Just how much aluminium aluminate must be formed by a self-neutralization of the amphoteric hydroxide will depend on the values for K_{Base} and K_{Acid} and on the solubility of aluminium hydroxide (nonionized Al(OH)_{3}). The two equilibrium equations may be combined: [AlO^{+}] × [AlO_{2}^{−}] × [H^{+}] × [HO^{−}] / [Al(OH)_{3}]^2 = K_{Base} × K_{Acid}. [p188] Since [H^{+}] × [HO^{−}] = K_{HOH}, and since [AlO^{+}] and [AlO_{2}^{−}] may be taken to represent ‹each› the concentration of the practically completely ionized aluminium aluminate AlO(AlO_{2}), we have[379] [Alum. Aluminate]^2 / [Alum. Hydroxide]^2 = (K_{Base} × K_{Acid}) / K_{HOH}, or [Alum. Aluminate] / [Alum. Hydroxide] = √[(K_{Base} × K_{Acid}) / K_{HOH}]. It is clear, that the smaller the ionization constants K_{Base} and K_{Acid} are, and the smaller the solubility of nonionized aluminium hydroxide [Alum. Hydroxide] is, the smaller must be the concentration of the aluminate formed to satisfy the conditions for equilibrium. Aluminium hydroxide is a typical ‹amphoteric hydroxide›, and the relations developed may be applied, ‹mutatis mutandis›, to the conditions of equilibrium for analogous amphoteric hydroxides, such as zinc, lead, chromic hydroxides, and so forth. Salt formation or self-neutralization will depend, in every instance, on the strength of the base and the acid formed, and on the solubility of the hydroxide.[380] With the aid of the preceding considerations the analytical reactions of aluminium, which are used to separate it from other elements and to identify it, may be readily understood. They will be discussed in connection with the analysis of the "Aluminium and Zinc Groups." «The Analysis of the Aluminium and Zinc Groups.»—The groups of metals which are here called the [p189] "‹Aluminium and Zinc Groups›" consist of two groups, which ordinarily are precipitated together in qualitative analysis, and which are then separated from each other. We may distinguish the "‹Aluminium Group›" of trivalent metal ions, including aluminium, ferric and chromium ions, and the "‹Zinc Group›" of bivalent metal ions, including zinc, nickelous, cobaltous, manganous and ferrous ions. Of the two groups, the ions of the second group, in agreement with their lower valence (see p. 172), form the ‹stronger bases›, and, as such, they are all capable of forming ‹comparatively stable salts› even with such very weak acids as hydrogen sulphide and carbonic acid. Ammonium sulphide, added to a solution of a salt of any one of the ions of the zinc group, precipitates the corresponding sulphide, sodium or ammonium carbonate precipitates the corresponding carbonate.[381] We have, for instance: FeCl_{2} + (NH_{4})_{2}S → FeS ↓ + 2 NH_{4}Cl, FeCl_{2} + Na_{2}CO_{3} → FeCO_{3} ↓ + 2 NaCl. Only one member of this group, zinc, forms an ‹amphoteric› hydroxide and advantage is taken of this in identifying zinc.