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COMMUNICATIONS TO THE EDITOR Cyclobutane Thermal Decomposition Rates at 1300-1500 K Publication costs assisted by Colgate University
Sir: Recent publications from other lab~ratoriesl-~ have indicated that rate constants for a number of unimolecular reactions, previously thought to be well characterized, actually become anomalously low at temperatures above -1100 Ke5 At least two quite different theoretical explanations have been put forward to account, partially or entirely, for the observed a n ~ m a l y . To ~ ~date, ~ , ~ all of the anomalously low rate data have come from absolute-rate single-pulse shock tube experiments where reactions were carried to high extents of con~ersion.~ Comparative-rate single-pulse shock tube studies on a number of these suspect systems, for example, the structural isomerization of cyclopropane to propene,’,’ have not indicated any deviation from strict Arrhenius behavior. This lack of agreement has hampered efforts to determine whether the reported anomaly is a characteristic behavior of these reactions, in need of theoretical justification, or merely an experimental artifact associated with high conversion in some absolute-rate studies. We wish to report here our initial results from a rate study of another system previously suggested as anomalous, cyclobutane 2 ethene, using an experimental technique not heretofore used for the study of these reactions. Our data support a continuation of the low temperature Arrhenius parameters for this reaction up to at least 1500 K. Reaction mixtures containing 5.0% cyclobutane in argon were heated by incident shock waves in a shock tube of rectangular cross section, previously described elsewhere;1° and cyclobutane dissociation rates were deduced by monitoring density gradients in the reacting gas behind the incident shock waves, via the laser schlieren method described by Kiefer et al.ll Fifteen experiments were run over the range 1308-1498 K, and all of these gave density profiles that showed evidence of approximately exponentially decaying endothermicity. One expects a constant density gradient behind a shock wave in a system which undergoes chemical reaction at a constant rate. However, for cyclobutane at these temperatures there will be significant percentages of decomposition within the time scale of our experiments, resulting in significantly lower reaction rates, decreasing rates of enthalpy change, and thus decreased laser beam deflection, as we observed. Extrapolation of the low temperature rate constant implies cyclobutane half-lives at 1300, 1400, and 1500 K of 5.5,1, and 0.2 ps, respectively. Below 1300 K there was no detectable endothermicity, presumably because the reaction was proceeding too slowly, and above 1500 K the initial exponential decay collapsed into the “spike” or dead time caused by passage of the shock front through the laser beam, and could not be resolved. Shocks in pure argon gave flat density profiles except for the shock front spike. Temperatures behind incident shocks were calculated from measured incident shock velocities, using an ideal, onedimensional shock model which assumed complete equipartition of energy and no chemical reaction. Enthalpy polynomials for cyclobutane were calculated from vibrational assignments given by Shimanouchi.12
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From each recorded density profile, laser beam deflection due to cyclobutane dissociation at “time zero” was estimated by extrapolating the exponential portion of the trace back to the middle of the spike, assumed to represent the time at which the shock front had reached the center of the laser beam cross section. From this datum, values for initial density gradient and reaction rate constant were calculated as described by Miller.lo Rate constants (k)thus obtained are shown in Figure 1. Also shown are the rate constants corrected to infinite pressure (km). Ratios of k/k, were interpolated from Forst method calculations by Frey, as reported by Barnard et a1.2 For each experiment, three points are shown, connected by a vertical line. These points correspond to assumed inert diluent gas (argon) collision efficiencies (Pp, pressure/pressure basis) of 0.01, 0.07, and 0.15, and reflect current lack of knowledge of the parameter under conditions of the present study. However, because of heavy reactant loading (5%) the fall-off corrections are not very sensitive to the value chosen. The collision efficiency for cyclobutane was assumed to be Figure 1 also shows Arrhenius lines deduced from static studies at lower temperat~res,’~ and from fully corrected high pressure rate constants obtained above 1100 K by Barnard et aL2 in their absolute rate single-pulse study. Clearly the present rate constants, even before correction for fall-off, are about an order of magnitude larger than the single-pulse shock tube results, while corrected rate constants from the present study lie close to, but slightly above, an extrapolation from earlier work at -700 K. There is no evidence of anomalous behavior below the upper limit of this study, 1500 K. The densitometric techniques used for our experiments avoid many potential sources of systematic error that may affect the absolute rate single-pulse method, such as nonideal shock reflection, turbulence behind reflected shocks, substantial boundary layer growth, and sampling of products of uncertain thermal history. However, the present method is more abstract in that the nature of processes occurring in the heated gas is assumed, and cannot be confirmed by conventional chemical analysis. A full description of the observed laser beam deflection hinges on the assumption that the apparently exponential deflection decay after passage of the shock front was directly related to cyclobutane dissociation. This assumption is supported by (a) the absence of beam deflection, except for the spike, from shocks run in pure argon; (b) measurements by Skinner et al.15 which indicated that further reaction of product ethene should be immeasurably slow under the present conditions; and (c) rates of decay of laser beam deflection which correlate well with decay rates predicted from the rate constants calculated from initial magnitudes of beam deflection. Our rate constants calculated from laser beam deflection are, of course, subject to various sources of error such as uncertainty in post-shock gas density (510%), index of refraction of cyclobutane (510% ), and estimated beam deflection at time zero (5a factor of 2). Contributing to the latter uncertainty are factors which lead to deviation from true exponential decay: unimolecular fall-off, small changes in bulk index of refraction as the reaction proceeds, and temperature drop due to reaction endothermicity. An additional problem is that equipartition of
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The Journal of Phys/cal Chemistry, Vol. 8 I, No. 19, 1977
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Communications to the Editor
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energy is not instantaneous upon passage of the shock front through the gas, so the reaction is not turned on instantaneously. Thus, there is some arbitrariness about the choice of time zero. Considering these factors and the 525 K possible systematic error in our temperature calculat i o n ~we , ~feel ~ the present data are in acceptable agreement with the low temperature rate ~ 0 n s t a n t s . l ~ Further study of this and other similar reactions previously reported to appear “anomalous” is in progress.
