$($a$)$ Differentiate the experimental reactors that are used to obtain kinetic data of catalytic reactions.

$($b$)$ With neat plots discuss the differences and limits for negligible and for strong pore diffusion resistance.

$($c$)1\frac{m^3}{h}$ of a gas containing A $)=(2\frac{\text{m}\text{o}\text{l}}{m^3}$ is fed to a plug flow reactor with recycle loop $(0\mathrm{.}02m_3$ loop volume, $3kg$ of catalyst$)$ and the composition of the exit stream from the reactor system is $0\mathrm{.}5$mol$\frac{A}{m^3}.$

Find the rate equation for the decomposition of A for:

$($i$).$ Very large recycle, $A3R,n=2$ and feed contains $50\%$A and $50\%$ inerts.

$($ii$).$ Very large recycle, $A3R,n=1,$ feed contains $50\%$A and $50\%$ inerts.

$($iii$).$ No recycle, $A3R,n=2,$ feed contains $25\%$A and $75\%$ inerts.

$($iv$).$ Very large recycle, $AR,n=\frac{1}{2}$