Kinetics of the thermal unimolecular reactions of cyclopropane and cyclobutane behind reflected shock waves

Barnard, J. A.; Cocks, Alan T.; Lee, Richard K-Y.

doi:10.1039/f19747001782

Cited by 29 publications

(21 citation statements)

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“…34 at very high temperatures, i.e. about 1100 K (37,38); however, recent evidence suggests that these results are incorrect and that the rate constants for these reactions can be represented by eq. 34 at least up to 1500 K (39).…”

Section: Future Developmentsmentioning

confidence: 99%

A reformulation of the theory of unimolecular reactions

Yau¹,

Pritchard²

1978

Can. J. Chem.

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PRITCHARD. Can. J. Chem. 56, 1389(19783 The theory of unimolecular reactions is reformulated in a way which makes no reference t o the concepts of a transition state, a reaction coordinate, or of an activated complex: the present theory is based, instead, on a simple master-equation approach using the estimated positions and lifetimes of the rotation-vibration energy levels of the molecule. The fundamental basis of this reformulation is that the unimolecular rate is derived from the perturbation of the normal modes of internal relaxation of the reactant molecule by the microscopic reaction processes. The thermal decompositions of cyclobutane, cyclopropane, ethyl isocyanide, ethyl chloride, and methyl isocyanide are examined in detail, and it is shown that not only is the present theory much easier to use than is conventional RRKM theory, but also that it gives better results.An Appendix provides a set of algorithms required for these calculations. Un appendice fournit l'ensemble d'algorithmes requis pour ces calculs.[Traduit par le journal]

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Section: Future Developmentsmentioning

confidence: 99%

A reformulation of the theory of unimolecular reactions

Yau¹,

Pritchard²

1978

Can. J. Chem.

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“…(5) and 897K. The five highest temperature points were obtained from experiments in shock tubes (14,15,18,19), for which temperatures are difficult to calculate and for which adjustments of k to k, are greater. For these reasons, data from shock tube experiments at even higher temperatures have been omitted.…”

Section: Discussionmentioning

confidence: 99%

“…In the studies of (3,4). It has now been the subject of at least 20 the collision efficiency at high temperatures (16,18, experimental studies (1,2,(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22) and at least three 20, 221, km was calculated starting with the above RRKM models (3,4, 23).…”

Section: Introductionmentioning

confidence: 99%

The pressure dependence of the rate of isomerization of cyclopropane at 897 K

Furue¹,

Pacey²

1982

Can. J. Chem.

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HIROSHI FURUE and PHILIP D. PACEY. Can. J. Chem. 60,916 (1982). The isomerization of cyclopropane has been studied in a flow reactor at 897 K and from 4 to 406 Tom. The pressure dependence of the rate constants from this work and from the literature have been compared with predictions obtained from two models based on the theory of Yau and Pritchard and from three RRKM models. The collisional deactivation efficiency was found to generally decline with increasing temperature. The average energy removed per collision was calculated by the method of Tardy and Rabinovitch and was found to have values from 15 to 23 kJ mol-I at 897 K. Combining the results of this work with data from the literature from 690 to 1038 K, the limiting high pressure rate constants follow the relation log k , = 15.50 k 0.14 -(276.0 k 2.1 kJ mol-')/2.3RT. HIROSHI FURUE Introductionselves, reliable, limiting high pressure values, k,, The isomerization of cyclopropane has played an based on extrapolation of data from a number of important part in the study of unimolecular reac-Pressures, have been obtained between 718 K and tions. Because it is a reasonably clean reaction 773K 2, 59 7). There have been six recent system, it was the subject of early, successful studies of the pressure dependence of the rate at experimental investigations (l,2). In turn, because higher temperatures (17-221, but the pressure of the availability of the experimental data, it was ranges were narrow and the authors did not extrapone of the first reactions used to test RRKM theory olate their data to determine k,. In the studies of (3, 4). It has now been the subject of at least 20 the collision efficiency at high temperatures (16, 18, experimental studies (1, 2, 5-22) and at least three 20, 221, km was calculated starting with the above RRKM models (3,4, 23).Arrhenius parameters determined at lower temperDespite this impressive body of work, some atures. Even these relatively precise Arrhenius questions remain. RRKM models which were de-Parameters can lead to an uncertainty in k, at veloped to reproduce the fall-off of the rate con-1mOK of50%-stant at low pressures at one temperature haveThe Purpose of the Present work is to study the been found to be unsuccessful at other tempera-reaction at high Pressures and high temperatures tures (4). It has been suggested (16,17) that this is using a flow system. Such a system can provide caused by a decline in P, the efficiency of collisions activation energies (24) and reaction orders (251, in removing excess vibrational energy, as the d 1n kld In P , with a precision of 2 or 3%. This temperature increases. The evidence for this is precision is not better than that of the activation strong for collisions of cyclopropane with small energy quoted above, soexperiments were restrict-

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“…To test this idea, a series of calculations was made for a mixture of 1% cyclopropane in argon, and compared with the reported results of Barnard, Cocks, and Lee [6]. Rate constants calculated form the observed disappearance of cyclopropane in single-pulse shock-tube experiments are shown in Figure 1, along with curve C which shows the apparent rate constants that would be calculated if the actual rate constant were that of curve B and wall cooling occurs.…”

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confidence: 96%

The importance of wall cooling in single‐pulse shock‐tube studies

Skinner

1977

Int J of Chemical Kinetics

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The first serious effort to correct kinetic data obtained from single-pulse shock tubes for the effects of wall cooling was made by Lifshitz and coworkers [l]. Allowing only for boundary-layer cooling behind the reflected shock, using Goldsworthy's equation [a], they showed that a few percent of the gas sample is substantially cooled in typical experiments. They concluded that the correction to rate constants calculated from the observed extent of reaction will be small if the extent of reaction is also small, but warned that boundary-layer effects may be serious at higher conversions of reactants to products.I n a paper on ethylene pyrolysis [3] we used the method of Lifshitz and coworkers, and also made an allowance for boundary-layer formation behind the incident shock, using the approach of Tschuikow-Roux and Marte (TM) [4]. When the incident shock boundary layer is considercd, that part of the sample near the wall is never heated to the full reflected shock temperature, whereas the Lifshitz calculation assumes a uniform temperature all across thc tube immediately behind the reflected wave.We have used two simplifying assumptions which suggwted themselves as we made trial calculations, and which can be shown to introduce errors of no more than 10% of the corrections to the rate constants. First we made all our calculations for the mid-point of the gas sample that was taken for analysis, rather than integrate over the length of the sample.Second, we noted that the temperature profiles in the boundary layer immediately behind the reflected shock wave, calculated by the TM method, had shapes not greatly different from those obtained by the Goldsworthy equation. By obtaining a time in the Goldsworthy equation that gave the best match with the T M curve (specifically, we matched the curves at the points corresponding to 0.96 of the free stream temperature) we were able to calculate temperature profiles in the reacting gas using only the Goldsworthy equation, avoiding the necessity of developing transition profiles between T M and Goldsworthy profiles.The size of the correction to the calculated rate constants increases with increasing sample size and with increasing heating time, and is typically between 5 and 20% for small degrees of conversion. 863

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Kinetics of the thermal unimolecular reactions of cyclopropane and cyclobutane behind reflected shock waves

Cited by 29 publications

References 1 publication

A reformulation of the theory of unimolecular reactions

A reformulation of the theory of unimolecular reactions

The pressure dependence of the rate of isomerization of cyclopropane at 897 K

The importance of wall cooling in single‐pulse shock‐tube studies

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