N$-$Butane, C$4$H$10,$ is to be isomerized to i$-$butane in a plug$-$flow reactor. This elementary reversible

reaction is to be carried out adiabatically in the liquid phase under high pressure using essentially

trace amounts of a liquid catalyst that gives a specific reaction rate of $31\mathrm{.}1$ h$1$ at $360$ K$.$ The feed

enters at $330$ K$.$

a$)$ Calculate the PFR volume necessary to process $163$ kmol$/$h at $70\%$ conversion of a mixture $90$

mol $\%$ n$-$butane and $10$ mol $\%$ i$-$pentane.

b$)$ Plot and analyze X$,$ Xe

$,$ T$,$ and rA down the length of the reactor.

c$)$ Calculate the CSTR volume for $40\%$ conversion