Electrode Potentials and the Nernst Equation
An electrode potential describes the tendency of a half-reaction to be reduced, measured relative to a reference under standard conditions. An electrode potentials & Nernst equation calculation updates a standard reduction potential \(E^\circ\) to the non-standard potential \(E\) by accounting for concentration, activity, and gas pressure through the reaction quotient \(Q\).
Core definitions and essential formulas
\[
E = E^{\circ} - \frac{R T}{z F}\,\ln Q
\]
\[
E = E^{\circ} - \frac{0.05916~\mathrm{V}}{z}\,\log_{10} Q \qquad (T=298~\mathrm{K})
\]
\[
Q=\frac{\prod a(\text{products})^{\nu}}{\prod a(\text{reactants})^{\nu}}
\]
\(E\) is the half-cell potential (V), \(E^\circ\) is the standard reduction potential (V), \(R\) is the gas constant, \(T\) is temperature in kelvin, \(F\) is the Faraday constant, and \(z\) is the number of electrons in the balanced half-reaction. \(Q\) is built from activities \(a\) raised to stoichiometric coefficients \(\nu\); electrons and pure solids/liquids are excluded because their activity is taken as \(1\). For aqueous solutes, \(a\) is often approximated by concentration in dilute solutions, and for gases by partial pressure relative to the standard state.
How to interpret results
A more positive \(E\) means a stronger tendency to be reduced (stronger oxidizing behavior for the species being reduced), while a more negative \(E\) means a stronger tendency to be oxidized. Because the Nernst term depends on \(\ln Q\), increasing \(Q\) (products favored in \(Q\)) makes \(E\) smaller, and decreasing \(Q\) makes \(E\) larger. Reported outputs commonly include \(E\), the computed \(Q\), and the direction of the shift relative to \(E^\circ\); values are in volts and depend on the stated temperature and input activities or concentrations.
- Temperature mismatch: using the \(0.05916\ \mathrm{V}\) constant when \(T \neq 298\ \mathrm{K}\).
- Wrong \(Q\): including solids/liquids or electrons in \(Q\), or inverting products and reactants.
- Incorrect \(z\): using the wrong electron count from the balanced half-reaction.
- Mixing units: treating pressures or concentrations inconsistently when approximating activities.
Micro example: For \(\mathrm{Zn^{2+} + 2\,e^- \rightarrow Zn(s)}\), \(Q=\dfrac{1}{[\mathrm{Zn^{2+}}]}\).
With \(E^\circ=-0.76\ \mathrm{V}\), \(z=2\), \([\mathrm{Zn^{2+}}]=0.010\ \mathrm{M}\) at \(298\ \mathrm{K}\),
\(E \approx -0.76 + \dfrac{0.05916}{2}\log_{10}(0.010) = -0.819\ \mathrm{V}\).
Use this tool to adjust half-cell potentials for nonstandard concentrations or gas pressures and to compare oxidizing and reducing strength under real conditions. Do not use it to obtain full cell voltage without combining two half-reactions; a common next step is building \(E_{\text{cell}}\) and linking it to \(\Delta_{r}G\) or equilibrium using cell thermodynamics.