Theory of the diffuse layer when a strong acid is reduced without supporting electrolyte

The value of the limiting current for reduction of a strong acid, HA, without supporting electrolyte is known to be twice the current value in a solution containing a supporting electrolyte. This enhancement is ascribed to acceleration of the flux of H+ toward the electrode by the electric field. Since the electrical neutrality equates [A−] with [H+], the depletion of H+ by the electrode reduction decreases also [A−] to zero. Consequently, no ion may be present near the electrode, indicative of infinite solution resistance. This is inconsistent with the experimental observation that the voltammogram is sigmoid. The inconsistency is discussed in this report by considering the Nernst–Planck equations and Poissonʹs equation for H+ and A− at the hemi-spherical electrode under the steady-state condition. Because of strong non-linearity in the differential equations, numerical solutions are obtained by combining the Newton method and the iterative method for simultaneous equations. They demonstrate the presence of two domains of collapse of the electrical neutrality. One domain close to the electrode has the relation [A−]>[H+] owing to the electroreduction of [H+], whereas the other domain further from the electrode has the opposite relation owing to the electrostatic effect. The non-zero value of [A−] is responsible for a finite value of the solution resistance and hence enables the voltammetric measurement to be made without a supporting electrolyte.