Standard electrode potential (data page)

The data below tabulates standard electrode potentials (E°), in volts relative to the standard hydrogen electrode (SHE), at:

• Temperature 298.15 K (25.00 °C; 77.00 °F);
• Effective concentration (activity) 1 mol/L for each aqueous or amalgamated (mercury-alloyed) species;
• Unit activity for each solvent and pure solid or liquid species; and
• Absolute partial pressure 101.325 kPa (1.00000 atm; 1.01325 bar) for each gaseous reagent — the convention in most literature data but not the current standard state (100 kPa).

The Nernst equation allows to calculate real electrode potentials by taking into account exact concentrations, gas pressure, and temperature measured under different experimental conditions.

Electrode potentials of successive elementary half-reactions, as commonly represented in Latimer diagrams, cannot be directly added, but can be correctly determined by adding the corresponding Gibbs free energy changes (∆G°) using the general formula ∆G° = –zFE°, i.e., the product of the number (z) of electrons transferred, the Faraday constant (F ≈ 96 485 coulombs/(mol  e⁻) ≈ 1.6022 E-19 coulomb/ e⁻) and the standard electrode potential (E°) in volt. In other words, volts cannot be directly summed up, but well electron-volts, or joules (coulombs × volts). So, F × E = 96 485 coulombs/(mol  e⁻) × 1 volt = 96 485 joules/(mol  e⁻).

For example, from Fe²⁺ + 2 e⁻ ⇌ Fe(s) (–0.44 V), the energy to form one neutral atom of Fe(s) from one Fe²⁺ ion and two electrons is 2 × 0.44 eV = 0.88 eV, or 84 907 J/(mol  e⁻). That value is also the standard formation energy (∆G_f°) for an Fe²⁺ ion, since  e⁻ and Fe(s) both have zero formation energy.

Data from different sources may cause table inconsistencies. For example: $${\displaystyle {\begin{alignedat}{4}&{\ce {Cu+ + e-}}&{}\rightleftharpoons {}&{\ce {Cu}}(s)&\quad \quad E_{1}=+0.520{\text{ V}}\\&{\ce {Cu^2+ + 2e-}}&{}\rightleftharpoons {}&{\ce {Cu}}(s)&\quad \quad E_{2}=+0.337{\text{ V}}\\&{\ce {Cu^2+ + e-}}&{}\rightleftharpoons {}&{\ce {Cu+}}&\quad \quad E_{3}=+0.159{\text{ V}}\end{alignedat}}}$$

In the hypothesis where the E₃ value should still be unknown because this half-reaction is an intermediate step difficult to measure or to control. It should be calculated from the two other values E₁ and E₂.
How to best proceed in an easy way as standard electrode potentials are not additive?

The simplest way to sum the Gibbs energies is to directly work in electron-volts (eV) without having to convert them in joules. It is because when summing up ∆G° = –zFE°, –F simplifies on both equation sides. This greatly facilitates the calculations, only requiring to know the number of electrons transferred and the standard electrode potentials:

∆G₃° + ∆G₁° = ∆G₂°

-1·FE₃ - 1·FE₁ = -2·FE₂

1·E₃ + 1·E₁ = 2·E₂

1·E₃ = 2·E₂ – 1·E₁

So, quite simply the result is:

$${\displaystyle E_{3}={\frac {2\cdot E_{2}-1\cdot E_{1}}{1}}=+0.154{\text{ V.}}}$$

Now, if the E₃ value is finally measured by an appropriate method with a good accuracy and sufficient precision under stable and properly controlled conditions and is +0.159 V as given here above, one would observe a slight difference between calculations and the experimental measurement.

Although the difference here is not important, nor very significant, the calculated value (+0.154 V) slightly differs (∆ = 0.005 V, or 5 mV) from the value of +0.159 V directly determined by experiment. The reason likely lies in small differences, or uncertainties, in the experimental conditions, or in the inconsistent use of slightly different values of physical constants needed to determine and to report the standard electrode potentials. This small discrepancy illustrates the need to correctly manage uncertainties and their propagation in such calculations.