    # Nernst Equation

Last Updated: 5/7/19 by Tim Paschkewitz ### 1Nernst Equation

There are many resources that describe the detailed background, derivation, and applications of this equation. Here, we present just a snippet to get you started.

To account for the possibility of non-unity activities in an electrochemical reaction, the Nernst equation (see below) can be used to express the equilibrium electrode potential $(E)$ in terms of the actual activities, $\displaystyle E = E^{0} + \frac{RT}{nF} \ln{\left(\frac{a_O}{a_R}\right)}$

where $E_0$ is the standard potential for the electrochemical couple,  $R$ is the Universal Gas Constant (8.314 J/mol K),  $T$ is absolute temperature,  $n$ is the number of electrons, and $F$ is Faraday's Constant (96,485 C/mol). Usually, the activities of molecules or ions dissolved in solution are assumed to be the same as their molar concentrations, so the Nernst Equation is often written as $\displaystyle E= E^{0' } + \frac{RT}{nF}\ln{\left(\frac{C_O}{C_R}\right)}$

where $E_0'$ is the formal potential for the electrochemical couple, $C_O$ and $C_R$ are the concentrations of the dissolved molecules or ions in the oxidized and reduced forms, respectively, at the surface of the electrode.  Note that any liquid or solid phase materials at the electrode surface (such as the solvent or the electrode itself) have unity activity and thus do not appear in the Nernst equation.

The formal potential is the measured half-cell potential when oxidized and reduced species are present at unity concentration.  In some cases formal and standard potential are the same value.

### 2References

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