Ion-Pair Formation

An ion pairA cation and an anion that are in intimate contact in solution rather than separated by solvent. An ion pair can be viewed as a species that is intermediate between the ionic solid and the completely dissociated ions in solution. consists of a cation and an anion that are in intimate contact in solution, rather than separated by solvent (Figure 17.2 "Ion-Pair Formation"). The ions in an ion pair are held together by the same attractive electrostatic forces that we discussed in Chapter 8 "Ionic versus Covalent Bonding" for ionic solids. As a result, the ions in an ion pair migrate as a single unit, whose net charge is the sum of the charges on the ions. In many ways, we can view an ion pair as a species intermediate between the ionic solid (in which each ion participates in many cation–anion interactions that hold the ions in a rigid array) and the completely dissociated ions in solution (where each is fully surrounded by water molecules and free to migrate independently).

Figure 17.2 Ion-Pair Formation

In an ion pair, the cation and the anion are in intimate contact in solution and migrate as a single unit. They are not completely dissociated and individually surrounded by solvent molecules, as are the hydrated ions, which are free to migrate independently.

As illustrated for calcium sulfate in the following equation, a second equilibrium must be included to describe the solubility of salts that form ion pairs:

The ion pair is represented by the symbols of the individual ions separated by a dot, which indicates that they are associated in solution. The formation of an ion pair is a dynamic process, just like any other equilibrium, so a particular ion pair may exist only briefly before dissociating into the free ions, each of which may later associate briefly with other ions.

Ion-pair formation can have a major effect on the measured solubility of a salt. For example, the measured K_sp for calcium sulfate is 4.93 × 10⁻⁵ at 25°C. The solubility of CaSO₄ should be 7.02 × 10⁻³ M if the only equilibrium involved were as follows:

In fact, the experimentally measured solubility of calcium sulfate at 25°C is 1.6 × 10⁻² M, almost twice the value predicted from its K_sp. The reason for the discrepancy is that the concentration of ion pairs in a saturated CaSO₄ solution is almost as high as the concentration of the hydrated ions. Recall that the magnitude of attractive electrostatic interactions is greatest for small, highly charged ions. Hence ion pair formation is most important for salts that contain M²⁺ and M³⁺ ions, such as Ca²⁺ and La³⁺, and is relatively unimportant for salts that contain monopositive cations, except for the smallest, Li⁺. We therefore expect a saturated solution of CaSO₄ to contain a high concentration of ion pairs and its solubility to be greater than predicted from its K_sp.

Incomplete Dissociation

A molecular solute may also be more soluble than predicted by the measured concentrations of ions in solution due to incomplete dissociation. This is particularly common with weak organic acids. (For more information about weak organic acids, see Chapter 16 "Aqueous Acid–Base Equilibriums"). Although strong acids (HA) dissociate completely into their constituent ions (H⁺ and A⁻) in water, weak acids such as carboxylic acids do not (K_a = 1.5 × 10⁻⁵). However, the molecular (undissociated) form of a weak acid (HA) is often quite soluble in water; for example, acetic acid (CH₃CO₂H) is completely miscible with water. Many carboxylic acids, however, have only limited solubility in water, such as benzoic acid (C₆H₅CO₂H), with K_a = 6.25 × 10⁻⁵. Just as with calcium sulfate, we need to include an additional equilibrium to describe the solubility of benzoic acid:

In a case like this, measuring only the concentration of the ions grossly underestimates the total concentration of the organic acid in solution. In the case of benzoic acid, for example, the pH of a saturated solution at 25°C is 2.85, corresponding to [H⁺] = [C₆H₅CO₂⁻] = 1.4 × 10⁻³ M. The total concentration of benzoic acid in the solution, however, is 2.8 × 10⁻² M. Thus approximately 95% of the benzoic acid in solution is in the form of hydrated neutral molecules—C₆H₅CO₂H(aq)—and only about 5% is present as the dissociated ions (Figure 17.3 "Incomplete Dissociation of a Molecular Solute").

Figure 17.3 Incomplete Dissociation of a Molecular Solute

In a saturated solution of benzoic acid in water at 25°C, only about 5% of the dissolved benzoic acid molecules are dissociated to form benzoate anions and hydrated protons. The remaining 95% exists in solution in the form of hydrated neutral molecules. (H₂O molecules are omitted for clarity.)

Although ion pairs, such as Ca²⁺·SO₄²⁻, and undissociated electrolytes, such as C₆H₅CO₂H, are both electrically neutral, there is a major difference in the forces responsible for their formation. Simple electrostatic attractive forces between the cation and the anion hold the ion pair together, whereas a polar covalent O−H bond holds together the undissociated electrolyte.