Problem $1.$ Effect of Catalyst Particle Shape on the Observed Rate.

The production rate of a heterogencously catalyzed, first$-$order reaction in a $0\mathrm{.}75-cm$ diameter spherical pellet is $R_A=-3\mathrm{.}25{10}^{-5}mo\frac{l}{c}{m}^3-s$ when the catalyst is exposed to pure, gaseous $A$ at a total pressure of $1$atm and a temperature of $525K.$ The activation energy $E_A=18,600ca\frac{l}{m}ol.$ Furthermore, the effective diffusivity of $A$ in the pellet is $D_{\text{K}\text{A}\text{e}}=0\mathrm{.}009c\frac{m^2}{s}$ at $525K$ and the mean pore size is small enough that the gaseous diffusion is primatily controlled by the Knudsen regime. The bulk fluid and the extemal surface concentrations can be assumed the same.

Find the production rate if the catalyst is changed to a cylindrical pellet that is $0\mathrm{.}5cm$ in diameter and has an overall length of $1\mathrm{.}0cm,$ and if the temperature is increased from $525K$ to $600K.$