KINETICSOF URANYL IONHYDROLYSIS AND POLYMERIZATION
We lastly wish to compare the two techniques on a problem for which the w-technique converges. We choose an example given by Streitwieser and XairI6the butadiene cation. The two methods are compared in Tables I11 and IV, where the initial charge densities are the same. The superiority of the present method is clear ; the w-technique still produces sizable variations in the third significant figure, even after 11 iterations, whereas the Y2-technique gives a reasonable answer in only one iteration. I t should be pointed out that it is
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not fair to make a direct comparison of the number of iterations the two methods take. The iterations of the Y2-technique are more complex than those of the wtechnique ; nonetheless, there is an appreciable saving in time with the present technique, in addition to its obvious advantage of succeeding where the w-technique fails. Acknowledgment. The authors wish to thank Dr. AI, Karplus, Dr. V. Schomaker, and Dr. E. B. Whipple for several helpful discussions.
Kinetics of Uranyl Ion Hydrolysis and Polymerization'
by M. P. Whittaker, E. M. Eyring, and E. Dibble2 Department of d h a i s t r y , University of Utah, Salt Lake City, Utah
(Received January 20, 1966)
Temperature jump relaxation times have been observed in acidic, aqueous solutions of uranyl ion that have been identified with the equilibrium 2 U 0 2 +
+
+ 2H20 + (U02)2kz
k -1
2H+. The rate constant k2 at 25" is found to have the value 116 M-I set.-'. This result is compared with the dimerization of chromate and vanadate ions.
Recently a number of workers have reported equilibrium constants for the hydrolysis and polymerization of uranyl ion in aqueous s0lution.3-~ In principle, such data permit the determination of rate constants for several over-all reactions using relaxation methods. A similar kinetic study of aqueous boric acid polymerization has been rep0rted.I The hydrolysis mechanism and equilibrium constants or uranyl ion in aqueous nitrate media proposed by Baes and Aleyer4 and also those proposed by Dunsmore, Hietanen, and Sill6nj were used as a basis for explaining relaxation times observed with a Joule heating-type temperature jump apparatus. The hydrolytic species and their corresponding equilibrium constants reported by Rush and Johnson6 were the basis for our calculations of rate constants in aqueous perchlorate medium. The calculated rate constants were essentially the same regardless of which set of equilibrium constants was used in their calculation provided that the
reaction responsible for the observed relaxation time was assumed to be the formation of dimer, (U02)2(OH)3+ or (U02)2(OH)22+ depending upon the hydrolysis scheme, from monomer.
Experimental For our experiments with uranyl nitrate, samples of (1) This research was supported in part by an equipment grant from the University of Utah research fund and by Grant AM-06231 from the National Institute of Arthritis and Metabolic Diseases of the C . S.Public Health Service. (2) National Science Foundation Undergraduate research participant. (3) R. M . Rush, J. S. Johnson, and K . A. Kraus, Inorg. Chem., 1, 378 (1962). (4) C. F. Baes, Jr.. and N. J. Meyer, ibid., 1, 780 (1962). ( 5 ) H . S.Dunsmore, S. Hietanen, and L. G. SillBn, Acta Chem. Scand.. 17, 2644 (1963). (6) R. hl. Rush and J. S. Johnson, J . P h y e . Chem.. 67, 821 (1963). (7) J. L. Anderson, E. M. Eyring, and M. P. Whittaker, ibid., 6 8 , 1128 (1964).
Volume 69, Number 7
Julu 1966
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Mallinckrodt analytical reagent grade uranyl nitrate were weighed out directly and dissolved in distilled, demineralized, boiled water. The pH of the sample was adjusted with Wasco reagent grade NaOH and deterinined with a Radiometer TTT-1 titrimeter. 1 i The ionic strength CI of each sample was made 0.5 A by the addition of hlerck reagent grade I
