The reaction for the catalytic partial hydrogenation of benzene to cyclohexene has of the form: C$\_6$H$\_6+2$H$\_2->$ C$\_6$H$\_10.$ Reactants are fed to a CSTR at $6$ atm and $170$oC$.$ The volumetric flow rate of the feed is $52$ L$/$min and hydrogen

is fed at twice the molar rate of benzene. The rate constant with respect to benzene is $45$ mol$/($kg catalyst.min.atm$3)$ and the activation energy is $80$ kJ$/$mol$.$

Finally, you are told that the system is isothermal and isobaric.

a$)$ Can you assume that the volumetric flow rate is constant in the system? Why?

b$)$ Find the catalyst weight required to obtain a conversion of $80\%.$