NOTES
162
The author wishes to thank the directors of British Titan Products Company Limited for permission to publish this note. ROLE OF MULTIPLE BONDING I N ELECTRON TRANSFER REACTIONS BYE. R. NIGHTINGALE, JR.~ Department of Chemistry, Universzty of Ptltsburgh, Pzttsburgh 2 % Pennsylvania Received J u l y 18, 1969
Factors which influence the rate and mechanism of oxidation-reduction reactions warrant consideration because the nature of the electron transfer process is so inadequately understood. One such factor whose role has not been previously assessed is that of bond order and the effect of resonance shortening. The only series of compounds for which sufficient data are available to permit interpretation appears to be that of the oxygenated halogenates, c103-, Clod-, Br03-, 1 0 3 - and IOk-. The present note concerns the effect of multiple bonding on the rate of the electron transfer process and correlates the character of the X-0 bond with the reactivity of the halogenates both in homogeneous solution and for electrode reactions. Experimentally, it is observed that the order of decreasing chemical reactivity IO3- > Br03- > C103-, Clod- parallels the shortening of the X-0 bond from that expected for the single covalent bond distance. The effect of this bond shortening upon the rate or mechanism of the electron transfer process is, of course, subject to the same limitations as the previous interpretations of bond shortening2-j since the nature of multiple bonding is not well understood. The classical treatment of Pauling6 relates bond shortening to the amount of double-bond character. However, this explanation is not satisfactory for heteropolar bonds because it fails to account for the shortening of the covalent bond distance and the increase in the bond energy caused by the partial ionic character of the bond. Furthermore, in species such as and Si04-4, the shortening is sufficient to predict complete double bonding and thus place a formal negative charge on the central atom which is contrary to the charge distribution predicted from electronegativities. Recently, Pauling7 has revised the original interpretation of bond shortening to account for the partial ionic character and partial a-bond character of heteropolar bonds. This treatment alleviates the objection of formal negative charge on the more electropositive central atom and retains the Pauling electroneutrality principle* that the electronic charge on each atom within a stable molecule is close to zero and in no case greater than f1 6 . (1) On leave from the University of Nebrsska, Lincoln 8, Nebraska. ( 2 ) V. Schomaker and D. P. Stevenson. J . A m . Cham. Soc., 63, 37 (1941). (3) A. F. Wells, J . Chem. Soc., 55 (1949). (4) M. Huggins, J . A m . Chem. Soc., 7 6 , 4126 (1953). (5) M. G. Brown, Trans. Faraday SOC.,66, 694 (1959). (6) L. Pauling, "The Nature of the Chemical Bond," Cornell University Press, 2nd Ed., Ithaca, N. Y.,1948. (7) L. Pauling, THISJOURNAL, 66, 361 (1952). ( 8 ) L. Paulina, J . Chem. SOC.,1461 (1048).
Vol. 64
Table I compares the interatomic distance and multiple bond character of the X-0 bonds in a series of oxygenated halogenates. With the exception of the periodate ion, the per cent. of abond character calculated considering partial ionic character and bond moment neutralization7 agrees well with the double bond character calculated using the older Pauling relation6; the calculated bond distances also agree rather closely with the experimental values. It seems probable that the failure of the periodate values to correspond more closely results from the failure of both theories to account adequately for the interaction between elements from the different periods with appreciably different electronegativities. Ninety per cent. double-bond character for periodate is too large because it fails to allow for the bond shortening due to the partial ionic character. Similarly, 25% a-bond character for periodate appears too small and suggests that the decrease in bond moment neutralization 1Vith periodic row number7 is too large, a t least for atoms with coordination number of four. If the excess shortening of the 1-0 bond is all attributed to partial a-bonding, the a-bond character of the 1-0 bond in periodate is calcula,ted as approximately 55y0. INTERATOMIC OF' X-0
TABLE I DISTANCE AND MULTIPLE BOKD CHARACTER BONDS IN OXYGENATED HALOGEKATES
Pauling single covalent bond length,'" 8. Experimentalbondlength,H. Per cent. double-bond charactef Schomaker-Stevenson single covalent bond length," A. Calcd. bond length? 8. Per cent. *-bond characterh
103-
BrOa-
ClOa-
Clod-
104-
1.99 1.83b
1.80 1.68'
1.F5 1.4Sd
1.65 1.4Se
1.99 1.79'
20
35
60
60
90
1.97 1.87 21
1.82
1.68 37
1.68 1.50 54
1.68 1.50 63
1,97 1.86 25
Calcd. from ref. 6. b NaI03. KBr03. NaC103. NaCIOa. f NaI04. 0 Calcd. from ref. 2. Calcd. from ref. 7. 5
e
Utilizing the partial a-bond concept, the decrease in chemical reactivity (vide infra) which accompanies the increasing a-bond character may be explained by the fact that increased a-bonding utilizes the oxygen p-orbitals and makes them less available for intermolecular bonding. Using this principle, the behavior of the iodate ion in aqueous solution recently has been attributed to lack of appreciable double-bond ~ h a r a c t e r . ~Conductance and viscosity data indicate that the iodate ion is appreciably hydrated whereas the Br03-, C103-, Clod- and IO4- ions are less extensively hydrated because of the increase in bond order. Doublebonding localizes the negative charge on the central halogen atom thereby rendering the charge less accessible for (presumably hydrogen) bonding with the solvent molecules. While extensive rate data are not available to permit a quantitative correlation between bond order and reactivity, several significant comparisons may be made. Halperin and Taube'" have studied the transfer of oxygen in the reaction of halogenates (9) E. R. Nightingale, Jr., and R. F. Benck, THISJOURNAL, 63, 1777 (1959). (10) J. Halperin and IT. Taiibo. J . A m . Chcm. Soc., 7 4 , 375 (1952).
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
