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Nerst Equation

Reviewed by Raghvendra GopalCheckmark
Last updated: August 10, 2020

What Does Nerst Equation Mean?

The Nernst equation is a formula that represents the relationship between an electrode potential and the solution concentration. The Nernst equation can be effectively used for the prediction of concentrations that are near the electrode surface at any given applied potential. This is possible provided the cells are able to respond quickly to changes that are made to the applied potential.

Potential of the working electrode is a factor that determines the kind of redox processes that tend to occur at the electrode's surface. However, extremely negative potentials tend to reduce analytes while positive potentials tend to oxidize them.

The Nernst equation is widely used because of its many use cases. This does come with some conditions that have to remain constant to receive accurate results. One of the uses of the equation is finding the relation that exists between the cell potential of an electrochemical cell, as well as, the standard cell potential, temperature and reaction quotient. However, in cases where these constants cannot be present, it is still possible to get the cell potentials of some electrochemical cells with the help of the Nernst equation.

This calculation can be done at any temperature, pressure and reactant concentration.


Corrosionpedia Explains Nerst Equation

The Nernst equation determines the voltage (cell potential) of an electrochemical cell or the concentration of one of the components of the cell.

The Nernst equation is represented as:

Ecell = E0cell – (RT/nF)ln(Q)


Ecell = Cell potential under nonstandard conditions (V).

E0cell = Cell potential under standard conditions, 298K (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.

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 = -nFE

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 -298K (25°) and 1 atm pressure.

The above equation is then written as: ∆Go = -nFEo

From thermodynamics: ∆G = ∆Go + RTln(Q)

Substituting ∆G = -nFE and ∆Go = -nFEo in above equations, then: -nFE = -nFEo + RTln(Q)

Divide both sides of the equation above by -nF, then we have:

Ecell = Eocell – RT/nFln(Q)

Limitation of the Nernst Equation

Very dilute solutions of an ion that is close to infinity in concentration can be expressed in terms of the ion concentration, but the ion concentration would not be equal to the ion activity in cases of solutions being of high concentrations. Using the Nernst equation correctly in such cases would require experimental measurements being conducted on the ion under observation.

Nernst Equation Applications

The Nernst equation can be used to find out:

  1. Emf of an electrochemical cell.
  2. Standard electrode potentials.
  3. Single electrode reduction or oxidation potential at any conditions.
  4. The pH of solutions and solubility of difficult soluble salts.
  5. Unknown ionic concentrations.

The Nernst equation is an important relation to find out the cell potential of an electrochemical reaction. It provides the relationship between the cell potential and the reaction quotient of a reaction. This equation can be used to find out the potentials of individual electrodes and the potential differences across a pair of half-cells. However, it is generally easier to apply the Nernst equation to one electrode at a time.


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