Nernst Equation Calculator
Calculate non-standard cell potentials using the Nernst equation with concentration, temperature, and pH effects on electrode and cell potentials.
Electromotive Force (EMF) Calculator
Calculate standard cell potential (EMF) from electrode potentials, predict reaction spontaneity, and determine Gibbs free energy for electrochemical cells.
E°cell⧉
1.100 V
Standard cell potential = E°cathode − E°anode
Cell Type⧉
Galvanic (spontaneous)
Positive EMF → reaction proceeds spontaneously
ΔG°⧉
-212.27 kJ/mol
Standard Gibbs free energy = −nFE°cell
log K⧉
37.21
Logarithm of the equilibrium constant
K⧉
1.62e+37
Equilibrium constant: K = exp(nFE°/RT)
Max Useful Work⧉
212.27 kJ/mol
Maximum non-expansion work obtainable = |ΔG°|
E° Cathode⧉
0.340 V
Standard reduction potential of the cathode half-reaction
E° Anode⧉
-0.760 V
Standard reduction potential of the anode half-reaction
Cell Potential Visual
E°cell
1.100 V
−3 V0 V+3 V
Standard Reduction Potentials (Electrochemical Series)
| Half-Reaction | E° (V) | Role in Your Cell |
|---|---|---|
| Li⁺/Li + 1e⁻ | -3.04 | |
| K⁺/K + 1e⁻ | -2.93 | |
| Ca²⁺/Ca + 2e⁻ | -2.87 | |
| Na⁺/Na + 1e⁻ | -2.71 | |
| Mg²⁺/Mg + 2e⁻ | -2.37 | |
| Al³⁺/Al + 3e⁻ | -1.66 | |
| Zn²⁺/Zn + 2e⁻ | -0.76 | ⬆️ Anode |
| Fe²⁺/Fe + 2e⁻ | -0.44 | |
| Ni²⁺/Ni + 2e⁻ | -0.26 | |
| Sn²⁺/Sn + 2e⁻ | -0.14 | |
| Pb²⁺/Pb + 2e⁻ | -0.13 | |
| H⁺/H₂ (SHE) + 2e⁻ | +0.00 | |
| Cu²⁺/Cu + 2e⁻ | +0.34 | ⬇️ Cathode |
| I₂/I⁻ + 2e⁻ | +0.54 | |
| Ag⁺/Ag + 1e⁻ | +0.80 | |
| Br₂/Br⁻ + 2e⁻ | +1.07 | |
| O₂/H₂O (acid) + 4e⁻ | +1.23 | |
| Cl₂/Cl⁻ + 2e⁻ | +1.36 | |
| Au³⁺/Au + 3e⁻ | +1.50 | |
| MnO₄⁻/Mn²⁺ + 5e⁻ | +1.51 | |
| F₂/F⁻ + 2e⁻ | +2.87 |
Common Battery EMFs
| Battery | Chemistry | E° (V) | vs. Your Cell |
|---|---|---|---|
| Zinc-Carbon | Zn/MnO₂ | 1.50 | -0.40 V |
| Alkaline | Zn/MnO₂ | 1.50 | -0.40 V |
| Lead-Acid | Pb/PbO₂ | 2.05 | -0.95 V |
| Nickel-Cadmium | Cd/NiOOH | 1.35 | -0.25 V |
| Lithium-Ion | LiCoO₂/C | 3.70 | -2.60 V |
| Zinc-Air | Zn/O₂ | 1.65 | -0.55 V |
Planning notes, formulas, and examples
About the Electromotive Force (EMF) Calculator
The electromotive force (EMF) of an electrochemical cell is the maximum potential difference between two electrodes when no current is flowing. It determines whether a redox reaction is spontaneous (positive EMF for galvanic cells) or requires external energy (negative EMF, indicating an electrolytic cell). The standard cell potential E°cell equals the difference between the cathode and anode standard reduction potentials.
Calculating EMF is central to understanding batteries, corrosion, electroplating, and biological electron transport. From the EMF, you can also calculate the standard Gibbs free energy change (ΔG° = −nFE°) and the equilibrium constant (ln K = nFE°/RT), connecting electrochemistry to thermodynamics. These relationships allow predictions of reaction feasibility, battery voltage, and the direction of electron flow.
This calculator lets you select electrode half-reactions from a comprehensive table, automatically computes E°cell, ΔG°, and K, handles both galvanic and electrolytic cell configurations, and shows the complete cell notation. It also provides a visual electrochemical series and contextualizes your cell potential against common battery chemistries.
