Converting Reference Electrode Potentials

When reading the literature we often find that the reported reference electrode is different to the one we've used for an experiment. Converting between different reference electrodes isn't difficult but it is slightly error prone. For example, if a potential is measured as being at +0.1 V (vs SCE) and we want to know what potential this is against a saturated Ag/AgCl electrode, how can we do the conversion? At 25^oC the SCE is +0.241 V (vs SHE) and the Ag/AgCl Sat. is +0.197 V (vs SHE). The simplest way forward is to draw out the different potential scales, as shown at the bottom of this article. This way we're less likely to make a mistake when adding and subtracting the relevant potentials. If you click 'convert' on the calculator below, the measured potential is marked up on the scale and we can see that for the above problem the converted potential is +0.144 V (vs Ag/AgCl Sat.) i.e. 0.1 V +0.241 V -0.197 V = +0.144 V.

Just be aware that the reported electrode values for different systems can vary a little in the literature. This seems to be especially true for mercury based electrodes. Consider the Mercury/Mercury Sulfate (Sat.) electrode, where Bard and Faulkner[1] give a value of +0.64 V vs SHE and The Handbook of Analytical Chemistry[2] gives a value of +0.65 V vs. SHE. The value of +0.64 V vs. SHE seems to be consistent (< 2 mV) with recent experiments on the proton/hydrogen redox couple. These discrepancies for the Mercury/Mercury Sulfate (Sat.) electrode are not ideal, but if we compare these two texts for their reported values of the Hg/HgO (0.1 M NaOH), the numbers don't even seem to vaguely agree. The Analytical Handbook reports a value of +0.165 V (vs NHE), whereas Bard and Faulkner give a value of 0.926 V (vs NHE)! Neither of these values actually seem to be completely accurate and if you are using a Hg/HgO reference electrode, I'd suggest you use this ACS Catalysis[3] paper to determine the 'best' potential for your electrode. For most other reference electrodes Ives and Janz[4] tends to be the primary literature source.

This variability in a standard electrode potential also arises in some other important cases. For example, consider the difference between the 'standard hydrogen electrode' (SHE) and the 'normal hydrogen electrode' (NHE). These two electrodes are often assumed to have exactly the same potential, but, this is not quite correct. For both the SHE and the NHE, the electrode potential is controlled by the proton/hydrogen redox couple: $$\mathrm{H^+} + e^- \rightleftharpoons \frac{1}{2}\mathrm{H_2}$$ However, the two reference potentials differ in their definitions of the proton solution phase composition.[5] The SHE is a hypothetical situation where the proton is at unit activity. Conversely, in the NHE the proton concentration is equal to 1 normal. A normal is a somewhat outdated measure of concentration and is, for a monoprotic acid, equal to its molar concentration. But, here's the key point, a solution containing one molar protons does not have unit activity. The activity coefficient (\( \gamma_\pm \)) has, under these conditions, a value of approximately 0.8. Consequently, if we consider the Nernst equation for the reaction: $$ E = E^{\minuso} - \frac{RT}{F} \ln \frac{c^{\minuso}p_{\mathrm{H_2}}^{1/2}}{\gamma_\pm c_{\mathrm{H^+}} {p^{\minuso}}^{1/2}} $$ where \(c^{\minuso} \) is the standard concentration (1 mol dm^-3), \(p^{\minuso} \) is the standard pressure (1 bar) and all other terms are as per usual. Then we can see at a one molar proton concentration, when we account for the non-unity activity coefficient, the potential of the NHE and SHE are expected to differ by approximately -5.7 mV. Furthermore, given that the activity coefficient varies not just as a function of the proton concentration but also depends on the identity of the acid,[6] the exact difference between the NHE and the SHE depends on the experimental system! In the calculator below a value of -5.7 mV is taken as the difference between the NHE and SHE, but as highlighted, this value should be taken with a pinch of salt.

These days when reading the literature it is advisable to assume that, unless stated otherwise, both the NHE and SHE refer to a hydrogen electrode with unit activity protons and that the historic differences have been set aside. This is the precisely the situation in Bard and Faulkner where the two electrodes are deemed to be equivalent.

Tabulated Values

[1] Bard, A. J., Faulkner, L. R. Electrochemical Methods: Fundamentals and Applications, 2nd Edition. United States: John Wiley & Sons (2000)
[2] Meites, Louis. Handbook of Analytical Chemistry, United States, McGraw-Hill Book Company (1963)
[3] Kawashima, Kenta, et al. "Accurate Potentials of Hg/HgO Electrodes: Practical Parameters for Reporting Alkaline Water Electrolysis Overpotentials." ACS Catalysis 13 (2023): 1893-1898
[4] David J. G., and George J. Janz. Reference Electrodes, Theory and Practice. New York: Academic (1961)
[5] Ramette, R. W. "Outmoded terminology: The normal hydrogen electrode." Journal of Chemical Education 64.10 (1987): 885
[6] McKay, H. A. C. "The activity coefficient of nitric acid, a partially ionized 1:1-electrolyte." Transactions of the Faraday Society 52 (1956): 1568-1573