In the Classroom
Historical Development of the Hydrogen Ion Concept n Carl E. Moore,* Bruno Jaselskis, and Jan Floria Chemistry Department, Loyola University of Chicago, Chicago, Illinois 60626 *
[email protected] The definition of the aqueous hydrogen ion over the years has undergone a number of fundamental changes. Each change has resulted in a new conceptual model. The result of these changes has been the pragmatic use of the proton (1) in aqueous solution in quantitative analysis as if it were an unencumbered entity, that is, a body that is neither complexed nor associated with other bodies. The development of the useful expressions such as the molar hydrogen ion concentration, [Hþ], and the hydration enthalpy of Hþ (2), and the extensive equations of aqueous solution chemistry have all been a consequence of this practical usage. These expressions, because they provide an incontestably correct stoichiometry, have become cornerstones of the vast field of aqueous solution chemistry. Initial Conceptions of the Hydrogen Ion The first conceptual model of the hydrogen ion appeared in a landmark paper on the electrolysis of water by Theodor von Grotthuss (3), in which he predicted the existence of a positive hydrogen entity in liquid water.1 This positive hydrogen entity was later identified in the von Helmholz laboratory (4).2 von Grotthuss postulated that the positive hydrogen entity moved through the solution from one water molecule to another. Via good insight, he reasoned that the generation of this particle occurred at the positive electrode but not inside the bulk of the water. von Grotthuss wrote, “all the molecules of the liquid situated in this circle would be decomposed and instantly recomposed: whence it follows, that this water, although undergoing the effect of the Galvanic action, will always remain water” (3, p 337). This depiction of a “proton wire” has become known as the von Grotthuss mechanism (5) and is still widely used two centuries later. In 1838, 30 years after the von Grotthuss contribution, Justus Liebig developed a model that defined acids in terms of replaceable hydrogen (6). After an additional four decades had elapsed, Svante Arrhenius, in his research (1883) on the dissociation of electrolytes, proposed a general paradigm postulating that all acids produce hydrogen ions (7). The early workers then put into use a model, defined by stipulation, that envisaged the hydrogen ion as being an unencumbered particle;a particle that could exist unattached to any of the entities existing in aqueous solution. They also observed that this particle, Hþ, reacted rapidly, and with the correct stoichiometry, with all types of bases. Consequently, the aqueous hydrogen ion in chemical equations was included in the mole and molarity concepts in which it was usually expressed as [Hþ], the molar hydrogen ion concentration. It was also expressed, for the sake of convenience, in terms of a negative logarithm of the molar hydrogen ion concentration as proposed in 1909 by Sorensen (8). 922
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Challenges to the Earlier Definitions In 1930, after almost one-half century of this model's use, I. M. Kolthoff (9) argued, using perspectives of solvation thermochemistry, that it was impossible for unencumbered protons to exist in aqueous solution.3 This paper by Kolthoff generated serious concerns in the analytical chemistry community, for it was no longer possible to confidently write [Hþ] because the simple unencumbered Hþ could not exist in aqueous solutions. Two decades later, in 1952, R. P. Bell (10) also reported that there could be essentially no free protons in aqueous solutions.4 Despite the notion that the unencumbered Hþ did not exist in aqueous solution, the pragmatic analytical chemists and the solution chemists continued to use the old established model of the unencumbered hydrogen ion because it gave a stoichiometry that agreed with experimental results. This problem led to the proposal of several procrustean models attempting to solve this quandary. Among these was the use of H3Oþ, the hydronium ion, the Brønsted acid, whose structure (11) was deduced from crystallographic studies of (H3Oþ)(ClO4-). Manfred Eigen (12) in Gottingen suggested that the hydrogen ion was associated with four waters forming H9O4þ, the Eigen ion. G. Zundel (13) proposed that the hydrogen ion was associated with two waters forming the H5O2þ ion, known as the Zundel ion. All of these representations fell short when later confronted with advancing knowledge of the water structure that was being developed. These newer extensive studies showed that the water molecules underwent widespread hydrogen bonding, producing a variety of water clusters in which the hydrogen ion was sequestered in some way (14). Clearly, the classical methods of defining the hydrogen ion had failed. Contemporary Conceptualizations of the Hydrogen Ion Moore and Jaselskis (15) pointed out that by still using the old nonencumbered concept of the hydrogen ion the definitional perspective of the hydrogen ion had been changed from definition by stipulation to a very different perspective of definition, namely, nominalism.5 Thus, by using a nominal definition, the Hþ term still could lay a claim to legitimacy. It has been shown by others that water molecules form clusters having up to 20 or more water molecules per cluster (16, 17), and that the hydrogen ions incorporated in the cagelike environments of these water clusters react very rapidly with bases, that is, on the order of pico seconds. These works suggest the following visualization of the aqueous hydrogen ion. Because the hydrogen ion is the smallest
