The reaction in gas phase: A $->$ R $+$ S$,$ is of first order with respect to reactant the A and its kinetic constant can be expressed as:

ln k $=34\mathrm{.}34-34222/$ T $($k in s$-1,$ T in K$)$

It is desired to feed $8000$ Kg$/$h of pure A $($M: $58$ g$/$mol$)$ to an adiabatic tubular reactor in steady state. If the inlet temperature is $1035$ K and the pressure is maintained

constant at $162$ kPa, what reactor volume is needed to achieve a conversion of

$20\%$ for A$.$

Data:

A: H$298=-216\mathrm{.}67($kJ$/$mol$)$

CpA $=26\mathrm{.}63+0\mathrm{.}183$ T $45\mathrm{.}8610-6$ T$2($J$/$mol K$)$

R: H$298=-61\mathrm{.}09($kJ$/$mol$)$

CpR $=20\mathrm{.}04+0\mathrm{.}0945$ T$-30\mathrm{.}9510-6$ T$2($J$/$mol K$)$

S: H$298=-74\mathrm{.}81$ kJ$/$mol

CpS $=13\mathrm{.}39+0\mathrm{.}077$ T $18\mathrm{.}7110-6$ T$2($J$/$mol K$)$