Acknowledgment. This research was supported by a Cottrell College Science Grant from the Research Corporation, and by the Colgate University Research Council. We thank Dr. Bansi Kalra and Messrs. Lorenzo Rocca and Bradley Shapiro for efforts which facilitated this project,
The Journal of Physlcal Chemistry, Voi. 81, No. 19, 1977
and Professor S. H. Bauer for allowing us to use his apparatus at Cornell University for this study. Supplementary Material Available: Details of the experimental procedure and experimental data and data reduction procedures (7 pages). Ordering information is available on any current masthead page. References and Notes (1) J. N. Bradleyand M. A. Frend, Trans. Faraday Soc.,67, 72 (1971). (2) J. A. Barnard, A. T. Cocks, and R. Y-K. Lee, J. Chem. Soc., Faraday Trans. 7 , 70, 1782 (1974). (3) J. A. Barnard, A. T. Cocks, and T. K. Parrott, J. Chem. Soc., Faraday Trans. 7 , 72, 1456 (1976). (4) J. A. Barnard and T. K. Parrott, J. Chem. Soc., Faraday Trans. 1, 72, 2404 (1976). (5) Actually, the onset of the anomaly correlates better with log k (Si) i= 3.0 than with temperature. (6) (a) H. Eyring and A-L. Lev, Proc. Natl. Acad. Sci., U.S.A., 72, 1717 (1975); (b) Chem. Eng. News, 53 (15), 27 (1975). (7) In the “absolute-rate” method, gas reaction temperatures are calculated from measurements of incident and/or reflected shock wave velocities; in the “comparative-rate” method, gas reaction temperatures are calculated from extent of reaction of an internal standard molecule, for which Arrhenius parameters are well known. (8) P. Jeffers, D. Lewis, and M. Sarr, J . Phys. Chem., 77, 3037 (1973). (9) P. Jeffers, C. Dasch, and S. H. Bauer, Int. J . Chem. Kinet., 5, 545 (1973). (10) J. Miller, Ph.D. Thesis, Corneii University, Ithaca, N.Y., 1974. (11) (a) J. H. Kiefer and R. W. Lutz, J . Chem. Phys., 44, 658 (1966); (b) W. D. Breshears, P. F. Bird, and J. H. Kiefer, ibki., 55, 4017 (1971). (12) T. Shimanouchi, Nati. Stand. Ref. Data Ser., Nati. Bur. Stand., No. 11 (1967). (13) Actual experimental data, intermediate and final calculated results, and a description of data reduction procedures are available as supplementary material. See paragraph at end of text regarding supplementary material. (14) S. W. Benson and H. E. O’Neai, Natl. Stand. Ref. Data Ser., Natl. Bur. Stand., No. 21 (1970). (15) (a) G. B. Skinner, R. C. Sweet, and S. K. Davis, J. Phys. Chem., 75, 1 (1971). (b) I f we were to assume that all of the product ethene didfurther decompose to C,H, -I-H, cyciobutane dissociation rates caicuhted from measured densi?, gradients woukl be lowered by about a factor of 8, which would stili leave k , values about an order of magnitude larger than those reported by Barnard et ai.’ Department of Chemistry Colga fe University Hamilton, New York 13346
D. K. Lewis” S. A. Felnsteln
Department of Chemistry State University College Cortland, New York 13045
P. M. Jeffers
Received May 5, 1977