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Vol. 87 No. 9 September 2010 pubs.acs.org/jchemeduc r 2010 American Chemical Society and Division of Chemical Education, Inc. 10.1021/ed100099m Published on Web 07/21/2010
In the Classroom
and lightest positively charged particle, it readily participates in hydrogen bonding to form networks of water clusters or cages and is readily relocated from within to the outside of these clusters or cages. While the kinetics of this process can be adequately described by classical physics, there are important corrections that necessitate the use of quantum mechanics (18). Thus, the hydrogen ion as an unencumbered Hþ in homogeneous solution can be treated from classical as well as quantum mechanical perspectives; its total concentration is equal to the Psummation of all hydrogen ion species in the water clusters, [Hþ(H2O)n]. As correctly envisioned by von Grotthuss, the unencumbered hydrogen ion can be released for a fleeting moment from these clusters to protonate other molecules or solid surfaces. Because the equilibrium for the resulting proton transfer reactions is not affected by the geometric details of the proton hydration shell, but only by the magnitude of its solvation free energy (19), the simple unencumbered proton concept used by the early workers retains its practical usefulness. Consequently, the pragmatic definitional philosophy of the early analytical and solution chemists of “if it works, don't fix it!” is thoroughly justified. Notes 1. The formula for the water molecule had not been established at this time. 2. The positive hydrogen entity was identified in the laboratory of von Helmholz (1896-1898) in Berlin. While doing electrical discharges through hydrogen gas, Eugene Goldstein observed some strange new rays at the cathode. He suggested that they be called “Canal Rays” until their identity could be established. Two years later (1898) Wilhelm Wien, also in von Helmholz's laboratory, discovered that these canal rays were hydrogen entities, later to be named protons (around 1907), and made the first measurements of the proton's charge to mass ratio. Eight years later, J. J. Thomson, using more refined experimental methods, also verified the existence of the proton as an independent particle and established a better value for the mass to charge ratio. See the citations in ref 4. 3. In ref 9, I. M. Kolthoff wrote “[A] value for Kbw = [H3Oþ]/ [Hþ][H2O] = 10þ130 is found. ...[We] see that in an aqueous solution no hydrogen-ions are present.” 4. In ref 10, R. P. Bell wrote “The fraction of protons which remain uncombined will be given roughly by e-E/RT, where E is the exothermicity: This fraction is therefore of the order of
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magnitude 10-190, which is equivalent to saying that the free proton does not exist at all in aqueous solution.” 5. Nominal definitions were developed by Aristotle nearly two millennia ago and are widely used in many areas.
Literature Cited 1. Moore, C. E.; Jaselskis, B.; von Smolinski, A. J. Chem. Educ. 1985, 62, 859–860. 2. Born, M. Z. Phys. 1920, 1, 45–48. 3. von Grotthuss, C. J. T. Tillochs Philos. Mag. 1806, 25, 330–339. 4. Goldstein, E. Berlin Akad. Monatsber. 1876, 279–295. Wien, W. Wiedmann's Ann. 1898, 65, 440–452. Thomson, J. J. Phil. Mag. 1907, 13, 561–575. 5. Agmon, N. Chem. Phys. Lett. 1995, 244, 456–462. Eisenberg, B. Biophys. J. 2003, 85, 3427–3428. Cukierman, S. Biochim. Biophys. Acta 2006, 1757, 876–885. Marx, D. Chem. Phys. Chem. 2006, 7, 1848–1870. 6. Liebig, J. Ann. Pharm. 1838, 26, 178–181. 7. Arrhenius, S. Recherches sur la Conductibilite Galvanique des Electrolytes. Thesis, Uppsala University, 1884. 8. Sorensen, S. P. L. C. R. Lab. Carlsberg 1909, 21, 131–304. 9. Kolthoff, I. M. Recl. Trav. Chim. 1930, 49, 409. 10. Bell, R. P. Acids and Bases: Their Quantitative Behavior; London Methuen and Co., John Wiley: New York, 1952; p 7. 11. Schriver, D. F.; Atkins, P.; Langford, C. H. Inorganic Chemistry; W. H. Freeman and Co.: New York, 1994; p 185. 12. Eigen, M. Angew. Chem., Int. Ed. Engl. 1964, 3, 1–19. 13. The Hydrogen Bond;Recent Developments and Experiments. II, Structure and Spectroscopy; Schuster, P., Zundel, G., Sandorfy, C., Eds.; North Holland: Amsterdam, 1976; pp 683-766. 14. Vuilleumier, R.; Borgis, D. J. Chem. Phys. 1999, 111, 4251–4266. 15. Moore, C. E.; Jaselskis, B. Microchim. Acta 1988, 129, 1–6. 16. Saykally, R. J.; Blake, G. A. Science 1993, 259, 1570–1575. 17. Castleman, A. W.; Wei, S.; Shi, Z. J. Chem. Phys. 1991, 94, 3268–3270. 18. Marx, D. Chem. Phys. Chem. 2006, 7, 1848–1870. Mitsuhito, M.; Asuka, F.; Takayuki, E.; Naohiko, M. Science 2004, 304, 1134– 1140. Tuckerman, M. E.; Marx, D.; Klein, M.; Parrinello, M. Science 1997, 275, 817–820. 19. Tawa, G. J.; Topol, I. A.; Burt, S. K.; Caldwell, R. A.; Rashin, A. A. J. Chem. Phys. 1998, 109, 4852–4863.
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