Electrode Potential
Given a metal electrode in a solution that contains ions of that metal, a potential difference between the metal and the solution will develop. This equilibrium is expressed as
The potential difference between the metal and the solution cannot be measured directly. You can measure the difference in potential between two electrodes in the solution. This involves two potential differences, one at each interface between electrode and solution. This potential difference can be measured by comparison with a reference electrode where the potential difference between the two phases is known. The ultimate reference is the normal hydrogen electrode, the potential of which is defined as zero.
Another type involves an inert metal in contact with a gas in equilibrium with ions in solution, such as the hydrogen or chlorine electrodes.
An equilibrium is established between the ions and adsorbed gas and the metal which determines the potential of the electrode. The normal hydrogen electrode consists of hydrogen ion activity of 1 and 1atm. H2 at 25°C.
In some cases the reduced and oxidized forms are in solution, e.g., Fe3+ and Fe2+. The inert metal serves as an electronic conductor between the two species. This is called a redox electrode.
The potential difference between the two phases, metal and solution, is represented by Df and is given by
fM and fS are called the inner or Galvani potentials of the two phases.
Each of these systems reaches equilibrium by the transfer of charge across the interface between the two phases. The Galvani potential has two distinct components. One is the Volta potential y which is the long range coulombic forces near the electrode and the surface potential c which is determined by short range effects of adsorbed ions and oriented water molecules. Thus the Galvani or inner potential is expressed as
The Volta potential can be measured directly. The surface potential cannot. Thus the Galvani potential can only be measured relative to a reference electrode.
Electrode potentials and activity: the Nernst equation
If we have the case of a metal in equilibrium
with its ions in solution, at equilibrium the electrochemical potential 
of the common species is equal in both phases. Suppose we had a
copper electrode in a solution that contained cupric ions. For the system
at equilibrium
For each phase the electrochemical potential consists of the chemical potential and a potential term. The chemical potential can further be separated into the standard chemical potential (unit activity) and an activity term. So the electrochemical potential for species i is given by
R is the gas constant 8.314 joule/mole·K, T is absolute temperature (K), F is the Faraday constant 96,485 coul/mole. This equation can be substituted for each phase in the equilibrium equation for copper. Then if we want the potential difference between the two phases we get
or
which is known as the Nernst equation. The logarithmic term can be generalized as ln of products of activities of reaction products (raised to powers of stoichiometric coefficients) divided by products of activities of reactants (raised to powers of stoichiometric coefficients).
This equation only applies to systems in equilibrium. At equilibrium there is no net current.
Applied to the general form
and replacing the difference in galvani potentials with E gives
The van’t Hoff reaction equation expresses free energy change for a chemical reaction as
where p and r indicate products and reactants. For the reaction Mn++ne=M this can be written
The free energy change is related to electrode potential by
and
This means that reduction of one mole of Mn+ to M requires passage of n Faradays, nF coulombs. Passage of charge nF through a potential difference of E volts constitutes work of nFE joules. This work, done at constant temperature and pressure is equal to the the decrease in free energy of the system, -DG.