RELAXATION SPECTRA OF MOLYBDATE POLYMERS
1575
quantitative explanation of the results reported here will require extensive ultrasonic absorption measurements as a function of frequency and concentration in the various solvents.
University for his assistance with the experiment and Mr. 0. E. Dial, Jr., of this laboratory for his assistance with the curve fitting. I wish to thank Professors Yeager and Stuehr of Case-Western Reserve University, and Dr. F. V. Hunt and Dr. H. Beedek of this laboratory for their helpful comments on the manuscript. This paper represents results in research sponsored under the Office of Naval Research and the National Science Foundation.
Acknowledgment. I wish to acknowledge Professor E. yeagerjs kindness in making it possible for me to perform this experiment a t the Department of Chemistry, Case-Western Reserve University. I n addition I wish t o thank Mr. A. Barksdale of Case-Western
Relaxation Spectra of Molybdate Polymers in Aqueous Solution. Ultrasonic Attenuation by Dan S. Honig and Kenneth Kustin* Department of Chemistry, Brandeia University, Waltham, Massachusetts 03164 (Received April 16, 1971) Publication costs assisted by the National Institutes of Health
Ultrasonic attenuation studies (7-214 MHa) were carried out on acidified solutions of sodium molybdate at an ionic strengtn of 1.0 M . The NatM004 concentration varied between 0.05 and 0.20 M , and the hydroM . A single relaxation time (7.1-9.10 X gen ion concentration extended from 5 X lo-’ to 3 X sec) was observed. This effect was assigned to a two-step mechanism consisting of protonations of Mood2and Mo~O~~B-.The following rate constants were thus determined: H+ M004’-, k = 5 X log M-‘ sec-’; H+ MoTO&, k = 7 X 1Olo M-l sec-’. The relatively low value obtained for reaction of H+ with Moo4*- was interpreted as indicating that addition of a proton to tetrahedral Mood2- ion is not simply a direct proton attachment process, but also involves conversion of M004~-to an octahedral configuration.
+
+
The kinetics of molybdenum(V1) isopolyanion formation has been studied by several investigator^.'-^ Rapid-mixing experiments demonstrated that both protonation and condensation were quite rapid, protonation being more s0.I The kinetics of polymerization have also been investigated with the temperaturejump m e t h ~ d ,but ~ only the overall monomer heptamer F ) octamer steps could be characterized. Relaxation times for these processes were all longer than 100 psec under the experimental conditions (pH 6.50-5.50, total [NaJiIo04] 0.01-0.25 M , ionic strength (NaNOa) 1.0 M , and 25°).4 Ultrasonic absorption experiments were undertaken in an attempt to observe (a) intermediate aggregation steps, (b) counterion binding of the polymers with sodium ion,6 or (c) the kinetics of any protolytic steps. The detection of intermediate steps was, from the outset, doubtful, as the most comprehensive equilibrium studies report no detectable polymers in Naf media below heptamer.6,6 Effects due to intermediates
*
would therefore be too small to o b ~ e r v e . On ~ ~ ~the other hand, protolytic and/or complexation equilibria should be ob~ervable.’~~
Results and Treatment of Data Acidified solutions of sodium molybdate, ionic strength, p, 1.0 M , were prepared as described prev i ~ u s l y ,without ~ degassing. Ultrasonic absorption measurements were carried out from 7 to 214 MHe (1) G. Sohwarzenbach and J. Meier, J . Imrg. Nucl. Chem., 8 , 302 (1958). (2) J. Asay and E. M. Eyring, unpublished results. (3) 0. Glemser and W. Holtje, Angew. Chern., Int. Ed. Engl., 5, 736 (1966). (4) D.S. Honig and K. Kustin, In.org.. C h m . , 11, 65 (1972). (5) J. Aveston, E. W. h a c k e r , and J. S. Johnson, ibid., 3, 735 (1964). (6) Y.Sasaki and L. G . Sill&, Ark. Kemi., 29, 253 (1967). (7) M.Eigen and L. De Maeyer, Tech. Org. Chem., 8, 895 (1963). (8) J. Stuehr and E. Yeager in “Physical Acoustics,” Vol. 2A, W. P. Mason, Ed., Academic Press, New York, N. Y., 1965, p 376. (9) Reference 8,p 398.
The JOUTTU~ of Physical Chemiatry, Vol. 76,No. 11, lQ79
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DANS. HONIGAND KENNETH KUSTIN
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parison of solutions 6 and 7 indicates that processes involving Mo04'- also contribute. No obvious indication of intermediate polymerization steps (e.g., dimerization, etc.) is observed. The possibility of (CYh)&em being due to complexation of Na+ with M004~can be ruled out (solution S), as would be expected.12 The full reaction scheme describing the kinetic behavior of molybdate monomer and heptamer a t frequencies from 7 to 220 MHz can be ~imp1ified.l~That is, at these pH's (
