Why is the Nernst slope about 59 mV per decade at room temperature?

Substituting R, T = 298 K, F, and converting natural to base-10 logarithms gives 2.303RT/F ≈ 0.0592 V, so each tenfold activity change shifts a one-electron electrode potential by roughly 59 mV.

Should the Nernst equation use concentrations or activities?

Strictly it uses activities; concentrations are an approximation valid only in dilute solutions, and deviations grow with ionic strength, which is why activity coefficients matter in accurate work.

Nernst Equation and Cell Potentials

The Nernst equation relates the equilibrium potential of an electrode or cell to the activities of the participating redox species, quantifying how concentration shifts the driving force of an electrochemical reaction.

Definition

An equation, E = E° − (RT/nF) ln Q, giving the equilibrium potential of an electrochemical half-cell or full cell as a function of the standard potential and the reaction quotient of species activities.

Scope

This topic covers the derivation and application of the Nernst equation, the meaning of standard electrode potentials, the additive construction of cell potentials from half-reactions, and the dependence of potential on temperature and concentration. It includes the use of the equation to predict reaction direction, calculate equilibrium constants from cell data, and interpret concentration cells.

Core questions

How does the potential of a half-cell change as the concentrations of oxidized and reduced species vary?
How are full-cell potentials assembled from tabulated half-cell reduction potentials?
How can equilibrium constants and free energies be extracted from measured cell potentials?
What is a concentration cell and how does it generate a potential from a single chemical species?

Key theories

Nernst equation: Derived from equating electrical and chemical work at equilibrium, it expresses electrode potential as a logarithmic function of species activities, reducing to E° at unit activity and predicting a 59 mV-per-decade shift per electron at 25 °C.
Additivity of half-cell potentials: A full cell's standard potential equals the cathode reduction potential minus the anode reduction potential, both referenced to the standard hydrogen electrode, allowing prediction of spontaneity from tabulated values.

Clinical relevance

The Nernst equation governs the response of pH meters, ion-selective electrodes, and biosensors, sets the open-circuit voltage of batteries, and quantifies membrane potentials in electrophysiology. It is the basis for potentiometric quantitative analysis.

History

Walther Nernst derived the relation in 1889 by combining thermodynamics with the osmotic theory of solutions, building on van 't Hoff's work on dilute solutions; the formulation became central to physical chemistry and was recognized by the 1920 Nobel Prize.

Key figures

Walther Nernst
Jacobus Henricus van 't Hoff

Seminal works

nernst1889
bard2001
atkins2018

Frequently asked questions

Why is the Nernst slope about 59 mV per decade at room temperature?: Substituting R, T = 298 K, F, and converting natural to base-10 logarithms gives 2.303RT/F ≈ 0.0592 V, so each tenfold activity change shifts a one-electron electrode potential by roughly 59 mV.
Should the Nernst equation use concentrations or activities?: Strictly it uses activities; concentrations are an approximation valid only in dilute solutions, and deviations grow with ionic strength, which is why activity coefficients matter in accurate work.