STRUCTURAL ISOMERIZATION OF CYCLOPROPANE
3459
Carbon-13 Kinetic Isotope Effect in the Structural Isomerization of Cyclopropane: Temperature and Pressure Dependence’
by L. B. Sims2and Peter E. Yankwich Noyes Laboratory of Chemistry, University of Illinois, Urbana, Illinois 61801 (Received April 7 , 1967)
The CI3 kinetic isotope effect in the structural isomerization of cyclopropane to propylene was measured in the pressure range 1-760 mm a t temperatures between 450 and 519”. The apparatus and procedure were proven by determinations of the first-order rate constant over the same ranges of experimental variables. Qualitatively, the C13 isotope effect exhibits the same behavior as that due to deuterium labeling: at high pressures it is relatively pressure independent, but below about 100 mm it decreases approximately linearly with log p . At 1 atm, k C t z a ~ a / k C ~ z z ~=~ a (0.995 Ha f 0.001) exp[(l9.1 f 2.O)/RT]. The C13 effect is about 0.8% a t 1 atm, falls to about 0.3% at 1 mm, and is surprisingly large for isotopy at only one carbon in the ring. The results indicate that the reaction coordinate involves considerable ring relaxation.
Introduction The gas-phase structural isomerization of cyclopropane to propylene is one of the most widely studied unimolecular reactions, and the detailed mechanism has long been the subject of controversy in the literature. Most often, discussion has revolved around two mechanisms proposed originally by Chambers and Ki~tiakowsky:~(1) hydrogen transfer, with little or no ring relaxation in the activated complex, and ( 2 ) ring opening t o form a trimethylene biradical-like complex with little or no hydrogen bridging. The importance of hydrogen transfer in the reaction coordinate is suggested by more recent observations of a large deuterium isotope effect at high pressure^.^^^ In addition to the structural isomerization, Rabinovitch, et al. ,I observed a geometrical cis-trans isomerization of sym-1,2-cyclopropane-dz with high-pressure Arrhenius parameters nearly identical with those observed for the structural isomerization,* suggesting similar mechanisms for the two processes. The most likely mechanism for the structural isomerization involves ring relaxation with hindered rotation of the end CH2 groups in the activated comp1ex.I Using the RRKM formulation of the theory of unimolecular reaction^,^,^^ Rabinovitch and his co-workers have shown that a complex involving both a relaxed ring structure and hydrogen bridging is able to account
adequately for the kinetics,” for the pressure and temperature dependences of the deuterium isotope effect, l 2 and for the inversion of the deuterium isotope effect at lo^ pressures,13as well as being consistent with the observed geometrical is~merization.~ The strongest evidence for ring relaxation in the reaction coordinate comes from the results on the ~
~~~
(1) Taken in part from the Ph.D. Thesis of L. B. Sims. (2) To whom correspondence should be addressed a t Department of Chemistry, University of Arkansas, Fayetteville, Ark. 72701. (3) See A. F. Trotman-Dickenson, “Gas Kinetics,” Butterworth and Co- Ltd., London, 1955, for a review and for early literature citations. (4) T. S. Chambers and G. B. Kistiakowsky, J . Am. Chem. SOC.56, 399 (1934). (5) A. T.Blades, Can. J . Chem., 39, 1401 (1961). (6) See also R. E. Weston, Jr., J. Chem. Phys., 26, 975 (1957). (7) B. S. Rabinovitch, E. W. Schlag, and K. B. Riberg, ibid., 28, 504 (1958). (8) E. W. Schlag and B. S. Rabinovitch, J . Am. Chem. Soc., 82, 5996 (1960). (9) R . A. Marcus and 0. K. Rice, J . Phys. Colloid Chem., 55, 894 (1951). (10) R. A. Marcus, J. Chem. P h g s . , 20,359 (1952). (11) D. W.Setser, Ph.D. Thesis, University of Washington, Seattle, Wash., 1961. (12) B. S. Rabinovitch, D. W. Setser, and F. W. Schneider, Can. J. Chem., 39, 2609 (1961). (13) B. S. Rabinovitch, P. W. Gilderson, and A. T . Blades, J . Am. Chem. Soc., 86, 2994 (1964).
