In the theory of the chemical reaction controlled (macroscopically) by diffusion it is assumed that the concentration gradient is discontinuous at the reaction zone. The theory works best for fast reactions for which the zone of reaction is extremely thin. Since reaction rates are finite, the zone of reaction must in reality have finite thickness and possess a structure with respect to the concentration and its gradient.
In this paper, the differential equation describing the concentration distribution in the reaction zone for very fast, but not infinitely fast, reactions is set up for second-and third-order kinetics. Similarity transformations which eliminate all dimensional constants are given for both sets of equations and boundary conditions. A solution obtained for the isothermal second order case using an analog computer is given. A reaction zone thickness is defined and used to establish the conditions under which transport from a dissolving, reacting sphere is diffusion controlled. A numerical calculation is given for the case of a CO2 bubble dissolving in an hydroxide solution.
By measuring the thickness of the reaction zone it should be possible to estimate the rates of reactions in solution. An example is given for the reaction occurring in a capillary connecting reservoirs containing solutions of the two reactants.