H$.$ D$.$ Martin, T$.$ Urbandk, and R$.$ Braun studied the kinetics of the gas phase pyrolysis of barrelene $[$bicyclo$(2\mathrm{.}2\mathrm{.}2)$octa$-2,5,7-$triene$]($B$)$ to benzene and acetylene.

$B{C}_6{H}_6+C_2{H}_2$

The following data are characteristic of the reaction as it occurs in a constant$-$volume batch reactor at $493K$ :

These researchers also indicated that for temperatures from $483$ to $523K,$ the activation energy for this reaction is $41\mathrm{.}7kcalmo{l}^{-1}.$ Use these data to ascertain the temperature at which a plug flow reactor should be operated if one desires to decompose $98\%$ of a pure barrelene feedstock when the barrelene enters the reactor at $2$atm. Barrelene is to be supplied at a volumetric flow rate of $1000f{t}^{3}mi{n}^{-1}$ to a

tubular reactor whose volume is $100f{t}^3.$ Comment on your answer.

What is the mean residence time of a fluid element in the reactor for operation at this temperature?