# Nerst Equation

Last updated: August 10, 2020

## What Does Nerst Equation Mean?

The Nernst equation is used to determine the voltage (cell potential) of an electrochemical cell or to find the concentration of one of the components of the cell.

Nernst equation is represented as:

Ecell = E0cell - (RT/nF) ln (Q)

Where:

Ecell = cell potential under nonstandard conditions (V)

E0cell = cell potential under standard conditions, 298 K (25°) and 1 atm pressure

R = gas constant, which is 8.31 (volt-coulomb)/(mol-K)

T = temperature (K)

n = number of moles of electrons exchanged in the electrochemical reaction (mol)

F = Faraday's constant, 96500 coulombs/mol

Q = reaction quotient, a function of the activities or concentrations of the chemical species involved in a chemical reaction

## Corrosionpedia Explains Nerst Equation

The Nernst equation is derived from electromotive force and Gibbs energy under nonstandard conditions.

Eo = Eo reduction - Eo oxidation

Since the change in Gibbs free energy (∆G) is also related to spontaneity of a reaction, ∆G and E are related. Specifically:

∆G = -n F E

Where, n is the number of electrons transferred in the reaction, F is the Faraday constant (96500 C/mol) and E is cell potential difference. Under standard conditions of -298 K (25°) and 1 atm pressure.

The above equation is then written as: ∆Go = -n F Eo

From thermodynamics: ∆G = ∆Go + R T ln (Q)

Substituting ∆G = -n F E and ∆Go = -n F Eo in above equations, then: -nFE = -nFEo +RT ln (Q)

Divide both sides of the equation above by -n F. Then we have:

Ecell = Eocell -RT/nF ln (Q) 