electrochemistry Electrochemistry is the branch of physical chemistry concerned with the relationship between electrical potential difference, as a measurable and quantitative phenomenon, and identifiable chemical change, with the potential difference as an out ...

, the electrochemical potential (ECP), ', is a

thermodynamic Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of ...

measure of

chemical potential In thermodynamics, the chemical potential of a species is the energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potential of a speci ...

that does not omit the energy contribution of

electrostatics Electrostatics is a branch of physics that studies electric charges at rest ( static electricity). Since classical times, it has been known that some materials, such as amber, attract lightweight particles after rubbing. The Greek word for a ...

. Electrochemical potential is expressed in the unit of J/ mol.

Introduction

Each

chemical species A chemical species is a chemical substance or ensemble composed of chemically identical molecular entities that can explore the same set of molecular energy levels on a characteristic or delineated time scale. These energy levels determine the wa ...

(for example, "water molecules", "sodium ions", "electrons", etc.) has an electrochemical potential (a quantity with units of energy) at any given point in space, 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⁺) dissolved uniformly in it, and an

electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical 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 dissolved sugar on one side and none on the other side, each sugar molecule will randomly

diffuse Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical p ...

around the water, until there is equal concentration of sugar everywhere. We say that the sugar molecules have a "

", 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 The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as the amount of work energy needed to move a unit of electric charge from a reference point to the specific point in ...

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 Semipermeable membrane is a type of biological or synthetic, polymeric membrane that will allow certain molecules or ions to pass through it by osmosis. The rate of passage depends on the pressure, concentration, and temperature of the molecule ...

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 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 mole is exactly equal to the electrochemical potential difference between the two regions.

Conflicting terminologies

It is common in electrochemistry and solid-state physics to discuss both the

and the electrochemical potential of the

electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have n ...

s. However, in the two fields, the definitions of these two terms are sometimes swapped. In electrochemistry, the ''electrochemical potential'' of electrons (or any other species) is the total potential, including both the (internal, nonelectrical) chemical potential and the electric potential, and is by definition constant across a device in equilibrium, whereas the ''chemical potential'' of electrons is equal to the electrochemical potential minus the local electric potential energy per electron. In solid-state physics, the definitions are normally compatible with this, but occasionally the definitions are swapped. This article uses the electrochemistry definitions.

Definition and usage

In generic terms, electrochemical potential is the

mechanical work In physics, work is the energy transferred to or from an object via the application of force along a displacement. In its simplest form, for a constant force aligned with the direction of motion, the work equals the product of the force stre ...

done in bringing 1 mole of an ion from a

standard state In chemistry, the standard state of a material (pure substance, mixture or solution) is a reference point used to calculate its properties under different conditions. A superscript circle ° (degree symbol) or a Plimsoll (⦵) character is use ...

to a specified

concentration In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: '' mass concentration'', '' molar concentration'', ''number concentration'', ...

and

. According to the

IUPAC The International Union of Pure and Applied Chemistry (IUPAC ) is an international federation of National Adhering Organizations working for the advancement of the chemical sciences, especially by developing nomenclature and terminology. It is ...

definition, 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

\bar_i = \mu_i + z_i F\Phi,

where: * ''_i'' is the electrochemical potential of species ''i'', in J/mol, * ''μ_i'' is the

of the species ''i'', in J/mol, * ''z_i'' is the valency (charge) of the ion ''i'', a dimensionless integer, * ''F'' is the

Faraday constant In physical chemistry, the Faraday constant, denoted by the symbol and sometimes stylized as ℱ, is the electric charge per mole of elementary charges. It is named after the English scientist Michael Faraday. Since the 2019 redefinition of ...

, in C/mol, * Φ is the local electrostatic potential, in V. In the special case of an uncharged atom, ''z_i'' = 0, and so ''_i'' = ''μ_i''. Electrochemical potential is important in biological processes that involve

molecular diffusion Molecular diffusion, often simply called diffusion, is the thermal motion of all (liquid or gas) particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size (mass) of ...

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 In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors. Common types of potential energy include the gravitational potenti ...

through which energy may be conserved. In

cell membranes The cell membrane (also known as the plasma membrane (PM) or cytoplasmic membrane, and historically referred to as the plasmalemma) is a biological membrane that separates and protects the interior of all cells from the outside environment (t ...

, the electrochemical potential is the sum of the

and the

membrane potential Membrane potential (also transmembrane potential or membrane voltage) is the difference in electric potential between the interior and the exterior of a biological cell. That is, there is a difference in the energy required for electric charges ...

Incorrect usage

The term ''electrochemical potential'' is sometimes used to mean an

electrode potential In electrochemistry, electrode potential is the electromotive force of a galvanic cell built from a standard reference electrode and another electrode to be characterized. By convention, the reference electrode is the standard hydrogen electrode ...

(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", 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).

References

External links