The equilibrium potential difference between two conducting phases in contact, most often an electronic conductor such as a metal or semiconductor on the one hand, and an ionic conductor such as an electrolyte solution (a solution containing ions) on the other. Electrode potentials are not experimentally accessible, but the differences in potential between two electronic conductors making contact with the same ionic conductor (that is, the difference between two electrode potentials) can be measured. A useful scale of electrode potentials can therefore be obtained when a particular electrode potential is set equal to zero by definition. There are several conventions, based on different definitions of the zero point on the scale of electrode potential, but all tables use the so-called standard hydrogen convention. See also: Electrode; Reference electrode
The interfacial potential difference is usually the consequence of the transfer of some charge carriers from one conducting phase to the other. For example, when a piece of silver, which contains silver ions and free, so-called conduction electrons, is in contact with an aqueous solution of silver nitrate, the only species common to the two phases are the silver ions. Their concentration (volume density) is constant in the metal but variable (from zero to the solubility limit of the silver salt used) in the solution. When more silver ions transfer from the solution to the metal than in the opposite direction, an excess of negatively charged nitrate ions remains in the solution, which therefore acquires a negative charge. However, the metal gains more silver ions than it loses, and therefore acquires a positive charge. Such a charge separation leads to a potential difference across the boundary between the two phases. The continued buildup of such charges makes the potential of the metal more and more positive with respect to that of the solution. This effect in turn leads to electrostatic repulsion of the silver ions in the solution phase immediately adjacent to the metal; these are the very metal ions that are candidates for transfer across the boundary. Consequently, the electrostatic repulsion decreases the tendency of silver ions to move from the solution to the metal, and eventually the process reaches equilibrium, at which point the tendency of ions to transfer is precisely counterbalanced by the repulsion of the candidate ions by the existing potential difference. At that potential, there is no further net transfer of charges between the contacting phases, although individual charges can still exchange across the phase boundary, a process which gives rise to the exchange current.
With a small number of metals, especially silver and mercury, interfacial equilibrium is often established rapidly, well within milliseconds. However, with most metals, the equilibrium state is reached much more slowly, especially when the electrode process involves bond breaking or other complicated reaction mechanisms. In some cases, equilibrium is never attained, and the equilibrium potentials can be known only through calculation.
For a metal in contact with its metal ions of valence z, the potential difference E can be expressed in terms of a standard potential E° (describing the affinity of the metal for its ions) and the concentration c of these ions in solution through the Nernst equation (1),
where R is the gas constant, T is the absolute temperature, and F is the Faraday.
When the metal ions in solution form a sparingly soluble salt, the solubility equilibrium can be used to convert a metal electrode responding to its own metal cations (positive ions) into an electrode responding to the concentration of anions (negative ions). Typical examples are the silver/silver chloride electrode, based on the low solubility of silver chloride (AgCl), and the calomel electrode, based on the poor solubility of calomel (Hg2Cl2).
An equilibrium potential difference between a metal and an electrolyte solution can also be established when the latter contains a redox couple, that is, a pair of chemical components that can be converted into each other by the addition or withdrawal of electrons, by reduction or oxidation respectively. In that case the metal often merely acts as the supplier or acceptor of electrons. When metal electrons are donated to the solution, the oxidized form of the redox couple is reduced; when the metal withdraws electrons from the redox couple, its reduced component is oxidized. Again, the buildup of a charge separation generates a potential difference, which counteracts the electrochemical charge transfer and eventually brings the process to equilibrium, a state in which the rate of oxidation is exactly equal to the rate of reduction. The dependence of the equilibrium electrode potential on the concentrations of and of the oxidized and reduced forms respectively is described by a Nernst equation of the form (2),
where n denotes the number of electrons () transferred between the oxidized species (Ox) and the reduced species (Red) in the reactions Red. A typical example is the reduction of hydrogen ions H+ to dissolved hydrogen molecules H2, and vice versa, in which case the reactions are 2H+ + 2e- H2, and for which the Nernst equation is of the form (3).
