Solubility

Key point: The solubilities of salts in water can be rationalized by considering lattice and hydration enthalpies. Lattice enthalpies play a role in solubilities, as the dissolution involves breaking up the lattice, but the trend is much more difficult to analyse than for decomposition reactions. One rule that is reasonably well obeyed is that compounds that contain ions with widely different radii are soluble in water. Conversely, the least water-soluble salts are those of ions with similar radii. That is, in general, difference in size favours solubility in water. It is found empirically that an ionic compound MX tends to be very soluble when the radius of M is smaller than that of X by about 80 pm. Two familiar series of compounds illustrate these trends. In gravimetric analysis, Ba2 is used to precipitate SO₄^2-, and the solubilities of the Group 2 sulfates decrease from MgSO₄ to BaSO₄ . In contrast, the solubility of the Group 2 hydroxides increases down the group: Mg(OH)₂ is the sparingly soluble ‘milk of magnesia’ but Ba(OH)₂ can be used as a soluble hydroxide for preparation of solutions of OH. The first case shows that a large anion requires a large cation for precipitation. The second case shows that a small anion requires a small cation for precipitation. Before attempting to rationalize the observations, we should note that the solubility of an ionic compound depends on the standard reaction Gibbs energy for

MX(s)→M⁺ (aq)+X^- (aq)

In this process, the interactions responsible for the lattice enthalpy of MX are replaced by hydration (and by solvation in general) of the ions. However, the exact balance of enthalpy and entropy effects is delicate and difficult to assess, particularly because the entropy change also depends on the degree of order of the solvent molecules that is brought about by the presence of the dissolved solute. The data in Fig. 3.51 suggest that enthalpy considerations are important in some cases at least, as the graph shows that there is a correlation between the enthalpy of solution of a salt and the difference in hydration enthalpies of the two ions. If the cation has a larger hydration enthalpy than its anion partner (reflecting the difference in their sizes) or vice versa, then the dissolution of the salt is exothermic (reflecting the favourable solubility equilibrium). The variation in enthalpy can be explained using the ionic model. The lattice enthalpy is inversely proportional to the distance between the centres of the ions:

Fig. 3.51 The correlation between enthalpies of solution of halides and the differences between the hydration enthalpies of the ions. Dissolution is most exothermic when the difference is large.

However, the hydration enthalpy, with each ion being hydrated individually, is the sum of individual ion contributions:

If the radius of one ion is small, the term in the hydration enthalpy for that ion will be large. However, in the expression for the lattice enthalpy one small ion cannot make the denominator of the expression small by itself. Thus, one small ion can result in a large hydration enthalpy but not necessarily lead to a high lattice enthalpy, so ion size asymmetry can result in exothermic dissolution. If both ions are small, then both the lattice enthalpy and the hydration enthalpy may be large, and dissolution might not be very exothermic.

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مواضيع ذات صلة

The Fermi level

Densities of states

Band formation by orbital overlap

The conductivities of inorganic solids

Nonstoichiometry

Intrinsic point defects

Thermal stabilities of ionic solids

The Born–Mayer equation

Structure maps

The radius ratio

Ionic radii

Characteristic structures of ionic solids