm{.}004,0\mathrm{.}003,0\mathrm{.}0025,0\mathrm{.}0018,0\mathrm{.}00125,0\mathrm{.}001]]$

If the reaction is carried out in two reactors in series with $40\%$ conversion in the first reactor and $85\%$ overall conversion, estimate the total volume of the two reactors when $($i$)$ the reactors are both mixed flow and $($ii$)$ the reactors are both plug flow.

$[10$ marks$]$