14.1 Why salts dissolve

Salts dissolve to varying degrees in polar solvents, not only water but also others such as alcohols that contain –OH groups. Also, dipolar aprotic solvents such as acetonitrile and dimethylsulfoxide support electrolyte dissolution. Metal cations are not as readily solvated by alcohols as they are in water, but dimethylsulfoxide and pyridine can even exceed the capacity of water to solvate metal ions. Nonetheless, most salts containing simple inorganic anions exhibit very low solubilities in organic solvents because of the difficulty these solvents have in effectively solvating simple inorganic anions.

The solubility of a salt is determined by the Gibbs energy of solvation Δ_solG°, which for the salt MX corresponds to the reaction

(14.1)

As shown in Fig. 14.1, whether or not this Gibbs energy change is negative is determined by the balance between the binding of the ions in the solid, represented by the lattice Gibbs energy Δ_latG° corresponding to

(14.2)

and the Gibbs energy of hydration

(14.3)

Using Hess’s law

(14.4)

14.2 Ions in solution

An ion in solution interacts with a solvent to create a range of regions with different structures about it. This is shown in Fig. 14.2, in which four separate regions are depicted: the primary solvation shell; the secondary solvation shell; a disordered region; and finally the bulk solvent. In the primary solvation shell, solvent molecules interact directly and strongly with the ion. In the secondary solvation shell, the solvent molecules are not in direct contact with the ion. However, they are influenced by the interaction of dipoles with the electrostatic field generated by the charge on the ion. At some distance away from the ion, the solvent is no longer influenced by the presence of the ion. This is region D, the bulk solvent. Polar protic solvents such as water and alcohols display a good deal of structure. Therefore, the structure of the secondary solvation shell is unlikely to match the structure of the bulk solvent. This leads to a disordered region C buffering the two. In less-structured solvents, this region is missing.

The ‘ideal’ solvation structure shown in Fig. 14.2 can only be achieved in very dilute solutions, on the order of 1 mM or less. It should also be borne in mind that the solvent molecules in the various regions are not static. They are in constant motion and are continuously being exchanged between regions.

Coordination complexes are well known in inorganic and organometallic chemistry. In these, metal ions take a central position and are coordinated by a number of ligands organized with well-defined symmetries. The first solvation shell, denoted A in Fig. 14.2, can be conceived of in an analogous fashion with water molecules acting as ligands, but in this case they are dynamic ligands. On average there will be a certain number of water molecules about the central ion (frequently six). The water molecules have a preferred orientation but they are free to move and exchange with the second shell and then beyond.

Nuclear magnetic resonance (NMR) can be used to probe the coordination sphere of some, but not all, metal ions in solution. The results of such investigations to determine the solvation number – the number of nearest-neighbor solvent molecules in solution – are shown in Table 14.1. It is found that temperature and pressure have very little effect on the solvation number. The clear result from these studies is that a solvation number of 6 is by far the most likely. Very small cations, such as Be²⁺, or cations that exhibit a peculiar square-planar coordination, such as Pt²⁺ and Pd²⁺, exhibit a lower solvation number of 4. Rather bulky solvents such as trimethyl phosphate (TMP) can also be forced to assume a solvation number of just 4. Only quite large cations, those of the lanthanides and actinides, are solvated by 8 or 9 molecules.

A number of kinetic methods have been developed to determine values related to the solvation number. These methods depend on the movement of solvated ions by observing diffusion, viscosity, conductivity, or transport numbers. Therefore, they often deliver numbers much different than 6 since these are measures of the number of solvent molecules that move with the ion. Values ranging from 1 to 12 or more are found.

Conspicuously absent from the NMR results are the important cations of the alkali and alkali earth metals. X-ray diffraction and neutron-scattering studies suggest solvation numbers ranging from 4 to 8.

The number of solvent molecules in the second solvation shell, region B in Fig. 14.2, is less accurately characterized. A value of 12 or more is likely, with larger cations such as the lanthanides and actinides having correspondingly more.

Anion solvation in water exhibits a wider range in solvation numbers in part due to the greater range of structures in the simple anions compared to bare metal cations. Diffraction and scattering show that solvation numbers range from 4 to 12 for most simple anions. A few specific values are: 7 or 8 for SO₄^2–; 8 for SeO₄^2– and ClO₄^–; 12 for CrO₄^2–, MoO₄^2– and WO₄^2–; and 4 or 5 for acetate. The nitrate ion has proved problematic with estimates ranging from 3 to 18.

