Let us begin with the consideration of an electric cell.[51] Figure 9.8 is a schematic representation of a cell.

A half cell is composed of a metallic electrode immersed in a salt solu­tion. Here, for simplicity, we have assumed that the salt cation is the singly ionized metal of the electrode. Thus, on the electrodes, electron capture and loss reactions can take place such as:

M^ + e_^ M1 [AG1] (9.41)

M2 <=; MJ+ e_ [-AG2] (9.42)

We give a positive value to the free energy release AG12 of the electron capture by an ion, since this a rather natural choice corresponding to the elementary atomic reactions.

If a conductor connects the two electrodes, an electron transfer between the two half cells can occur which results in the possible reactions

M+ + M2 ) M+ + M1 [AG = AG1 — AG2] (9.43)

M+ + M2 ^ M+ + M1 [AG = AG2 — AG1]. (9.44)

The direction of the electron transfer depends upon the sign of AG = AG1 — ag2. If AG > 0, electrons will flow from right to left, and

therefore a positive current will flow from left to right. A positive potential

V will be established between the left and the right electrodes. Assume that a mole of M1 is produced.[52] The number of electrons transferred is thus equal to the Avogadro’s number, and the amount of charge transferred is a Faraday, i. e.

1 Faraday =(1.6 x 10-19)x(6 x 1023) = 96 000 Coulomb. (9.45)

The work done by this transfer is therefore

W = 96 000 x V. (9.46)

Neglecting resistive losses, this work has to be provided by the molecular free energy change AG, so that

AG = 96 000 V (9.47)

V = 1.04 x 10-5AG. (9.48)

The generalization of these equations to the case when the M1 ions are the n1 charged M?+ species is straightforward and yields

M?+ + n2M2 ) Mn22+ + n1M1 [AG] (9.49)

AG = 96000n1 V (9.50)

a g

V = 1.04 x 10-5——- . (9.51)

n1

In practice, electro-chemists use a standard reference for each element which is the cell of the element associated with the hydrogen cell H2/H+ with the reaction 2H+ + 2e- ) H2 with one molar electrolyte concentration and normal temperature and pressure conditions. By convention the value of AG for the hydrogen cell under these conditions is assumed to be 0. Each ionic state of elements is, therefore, characterized by the standard potential
of the cell it forms with the standard hydrogen half-cell, as well as by its free energy relative to that of H+:

AG0 = 96 500nV0 (9.52)

AG

V0 = 1.04 x 10—5——— — . (9.53)

n

Metals easily lose their electrons to hydrogen, and are therefore characterized by a negative value of both V0 and AG0. When the standard conditions are not fulfilled, equation (9.4) allows us to get

AG = AG0 + RT ln(K) (9.54)

which reads, for reaction (II),