Develop a model equation, in final, integrated algebraic form, to determine the total transfer rate of ethylene WA, units mole A/time, product of flux and surface area) into the cylindrical catalyst pellet. The model equation should include terms for the diffusion coefficient (D Ae), the dimensions of the pellet (R_o, R₁, L), and concentration of ethylene. If the required transfer rate of ethylene. If the required transfer rate of ethylene (A) into a single pellet is 9.238 X 10^-6 gmole/s, what is the required R₁, in units of cm, if the catalyst surface is fixed at R_o = 0.5 cm? It will also be necessary to calculate the effective diffusion coefficient as part of the problem solution.