Nernst Equation
The Nernst equation E = E° - (RT/nF)ln(Q) relates cell potential to standard potential, temperature, and reaction quotient. It predicts electrode potentials and battery behavior under non-standard conditions.
Why This Chemistry Calculation Matters
Why: The Nernst equation is fundamental for predicting battery voltage, corrosion behavior, and electrochemical sensor response under real-world conditions.
How: Measure or look up E°, determine Q from concentrations, apply E = E° - (RT/nF)ln(Q). At 25°C use E = E° - (0.0592/n)log₁₀(Q).
- ●At 25°C, RT/nF ≈ 0.0257 V; per decade of Q change, E shifts by 0.0592/n V.
- ●E > 0 means galvanic (spontaneous); E < 0 means electrolytic.
- ●K = exp(nFE°/RT) gives equilibrium constant from standard potential.
- ●Batteries and fuel cells rely on Nernst behavior for voltage prediction.
Sample Examples
🔋 Daniell Cell
Zn|Zn²⁺||Cu²⁺|Cu - Classic galvanic cell
⚡ Hydrogen Electrode
Standard Hydrogen Electrode (SHE) at different pH
⚗️ Zn-Cu Galvanic Cell
Concentration cell with different concentrations
🔬 Ag-Cu Cell
Silver-copper cell with concentration effects
🔋 Lead-Acid Battery
Automotive battery chemistry
🔋 Ni-Cd Battery
Rechargeable battery system
⚙️ Fe-Cu Cell
Iron-copper galvanic cell
📊 Concentration Cell
Same electrodes, different concentrations
Calculate Cell Potential
⚠️For educational and informational purposes only. Verify with a qualified professional.
🔬 Chemistry Facts
At 25°C, E shifts 59.2/n mV per decade change in Q.
— IUPAC
Lead-acid battery: E° ≈ 2.05 V; Zn-Cu Daniell: E° = 1.10 V.
— Electrochemistry
ΔG = -nFE links cell potential to thermodynamic spontaneity.
— Thermodynamics
E = 0 at equilibrium; then E° = (RT/nF)ln(K).
— Nernst
What is the Nernst Equation?
The Nernst equation is a fundamental relationship in electrochemistry that relates the cell potential (E) of an electrochemical cell to the standard cell potential (E°), temperature, and the reaction quotient (Q). It allows us to predict how cell potential changes with concentration and temperature.
🔬 Key Concepts
Cell Potential (E)
The voltage or electromotive force (EMF) of an electrochemical cell. It determines whether a reaction is spontaneous (E > 0) or requires energy input (E < 0).
Standard Potential (E°)
The cell potential under standard conditions (1 M concentrations, 1 atm pressure, 25°C). This is a constant for a given redox reaction.
Reaction Quotient (Q)
Similar to the equilibrium constant, but calculated using current concentrations rather than equilibrium concentrations. Q = [products] / [reactants].
Temperature Effect
Temperature affects cell potential through the RT/nF term. At 25°C, this simplifies to 0.0592/n volts per log₁₀ unit.
How to Use the Nernst Equation
The Nernst equation can be applied in several ways depending on what information you have and what you want to calculate.
📐 Calculation Methods
1. Calculate Cell Potential
Given standard potential, number of electrons, reaction quotient, and temperature:
At 25°C: E = E° - (0.0592/n)log₁₀(Q)
2. Calculate from Half-Cells
Use standard reduction potentials for anode and cathode:
Then apply Nernst equation with concentrations
3. Calculate Equilibrium Constant
At equilibrium (E = 0), the Nernst equation gives:
Large K values indicate spontaneous reactions
When to Use the Nernst Equation
The Nernst equation is essential in many electrochemical applications, from battery design to corrosion prevention.
Battery Design
Predict cell voltage under different conditions. Essential for designing batteries with optimal performance.
- Lead-acid batteries
- Lithium-ion cells
- Fuel cells
Corrosion Prevention
Understand electrochemical corrosion processes. Predict which metals will corrode and design protection systems.
- Galvanic corrosion
- Cathodic protection
- Sacrificial anodes
Analytical Chemistry
Use electrochemical cells for quantitative analysis. Measure concentrations using potentiometry and voltammetry.
- pH electrodes
- Ion-selective electrodes
- Electrochemical sensors
Nernst Equation Formulas
General Nernst Equation
Where: E = cell potential, E° = standard potential, R = gas constant (8.314 J/mol·K), T = temperature (K), n = electrons transferred, F = Faraday's constant (96485 C/mol), Q = reaction quotient
Simplified Form (25°C)
At 25°C, RT/F = 0.0257 V, and converting to base-10 logarithm gives 0.0592 V per decade
Standard Cell Potential
Standard potential is the difference between cathode (reduction) and anode (oxidation) potentials
Equilibrium Constant
At equilibrium, E = 0, so E° = (RT/nF)ln(K). Large K values indicate spontaneous reactions.
Gibbs Free Energy
Relates cell potential to thermodynamic spontaneity. Negative ΔG means spontaneous reaction.
📚 Official Data Sources
⚠️ Disclaimer: This calculator uses IUPAC-recommended electrochemical conventions. For precise work, consult the IUPAC Gold Book, NIST reference data, and Bard & Faulkner, Electrochemical Methods.
Standard Reduction Potentials (25°C)
Standard reduction potentials (E°) measured vs. Standard Hydrogen Electrode (SHE). More positive values indicate stronger oxidizing agents.
| Half-Reaction | E° (V) | Description |
|---|---|---|
| F₂ + 2e⁻ → 2F⁻ | +2.87 | Strongest oxidizing agent |
| O₃ + 2H⁺ + 2e⁻ → O₂ + H₂O | +2.07 | Ozone |
| S₂O₈²⁻ + 2e⁻ → 2SO₄²⁻ | +2.01 | Persulfate |
| H₂O₂ + 2H⁺ + 2e⁻ → 2H₂O | +1.78 | Hydrogen peroxide |
| MnO₄⁻ + 8H⁺ + 5e⁻ → Mn²⁺ + 4H₂O | +1.51 | Permanganate |
| Cl₂ + 2e⁻ → 2Cl⁻ | +1.36 | Chlorine |
| Cr₂O₇²⁻ + 14H⁺ + 6e⁻ → 2Cr³⁺ + 7H₂O | +1.33 | Dichromate |
| O₂ + 4H⁺ + 4e⁻ → 2H₂O | +1.23 | Oxygen reduction |
| Br₂ + 2e⁻ → 2Br⁻ | +1.09 | Bromine |
| NO₃⁻ + 4H⁺ + 3e⁻ → NO + 2H₂O | +0.96 | Nitrate |
| Ag⁺ + e⁻ → Ag | +0.80 | Silver |
| Fe³⁺ + e⁻ → Fe²⁺ | +0.77 | Iron(III)/Iron(II) |
| I₂ + 2e⁻ → 2I⁻ | +0.54 | Iodine |
| Cu²⁺ + 2e⁻ → Cu | +0.34 | Copper |
| 2H⁺ + 2e⁻ → H₂ | 0.00 | Standard Hydrogen Electrode (SHE) |