Nernst Equation Calculator
Enter the standard potential E°, electrons transferred n and reaction quotient Q; at 25 °C the Nernst equation E = E° − (0.0592/n)·log Q instantly gives the electrode (cell) potential.
Input Data
Results
At a glance:The Nernst equation (proposed by the German chemist Walther Nernst in 1889) is one of the most important equations in electrochemistry; it describes how an electrode or cell potential changes as the concentrations (activities) of reactants and products deviate from the standard state. In full form E = E° − (RT / nF)·ln Q, where E is the actual electrode (cell) potential, E° the standard potential (all activities = 1), R the gas constant (8.314 J/(mol·K)), T the absolute temperature (K), n the electrons transferred in the redox reaction, F the Faraday constant (96485 C/mol) and Q the reaction quotient. At the most common 25 °C (298.15 K), substituting the constants and converting ln to log₁₀ (ln x = 2.303 log x) gives (RT/F)·2.303 ≈ 0.0592 V, so the Nernst equation simplifies to the hand-calculable form E = E° − (0.0592 / n)·log₁₀Q. Using this tool's default: E° = 1.10 V, n = 2, Q = 10, then E = 1.10 − (0.0592/2)×log₁₀(10) = 1.10 − 0.0296×1 = 1.0704 V. The physical meaning: it links 'thermodynamics (concentration, activity)' with 'potential'. The reaction quotient Q reflects how far the system deviates from standard state — when Q < 1 (few products, many reactants) log Q < 0, so E > E° (more driving force); when Q > 1 (many products) log Q > 0, so E < E° (less driving force); when Q = 1 (standard state) log Q = 0, so E = E°. As the battery discharges, products accumulate and Q grows, so E gradually falls until equilibrium (Q = K, E = 0) where the battery does no more electrical work — exactly why batteries 'run out'. Applications: computing non-standard electrode/cell potentials (e.g. concentration cells); the working principle of pH meters and ion-selective electrodes; back-calculating ion concentration from measured potential (potentiometric titration); and understanding biological membrane potentials (Nernst potential). Notes: the 0.0592 coefficient only holds at 25 °C; n comes from the balanced half-reactions; Q is written like K (products over reactants, stoichiometric powers), pure solids/liquids have activity 1; this calculator uses the 25 °C simplified form and requires Q > 0.
Formula
Full form: E = E° − (RT / nF)·ln Q.
At 25 °C: E = E° − (0.0592 / n)·log₁₀Q.
Q = 1 (standard state) gives E = E°; at equilibrium E = 0 and Q = K.
Q is written like the equilibrium constant (products / reactants).
$$E = E^{\circ} - \dfrac{0.0592}{n} \log_{10} Q$$How to Use
- Enter the standard electrode (cell) potential E° (V, may be positive or negative).
- Enter the electrons transferred n in the balanced reaction.
- Enter the reaction quotient Q (1 at standard state); the right panel instantly shows E.
Nernst equation examples (E° = 1.10 V, n = 2, 25 °C)
| Reaction Quotient Q | log₁₀Q | Potential E (V) |
|---|---|---|
| 0.1 | −1 | 1.1296 |
| 1 | 0 | 1.1000 |
| 10 | 1 | 1.0704 |
| 100 | 2 | 1.0408 |
Q < 1 raises potential; Q > 1 lowers it; the 0.0592 coefficient only holds at 25 °C.
Case Studies
Cell potential under non-standard conditions
Cu–Zn cell E° = 1.10 V, n = 2, reaction quotient Q = 10.
E = 1.10 − (0.0592/2)×log 10 = 1.10 − 0.0296 = 1.0704 V.
Q > 1 means more products, so the potential is slightly below the standard value.
Verification at standard state
When all species have activity 1, Q = 1.
log 1 = 0, so E = E° − 0 = E°.
The Nernst equation reduces to the standard potential at standard state.
FAQ
What does the Nernst equation do?
It describes how the actual electrode or cell potential changes as reactant/product concentrations (activities) deviate from standard state: E = E° − (0.0592/n)·log Q at 25 °C. It is the core electrochemistry equation linking concentration to potential.
Where does 0.0592 come from?
It is (RT/F)×2.303 evaluated at 25 °C: R = 8.314, T = 298.15 K, F = 96485 C/mol, giving about 0.0592 V. This coefficient only holds at 25 °C; other temperatures need recomputation.
How is the reaction quotient Q written?
Q is written like the equilibrium constant K: product activities to their stoichiometric powers divided by reactant activities to theirs. Pure solids and liquids have activity 1; dilute solutions approximate activity with concentration.
What is the difference between Q=1 and equilibrium?
Q = 1 means all species have activity 1 (standard state), so E = E°. Equilibrium is Q = K (the equilibrium constant), where E = 0 and the cell does no electrical work. They are different states.
What value should n take?
n is the moles of electrons transferred in the balanced redox reaction, e.g. Zn + Cu²⁺ → Zn²⁺ + Cu transfers 2 electrons, so n = 2. Different reactions have different n, read from the balanced half-reactions.
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.