Two different shapes are being considered for a catalyst particle: spherical and cylindrical. The particle will be made up of three layers, with either a spherical or cylindrical inert solid core coated with a catalyst and surrounded with a permeable outer layer. The outer layer will be made up of a highly porous material with a void fraction of $0\mathrm{.}60.$ The particle will be suspended in a gas stream of mixture A and $B$ maintained at a constant concentration of $c_{A,\text{i}\text{n}\text{f}}.$ A diffuses into the particle and reacts at the surface of the catalyst in the heterogeneous reaction

$AB$

with surface reaction rate constant $k_s.$ Compare the flux and mole fraction of species $A$ at the catalyst surface for a reaction carried out at $300C$ and $1\mathrm{.}0$atm with $k_s=2\mathrm{.}0c\frac{m}{s},D_{AB}=0\mathrm{.}30c\frac{m^2}{s},$ and $50$mole$\%$A maintained in the gas phase for each particle shape. The distance from the center of a radial cross section of the particle to the catalyst surface is $0\mathrm{.}3cm,$ and the outer radius is $0\mathrm{.}5cm.$ If needed, assume the tortuosity of the porous material is $1\mathrm{.}65.$ Consider only radial diffusion.