Voltammetry of labile metal—complex systems with induced reactant adsorption. Theoretical analysis for any ligand-to-metal ratio

The validity of the hypothesis of ligand excess is discussed for the voltammetric reduction of a metal ion (M) in the presence of a ligand (L). The following basic assumptions are made: (i) formation of the electroinactive ML complex, (ii) equal mobility of species M, ML and L, (iii) reversible charge transfer, (iv) labile complex and (v) Langmuirian adsorption of the ligand and the complex. The model proposed is solved rigorously for normal pulse polarography (NPP) in the four possible cases assuming either ligand excess or ligand deficiency or either adsorption or non-adsorption. For the case without adsorption, the assumption of ligand excess affects only the increasing part of the NPP wave independent of the total ligand-to-metal ratio. Then (I_NNP)_lim has the same value for both ligand excess and ligand deficiency while E differs, thus preventing the use of the DeFord—Hume method to obtain the stability constant. An analytical expression for E is performed, which allows the evaluation of the stability constant at any total ligand-to-metal ratio and provides a quantitative estimation of the error made by applying the classical procedure assuming ligand excess. In the presence of adsorption, the assumption of ligand excess modifies the whole wave. The discrepancy between the currents obtained from the hypothesis of ligand excess with respect to that with ligand deficiency is even higher for the case with adsorption than for the case without adsorption.