# Electrochemical potential

The electrochemical potential is the chemical potential of an ion in an electrical potential . ${\ displaystyle {\ overline {\ mu}} _ {i}}$ ${\ displaystyle \ mu _ {i}}$ ${\ displaystyle i}$ ${\ displaystyle \ varphi}$

${\ displaystyle {\ overline {\ mu}} _ {i} = \ mu _ {i} + z_ {i} \ mathrm {F} \ varphi}$
• ${\ displaystyle z_ {i}}$ Charge number of the ion
• F, Faraday's constant , F = 96485.33 C / mol
• ${\ displaystyle \ varphi}$, Local electrical potential

${\ displaystyle {\ overline {\ mu}} _ {i}}$Specifies how much work has to be done to increase the amount of ion species from to in a system at constant pressure , constant temperature and constant amounts of substance for all other system components . ${\ displaystyle P}$${\ displaystyle T}$${\ displaystyle i}$${\ displaystyle n_ {a}}$${\ displaystyle n_ {e}}$

${\ displaystyle \ Delta G = \ int _ {n_ {a}} ^ {n_ {e}} {\ overline {\ mu}} _ {i} \, dn_ {i} = 0}$

(Under the conditions mentioned, the work to be done is equal to the change in the Gibbs energy of the system. Compare chemical potential .) ${\ displaystyle \ Delta G}$

Since every potential difference describes the ability of a system to do work, passive chemical reactions with the participation of ions continue until the electrochemical potentials of all system components have equalized. The consideration of this principle at phase boundaries, which are permeable to only one type of ion, explains how the glass electrode works as a pH measuring device as well as the development of the Donnan potential (according to Frederick George Donnan ) on biological membranes and leads to the derivation of the Nernst equation .

The concept is not limited to ions, but can be applied to all electrically charged particles. For example, the Fermi energy of the electrons in a solid is equal to their electrochemical potential at temperature . The equalization of the electrochemical potentials of the electrons across the contact area between a metal and a semiconductor leads to the formation of a Schottky barrier , which is important in semiconductor technology. ${\ displaystyle T = 0 ~ \ mathrm {K}}$

The potential E of an electrode is a particularly important potential in electrochemistry and depends directly on the electrochemical potential discussed here, but differs from the strict definition of the electrochemical potential given here: E is an electrical voltage, i.e. one energy per charge, which but potential treated here is one energy per mole. ${\ displaystyle {\ overline {\ mu}} _ {i}}$${\ displaystyle {\ overline {\ mu}} _ {i}}$