This table lists the ionic species that are most likely to be present, depending on pH, in aqueous solutions of binary salts of metal ions. The existence must be inferred on the basis of indirect evidence provided by modelling with experimental data or by analogy with structures obtained by X-ray crystallography.
Introduction When a salt of a metal ion, with the generic formula MXn, is dissolved in water, it will dissociate into a cation and anions.
M X n → M n + ( a q ) + n X − ( a q ) {\displaystyle MX_{n}\rightarrow M^{n+}(aq)+nX^{-}(aq)}
(aq) signifies that the ion is aquated, with cations having a chemical formula [M(H2O)p]q+ and anions whose state of aquation is generally unknown. For convenience (aq) is not shown in the rest of this article as the number of water molecules that are attached to the ions is irrelevant in regard to hydrolysis. This reaction occurs quantitatively with salts of the alkali-metals at low to moderate concentrations. With salts of divalent metal ions, the aqua-ion will be subject to a dissociation reaction, known as hydrolysis, a name derived from Greek words for water splitting. The first step in this process can be written as
M n + + O H − {\displaystyle M^{n+}+OH^{-}} ⇌ M ( O H ) ( n − 1 ) + {\displaystyle M(OH)^{(n-1)+}}
When the pH of the solution is increased by adding an alkaline solution to it, the extent of hydrolysis increases. Measurements of pH or colour change are used to derive the equilibrium constant for the reaction. Further hydrolysis may occur, producing dimeric, trimeric or polymeric species containing hydroxy- or oxy- groups. The next step is to determine which model for the chemical processes best fits the experimental data.
Model selection The model is defined in terms of a list of those complex species which are present in solutions in significant amounts. In the present context the complex species have the general formula [MpOq(OH)r]n±. where p, q and r define the stoichiometry of the species and n± gives the electrical charge of the ion. The experimental data are fitted to those models which may represent the species that are formed in solution. The model which gives the best fit is selected for publication. However, the pH range in which data may be collected is limited by the fact that an hydroxide with formula M(OH)n will be formed at relatively low pH, as illustrated at the right. This will make the process of model selection difficult when monomers and dimers are formed. and virtually impossible when higher polymers are also formed. In those cases it must be assumed that the species found in solids are also present in solutions. The formation of an hydroxo-bridged species is enthalpically favoured over the monomers, countering the unfavourable entropic effect of aggregation. For this reason, it is difficult to establish models in which both types of species are present.
Monomeric hydrolysis products The extent of hydrolysis can be quantified when the values of the hydrolysis constants can be determined experimentally. The first hydrolysis constant refers to the equilibrium
M n + ( a q ) {\displaystyle M^{n+}(aq)} ⇌ M ( O H ) ( n − 1 ) + ( a q ) + H + {\displaystyle M(OH)^{(n-1)+}(aq)+H^{+}}
The association constant for this reaction can be expressed as
K = [ M ( O H ) ] [ M ] [ O H ] {\displaystyle K={\frac {[M(OH)]}{[M][OH]}}} (electrical charges are omitted from generic expressions) Numerical values for this equilibrium constant can be found in papers concerned only with metal ion hydrolysis. However, it is more useful, in general, to use the acid dissociation constant, Ka.
K a = [ M ] [ H ] [ M ( O H ) ] {\displaystyle K_{a}={\frac {[M][H]}{[M(OH)]}}}
and to cite the cologarithm, pKa, of the value of this quantity in books and other publications. The two values are constrained by the relationship
log K(association) * log K(dissociation) = pKw pKw refers to the self-ionization of water: pK = log (1/K) = -log(K). Further monomeric complexes may be formed in a stepwise manner.
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