Analytical solution for the steady-state diffusion and migration involving multiple reacting ions - Application to the identification of Butler-Volmer kinetic parameters for the ferri-/ferrocyanide redox couple

An analytical solution for the one-dimensional steady-state transport of ions in an electrolyte towards a planar electrode is obtained. This electrolyte contains more than one electroactive species and any number of non-reacting species. The mass and charge transport equations give rise to an implicit form of a set of non-linear algebraic equations which must be solved numerically. The solution is generally applicable and can deal with any kind of overpotential relation at the electrode. The analytical solution is used to determine the mass and charge transport parameters for the Fe(CN)(6)(3-/4-) redox couple in a KCl solution for two different electrolyte concentrations (0.03 M Fe(CN)(6)(3-/4-)+1.0 M KCl and 0.005 M Fe(CN)(6)(3-/4-)+0.2M KCl). The agreement between the experimental and analytical current densities is perfect for both electrolyte solutions under investigation. It is shown that, although an excess of supporting electrolyte is added, neglecting migration results in an under/overestimation of the diffusion coefficient of ferri-/ferrocyanide of 3 to 5% for the Fe(CN)(6)(3-/4-)/KCl ratios investigated. Furthermore, a mathematical background is given for the wide range of values found in the literature for the charge transfer coefficient and the rate constants of the ferri-/ferrocyanide redox system. The same approach can also be useful for other systems, as to parameter identification procedures. (C) 1997 Elsevier Science S.A.