Nernst Equation Calculator | Cell Potential at Non-Standard Conditions
Calculate electrochemical cell potential at any temperature and concentration using the Nernst equation E = E° − (RT/nF)ln Q. Supports concentration cell calculations (E° = 0), temperature variation, and solving for unknown ion concentrations when the measured potential is known.
PRESETS
STANDARD REDUCTION POTENTIALS (E° REFERENCE)
Cell potential E (V)
1.1336
Spontaneous (E > 0)
Q (reaction quotient)
0.1000
ln Q = -2.3026
E° (standard)
1.104 V
ΔE = 0.0296 V from standard
STEP-BY-STEP
RT/(nF) = (8.314 × 298.15) / (2 × 96485) = 0.012846 V
ln(Q) = ln(0.1000) = -2.3026
E = E° − RT/(nF) × ln(Q)
E = 1.104 − 0.012846 × -2.3026
E = 1.1336 V
E AT DIFFERENT TEMPERATURES
| T (K) | E (V) | Spontaneous? |
|---|---|---|
| 273 | 1.1311 | Yes |
| 298.15 | 1.1336 | Yes |
| 350 | 1.1387 | Yes |
| 400 | 1.1437 | Yes |
What Is the Nernst Equation Calculator | Cell Potential at Non-Standard Conditions?
Calculate electrochemical cell potential at any temperature and concentration using the Nernst equation. Supports direct Q entry, species-by-species concentration input, concentration cells (E° = 0), and reverse calculations to find Q from a measured potential.
Formula
E = E° − (RT/nF) × ln(Q) at 25 °C: E = E° − (0.05916/n) × log₁₀(Q)
How to Use
- 1
Select a mode: Direct Q (enter Q directly), Concentrations (enter species concentrations and stoichiometry), Concentration Cell (same half-reaction at two concentrations), or Reverse (find Q from measured E).
- 2
Click a half-cell preset button to fill in a known E° value, or type your cell's standard potential.
- 3
Enter n (number of electrons transferred) and temperature T in Kelvin (default 298.15 K).
- 4
For Direct Q mode: enter the reaction quotient Q (dimensionless ratio of product to reactant activities).
- 5
For Concentrations mode: add each species with its concentration (M), stoichiometric coefficient, and whether it is a product or reactant.
- 6
Read the cell potential E (V), Q, and spontaneity verdict (E > 0 = spontaneous).
- 7
Check the temperature variation table to see how E changes at 273 K, 298 K, 350 K, and 400 K.
Choose a mode (Direct Q, Concentrations, Concentration Cell, or Reverse), enter E°, n, T, and the relevant concentrations or Q.
Example Calculation
Daniell cell at non-standard conditions: Zn|Zn²⁺(0.1 M)||Cu²⁺(1.0 M)|Cu. E° = 0.342 − (−0.762) = 1.104 V, n = 2, T = 298 K. Q = [Zn²⁺]/[Cu²⁺] = 0.1/1.0 = 0.1. E = 1.104 − (0.025693/2)×ln(0.1) = 1.104 + 0.0296 = 1.133 V.
Understanding Nernst Equation | Cell Potential at Non-Standard Conditions
Standard Reduction Potentials at 25 °C
All potentials are measured relative to the standard hydrogen electrode (SHE) at E° = 0.000 V. Higher (more positive) E° means stronger oxidising agent. Cell voltage = E°_cathode − E°_anode.
