in which KAcid and KBase represent the ionization constants of the acid and the base, as given in the tables (pp. [104] and [106]), and α is the degree of ionization of the salt.
For the cyanide of a base, which is as weak a base as hydrocyanic acid is an acid, we find that the decomposition by water, at 25° in a 0.1 molar solution, must comprise 99.35%[375] of the salt, in order to establish equilibrium. In the case of potassium cyanide, in 0.1 molar solution, only 1.3% of the salt is decomposed (p. [182]).
Now, if both the free base and the free acid are very difficultly soluble, then the concentrations [MeOH] and [HX], respectively, in the solution cannot go beyond a certain minute limit. In view,[376] then, of the very small value, KBase, of the ratio [Me+] × [HO−] / [MeOH] and the minute value that the second term [MeOH] has under these conditions, the first term [Me+] × [HO−] must have a correspondingly smaller value. It is clear, therefore, that in such a solution neither the nonionized base, MeOH, nor its ion, Me+, can exist in more than minute quantities when the equilibrium constants are satisfied. The same conclusion is reached regarding the [p186] possibility of the existence of the difficultly soluble acid HX and its ion X−, in more than minimal quantities. Since, then, neither the ion Me+ nor the ion X− can be present in more than traces, their salt, MeX, which is considered readily ionizable, also cannot exist in aqueous solutions, except in traces.
The quantitative relations are evident from the equilibrium equation (p. [185]): [Me+] × [X−] / ([HX] × [MeOH]) = α2 [Salt]2 / ([Acid] × [Base]) = KAcid × KBase / KHOH = K. It is evident that the concentration of the salt, [Salt], which is capable of existence in aqueous solution, is, in the first place, the smaller the smaller the values for KAcid and KBase are, i.e. the weaker the acid and the base are; and, in the second place, it is the smaller the smaller the values for [Acid] and [Base] are, which, in the present instance, represent the concentrations of the difficultly soluble acid and base in saturated solution, i.e. their solubilities.
We reach the conclusion that salts of very weak bases and very weak acids are very considerably decomposed by water, and, if both the acid and the base are difficultly soluble in water, the decomposition is practically complete. Conversely, such a very weak, difficultly soluble base will not combine with a very weak, difficultly soluble acid to form a salt in the presence of water. An instance of the first kind is found in the case of aluminium sulphide, the salt of a very weak, difficultly soluble base, aluminium hydroxide, with a rather little soluble, weak acid, hydrogen sulphide (see table, p. [104]). We find that when a piece of aluminium sulphide, prepared by dry methods, is dropped into water (exp.), a precipitate of aluminium hydroxide is immediately formed and evolution of hydrogen sulphide occurs. We have
Al2S3 ⇄ 2 Al3+ + 3 S2−,
6 HOH ⇄ 6 HO− + 6 H+
2 Al3+ + 6 HO− ⇄ 2 Al(OH)3 ↓
3 S2− + 6 H+ ⇄ 3 H2S ↑.
An instance where a very weak insoluble acid will not combine, appreciably, with a very weak insoluble base, is found in the case of aluminium hydroxide. A development of the equilibrium equations for its ionization as a base and its ionization as an acid would show, that all the constants would be readily satisfied, when a very minute quantity of dissolved ionized aluminium aluminate is formed. [p187]
Self-Neutralization of Amphoteric Hydroxides.
[AlO2−] × [H+] / [Al(OH)3] = KAcid.
Similarly, for the basic ionization,[378] Al(OH)3 ⇄ (AlO)+ + HO− + H2O, we have