Microscopic Equilibria
T
eaching equilibria to chemistry students is usually done at the coarsest level, by writing quantitative expressions portraying the concentrations of the equilibrium reaction's reactants and products. The descriptions are macroscopic, they involve solution properties such as pH or pM, and they do not require explicit structures of the equilibrium components. More detailed descriptions are used for equilibria with multiple structural variants of the same overall composition. Equilibrium descriptionsthat take structure explicitly into account are called microscopic equilibria. Microscopic equilibria for polyprotic acids identify the site of proton ionization within the polyprotic acid. For molecules with multiple (but localized) electron donor/acceptor sites, the microscopic equilibria describe the state of oxidation of each site. Another example is the location of metal ions bound to ligands having multiple metal-binding sites. The macroscopic observables of pH, potential, and pM give no insight into the microscopic equilibria; structure-sensitive(and generally spectroscopic) tools are required. An even deeper description of microscopic equilibria would include the occurrence of any multiplicity of molecular conformations lying in energy wells relative to kT, because the different conformations could have differing microscopic equilibrium constants for nominally the same site of protonation. I have presented this little tutorial to explain what is meant by microscopic equilibria because, in my experience, a startling proportion of otherwise well-educated chemists do not appreciate that quantitative relations for microscopic equilibria are possible or important. I believe this reflects a deficiency in teaching about chemical equilibrium and, because it is most often taught by analytical faculty, it is our deficiency. Teaching of equilibrium chemistry, at the beginning or advanced levels, commonly omits the facts, nay, even the existence, of microscopic equilibria. Our textbooks mention it briefly in passing, if at all. Students learn that ionization of protonated glycine involves two equilibrium equations, the first of which tells about the car-
462 A Analytical Chemistry, August 1, 1995
boxylic acid site; the fact that the equilibrium equations themselves are uninformative about the site of proton loss is finessed. Examples of similar multiple pKas tend to be avoided because of ambiguity of the ionization site. In my experience, introducing the student to the microscopic concept using polyprotic acids is not hard, and the consideration of actual structures helps to lend reality to equilibrium equations. (Students can be unhappy to learn that the macroscopic concepts they have been previously taught have left out a lot of chemical truths.) Nice examples of microscopic equilibria include cysteine, which has three macroscopic pKas but five microscopic ones, and diethylenetriamine, which accepts a first equivalent of protons by putting 41%of them on each primary amine and 18%on the central base site. There is a larger importance in learning about microscopic equilibria than a sense of completeness. How are equilibria used? Some cases are functional, such as seeking to control a macroscopic property like pH (i.e., a buffer) to in turn affect some other chemical process; the microscopic concept isn't needed then. Analytical chemistry (and chemistry at large) has, however, an increasing orientation to biological reaction systems. In those systems, multiple proton ionization (and other kinds of binding) sites are more likeIy to exist, and the pattern of these ionizationsmay directly affect chemical reactivity. The clustering of bases around enzyme active sites is an example; I would guess that others could be found in permeation rates of multiplyfunctionalized drugs through lipid membranes. In general, the current understanding of complex biological molecules does not include a quantitative understanding of their microscopic protonation (and other) equilibria, or how these may affect their chemical reactivity for analytical or other purposes. Therein lies a research frontier. Students should be prepared to confront problems such as these.
