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Nernst Equation Calculator - Online Electrochemical Potential

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Nernst Equation Parameters
V

For reaction: a·Ox + n·e⁻ → b·Red, the reaction quotient is Q = [Red]b / [Ox]a
Pure solids & liquids have activity = 1

M
M
Calculated Q = 1.000
Result
Cell Potential (E)
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Enter parameters and click Calculate to see the result.

Calculation steps will appear here after you click Calculate.

About the Nernst Equation

The Nernst equation, formulated by German physical chemist Walther Nernst in 1889, relates the reduction potential of an electrochemical reaction to the standard electrode potential, temperature, and activities (often approximated by concentrations) of the species involved.

E = E° − (RT/nF) · ln(Q)

Where:

  • E = Cell potential under non-standard conditions (V)
  • E° = Standard reduction potential (V)
  • R = Universal gas constant = 8.314 J/(mol·K)
  • T = Temperature in Kelvin (K)
  • n = Number of electrons transferred
  • F = Faraday constant = 96,485 C/mol
  • Q = Reaction quotient (dimensionless)

At 25°C (298.15 K), the equation simplifies to:
E = E° − (0.0592/n) · log₁₀(Q)

Key Insights
  • Q = 1: E = E° (standard conditions)
  • Q < 1: More reactants than products → E > E° (more favorable reduction)
  • Q > 1: More products than reactants → E < E° (less favorable reduction)
  • E > 0: Spontaneous reaction (galvanic/voltaic cell)
  • E < 0: Non-spontaneous reaction (requires external power — electrolytic cell)
  • E = 0: System at equilibrium (ΔG = 0)
  • Temperature effect: Higher T amplifies the correction term, making concentration differences more impactful.
Frequently Asked Questions (FAQ)

The Nernst equation is used to calculate the electrochemical cell potential under non-standard conditions. It accounts for the effects of temperature and concentration on the cell voltage. Key applications include predicting battery performance under varying conditions, understanding ion-selective electrodes (like pH meters), analyzing corrosion processes, studying biological membrane potentials, and designing electrochemical sensors.

E° (standard reduction potential) is the potential measured under standard conditions: all solutes at 1 M concentration, all gases at 1 atm pressure, and temperature at 25°C (298.15 K). E is the actual cell potential when concentrations, temperature, or pressure deviate from standard conditions. The Nernst equation bridges these two values by applying a correction based on the reaction quotient Q.

For a reduction half-reaction: a·Ox + n·e⁻ → b·Red, the reaction quotient is Q = [Red]b / [Ox]a. Here, [Ox] and [Red] represent the activities (approximated by molar concentrations for dilute solutions). Pure solids (like metal electrodes) and pure liquids (like water) have an activity of 1 and are omitted from the Q expression. For example, in the Cu²⁺/Cu half-cell (Cu²⁺ + 2e⁻ → Cu), Q = 1/[Cu²⁺] because solid copper has activity = 1.

The Nernst equation fundamentally uses the natural logarithm (ln) because it derives from thermodynamic principles (ΔG = ΔG° + RT·ln(Q) and ΔG = −nFE). However, for convenience at 25°C, the equation is often converted to base-10 logarithm: E = E° − (0.0592/n)·log₁₀(Q). The factor 0.0592 comes from (RT/F)·ln(10) at 298.15 K. Our calculator uses the precise natural log formulation and automatically adjusts for any temperature you enter.

Temperature directly affects the RT/nF term in the Nernst equation. As temperature increases, the correction term becomes larger in magnitude, meaning concentration differences have a greater impact on the cell potential. At higher temperatures, the same concentration ratio produces a larger deviation from E°. This is why battery performance can vary significantly with temperature — a phenomenon accounted for by the Nernst equation. At 0°C (273.15 K), RT/F ≈ 0.0235 V; at 100°C (373.15 K), RT/F ≈ 0.0322 V.

The value n represents the number of electrons transferred in the balanced half-reaction. It appears in the denominator of the correction term (RT/nF), meaning that reactions involving more electrons are less sensitive to concentration changes. For example, a one-electron transfer (n=1) shows a 59.2 mV change per 10-fold concentration change at 25°C, while a two-electron transfer (n=2) shows only a 29.6 mV change. Always use the number of electrons from the balanced half-reaction.

Yes! A concentration cell uses two identical electrodes with different ion concentrations. In this case, E° = 0 (since both half-cells have the same standard potential), and the Nernst equation simplifies to E = −(RT/nF)·ln([ion]₁/[ion]₂). The voltage arises purely from the concentration difference, driving ions from the higher concentration side to the lower concentration side until equilibrium is reached. This principle is used in pH meters and ion-selective electrodes.

Common mistakes include: (1) Using the wrong sign — remember E = E° − (RT/nF)·ln(Q), not plus. (2) Incorrect n value — always count electrons from the balanced half-reaction, not the overall reaction. (3) Forgetting to convert temperature to Kelvin — using Celsius directly gives incorrect results. (4) Including solids/liquids in Q — pure phases have activity = 1. (5) Confusing Q and K — Q is the reaction quotient at any moment; K is the equilibrium constant (when E=0). (6) Using log₁₀ with the ln formula — at 25°C, use 0.0592 with log₁₀, or 0.0257 with ln.

The Goldman-Hodgkin-Katz (GHK) equation extends the Nernst equation for biological membranes permeable to multiple ions (Na⁺, K⁺, Cl⁻, Ca²⁺). While the Nernst equation calculates the equilibrium potential for a single ion, the Goldman equation computes the resting membrane potential considering multiple ions and their relative permeabilities. The Nernst equation gives the equilibrium potential for K⁺ as about −90 mV and for Na⁺ as about +60 mV in typical neurons, while the Goldman equation yields the resting potential of approximately −70 mV.

The Nernst equation has wide-ranging applications: pH measurement (glass electrode responds to H⁺ concentration following Nernstian behavior at 59.2 mV/pH unit), battery design (predicting voltage under different state-of-charge conditions), corrosion science (calculating corrosion potentials in different environments), electroplating (optimizing deposition conditions), fuel cells (predicting performance under varying gas pressures), biosensors (glucose sensors, ion-selective electrodes), and neurophysiology (understanding action potentials and synaptic signaling).
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