It is not possible to measure the electrode potential of a single electrode in isolation. This idea can be explained very simply:

If we consider that the reaction at an electrode is actually a half reaction, one half of a redox process, it is obvious that to maintain the overall number of electrons, there must be an associated half reaction occurring. This other half-reaction must either involve another redox couple, with its own associated potential, or the transfer of free electrons, which is an energetically very disfavoured process that to all intents and purposes is never observed.

We thus take the step of defining one electrode as having a potential of zero volts, and measuring all other electrode potentials relative to this electrode.

The electrode selected for this purpose is the Standard Hydrogen Electrode (SHE), which consists of a platinum electrode coated with a thin layer of platinum black (a finely divided form of platinum which provides more catalytic sites for the reaction). The electrode is dipped into an aqueous solution of 1.18M hydrochloric acid (which corresponds to an activity of one for the hydrogen ions), and hydrogen gas at a pressure of one atmosphere is bubbled over the electrode surface. It is represented as follows:

Pt | H2(g) | H+(aq) , Eº = 0

The standard potential, Eº, of any other couple is then assigned by constructing a cell in which it forms the right-hand electrode, and the standard hydrogen electrode is the left-hand electrode.

For example, the standard potential of the Cu²⁺/Cu couple is the standard potential of the following cell:

Pt | H_2(g) | H⁺_(aq) Cu²⁺_(aq) | Cu_(s)

Note that although standard potentials are written as though they refer to a half-reaction, eg

Cu²⁺_(aq) + 2e^- => Cu_(s) Eº = +0.34V

it is implicit in their definition that they actually refer to the overall reaction

Cu²⁺_(aq) + H_2(g) => Cu_(s) + 2H⁺_(aq) Eº = +0.34V

The standard potential of a cell formed from any two electrodes can be calculated as the difference of the standard potentials of the two electrodes. The standard cell potential is given by the value Eº_right - Eº_left , where the standard potentials refer to the electrodes that make up the cell.

An important feature of standard cell potentials and standard potentials is that they are not molar quantities. i.e. multiplication of the chemical equation for a half-reaction or cell reaction by a number does not change the value of the standard potential for the reaction. (In terms of the equations which govern these properties, it can be seen that this is because the numerical factor multiplies both the standard Gibbs energy for the reaction, which is a molar quantity, and the ν, the number of electrons transferred in the reaction. There is thus no change in the value of Eº, which depends upon the ratio of these two quantities.) Thus:

Cu²⁺_(aq) + 2e^- => Cu_(s) ΔGº_r = - 65.49kJ Eº = +0.34V , ν = 2

2Cu²⁺_(aq) + 4e- => 2Cu_(s) ΔGº_r = - 130.98kJ , Eº = +0.34V , ν = 4