| Half-reaction (reduction) | E° (V) | n | Notes |
|---|---|---|---|
| F₂ + 2e⁻ → 2F⁻ | +2.87 | 2 | Strongest common oxidiser |
| MnO₄⁻ + 8H⁺ + 5e⁻ → Mn²⁺ + 4H₂O | +1.51 | 5 | Permanganate in acid |
| Au³⁺ + 3e⁻ → Au | +1.50 | 3 | Gold reduction |
| Cl₂ + 2e⁻ → 2Cl⁻ | +1.36 | 2 | Halogen reduction |
| Ag⁺ + e⁻ → Ag | +0.80 | 1 | Silver electrode |
| Fe³⁺ + e⁻ → Fe²⁺ | +0.77 | 1 | Iron(III/II) |
| Cu²⁺ + 2e⁻ → Cu | +0.34 | 2 | Copper electrode (Daniell cathode) |
| 2H⁺ + 2e⁻ → H₂ | 0.000 | 2 | SHE reference |
| Zn²⁺ + 2e⁻ → Zn | −0.76 | 2 | Zinc electrode (Daniell anode) |
| Li⁺ + e⁻ → Li | −3.04 | 1 | Strongest common reducer |
Nernst Equation Forms at Different Temperatures
| Form | Equation | RT/F constant | 0.0592/n factor valid? |
|---|---|---|---|
| General (any T) | E = E° − (RT/nF) ln Q | — | No |
| 25 °C (298.15 K), ln form | E = E° − (0.025693/n) ln Q | 0.025693 V | No |
| 25 °C, log₁₀ form | E = E° − (0.05916/n) log₁₀ Q | — | Yes (≈ 0.0592) |
| 37 °C (310 K, body temp) | E = E° − (0.02671/n) ln Q | 0.026706 V | No (use 0.0615/n) |
| 0 °C (273.15 K) | E = E° − (0.023526/n) ln Q | 0.02353 V | No (use 0.0542/n) |
Electrochemistry Applications
- ›Galvanic cells (batteries): the Nernst equation predicts voltage at non-standard concentrations — a discharged battery has Q approaching K, so E → 0.
- ›pH electrodes: the glass electrode output shifts −59.16 mV per pH unit at 25 °C, directly from the Nernst equation with n = 1.
- ›Concentration cells: two half-cells of the same material at different concentrations generate voltage E = (RT/nF) ln([high]/[low]).
- ›Corrosion prediction: if E_cell > 0 in a metal-electrolyte system, corrosion is thermodynamically spontaneous.
- ›Chlor-alkali process: electrolysis of brine uses the Nernst equation to determine the minimum applied voltage.
- ›Fuel cells: H₂/O₂ fuel cells have E° = 1.23 V; under operating conditions the Nernst equation gives the actual open-circuit voltage.
- ›Biological membranes: the Nernst potential E = (RT/zF) ln([ion]_out/[ion]_in) determines resting membrane potential for each ion species.
Frequently Asked Questions
What is the reaction quotient Q in the Nernst equation?
Q = [products]^stoich / [reactants]^stoich, the same expression as the equilibrium constant K but evaluated at current (not equilibrium) concentrations. When Q = K, the cell is at equilibrium and E = 0.
Why does cell voltage change with concentration?
The Nernst equation shows E depends on (RT/nF) ln Q. Increasing product concentration (higher Q) decreases E; increasing reactant concentration (lower Q) increases E. A nearly discharged battery has Q approaching K, so E drops to zero.
What is a concentration cell?
A concentration cell uses identical electrodes in solutions of different concentrations. E° = 0 because both half-reactions are the same, but the Nernst term (RT/nF) ln([high]/[low]) gives a non-zero voltage. The cell drives current until concentrations equalise.
How does temperature affect the Nernst equation?
Temperature enters via the RT/nF prefactor. At higher T the Nernst correction is larger, so concentration effects are amplified. At 25 °C the log₁₀ factor is 0.0592/n; at 37 °C it is 0.0615/n. Standard E° values are also slightly temperature-dependent, but this calculator uses the 25 °C values.
What is the relationship between E and ΔG?
ΔG = −nFE. A positive E means negative ΔG, so the reaction is spontaneous. At standard conditions ΔG° = −nFE°. This directly links electrochemistry to thermodynamics — you can use this calculator to find ΔG of any redox reaction.
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