Extend the Smoluchowski model for diffusion into a reactive sphere of radius a, by assuming that the reaction rate at the spherical surface is proportional to concentration of incoming solute at the surface. Letting K be the first order reaction rate constant, per unit area at the surface (cm/sec), derive an equation for the steady rate of reaction, given a source of diffusing reactant of concentration Co at infinite distance from the reactive sphere. Derive a dimensionless parameter that determines whether flux is diffusion or reaction limited.