In Chapter 4 we previously encountered the radial distribution function g(r). This is a measure of the probability of finding a particle at a given distance away from some chosen point. In the present case, we choose the center of the solvated ion as the origin of our coordinates. An example of a radial distribution function is given in Fig. 14.3. The first peak represents the nearest-neighbor distance, in this case for Zn²⁺ in an aqueous solution. The distance from the Zn²⁺ to the H and O atoms of the solvating H₂O molecules are slightly shifted with respect to one another. This is expected because the partially negative O atom in H₂O is attracted to the positive charge on Zn²⁺ while the partially positive H atoms are repelled. The mean distances measured by diffraction and scattering for solvation closely track the distances observed in crystal hydrates. Increasing the charge on the ion shortens the ion–solvent internuclear separation. For example, this distance drops from 0.212 nm in [Fe(OH₂)₆]²⁺ as compared to 0.205 nm in [Fe(OH₂)₆]³⁺. A first approximation to these distances can be made by taking the sum of the ionic radius for the appropriate coordination number – often called the Shannon radius – and the mean radius of the water molecule. The radius of a water molecule is approximately 0.138 nm. A number of representative values for the metal ion to oxygen distance are given in Table 14.2.

14.3 The thermodynamic properties of ions in solution

14.3.1 Enthalpy of hydration

The enthalpy change upon the dissolution of an ionic compound can be readily measured by calorimetry, assuming its solubility is sufficiently high. For a sparingly soluble salt, the temperature dependence of its solubility and application of the integrated form of the van’t Hoff equation are used to obtain the enthalpy of solution.

However, an ion cannot be made in solution in the absence of a counterion because a solution must remain neutral. Therefore, the enthalpy/entropy/Gibbs energy of formation of a single ion cannot be measured directly in solution. It is possible to estimate the absolute enthalpy of hydration of an ion. If we choose one to estimate accurately, then all other ions could have their values set by transitivity. That is, if we knew the absolute enthalpy change caused by dissolving 1 mol of H⁺ (at infinite dilution), then by measuring the enthalpy change caused by dissolving 1 mol of HCl, HBr and HI, we could determine the molar enthalpy of hydration of Cl^–, Br^– and I^–. We could then measure the enthalpy of solution of the metal salts MX_n and so on to determine the molar enthalpies of hydration of the metal ions Mⁿ⁺, and so forth.

This has been done to measure Δ_hydH_m°(H⁺) by a series of experiments involving a number of salts HX with increasingly large anions X^–. As the size of the anion increases, the Δ_hydH_m°(X^–) tends to zero. By extrapolating the data to infinitely large and negligibly solvated X^–, the value for Δ_hydH_m°(H⁺) is obtained. In this manner, the value Δ_hydH_m°(H⁺) = –1091 kJ mol^–1 has been obtained. This value corresponds to the enthalpy change for the reaction

The enthalpy of hydration depends on the size and charge of the ion. The greater the charge and the smaller the ion, the greater the enthalpy of hydration. The value for H⁺ is particularly large compared to that of Li⁺ (–515 kJ mol^–1). As expected, Δ_hydH_m°(Cs⁺) = –263 kJ mol^–1 is much less than the value for the smaller Li⁺. Doubling the charge greatly increases the enthalpy of hydration; for example, Δ_hydH_m°(Be²⁺) = –2487 kJ mol^–1 and Δ_hydH_m°(Ba²⁺) = –1304 kJ mol^–1. Similar trends also hold for anions with Δ_hydH_m°(F^–) = –503 kJ mol^–1 and Δ_hydH_m°(I^–) = –298 kJ mol^–1, while Δ_hydH_m°(SO₄^2–) = –1145 kJ mol^–1.

The enthalpy of solvation also depends on the solvent. As mentioned above, many polar solvents actually solvate cations more effectively than water. However, they tend to solvate anions less effectively. This is quantified directly by the enthalpy of transfer Δ_transH_m° defined by

(14.5)

where Δ_solH_m° is the molar enthalpy change of solution in a solvent other than water. Several values for the enthalpy of transfer are shown in Table 14.3.

	NH3(l)	CH3OH	CH3CN	(CH3)2SO	HMPA
K+	–30	–30	–26	–47	–64
Ag+	–102	–35	–61	–69
Ba2+	–101	–85	–22	–102	–156
Cl–		+8	+20	+19

(CH₃)₂SO = DMSO = dimethylsulfoxide; HMPA = hexamethylphosphoramide.

14.3.2 Enthalpy, entropy and gibbs energy of ion formation in solutions

For thermodynamic calculations, we need to establish the values of entropy, enthalpy and Gibbs energy. Rather than using a scale based on absolute entropies and enthalpies, it is easier to construct a scale based on relative values. This is done by selecting one reaction as a standard against which all other values are measured. We chose H⁺(aq) as the standard ion. The corresponding the reaction is

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