Perspectives on Speciation

An important consideration about speciation is the dissociation reaction stoichiometry of reactions that form H⁺. The concept of hydration was discussed in Section 18.1. Positive ions usually require water of hydration, and do not float freely in solution as implied by Eqn. 18.4. For example, the species H₉O₄⁺ is spectroscopically identifiable even at the normal boiling point of water.¹⁰ However, the generally accepted method of writing the reaction is given by Eqn. 18.4 with the understanding that it is actually hydrated. Nevertheless, omitting the water of hydration in the reactions can lead to unexpected results from calculations in mixed solvents. When water is the dominant solvent, there is sufficient water to hydrate the ions. However, at lower concentrations of water, Eqn. 18.4 has no requirement for water of hydration to be present. A more realistic method of writing reactions that form H⁺ is to write them including at least one water, for example,

where H₃O⁺_(aq) is known as the hydronium ion. For acetic acid, the ionization forming hydronium can be written

In this manner, at least some water of hydration must be present for ionization to occur. When the dissociation reactions are written this way, it has no effect on the equilibrium constants from the literature which are measured when the activity of water is essentially one. On the other hand, when Gibbs energies are used, the Gibbs energy and enthalpy of formation of the hydronium includes the corresponding energy and enthalpy of formation for water, resulting in the same Gibbs energies and enthalpies of reaction for Eqns. 18.14 and 18.4, and the same equilibrium behavior when water is the dominant component. When the speciation is calculated in a mixture with small concentrations of water where the activity of water deviates from unity, Eqns. 18.4 and 18.14 lead to different results. For example, the dissociation of H₂SO₄ requires water, as seen in Fig. 18.1, but a dissociation in terms of H⁺ would result a dissociation in pure sulfuric acid. The requirement for a solvent in the dissociation reaction is more realistic in aqueous systems.¹¹ Despite the importance of the hydration water in calculations, the convention in the literature is to write the reactions using only the H⁺ ion, and we follow that convention here where we work with dilute aqueous solutions.

The nature of hydration changes with concentration. As the ion concentrations increases, the ions are often paired with counter-ions and are called ion pairs. Ion pairs often contain water between them. Under other circumstances water is excluded from within the pair and the pair is hydrated. The ion pair phenomenon is used in ion pair chromatography (IPC) to influence the retention time using ions that are bulky or interact strongly with the solid stationary phase.

Charge Balance

When ions are dissolved in solution, an extra constraint of charge balance is needed, which is often called the condition of electroneutrality. The net charge on a solution must be zero. Electroneutrality can be expressed using moles, molarity, or molality. This condition provides an important constraint that is used in all calculations, supplementing the component balances and equilibrium constraints. Note that the charge balance always uses concentrations, not activities.

Approximate Calculations

We begin quantitative discussion by using concentrations instead of activities. We expect that students can make the transition to activities as their skill level develops. Further, as we show, the calculations using concentrations are frequently the first step to a more rigorous solution including activities. To avoid clumsy notation, we write many equilibrium constant relations using concentrations instead of activities. When a solution is dilute, we also use concentration in place of molality without further description. Near the end of the chapter we provide a complete example using activities.