6.S: Equilibrium Chemistry (Summary)

Analytical chemistry is more than a collection of techniques; it is the application of chemistry to the analysis of samples. As we will see in later chapters, almost all analytical methods use chemical reactivity to accomplish one or more of the following: dissolve the sample, separate analytes from interferents, transform the analyte to a more useful form, or provide a signal. Equilibrium chemistry and thermodynamics provide us with a means for predicting which reactions are likely to be favorable.

The most important types of reactions are precipitation reactions, acid–base reactions, metal-ligand complexation reactions, and redox reactions. In a precipitation reaction two or more soluble species combine to produce an insoluble product called a precipitate, which we characterize using a solubility product.

An acid–base reaction occurs when an acid donates a proton to a base. The reaction’s equilibrium position is described using either an acid dissociation constant, K_a, or a base dissociation constant, K_b. The product of K_a and K_b for an acid and its conjugate base is the dissociation constant for water, K_w.

When a ligand donates one or more pairs of electron to a metal ion, the result is a metal–ligand complex. Two types of equilibrium constants are used to describe metal–ligand complexation—stepwise formation constants and overall formation constants. There are two stepwise formation constants for the metal–ligand complex ML₂, each describing the addition of one ligand; thus, K₁ represents the addition of the first ligand to M, and K₂ represents the addition of the second ligand to ML. Alternatively, we can use a cumulative, or overall formation constant, β₂, for the metal–ligand complex ML₂, in which both ligands are added to M.

In a redox reaction, one of the reactants undergoes oxidation and another reactant undergoes reduction. Instead of using an equilibrium constants to characterize a redox reactions, we use the potential, positive values of which indicate a favorable reaction. The Nernst equation relates this potential to the concentrations of reactants and products.

Le Châtelier’s principle provides a means for predicting how a system at equilibrium responds to a change in conditions. If we apply a stress to a system at equilibrium—by adding a reactant or product, by adding a reagent that reacts with one of the reactants or products, or by changing the volume—the system responds by moving in the direction that relieves the stress.

You should be able to describe a system at equilibrium both qualitatively and quantitatively. You can develop a rigorous solution to an equilibrium problem by combining equilibrium constant expressions with appropriate mass balance and charge balance equations. Using this systematic approach, you can solve some quite complicated equilibrium problems. If a less rigorous answer is acceptable, then a ladder diagram may help you estimate the equilibrium system’s composition.

Solutions containing relatively similar amounts of a weak acid and its conjugate base experience only a small change in pH upon adding a small amount of a strong acid or a strong base. We call these solutions buffers. A buffer can also be formed using a metal and its metal–ligand complex, or an oxidizing agent and its conjugate reducing agent. Both the systematic approach to solving equilibrium problems and ladder diagrams are useful tools for characterizing buffers.

A quantitative solution to an equilibrium problem may give an answer that does not agree with experimental results if we do not consider the effect of ionic strength. The true, thermodynamic equilibrium constant is a function of activities, a, not concentrations. A species' activity is related to its molar concentration by an activity coefficient, γ. Activity coefficients can be calculated using the extended Debye-Hückel equation, making possible a more rigorous treatment of equilibria.

6.12.1 Key Terms

acid acid dissociation constant activity activity coefficient amphiprotic base base dissociation constant buffer buffer capacity charge balance equation common ion effect cumulative formation constant dissociation constant enthalpy entropy equilibrium

equilibrium constant extended Debye‑Hückel equation formation constant Gibb’s free energy half‑reaction Henderson–Hasselbalch equation ionic strength ladder diagram Le Châtelier’s principle ligand mass balance equation metal–ligand complex method of successive approximations monoprotic Nernst equation

oxidation oxidizing agent pH scale polyprotic potential precipitate redox reaction reducing agent reduction standard‑state standard potential steady state stepwise formation constant solubility product

References

1. Quilez, J. Chem. Educ. Res. Pract. 2004, 5, 69–87 (http://www.uoi.gr/cerp).
2. lthough not specifically on the topic of ladder diagrams as developed in this section, the following sources provide appropriate background information: (a) Runo, J. R.; Peters, D. G. J. Chem. Educ. 1993, 70, 708–713; (b) Vale, J.; Fernández-Pereira, C.; Alcalde, M. J. Chem. Educ. 1993, 70, 790–795; (c) Fernández-Pereira, C.; Vale, J. Chem. Educator 1996, 6, 1–18; (d) Fernández-Pereira, C.; Vale, J.; Alcalde, M. Chem. Educator 2003, 8, 15–21; (e) Fernández-Pereira, C.; Alcalde, M.; Villegas, R.; Vale, J. J. Chem. Educ. 2007, 84, 520–525.
3. See, for example, (a) Bower, V. E.; Bates, R. G. J. Res. Natl. Bur. Stand. (U. S.) 1955, 55, 197–200; (b) Bates, R. G. Ann. N. Y. Acad. Sci. 1961, 92, 341–356; (c) Bates, R. G. Determination of pH, 2nd ed.; Wiley-Interscience: New York, 1973.
4. (a) Lambert, W. J. J. Chem. Educ. 1990, 67, 150–153; (b) http://www.bioinformatics.org/JaMBW/5/4/index.html.
5. Lister, M. W.; Rivington, D. E. Can. J. Chem. 1995, 33, 1572–1590.
6. Davies, C. W. Ion Association, Butterworth: London, 1962.

Contributors

David Harvey (DePauw University)