It frequently happens that we have to deal, simultaneously, with conditions of chemical and of physical equilibrium, obtaining in the same system. For instance, a gas like carbon dioxide, in contact with its saturated solution in water, is in equilibrium with the dissolved carbon dioxide, and this, in turn, is in equilibrium with its hydrate, carbonic acid. A substance may be distributed between two solvents and show a different molecular weight in the two (see p. 18); it may exist, in the one, primarily in polymeric form, and only to a slight extent in the simple form, the two forms being in equilibrium (chemical equilibrium). In the other solvent, it may exist only in its simple molecular form, and this will be in equilibrium with the same simple molecular form in the first solvent (physical equilibrium). In matters dealing with the solubility of electrolytes in water, and, therefore, in questions of their ‹precipitation› or ‹solution›, such simultaneous conditions of chemical and physical equilibrium are constantly occurring. Since qualitative analysis deals to a very considerable extent with just such precipitates of salts, acids and bases, these cases are of particular importance to us. «Earlier Derivation of the Solubility-Product Principle.»—A very simple relation was derived by Nernst[291] for the combined conditions of chemical and of physical equilibrium, where difficultly soluble electrolytes (precipitates) were concerned. We shall develop the relation first for a simple salt, such as silver acetate. When water is added to solid silver acetate, the salt will dissolve. If an excess of the acetate is used, equilibrium will result between the solid salt and its solution, when the solution is saturated at the temperature used. As the salt dissolves, it is more or less ionized, and in the saturated solution we have a [p140] condition of chemical equilibrium between the salt and its ions: CH_{3}COOAg ⇄ CH_{3}COO^{−} + Ag^{+}. (1) If the law of chemical equilibrium is applied to this reversible action, we have (p. 98) [CH_{3}COO^{−}] × [Ag^{+}] / [CH_{3}COOAg] = K_{Ionization}. I The nonionized silver acetate is present in two phases, in the solid phase and also in solution: CH_{3}COOAg ↓ ⇄ CH_{3}COOAg. (2) Applying the law of physical equilibrium to this system, we have further (p. 121) [CH_{3}COOAg] / [CH_{3}COOAg]_{solid} = K. II