The Elements of Qualitative Chemical Analysis, vol. 1, parts 1 and 2. / With Special Consideration of the Application of the Laws of Equilibrium and of the Modern Theories of Solution. - Julius Stieglitz

The potential differences, given in the table, are based on the assumption that the absolute zero of potential is at such a point, that the so-called standard normal calomel electrode has a value of +0.56 volt relative to this zero (cf. Ostwald, Z. phys. Chem., 36, 97 (1901)). The exact determination of this value is a very difficult matter. Recently Palmaer (ibid., 59, 129 (1907)), located the absolute zero at a point 0.04 volt more positive than the above, making the absolute potential of the normal calomel electrode, approximately, +0.52 volt. To refer potentials, given in this book, to this new zero, one would subtract 0.04 volt from all positive potentials and add 0.04 to the numbers representing negative potentials (e.g. E. P._Zn,Zn²⁺ would become −0.569 in place of −0.529 volt). Since the equilibrium (solution-tension) constants are calculated from the potential differences referred to the absolute zero (p. [259]), any change in the zero involves corresponding changes in the values of the equilibrium constants, as calculated for this book. However, it should be noted that all potential differences would be corrected by the same constant quantity (0.04 volt for Palmaer's zero): all the equilibrium constants for univalent metallic ions would be increased proportionally to a constant factor c (c is very nearly equal to 5, for Palmaer's zero), the equilibrium constants for bivalent metallic ions would be increased proportionally to c², etc. The equilibrium ratio for two metals and their ions would in no wise be changed by these alterations: e.g. for the equilibrium between zinc and copper and [p296] their ions (p. [267]), K_equil. = K_Zn²⁺ / K_Cu²⁺; the factor c² would be introduced into both terms of the ratio and would not affect the value of the latter. For the condition of equilibrium between silver and copper and their ions (p. [267]) K_equil. = K_Ag⁺² / K_Cu²⁺, and since (c)² = c², this equilibrium ratio would also not be affected. For elements, which produce negative ions, the corresponding correction factors would be 1 / c, 1 / c², etc., and the equilibrium relations between two such elements and their ions likewise would remain unchanged. Since these equilibrium relations are the significant ones in this work, and since our conclusions have been based on them, it is clear that a change in the absolute zero would not affect the conclusions reached.

On account of the uncertainty attaching to the determination of the absolute zero of potential, it is preferred, in practice, to report the experimentally determined potentials as measured against a constant, well-defined electrode (such as the calomel electrode or a hydrogen electrode) and thus to eliminate the variation, which a change in the determination of the zero potential would make necessary. However, for an elementary discussion of oxidation-reduction reactions, from the same viewpoint as is used in considering all other reversible chemical actions, the idea of the absolute potential has certain advantages, making a uniform treatment possible.

1. Meaning of K_Ion. Under K_Ion is given, for each element, the concentration of its ion, with which the element would be directly in equilibrium at the ordinary temperature (see p. [258]). The constants for gaseous elements represent the constants of the gases under atmospheric pressure.

2. The Condition for Equilibrium between Two Elements and Their Ions. The condition of equilibrium in a system of two elements and their ions may be found with the aid of the constants K_Ion, as follows: For Zn ↓ + Cu²⁺ ⥂ Zn²⁺ + Cu ↓ we have for the condition of equilibrium (see p. [267])

[Zn²⁺] / [Cu²⁺] = K and
K = K_Zn²⁺ / K_Cu²⁺ = 1.4E17 / 8.3E−22 = 1.7E38.

Zinc-ion must be present in enormous excess in the condition of equilibrium and zinc will precipitate copper from solutions of cupric salts until this relation is established. The suppression of the cupric-ion—by precipitation in the form of insoluble salts or by conversion into very stable complex ions—makes [Cu²⁺] exceedingly small and makes it increasingly difficult for zinc to precipitate copper, and, under certain conditions, the ordinary course of the action may be reversed (p. [268]).

For Cu ↓ + 2 Ag⁺ ⥂ Cu²⁺ + 2 Ag ↓, we have (p. [267])

[Cu²⁺] / [Ag⁺]² = K and
K = K_Cu²⁺ / K_Ag⁺² = 8.3E−22 / (6E−19)² = 2.3E15.

3. Potential Differences Calculated with the Aid of K_Ion. For metallic elements, which send out positive ions, in contact with an aqueous solution containing the ion in concentration [C], the potential difference is (see p. [261])

ε_Me, Ion^v = (0.0575 / v) log([C] / K_Ion) volts,