Luther’s rule

Liquids, miscible, 382 partially miscible, 406 immiscible, 409 Litre-atmosphere, 48 Luther s rule, 480... 

While some metals, such as zinc, enter the solution as ions of always the same valency, other metals (e. g. Cu, Hg, Sn, Pb, Cr, An, Fe, Co, Ni, Tl) can form ions of different valencies in the anodic process. In order to solve the problem of ionization in stages Luther s rule is applied. 

Luther s rule -> Luther studied the relation between the standard electrode -> potentials of metals that can exist in more than one oxidation state. For some electrochem-ically reversible systems (- reversibility) he showed theoretically and experimentally that for a metal Me and its ions Me+ and Me2+ the following relation holds (in contemporary nomenclature) for the -> Gibbs energies of the redox transitions ... 

This mathematical relationship expresses Latimer-Luther s rule. We infer from it the fact that it is unnecessary to calculate the standard molar free enthalpy changes, but this result is not general. The rule is valid only for processes that involve only redox phenomena. This was not the case in the examples given before. 

Let s recall that the handling of the free enthalpies of redox reactions permits us to calculate unknown standard potentials (see Sect. 2.11 in Chap. 2). This point is also important for the calculation of cell potentials, namely, for the calculation of the electrical charges brought by the electrodes (see below) not all redox couples appear in Tables 13.1-13.3. The standard potentials of the other couples may be calculated by using the additivity of the free enthalpies of the physical or chemical equivalent processes or with the help of Latimer-Luther s rule (see Chap. 2). 

Obviously, the slope values of the segments OA, OB, OA, and OB are the standard potential values of the corresponding couples. The slopes of segments AB andA B are, equal to the standard potentials Cu +/Cu+ and Hg +/Hg2+, respectively. This is a consequence of the additivity of the free enthalpies and, more precisely in this case, of Latimer-Luther s rule (see Chap. 2). 

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