Mixed potential

Abstract

If a typical chemistry graduate were shown a copper wire immersed in a solution of copper sulfate and invited to talk about the factors controlling the potential of that, wire relative to the potential of some reference electrode dipped into the same solution, it is likely that, the answer would be reasonably complete. However, if the same graduate were asked the same question concerning a copper wire dipped into a solution of ferric sulfate, it is probable that the response would be far less satisfactory. The problem, as we see it., is not so much that chemists are confused about the potentials of reacting systems, sometimes called mixed potentials for reasons that will emerge later, but that they know almost, nothing whatsoever about the topic. Two factors have contributed to this state of ignorance. The first is that most university courses give a thorough grounding in electrochemical thermodynamics, but electrode kinetics, which are essential to an understanding of mixed potentials, are treated in a much more cursory fashion. The shadow of Bockris's Nernstian hiatus (1) still lies heavily upon the chemistry curriculum. The second factor is the mathematical emphasis given to electrode kinetics, so often starting with the derivation of the Butler-Volmer equation from absolute rate theory, rather than the experimentally observed current-potential curves (2). In addition, the importance of mixed potentials in a wide variety of practical fields, especially corrosion and hydrometallurgical processing, is often omitted from textbooks of electrochemistry (2,3), and virtually never mentioned in standard texts on chemistry. In this paper, we present a largely experimental approach to the concept of mixed potentials, pointing out the close parallel that exists between equilibrium potentials and mixed potentials. We then discuss a number of important examples of mixed potentials. The Equilibrium Potential of a Redox Couple We will take, as our example of the redox couple, the hex-acyanoferrate(ll)-hexacyanoferrate(III) system on an inert gold electrode. It is convenient to measure the rate of an electrochemical reaction in terms of the current flowing through the electrode. This varies with the electrode potential; a plot of current against electrode potential is known as a polarization curve. Since the shape of the polarization curve generally depends, at least in part, on diffusion of reactants to, or products from, the electrode surface, the design of the electrode and the way the solution is stirred must be such that, convection is a reproducible process. This result is most satisfactorily achieved by constructing the electrode in the form of a disk which can be rotated about its axis under conditions of laminar flow (4). Accordingly, we will suppose that the polarization curves for the hexacyanoferrate system and all other systems considered in this paper are measured at rotating disk electrodes. We will also suppose that the polarization measurements are made in the presence of a large excess of inert electrolyte; sodium hydroxide is a convenient choice for the hexacyano-ferrate redox couple. By carrying out the measurements in the presence of a large excess of indifferent electrolyte compli-1 Author to whom correspondence whould be sent. cations in the form of unwanted potential drops due to a high solution resistance are minimized. The addition of an inert, electrolyte to the solution containing the redox couple under investigation has a second advantage, namely that, by suppressing the electric field in the solution, it reduces the ion migration. Three electrodes are needed for the measurement of a polarization curve: the working electrode, which in our case is a rotating-disk electrode; the counter or auxiliary electrode which carries the current flowing through the working electrode ; and the reference electrode against which the potential of the working electrode is measured. It is common practice these days to make potentiostatic measurements, a poten-tiostat being a device for fixing the potential of the working electrode at some preselected value (5). The current flowing through the electrode is then a unique function of electrode potential. Alternatively, the measurements may be made galvanostatically (i.e,, at some chosen current). However, in this case, the potential is not always a unique function of current. The conventions adopted concerning the sign of potentials and currents are those recommended by IUPAC (6): (1 > The potentials quoted are reduction potentials on the standard hydrogen scale. (2) The anodic (oxidation) currents are considered positive and the cathodic (reduction) currents negative. All current-voltage curves are then displayed on Cartesian coordinates. It should he noted that some discussions of mixed potentials assume all currents are positive (7). However, we believe, and will show below, that there are positive teaching advantages in adhering to the IUPAC convention. Using a potentiostat, the potential-current curve 1(a) given in Figure 1 was obtained for the oxidation of a 0.002 mol dm-* solution of hexacyanoferrate! II). dm' 3 KOH, at a rotating platinum disk electrode. Rotation speed 900 RPM electrode area 6.00 X 10 8 m3. (a) Polarization curve for the oxidation of 2 X 10 3 mol dm'3 hexacyanoferrate(ll) (b> Polarization curve for fhe reduction of 3 X 10-3 mol dm'3 hexacyanoferrate(lll). (c) Polarization curve for a mixture of 2 X W 3 mol dm-3 hexacyanoferrate(ll) and 3 X 10 3 mol dm'3 hexacy-anoferrate(lll) The points marked X were calculated by adding (a) and (b)