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.

by Julius Stieglitz

[CH₃COO⁻] × [Ag⁺] = K_Ionization × K_{mol. sol.} =
K_{Solubility-Product}.

IV

Further, if the assumption is made that the presence of foreign electrolytes, in not too concentrated solutions, does not affect either the molecular solubility, K_{mol. sol.}, of silver acetate or its tendency to ionize—as expressed in K_Ionization—then, the [p141] relation, which has been developed, would hold for saturated aqueous solutions of silver acetate in the presence of foreign electrolytes, as well as for a saturated, pure, aqueous solution. A single, simple equation would thus express the conditions for simultaneous chemical and physical equilibrium between a difficultly soluble ionogen, of the type of silver acetate, and its saturated solutions, at a given temperature, in the presence or the absence of foreign electrolytes.

The Solubility- or Ion-Product Principle.

Criticism of the Derivation of the Principle.

It appears, however, that while the soundness of this theoretical development of the relations expressed by the solubility-product must be questioned, nevertheless as a matter of experiment, the product of the ion concentrations of a difficultly soluble salt is found, in dilute solutions, to be a constant, or sufficiently close to a constant to satisfy all but the most rigorous requirements.[295]

It is, in fact, quite evident, that a decreasing value for the second term of the ratio I—namely, for [CH₃COOAg], the molecular solubility of the salt—as the total concentration of the electrolytes present increases, together with an increasing value for the whole ratio I under the same conditions, are not incompatible with a constant value of the first term of the ratio. That is, the product of the ion concentrations, [CH₃COO⁻] × [Ag⁺], may well remain constant (equation IV), or approximately constant, in dilute salt solutions, even if equations I and III do not hold for salt solutions. [p143]

Whether in the case of all difficultly soluble salts, as the total salt concentration increases, the increasing values of the chemical equilibrium ratio (equation I) will be so nicely balanced by the decreasing values of the molecular solubility, that the first term of the first ratio (the solubility-product) will always be constant, is a question demanding further extended investigation.[296] The range of the investigation must be extensive, because it must include several other classes[297] of salts (e.g. Me₂X, MeY₂, etc.), for which the first equation has a different form; for instance, for Me₂X,

[Me⁺]² × [X²⁻] / [Me₂X] = K.

For the present we must remain content with the result of the past investigations and consider the principle of the constant solubility-product to be essentially an empirical one. It is an extremely convenient condensation, into a very simple mathematical form, of the main factors involved in the precipitation and solution of difficultly soluble salts, acids, and bases. It should be used with due knowledge of its character and limitations.