Nernst equation

In electrochemistry, the Nernst equation is an equation that relates the reduction potential of an electrochemical reaction (half-cell or full cell reaction) to the standard electrode potential, temperature, and activities (often approximated by concentrations) of the chemical species undergoing reduction and oxidation. It is the most important equation in the field of electrochemistry. It is named after the German physical chemist who first formulated it, Walther Nernst.

The Nernst equation is easily derived from the standard changes in the Gibbs free energy associated with an electrochemical transformation. For any electrochemical reduction reaction of the form ${\displaystyle Ox+ze\rightarrow Red}$, standard thermodynamics says that the actual free energy change ${\displaystyle \Delta G}$ is related to the free energy change under standard conditions ${\displaystyle \Delta G^{\ominus }}$ by the relationship ${\displaystyle \Delta G=\Delta G^{\ominus }+RT\ln(Q)}$, where Q is the reaction quotient. The electrochemical potential E associated with an electrochemical reaction of the form ${\displaystyle Ox+ze\rightarrow Red}$ is defined as the decrease in Gibbs free energy per Coulomb of charge transferred, which leads to the relationship ${\displaystyle \Delta G=-zFE}$. The constant F (the Faraday constant) is a units conversion factor ${\displaystyle F=N_{\text{A}}q}$ where NA is Avogadro's number and q is the fundamental electron charge. This immediately leads to the Nernst Equation.

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