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

Typical custom and commercial hanging mercury drop electrodes have the geom etry of a spherical cap formed by the plane of the lower surface of the ele ctrode holder cutting off the top of the drop, To conduct accurate quantita tive measurements by voltammetry, it is necessary to be able to account for the effects of solution resistance, R-u. A method of determining the solut ion resistance is proposed and tested. The method involves making measureme nts of a test reaction (in this case, oxidation of ferrocene) by cyclic vol tammetry at scan rates where resistance effects are important and at more t han one concentration. When the data are analyzed by digital simulation, it is found that only one value of R-u will provide adequate matches between simulation and experiment at all concentrations. An approximate equation ha s been derived that allows calculation of R-u from the dimensions of the sp herical-cap electrode and the solution resistivity. The calculated values o f R-u for electrodes of three different sizes agreed well with the measured values. Error analysis was performed for a particular measurement, the det ermination of the standard heterogeneous electron-transfer rate constant, k (s), by cyclic voltammetry, and it was shown that uncertainty in R-u puts a n upper limit of about 1 cm/s for the determination of k(s) with the hangin g mercury drop electrodes used in this study.