744
KARLHEINZINGER AND RALPHE. WESTON, JR.
I n conclusion, the present) investigation indicates clearly that primary amines can rotate in their crystal lattices over hindering potential energy barriers in a temperature region not far below their melting points. The extreme sharpness of the drop in the dielectric constant at the transition testifies to the purity of the materials. The secondary amines do not, show a transition to a rotator phase as evidenced by the sharp drop in their dielectric constants a t the freezing points and
by the absence of any appreciable loss in their solid phases.
Acknowledgments. The authors wish to express their thanks to Professor P. J. Graham for the computer programming. The static dielectric contant measurements and the evaluation of the thermodynamic parameters were done by 14. S. Mathur, Research Assistant on the project.
Isotopic Fractionation of Hydrogen between Water and the Aqueous Hydrogen Ion'
by Karl Heinzinger2 and Ralph E. Weston, Jr. Department of Chemistry, Brookhaven National Laboratory, U p t o n , New York
(Received August 13, 1969)
The fractionation of hydrogen isotopes between aqueous solutions of perchloric acid and the vapor phase in equilibrium with the solutions has been measured at 13.5'. With the usual assumption that the proton is solvated in the form H30+,the separation factor thus obtained can be used to calculate the equilibrium constaiit, K L , for the isotope exchange equilibrium, H 2 0 HzDO+ = HDO H30+. The value of 0.96 f 0.02 determined in this work is in good agreement with values obtained by other, generally indirect, methods. It is shown that our results are consistent with those obtained by other types of measurement only if the proton is formulated as H30+.
+
Some thirty years ago, an explanation for the kinetic behavior of acid-catalyzed reactions in mixtures of light and heavy water was proposed by Gross and coworkers3-5 and by Butler and co-workers.6-8 They developed a theory for the effect of deuterium in the aqueous solvent on the ionization constants of weak acids and on the experimental rate constant of acidcatalyzed reactions following the mechanism
8
+ H+
SH+ (rapid)
SH + --+product (rate-determining) In a solvent composed of light and heavy water, the isotopic composition of the solvated hydrogen ion T h e Journal of Physical Chemistry
+
differs from that of the solvent. These two quantities are related by equilibrium constants such as
( I ) Research performed under the auspices of the 5. S. Atomic Energy Commission. (2) On leave from the Max Planck-Institut fur Chemie, Main., Germany. (3) P. Gross, H. Steiner, and F. Krauss, Trans. Faraday Soc., 32, 877 (1936). (4) P. Gross and H. Wischen, ibid.,32, 879 (1936). (5) P. Gross, H. Steiner, and €1. Suess, ibid., 32, 883 (1936). (6) J. C. Hornel and J. A. V. Butler, J . Chem. Soc., 1361 (1936). (7) W. J. C. Orr and J. A. V. Butler, ihid., 330 (1937). (8) W. E. Nelson and J. A. V. Butler, ibid., 958 (1938).
ISOTOPIC FRACTION.ATION OF HYDROGEN
745
This may be recognized as the equilibrium constant for the isotope exchange reaction H2O
+ HzDO+ = HDO + H30'
(2)
A further simplification results from the assumption of the rule of the geometric mean9 as applied to the isotopically homologous series H 3 0+, H2D0+, HD2O1+, and D30+. This makes it possible to relate all the equilibria such as (2) to a single one, which has traditionally been described by the equilibrium constant L. 2D30+
+ 3Hz0
=
2H30f
+ 3D2O
(3)
The isotopic fractionation between solvent and hydronium ion is reflected in the behavior of the rate constant as a function of the isotopic content of the solvent. For this reason, the kinetic behavior of acidcatalyzed reactions in mixtures of light and heavy water has been used for many years as a criterion of a mechanism which involves a rapid equilibrium between reactant and hydrogen ion. A few years ago, this problem was examined again by Purlee,lo who re-evaluated L from modern data. His paper was rapidly followed by several other communications on the subject. In oiie of these, Gold1' points out that in most of the data used by Purlee the value of L is extremely sensitive to small errors in the experimental values of rate constants. He also showed that similar solvent isotope effects may be expected in reactions which have a proton transfer as the rate-determining step. Swain and co-workers1"13 evaluated L from the vibrational frequencies of H30+ and D30+, and also from a somewhat different treatment of electrochemical data than that of Purlee, obtaining a value of L about 25% lower than Purlee's value. Halevi, Long, and Paul14 have also discussed this problem, and in particular, have emphasized the importance of the changing medium on ionic activity coefficients. Recently, Kresge'j has derived, very generally, the equations for protolytic reactions in mixtures of H 2 0 and D20. Equilibrium and rate expressions for both rapid and rate-determining proton transfer reactions are considered. Until very recently there has been no direct measurement of an equilibrium constant related to L. There now are two sets of experiment^'^^" which give data leading directly to L. These depend upon the fact that the position of the proton n.m.r. peak in an aqueous acid solution is related to the concentration of the hydrogen ion. By measuring this shift in H 2 0 and in a mixture of D2O and H20, it is possible to obtain relative hydrogen ion concentrations in the two solvents and thus to evaluate L. The agreement
between these two sets of experiments is within experimental error. In this type of measurement, it is tacitly assumed that there is no significant contribution to the n.m.r. shift from the water molecules solvating the anion. We have now made a direct measurement of the equilibrium constant K L using a quite different technique. Essentially, this involves the determination of the isotopic composition of the water in an aqueous acid solution by measuring the D / H ratio of the vapor phase (which contains only water) in equilibrium with the acid solution. Knowing the analogous separation factor for pure water and the isotopic composition of the entire liquid phase together with the concentration and extent of dissociation of the acid, one can calculate K, . Principle of the Measurement. The equation which relates the separation factor between vapor and liquid of a n aqueous acid solution to the desired equilibrium constant KL can be derived by the same method as that used by WetzelLgto describe the fractionation in an azeotropic acid-water mixture. In our experiments the atom fraction of deuterium is so small (-3 X that molecular species coiitaining more than one deuterium atom need not be considered. In addition, NHDO
