The Nernst equation describes how the electrochemical potential of a redox reaction depends on temperature and on the concentrations of the substances involved. It is one of the most important tools in electrochemistry and explains, among other things, why pH electrodes work and how the redox potential (ORP) of water arises — for example during the electrolysis of water or in water ionisers. This article explains the formula, derivation and applications with worked examples.
Nernst Equation Calculator
| Cell potential E (V) | |
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| Slope (mV/decade) |
E = E° − (R·T / n·F)·ln Q, with R = 8.314 J/mol·K, F = 96,485 C/mol. At 25 °C the slope 2.303·R·T/F ≈ 59.16 mV per decade.
What is the Nernst equation?
Named after the chemist Walther Nernst (Nobel Prize 1920), the equation links the standard potential of a reaction (measured under standardised conditions) with the actual potential under real conditions. It answers the question: how does the voltage of an electrochemical cell shift when concentration or temperature changes?
The formula
- E = actual electrode potential
- E° = standard potential
- R = universal gas constant (8.314 J/mol·K)
- T = temperature in kelvin
- n = number of electrons transferred
- F = Faraday constant (96,485 C/mol)
- Q = reaction quotient (ratio of concentrations)
For room temperature (25 °C or 298 K) and switching from the natural to the base-10 logarithm, the equation simplifies to the practical form:
The factor 0.0592 V (often rounded to 59 mV) is the reason the potential shifts by about 59 mV (divided by n) per tenfold change in concentration.
Derivation in brief
The Nernst equation follows from thermodynamics. The starting point is the Gibbs free energy of reaction:
- ΔG = ΔG° + R·T·ln Q
- Relation to voltage: ΔG = −n·F·E and ΔG° = −n·F·E°
- Substituting and rearranging gives: E = E° − (R·T)/(n·F) · ln Q
The equation therefore links energy (ΔG) directly to a measurable voltage (E).
Worked example
A classic example is pH measurement. A hydrogen or glass electrode responds to the H⁺ concentration. Per pH unit (i.e. per tenfold change in H⁺), the potential changes by about 59 mV (for n = 1 at 25 °C). This very behaviour is what makes pH electrodes possible — they are the Nernst equation applied.
The theoretical decomposition voltage of water (1.23 V) also follows from the standard potentials of the half-reactions — a direct link to water electrolysis.
Redox potential (ORP) and water ionisers
The frequently advertised "negative redox potential" (ORP) of ionised water is essentially a Nernst quantity: it depends on dissolved substances, dissolved hydrogen and, above all, the pH value. Because the ORP value is so strongly influenced by measurement conditions, it should be treated with caution as a sole quality indicator.
To put the marketing claims around ORP into context, the article on Kangen water shows the practical application — and the article on the ppm value covers the separate question of how much hydrogen (H₂) is actually dissolved. Both quantities are often mixed up in marketing but are physically different.
Frequently asked questions (FAQ)
What is the Nernst equation used for?
It calculates the actual potential of a redox reaction at real concentrations and temperatures — the basis for batteries, pH measurement, ORP and corrosion chemistry.
What is the Nernst equation?
E = E° − (R·T)/(n·F) · ln Q. At 25 °C it simplifies to E = E° − (0.0592/n) · log Q.
What does the value 0.0592 V mean?
It is (R·T/F)·ln 10 at 25 °C. It describes that the potential shifts by about 59 mV (divided by n) per tenfold change in concentration.
What does the Nernst equation have to do with water?
It explains the redox potential (ORP) of water, the function of pH electrodes, and the theoretical decomposition voltage during electrolysis.
