On the determination of limiting current density from uncertain data

Abstract

The technique for determining the limiting current from I/E curves is normally simple. However, in the absence of a clearly de®ned plateau it is not straightforward. In a recent study of the concentration of nitric acid by electro-electrodialysis (membrane electrolysis), Robbins [2] plotted the normalized resistance E=I†= E=I†max against the reciprocal current density (1/I) corrected for catholyte acid concentration, in order to elucidate the cathodic reactions. He based his plot upon the work of Kuppinger et al. [3] but was unable to ®nd a theoretical basis for the apparent relationship between the minimum point in the curves and the mass transfer coecient. The purpose of this paper is twofold. First, it is to reintroduce the E=I against 1/I plot as a basis for the determination of the limiting current. Second, it is to show that the previously presented method using this approach [4] is mathematically incorrect. In fact, the authors never justi®ed their mathematical methodology but stated that the point at which the negative slope cuts the positive slope in the curve E=I against 1/I , is designated as a `limiting current density' because of its apparent relation (our emphasis) to di€usion. The point of intersection used by them will be clearly de®ned later and contrasted with other methodologies. Our proposed approach was tested for the reduction of oxygen and Fe(CN)3y 6 . The reduction of ferric cyanide ions was carried out in a commercially available laboratory electrolyser, the FM01-LC cell supplied by ICI, and oxygen reduction was carried out in a conventional ow cell constructed in our laboratory, both on a reticulated vitreous carbon electrode (RVC).