NOTES
Jan., 1960 with sulfite. I n acid medium, the reaction of iodate and bromate with sulfite is very rapid" whereas the reaction of chlorate, which possesses a considerably larger bond order, proceeds a t a measurable velocity.12 The exchange of oxygen between iodate and water is immeasurably rapid, while both bromate and chlorate exchange with half-times of the order of many hours.'O Halperin and Taube suggest that the difference between the oxygen lability of iodate and of bromate and chlorate may lie in the tendency for iodine to assume coordination numbers greater than 3 or 4, but there is no evidence for the existence of a stable para-iodate or similarly hydrated species in aqueous solution. However, the ability to expand the coordination sphere is related to the absence of appreciable multiple bond character and the availability of the d-orbitals, and the role of bond hybridization cannot adequately be evaluated without further exchange data, particularly for perchlorate and periodate. Further information is available from a study of the electrode processes. I n pH 0 medium, the half-wave potentials for the reduction of IO4-, IO3- and Br03- a t the dropping mercury electrode (d.m.e.) are 0.38,13 0.06,14 and - 0.1114 v. us. s.c.e.. respectively. Chlorate and perchlorate are not reduced a t the d.m.e. Measuring the overpotential as the difference between the standard electrode potential and the half-wave potential, the overpotentials for the reduction of IO4-, IO3- and BrOa- are 1.2, 0.7 and 1.3 v., respectively. The overpotential for a slow (irreversible) reaction is related, though not in a simple maniier, to the rate of the electrode reaction, and we estimate the relative rates of reduction as 1 0 3 - > BrO3- _> IO4-. Assuming the bond hybridization to be invariant, the effect of the number of coordinating atoms may be illustrated by comparing, for example, the iodate and periodate ions. For the completely a-bonded structure, the formal charge on the iodine atom is more positive in periodate than in iodate. However, the greater a-bonding in periodate reduces more effectively this formal charge and leaves the iodine atom less electropositi1.e than in iodate. The iodate ion is therefore more reactive because of the more electrophilic iodine atom a i d the greater availability of the oxygen p-orbitals. Recently, GierstI5 has measured the rates of reduction of iodate and bromate in alkaline medium a t 25' a t a mercury electrode. For a rate constant of cm./sec., the potentials for the iodate and bromate reduction are - 1.05 :ind - 1.45 v. 2's. s.c.e., respectively, corresponding to overpotentials of about 1.06 and 1.81 v.16 The values for a ~ are , 0.96 for iodate and 0.65 for bromate,15where a iq the transfer coefficient. Assuming of electrons transferred in the that the number
+
+
(11) 9. Sehwickor, Chem. Zentr., 15, 845 (1891). (12) A. C. Pu'ixon and K. B. Krauskopf, J. A m . Chem. Soc., 64, 4606 (1932). (13) P. Souchay, A n a l . China. A c t a , 2, 17 (1948). (14) I. hl. Kolthoff and E. F.Orlemsn, J . Am. Chem. Sac.. 64,1044, 1970 (1942). (15) L. Gierst, private communication. (16) From these data, the reaction rates may be calculated for any arbitrary value of overpotential. For instance, the ratio of the rate of reduction of iodate t o t h a t of bromate is approximately 10%a t a constant ovcrootential of 1.4 v.
163
rate determining step is two in each case, the values for the transfer coefficient of 0.48 for iodate and 0.32 for bromate are congruous with the increase in the bond order for these species. The fact that chlorate cannot be reduced a t the mercury electrode suggests that the transfer coefficient is sufficiently small to preclude an appreciable reaction rate prior to the hydrogen evolution. Acknowledgment.-Stimulating discussions with Dr. D. H. McDaniel are gratefully acknowledged.
THE INTERMOLECULAR FORCE CONSTANTS O F RADOS BY GEORGEA. MILLER Contiibution from the Chemistry Department, Georgia Institute of Technology, Atlanta, Georgia Received J u l y 9, 1969
In a recent article, Srivastava and Saxena' have calculated the Lennard-Jones(6-12) potential parameters of radon. Their method involves a correlation of the thermal diffusion of mixtures of rare gases with a function of their molecular weights. The values they have obtained, u = 4.48 A. and E/JC = 484"K., lead to an unusually high dispersion energy of 2.16 X lop5'erg cm.6. It is the purpose of this paper to estimate the potential parameters by other means. First, the Dolarizabilitv of radon will be estimated using
