Evaluation of uncompensated solution resistance for electrodes with spherical-cap geometry

Typical custom and commercial hanging mercury drop electrodes have the geometry of a spherical cap formed by the plane of the lower surface of the electrode holder cutting off the top of the drop. To conduct accurate quantitative measurements by voltammetry, it is necessary to be able to account for the effects of solution resistance, Ru. A method of determining the solution resistance is proposed and tested. The method involves making measurements of a test reaction (in this case, oxidation of ferrocene) by cyclic voltammetry at scan rates where resistance effects are important and at more than one concentration. When the data are analyzed by digital simulation, it is found that only one value of Ru will provide adequate matches between simulation and experiment at all concentrations. An approximate equation has been derived that allows calculation of Ru from the dimensions of the spherical-cap electrode and the solution resistivity. The calculated values of Ru for electrodes of three different sizes agreed well with the measured values. Error analysis was performed for a particular measurement, the determination of the standard heterogeneous electron-transfer rate constant, ks, by cyclic voltammetry, and it was shown that uncertainty in Ru puts an upper limit of about 1 cm/s for the determination of ks with the hanging mercury drop electrodes used in this study.