The Nernst Equation: Why Concentration Shifts Electrode Potential

Standard potential is only the starting point

A cell's standard electrode potential E° is measured under fixed reference conditions — typically 1 M concentrations, 1 atm partial pressure, 25°C. Real electrochemical cells, real batteries and real biological membranes almost never sit exactly at those conditions, and the potential shifts measurably as concentrations, temperature or pressure move away from standard. The Nernst equation (Walther Nernst, 1889) quantifies exactly how much:

E = E° − (RT/nF)·ln(Q)

Here R is the gas constant, T the absolute temperature, n the number of electrons transferred in the half-reaction, F the Faraday constant (charge per mole of electrons), and Q the reaction quotient — the same ratio of product to reactant concentrations (or activities) used in equilibrium expressions, but evaluated at the current, not necessarily equilibrium, concentrations. At standard conditions Q = 1, ln(1) = 0, and E collapses back to E° exactly, which is a useful sanity check on the formula.

Why concentration moves the potential

Electrode potential reflects the thermodynamic driving force for the reaction, which depends on how far the system is from equilibrium. Raise the concentration of the products of the reduction half-reaction (or lower the reactants) relative to standard, and Q rises, ln(Q) rises, and E decreases — the reaction has less driving force left because it's already closer to where a high-product concentration would naturally push it toward equilibrium. Conversely, depleting the products (or raising reactant/oxidised-species concentration) lowers Q and raises E, since there's more thermodynamic distance left for the reaction to still go forward. This is exactly why a battery's voltage sags as it discharges — reactants are consumed, products accumulate, Q climbs, and E falls, even though the electrodes themselves haven't chemically changed.

The at-25°C shortcut, and why temperature matters more broadly

At room temperature (298 K) with base-10 logarithms, RT/F works out to about 0.0592 V per electron transferred, giving the commonly memorised form E = E° − (0.0592/n)·log₁₀(Q). But that constant is only valid at that specific temperature — RT/nF is directly proportional to T, so a cell running significantly hotter or colder (a car battery in winter, an industrial electrolysis cell) has a measurably different concentration sensitivity, and the 0.0592 shortcut quietly stops being accurate. The general form with ln and explicit T is the one that's actually always correct.

A worked single-electron example

Consider a metal/metal-ion half-cell, M²⁺ + 2e⁻ → M, with E° = +0.34 V (this is close to the copper couple) and n = 2. Dilute the M²⁺ concentration from 1 M down to 0.01 M at 25°C:

E = 0.34 − (0.0592/2)·log₁₀(1/0.01)
  = 0.34 − 0.0296·log₁₀(100)
  = 0.34 − 0.0296·2
  = 0.34 − 0.0592
  = 0.281 V

A hundred-fold dilution of the metal ion drops the potential by about 59 mV — small compared to E° itself, but very measurable, and exactly the mechanism behind ion-selective electrodes: a pH electrode, for instance, is a Nernst-equation device that reports hydrogen-ion concentration precisely because its measured potential is a known logarithmic function of [H⁺].

Why cells (and neurons) are Nernst-equation devices too

The same equation, applied per ion species across a membrane rather than at a metal electrode, gives the Nernst potential (equilibrium potential) for that ion — the membrane voltage at which the electrical and concentration gradients for that ion exactly balance. This is the starting point for understanding resting membrane potential and action potentials in neurons: the sodium and potassium Nernst potentials, weighted by each ion's membrane permeability, set the baseline the cell's electrical activity operates around.

Frequently asked questions

Try it live

Everything above runs in your browser — open Nernst Equation Simulator and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.