Editing Electrochemical potential (section)

==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 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<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 electrochemical 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 electrochemical potentials of the two regions are different, more molecules will move to the lower electrochemical 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 mole is exactly equal to the electrochemical potential difference between the two regions.