# Nernst Equation Calculator

> Computes the cell (or electrode) potential under non-standard conditions with the Nernst equation E = E° − (RT/nF)·ln Q, the textbook 0.0592/n·log Q form at 25 °C, the Gibbs energy ΔG = −nFE and the equilibrium constant from E°.

- Calculator id: `nernst-equation` · Category: Chemistry (`chemistry`) · Tool name: `calculate_nernst_potential`
- Canonical page: https://tttkmbb.com/chemistry/nernst-equation · This document: https://tttkmbb.com/chemistry/nernst-equation.md · JSON definition: https://tttkmbb.com/chemistry/nernst-equation.json

## Purpose

Computes the cell (or electrode) potential under non-standard conditions with the Nernst equation E = E° − (RT/nF)·ln Q, the textbook 0.0592/n·log Q form at 25 °C, the Gibbs energy ΔG = −nFE and the equilibrium constant from E°.

**Use when:** You know a standard potential and the concentrations (reaction quotient) of an electrochemical cell or half-cell and need its actual potential, ΔG or K, including at temperatures other than 25 °C.

**Do not use when:** You need the mass deposited or charge passed during electrolysis (use faraday-electrolysis), or the pH of a solution from concentrations (use ph).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `standard_potential_v` | number | V | required | Standard cell potential E°cell (cathode − anode) or standard reduction potential of the half-reaction, in volts. (min -10, max 10) |
| `electrons` | integer |  | required | Number of moles of electrons in the balanced cell reaction (2 for Zn + Cu²⁺ → Zn²⁺ + Cu). (min 1, max 20) |
| `reaction_quotient` | number |  | required | Q = product activities / reactant activities with stoichiometric exponents, e.g. [Zn²⁺]/[Cu²⁺]; pure solids and liquids are omitted. Use Q = 1 for standard conditions. (> 0) |
| `temperature` | number |  | optional, default 25 | Cell temperature in temperature_unit. |
| `temperature_unit` | enum: celsius \| kelvin |  | optional, default "celsius" | Unit of the temperature inputs; the calculation uses kelvin (K = °C + 273.15). |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `cell_potential_v` | number | V | E = E° − (RT/nF)·ln Q at the given temperature. |
| `nernst_correction_v` | number | V | Amount subtracted from E°; negative when Q < 1. |
| `rt_over_nf_v` | number | V | Thermal voltage divided by n (0.025693/n V at 25 °C). |
| `cell_potential_25c_log_form_v` | number | V | E° − (0.0592/n)·log10 Q, the textbook approximation valid at 25 °C regardless of the temperature entered. |
| `gibbs_energy_kj_per_mol` | number | kJ/mol | −n·F·E: negative for a spontaneous reaction as written. |
| `standard_gibbs_energy_kj_per_mol` | number | kJ/mol | −n·F·E°. |
| `log10_equilibrium_constant` | number |  | n·F·E° / (R·T·ln 10) at the given temperature. |
| `equilibrium_constant_scientific` | string |  | K = exp(nFE°/RT) in scientific notation. |
| `spontaneous` | string |  | Whether the reaction as written is spontaneous at the given Q (E > 0), at equilibrium (E = 0) or non-spontaneous (E < 0). |
| `temperature_k` | number | K | Absolute temperature used. |

## Formula

`E = E° − (R × T / (n × F)) × ln Q with R = 8.314462618 J/(mol·K), F = 96485.33212 C/mol; at 25 °C E ≈ E° − (0.0592 / n) × log10 Q; ΔG = −n × F × E; ΔG° = −n × F × E°; ln K = n × F × E° / (R × T)`

Concentrations are used in place of activities, which is accurate for dilute solutions; the constant 0.05916 V is RT·ln10/F at 298.15 K (0.0592 in most textbooks). E° is taken as temperature-independent, so the temperature only enters through RT/nF.

## Data Sources

- OpenStax Chemistry 2e – 17.4 Potential, Free Energy, and Equilibrium — https://openstax.org/books/chemistry-2e/pages/17-4-potential-free-energy-and-equilibrium (textbook, retrieved 2026-09-24)
- Wikipedia – Nernst equation — https://en.wikipedia.org/wiki/Nernst_equation (reference, retrieved 2026-09-24)
- NIST – CODATA internationally recommended values of the fundamental physical constants (Faraday constant F = 96 485.33212 C/mol, exact) — https://physics.nist.gov/cuu/Constants/index.html (standard, retrieved 2026-09-24)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/nernst-equation?standard_potential_v=…&electrons=…&reaction_quotient=…`
- `POST https://tttkmbb.com/api/v1/calculate/nernst-equation` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/nernst-equation · OpenAPI operationId `calculate_nernst_potential` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "nernst-equation", "inputs": {…}}`

## Example

- Zn/Cu cell, E° 1.10 V, [Zn²⁺]/[Cu²⁺] = 100, 25 °C: inputs `{"standard_potential_v":1.1,"electrons":2,"reaction_quotient":100,"temperature":25}` → `{"cell_potential_v":1.04084,"nernst_correction_v":0.05916,"rt_over_nf_v":0.012846,"cell_potential_25c_log_form_v":1.0408,"gibbs_energy_kj_per_mol":-200.852,"standard_gibbs_energy_kj_per_mol":-212.268,"log10_equilibrium_constant":37.1877,"spontaneous":"Spontaneous as written (E > 0)"}`
- E° 0.34 V, n = 2, Q = 0.001 at 50 °C: inputs `{"standard_potential_v":0.34,"electrons":2,"reaction_quotient":0.001,"temperature":50}` → `{"cell_potential_v":0.43618,"rt_over_nf_v":0.013923,"nernst_correction_v":-0.09618,"cell_potential_25c_log_form_v":0.4288,"temperature_k":323.15}`

```
GET https://tttkmbb.com/api/v1/calculate/nernst-equation?standard_potential_v=1.1&electrons=2&reaction_quotient=100&temperature=25
```

## Limitations

You need the mass deposited or charge passed during electrolysis (use faraday-electrolysis), or the pH of a solution from concentrations (use ph). Concentrations are used in place of activities, which is accurate for dilute solutions; the constant 0.05916 V is RT·ln10/F at 298.15 K (0.0592 in most textbooks). E° is taken as temperature-independent, so the temperature only enters through RT/nF. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**How do I build Q?**

Write the overall cell reaction, then Q = (products)/(reactants) with each concentration raised to its coefficient, omitting solids, pure liquids and the solvent; gases enter as partial pressure in bar (or atm).

**Why do the exact and 0.0592 values differ?**

The 0.0592/n·log Q form is the Nernst equation evaluated at 25 °C. At other temperatures use cell_potential_v, which uses RT/nF at the temperature entered.

**Does this work for a single half-cell?**

Yes: enter the standard reduction potential, the electrons of the half-reaction and Q = [reduced]/[oxidized] to get the electrode potential versus SHE.

## Related

- [Faraday's Law of Electrolysis Calculator](https://tttkmbb.com/chemistry/faraday-electrolysis.md) — Charge, mass and time in electrolysis with the same Faraday constant.
- [pH Calculator](https://tttkmbb.com/chemistry/ph.md) — Convert [H⁺] for hydrogen-electrode or pH-dependent potentials.
- [Logarithm Calculator](https://tttkmbb.com/math/logarithm.md) — Natural and base-10 logarithm arithmetic.