Nernst Equation
The Nernst equation relates the electrode potential of a half-cell (or full cell) to the standard electrode potential and the reaction quotient Q, accounting for the actual concentrations or partial pressures of reactants and products at any temperature. It shows that the cell potential decreases as products accumulate and reactants are consumed, reaching zero at equilibrium when the cell is fully discharged. The equation is critical for predicting cell behaviour under non-standard conditions and forms the basis of pH measurement using electrochemical sensors.
Key Formula
E = E° - (RT / nF) × ln(Q)
LaTeX: E = E° - \frac{RT}{nF} \ln Q
| Symbol | Meaning | Unit |
|---|---|---|
| E | Cell potential under non-standard conditions | V |
| E° | Standard cell potential | V |
| R | Universal gas constant (8.314) | J mol⁻¹ K⁻¹ |
| T | Absolute temperature | K |
| n | Number of moles of electrons transferred | mol |
| F | Faraday constant (96485) | C mol⁻¹ |
| Q | Reaction quotient | dimensionless |
Worked Example
Problem
A Daniel cell (Zn|Zn²⁺||Cu²⁺|Cu) operates at 25 °C with [Zn²⁺] = 0.10 mol L⁻¹ and [Cu²⁺] = 1.0 mol L⁻¹. E° = 1.10 V, n = 2. Calculate the cell potential.
Solution
Step 1: Write Q. Reaction: Zn + Cu²⁺ → Zn²⁺ + Cu. Q = [Zn²⁺]/[Cu²⁺] = 0.10/1.0 = 0.10 Step 2: At 25 °C, RT/F = 0.02569 V. So (RT/nF) = 0.02569/2 = 0.012845 V Step 3: E = 1.10 − 0.012845 × ln(0.10) = 1.10 − 0.012845 × (−2.3026) = 1.10 + 0.02958 ≈ 1.13 V
Answer
E ≈ 1.13 V
Nernst Equation at 25 °C — Common Forms
| Form | Expression | When Used |
|---|---|---|
| General (any T) | E = E° − (RT/nF) ln Q | Any temperature |
| At 25 °C (natural log) | E = E° − (0.02569/n) ln Q | T = 298 K, ln form |
| At 25 °C (log₁₀) | E = E° − (0.0592/n) log Q | T = 298 K, common log form |
| At equilibrium | E = 0, Q = K | Cell fully discharged |
| Link to ΔG | ΔG = −nFE | Thermodynamic interpretation |
Interactive Tools
Wolfram Alpha – Nernst Equation
Compute cell potentials at non-standard conditions using the Nernst equation
Open ToolKhan Academy – Nernst Equation
Step-by-step explanation with worked examples and practice problems
Open ToolDesmos Graphing Calculator
Use to plot cell potential vs. concentration using the Nernst equation
Open Tool
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Related Terms
Standard Electrode Potential
The standard electrode potential (E°) is the potential difference developed at an electrode when it is in contact with a 1 mol L⁻¹ solution of its ions at 25 °C (298 K) and 1 atm pressure, measured relative to the standard hydrogen electrode (SHE), which is assigned a potential of exactly 0.00 V. Positive values of E° indicate a greater tendency for reduction (the species is a stronger oxidising agent), while negative values indicate a tendency for oxidation. Standard electrode potentials are tabulated and used to predict the feasibility of redox reactions and to calculate cell EMFs.
Cell EMF
The electromotive force (EMF) of an electrochemical cell is the maximum potential difference between the two electrodes when no current is flowing (open-circuit condition), representing the driving force for electron transfer in the external circuit. It is determined by the difference in the electrode potentials of the cathode and anode and is directly related to the Gibbs free energy change of the reaction by ΔG° = −nFE°. A positive cell EMF indicates a spontaneous reaction (ΔG < 0), while a negative cell EMF indicates a non-spontaneous reaction under the given conditions.
Galvanic Cell
A galvanic cell (also called a voltaic cell) is an electrochemical device that converts chemical energy into electrical energy through spontaneous redox reactions occurring at two electrodes separated by an electrolyte. The oxidation half-reaction occurs at the anode (negative terminal) and the reduction half-reaction occurs at the cathode (positive terminal), with electrons flowing through an external circuit. Galvanic cells are the basis of all batteries and are fundamental to understanding energy storage and conversion in chemistry.
Named after German chemist Walther Hermann Nernst (1864–1941), who derived the equation around 1889. Nernst received the Nobel Prize in Chemistry in 1920 for his work in thermochemistry.