5-20. Concentrations of Reactive Solutes in Suspensions This problem concerns dilute suspensions of spheres in which a solute reacts irreversibly within the particles. It is desired to determine the steady concentration of the solute, inside and outside a sphere, created by an imposed concentration gradient in the bulk solution. As in Example 5.8-4, the spheres are of radius a, the sphere/liquid partition coefficient is K, and the imposed gradient at r= is C=Gez. There are no reactions in the liquid and the coordinates are as in Fig. 5-11. (a) Suppose that the reaction is zeroth order, with a volumetric rate of consumption k0. Show that the internal concentration (C) and external concentration (C) can each be constructed using linear superposition as C(r,)=C(r,)+h(r),C(r,)=C(r,)+H(r) where C and C are the corresponding solutions for an unreactive solute. Determine h(r) and H(r) and show that the concentration in the liquid is C(r,)=A+Gr+ra3(rG3Dk0) where is defined in Eq. (5.8-57). (Hint: The results in Example 5.8-4 make it unnecessary to repeat the solution for the unreactive case.) (b) Assume now that the reaction is first order, with a rate constant k1. Show that no solution exists for this case