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In [[electrochemistry]], the '''electrochemical potential''', <math>\bar{\mu}</math>, sometimes abbreviated to ECP, is a [[thermodynamic]] measure that combines the concepts of energy stored in the form of [[chemical potential]] and [[electric charge|electrostatics]]. Electrochemical potential is expressed in the unit of [[Joule|J]]/[[Mole (unit)|mol]].
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==Introduction==
 
Each [[chemical species]] (for example, "water molecules", "sodium ions", "electrons", etc.) has an electrochemical potential (a quantity with units of energy) at any given location, which represents how easy or difficult it is to add more of that species to that location. If possible, a species will move from areas with higher electrochemical potential to areas with lower electrochemical potential; in equilibrium, the electrochemical potential will be constant everywhere for each species (it may have a different value for different species). For example, if a glass of water has sodium ions (Na<sup>+</sup>) dissolved uniformly in it, and an [[electric field]] is applied across the water, then the sodium ions will tend to get pulled by the electric field towards one side. We say the ions have [[electric potential energy]], and are moving to lower their potential energy. Likewise, if a glass of water has a lot of [[Dissolution (chemistry)|dissolved]] sugar on one side and none on the other side, each sugar molecule will randomly [[Molecular diffusion|diffuse]] around the water, until there is equal concentration of sugar everywhere. We say that the sugar molecules have a "[[chemical potential]]," which is higher in the high-concentration areas, and the molecules move to lower their chemical potential. These two examples show that an [[electrical potential]] and a chemical potential can both give the same result: A redistribution of the chemical species. Therefore it makes sense to combine them into a single "potential", the ''electrochemical potential'', which can directly give the ''net'' redistribution taking ''both'' into account.
 
It is (in principle) easy to measure whether or not two regions (for example, two glasses of water) have the same electrochemical potential for a certain chemical species (for example, a solute molecule): Allow the species to freely move back and forth between the two regions (for example, connect them with a [[semi-permeable membrane]] that lets only that species through). If the chemical potential is the same in the two regions, the species will occasionally move back and forth between the two regions, but on average there is just as much movement in one direction as the other, and there is zero net migration (this is called "diffusive equilibrium"). If the chemical potentials of the two regions are different, more molecules will move to the lower chemical potential than the other direction.
 
Moreover, when there is ''not'' diffusive equilibrium, i.e., when there is a tendency for molecules to diffuse from one region to another, then there is a certain [[Thermodynamic free energy|free energy]] released by each net-diffusing molecule. This energy, which can sometimes be harnessed (a simple example is a [[concentration cell]]), and the free-energy per molecule is exactly equal to the electrochemical potential difference between the two regions.
 
== Conflicting terminologies ==
{{see also|Fermi level}}
 
It is common in both solid-state physics and electrochemistry to discuss the [[chemical potential]] and electrochemical potential of an [[electron]]. However, in the two fields, the definitions of these two terms are sometimes swapped. In electrochemistry, the ''electrochemical potential'' of an electron (or any other species) is by definition constant across a device in equilibrium, while the ''chemical potential'' is equal to the electrochemical potential minus the local [[electric potential energy]] of the electron.<ref>See, for example, ''Electrochemical Methods'' by Bard and Faulkner, 2nd edition, Section 2.2.4(a),4-5.</ref> In solid-state physics, the opposite definitions are occasionally<ref>See, for example, ''Solid State Physics'' by Ashcroft and Mermin, page 593.</ref> (but not always)<ref>See, for example, ''Introduction to solid-state theory'' by Otfried Madelung [http://books.google.com/books?id=yK_J-3_p8_oC&pg=PA198 page 198]</ref> used, where the ''chemical potential'' of an electron is by definition constant across a device in equilibrium; while the ''electrochemical potential'' is equal to the chemical potential minus the local [[electric potential energy]] of an electron.
 
This article uses the electrochemistry definitions.
 
== Definition and usage==
 
In generic terms, electrochemical potential is the [[mechanical work]] done in bringing 1 mole of an ion from a [[standard state]] to a specified [[concentration]] and [[electrical potential]]. According to the [[IUPAC]] definition,<ref>IUPAC Gold Book, http://goldbook.iupac.org/E01945.html</ref> it is the partial molar Gibbs energy of the substance at the specified electric potential, where the substance is in a specified phase. Electrochemical potential can be expressed as
 
:<math>\bar{\mu}_i=\mu_i + z_iF\Phi</math>,
 
where:
* <math>\bar{\mu}_i</math> is the electrochemical potential of species i, J/mol
* <math>\mu_i</math> is the [[chemical potential]] of the species i, J/mol
* <math>z_i</math> is the valency (charge) of the ion i, dimensionless
* <math>F</math> is [[Faraday constant|Faraday's Constant]], C/mol
* <math>\Phi</math> is the local electrostatic potential, V.
 
In the special case of an uncharged atom, <math>z_i</math> = 0 and so <math>\bar{\mu}_i=\mu_i </math>.
 
Electrochemical potential is important in biological processes that involve [[molecule|molecular]] [[diffusion]] across membranes, in electroanalytical chemistry, and industrial applications such as batteries and fuel cells. It represents one of the many interchangeable forms of [[potential energy]] through which energy may be [[conservation of energy|conserved]].
 
In [[cell membranes]], the electrochemical potential is the sum of the [[chemical potential]] and the [[membrane potential]].
 
==Incorrect usage==
The term ''electrochemical potential'' is sometimes used to mean an [[electrode potential]] (either of a corroding electrode, an electrode with a non-zero net reaction or current, or an electrode at equilibrium). In some contexts, the electrode potential of corroding metals is called "electrochemical corrosion potential",<ref>Grover, D.J.: [http://dspace.mit.edu/bitstream/handle/1721.1/39772/37471582.pdf Modeling water chemistry and electrochemical corrosion potential in boiling water reactors], MIT thesis, 1996</ref> which is often abbreviated as ECP, and the word "corrosion" is sometimes omitted. This usage can lead to confusion. The two quantities have different meanings and different dimensions: the dimension of electrochemical potential is energy per mole while that of electrode potential is voltage (energy per charge).
 
==See also==
* [[Fermi level]]
* [[Electrochemical gradient]]
* [[Membrane potential]]
* [[Concentration cell]]
 
==References==
{{Reflist}}
 
==External links==
* [http://www.life.uiuc.edu/crofts/bioph354/lect9.html Electrochemical potential] - lecture notes from University of Illinois at Urbana-Champaign
 
{{DEFAULTSORT:Electrochemical Potential}}
[[Category:Electrochemistry]]
[[Category:Thermodynamics]]

Revision as of 23:53, 13 February 2014

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