$(25$ marks$)$ A gas phase hydrogenation reaction $A+H_{2}C$ takes place in a CSTR$,$ using mixing and

the presence of an inert to keep the temperature and the concentration of hydrogen within safe limits$.$

The feed contains equal amounts of three components: $A,H_2,$ and the inert, at a total molar flow rate

of $2\mathrm{.}1mo\frac{l}{m}in.$ The reaction is first order with respect to A and $H_2,$ and occurs at constant pressure.

a$.$ Determine the mean residence time in the reactor required to obtain $75\%$ conversion of $A,$ and

the corresponding inlet volumetric flow rate, given that the reaction rate constant is $0\mathrm{.}75Lmo{l}^{-1}$

$mi{n}^{-1},$ and the feed concentration of $A$ is $0\mathrm{.}50mo\frac{l}{L}.$

b$.$ Assuming the same residence time as calculated in $($a$),$ would the conversion obtained from the

segregated flow model $($with the RTD for back$-$mixed flow$)$ be greater than, less than, or equal to

$75\%?$ Either a calculation or discussion with justification is acceptable.

$($a$)$ ANSWER: $24$min;$1\mathrm{.}4\frac{L}{m}in$