When This Page Helps
This calculator simplifies electrochemistry computations — select half-reactions, quickly get cell potential, free energy, and equilibrium constant. Perfect for students studying redox chemistry and engineers designing electrochemical cells.
How to Use the Inputs
- Select the cathode (reduction) half-reaction from the dropdown or enter a custom E° value.
- Select the anode (oxidation) half-reaction — the calculator automatically reverses the sign.
- The standard cell EMF is calculated as E°cell = E°cathode − E°anode.
- Enter the number of electrons transferred (n) for energy and equilibrium calculations.
- Review the Gibbs free energy, equilibrium constant, and spontaneity prediction.
- Use the preset buttons to load common battery and cell configurations.
- Compare your cell potential against the battery reference table.
Formula used
E°cell = E°cathode − E°anode. ΔG° = −nFE°cell, where n = moles of electrons transferred, F = 96,485 C/mol. ln K = nFE°cell / (RT), where R = 8.314 J/(mol·K), T = temperature (K).Example Calculation
Result: E°cell = 1.10 V, ΔG° = −212.3 kJ/mol
For the Daniell cell: E°cell = 0.34 − (−0.76) = 1.10 V. With n = 2: ΔG° = −2 × 96,485 × 1.10 = −212,267 J/mol = −212.3 kJ/mol. The positive EMF confirms spontaneity.
Tips & Best Practices
- All standard potentials are referenced to the standard hydrogen electrode (SHE) at 0.00 V.
- When writing cell notation, the anode is on the left: Zn|Zn²⁺||Cu²⁺|Cu.
- For half-reactions involving H⁺ or OH⁻, the potential changes with pH — use the Nernst equation.
- A larger positive E°cell means a more thermodynamically favorable (more spontaneous) reaction.
- The equilibrium constant K is exponentially sensitive to E°cell — small voltage changes mean huge K changes.
- Real battery output voltage is always less than E°cell due to internal losses.
The Electrochemical Series
The electrochemical series ranks elements by their standard reduction potentials, from the most negative (strongest reducing agents like Li at −3.04 V) to the most positive (strongest oxidizing agents like F₂ at +2.87 V). This series predicts which redox reactions are spontaneous: a species higher in the series (more positive E°) will oxidize a species lower in the series (more negative E°). The series is fundamental to understanding corrosion, battery design, and metallurgical extraction.
Connecting EMF to Thermodynamics
The relationship ΔG° = −nFE° is one of the most powerful equations in chemistry, bridging thermodynamics and electrochemistry. A positive E° means negative ΔG° (spontaneous). The equilibrium constant relationship K = exp(nFE°/RT) shows that even moderate cell potentials correspond to enormous equilibrium constants. For example, the Daniell cell (E° = 1.10 V, n = 2) has K ≈ 10³⁷ — essentially irreversible under standard conditions.
Practical Applications in Battery Technology
Understanding EMF is crucial for battery design. Lead-acid batteries (E° ≈ 2.0 V), lithium-ion (E° ≈ 3.6 V), and zinc-air (E° ≈ 1.65 V) all have their cell potentials determined by the electrode materials chosen. Multi-cell batteries connect individual cells in series to achieve higher voltages. The theoretical energy density is determined by E° and the molar masses of the active materials.
Sources & Methodology
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Frequently Asked Questions
Electromotive force is the maximum voltage a cell can produce under standard conditions with no current flow. It's the thermodynamic driving force for the redox reaction.
The electrode with the more negative (less positive) standard reduction potential is the anode (oxidation occurs). The more positive electrode is the cathode (reduction occurs) in a galvanic cell.
By convention, E°cell = E°(reduction at cathode) − E°(reduction at anode). Since oxidation occurs at the anode, subtracting its reduction potential effectively adds its oxidation potential.
A negative E°cell means the reaction is non-spontaneous under standard conditions. An external voltage greater than |E°cell| must be applied to force the reaction (electrolysis).
Standard EMFs are accurate for standard conditions (1 M, 1 atm, 25°C). For non-standard conditions, use the Nernst equation to adjust for actual concentrations and temperatures.
The EMF gives the theoretical maximum voltage. Real batteries deliver less due to internal resistance, overpotentials, and concentration gradients. Actual voltage = EMF − IR − overpotentials.
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