Redox potentials involving a gas are often established slowly, if at all. For determinations of such a redox potential, platinum is often used as the metal, because it is chemically and electrochemically stable. See also: Oxidation-reduction
Electrode potentials can also be established at double phase boundaries, such as that between two aqueous solutions separated by a glass membrane. This glass electrode is commonly used for measurements of the pH, a measure of the acidity or basicity of solutions. The mechanism by which the glass electrode operates involves ion exchange of hydrogen ions at the two glass-solution interfaces. See also: Ion exchange
In all the above examples, the two contacting phases can have only one type of charge carrier in common. Usually, no equilibrium potential difference is established when more than one type of charge carrier can cross the interface, but often (depending on the nature of the metal and of the chemical components of the solution, and sometimes also depending on the geometry of the contact region) an apparently stable potential can still be obtained, which corresponds to zero net charge transfer. This can be a so-called mixed potential, important in metal corrosion, or a junction potential, which figures in most measurements of electrochemical potentials and usually limits the accuracy and precision of such measurements, including that of the pH. See also: Corrosion; Electrochemical series
In determining electrode potentials, there are several complications. In the first place, it follows from thermodynamics that the Nernst equation should be written in terms of activities rather than concentrations. The difference between these two parameters is often small but seldom completely negligible. The problem is that the activities of ions (in contrast to those of neutral molecules) are not experimentally accessible, although there are theoretical models that allow their estimation in sufficiently dilute solutions. See also: Activity (thermodynamics)
Second, measurements of potential differences always involve the potential difference between two metals rather than that between a metal and a solution. Therefore, electrode potentials as defined above cannot be measured either. The latter complication is circumvented by setting the electrochemical potential of one particular metal-solution interface equal to zero by definition. W. Nernst suggested that a normal hydrogen electrode be used as the common zero point; he defined this as a metal in contact with a solution saturated with hydrogen gas at 1 atm partial pressure and containing 1 mole of a monoprotic acid per liter. However, it was soon found that the nature of the acid used, and the presence of other components in the solution, would affect the potential of such an electrode—a reflection of the fact that the electrode responds to the activity rather than the concentration of the hydrogen ions. The problem here is that the activity of ions (including that of hydrogen ions) is not known, except at or near infinite dilution. Thus the standard hydrogen electrode, defined in terms of hydrogen ion activity rather than concentration, is not experimentally realizable. An alternative definition, in terms of an acid activity, has an anion sensitivity similar to the original definition in terms of concentrations. Moreover, use of the hydrogen electrode can lead to a high liquid junction potential, whereas use of the standard calomel electrode tends to reduce it. In practice, therefore, other electrodes are often used, such as silver–silver chloride electrode or a calomel electrode. In many areas of electrochemistry, the de facto reference electrode is the saturated calomel electrode, which consists of mercury plus calomel in a saturated aqueous solution of potassium chloride (KCl). The standard hydrogen electrode is used mostly for physico-chemical calculations.
Because these measurements involve a potential difference, there has been considerable confusion about the definition of that difference; that is, whether it is defined as the potential of the metal minus that of the solution, or the other way around. This is a matter of a sign convention. The problem is usually framed in terms of oxidation potentials versus reduction potentials. In 1953 the international community settled on the latter and simply called them electrode potentials.
Another zero point is often used to anchor the scale of electrode potentials of semiconductor electrodes. Here the reference point is the work function, that is, the electrical work necessary to remove an electron from the interior of the phase to a far-away position in vacuum. This is, theoretically, a more meaningful scale. Unfortunately, the work function is not known with sufficient accuracy and precision to make this scale practical. See also: Work function (thermodynamics)
There are other factors besides charge transfer that can cause interfacial potential differences. Oriented dipolar molecules at interfaces can give rise to interfacial potential differences, even though they represent a charge separation within a layer of only molecular dimensions. Similarly, adsorbed molecules and ions can affect the interfacial potential difference when their adsorption involves a partial charge transfer. None of these phenomena affect the thermodynamic potentials, but they have effectively blocked attempts to define an absolute potential that is both practical and theoretically meaningful.
There are four main applications for measurements of electrode potentials: (1) in the establishment of the oxidative and reductive power of redox systems, the so-called electromotive series; (2) as concentration probes, such as in pH measurements; (3) as sources of chemical equilibrium data; and (4) as the primary (or independent) variable in studies of electrode reactions.
The electromotive series is a listing of redox couples in the order of their potentials. The most positive potentials correspond to the strongest oxidants, while most negative potentials identify the strongest reductants. This series therefore serves to organize redox systems according to their oxidative or reductive power. See also: Electromotive force (cells)
A combination of two electrodes can be employed to determine the concentration of a particular species in a sample solution. One of the two electrodes is the indicator electrode, sensitive to a particular ionic species in the sample solution. The other, reference electrode typically comprises a separate compartment containing a metal in contact with its sparingly soluble salt and an excess of the anion of that salt (as in the calomel and silver/silver chloride electrodes), or with a redox couple such as the combination of iodide and triiodide ions. The solution in the reference electrode compartment then makes contact with the sample solution through a very constrictive contact, such that solution mixing is minimized. Moreover, the nature of the solution in the junction is chosen so that the potential difference across that liquid junction will be as small as possible. This can be achieved by using a high concentration of a salt with, as much as possible, equitransferent ions (ions that have near-equal mobilities, such as in KCl or NH4NO3). Under those conditions the liquid junction potential can often be neglected, and the Nernst equation can be written in terms of measurable potentials and concentrations. This is the basis of the measurement of pH using the combination of a glass electrode and a calomel, silver/silver chloride or iodide/triiodide reference electrode. Many other indicator electrodes are available, responding in a similar fashion to different cations and anions. There are also electrodes that respond to neutral compounds. Such electrodes are often based on the presence of an immobilized enzyme. For instance, when an enzyme reacts with its substrate, it may release or consume hydrogen ions. The electrode then responds to the resulting change in the concentration of hydrogen ions and, therefore, indirectly to the enzyme substrate. See also: Ion-selective membranes and electrodes
Because equilibrium potentials can be correlated with chemical equilibrium constants, measurements of the potentials of electrochemical cells are a major source of numerical information about equilibrium constants. Measurements of electrode potentials not involving liquid junctions can yield data accurate to about 10 microvolts, from which salt activities (but not the corresponding ionic activities) can be calculated. Measurements involving liquid junctions (such as pH measurements using reference electrodes with liquid junctions) are much less reliable, because of the uncertainties in the liquid junction potentials, of the order of one or a few millivolts.
The rates of electrode reactions depend strongly (typically, exponentially) on the electrode potential, and most measurements of the rates of electrode reactions are therefore performed under tight control of this potential, often using a specialized instrument called a potentiostat or, in biophysical applications, a voltage clamp. See also: Biopotentials and ionic currents; Electrochemistry