Volume 71, Number 11 October 1967
L. B. SIMSAND PETERE. YANKWICH
3460
geometrical cis-trans isomerization and, though seemingly irrefutable, is somewhat indirect. Examination of the related carbon isotope effect should provide a more direct route for obtaining such information. The RRKM calculated kinetic quantities" are found to be relatively insensitive to details of the activated complex structure and vibrational frequency pattern. The various hydrogen and carbon kinetic isotope effects depend upon the isotope shifts in the normal molecule and activated complex vibration frequencies. The nonskeletal vibrations are very sensitive to deuterium substitution and virtually unaffected by carbon isotopy; the deuterium isotope effect thus provides information about hydrogen transfer and bridging. The skeletal or ring mode vibrations are not very sensitive to hydrogen isotopy but are strongly affected by substitution of C13 for C l 2; the CI3 isotope effect should permit one to obtain detailed information on these complex frequencies, particularly if the experimental conditions cover suitable ranges of temperature and pressure. Heretofore, the only results available for the C13 isotope effect have been those of Weston,6 who found =
1.0072
f
0.0006
(1)
at 492" and 1 atm pressure. Such a datum does not suffice to demonstrate conclusively the importance of ring relaxation or to make possible comparisons with theory. The object of the investigation reported here was to provide a temperature-pressure map of the C13 kinetic isotope effect adequate to support such analysis.
Experimental Section Materials. Cyclopropane (Matheson Co., 95%) was purified by repeated distillation in vacuo between traps at -78 and -196" until no impurities were detectable by gas chromatography and the mass spectrum agreed well with that reported in the literature.14 Propylene (Phillips Petroleum Co., Research grade) was purified similarly. A p p a r a t u s and Procedure. A conventional highvacuum apparatus was used for gas handling and for introduction of cyclopropane into a 1400-cc Vycor reaction vessel heated by a furnace assembly similar to that described by Chesick. l5 The temperature was regulated by means of a gas thermometer controller like that described by LarsonI6 and measured using PtPt-lO% Rh thermocouples placed at several positions on the surface of the reaction vessel and in wells extending into it. The temperature was homogeneous over the reactor to within =k0.05" in all runs and its drift was less than 1" in the longest experiment. The reaction temperatures cited are believed accurate to 0.2". The Journal of Physical Chemistry
For reactions at pressures above 1 cm, cyclopropane was introduced into the preheated reactor from a storage bulb on the vacuum line and the pressure measured with a mercury manometer; for lower reaction pressures, cyclopropane was expanded into the reaction vessel from a small calibrated section of the inlet line and the pressure calculated from a predetermined expansion factor" or, in some cases, measured with a McLeod gauge. The degree of reaction in individual runs lay between 10 and 50%; the reaction was quenched by opening the reactor to a trap at -196". Propylene and unreacted cyclopropane were separated by gas chromatography, using a 3-m column of dodecyl phthalate on 30/50 ASTN firebrick, and the fraction of reaction (f) was determined to z k l % from the ratio of the integrated peak areas. Unreacted cyclopropane (A) and propylene (P) were each oxidized at 600" over copper oxide wire and the resulting carbon dioxide was purified by vacuum sublimation. Isotope Analyses. All samples of carbon dioxide were equilibrated for 24 hr with standard water'* to eliminate possible effects of oxygen isotope fractionation arising in the oxidations. The m / e 45/44 ratios were measured with a Consolidated-Nier Isotope-Ratio mass spectrometer modified by replacement of the original dc amplifiers with a master-slave pair of vibrating-reed electrometers (Applied Physics Corp.) . The isotope ratios R, and R p , from measurements on carbon dioxide obtained from combustion of unreacted cyclopropane and propylene, respectively, were corrected as required for the effects of incomplete oxidation; in addition, the corrections described in previous publications from this l a b o r a t ~ r y ' ~were - ~ ~ applied. The imprecision of individual R values was f0.003%.
Results The apparatus and procedures were proven by determinations of the first-order rate constant k, for the structural isomerization at each of the experimental temperatures (450.3, 474.0, 493.9, and 513.8") and over (14) American Petroleum Institute, Research Project No. 44, "Catalog of Mass Spectral Data," spectra no. 115,172,and 181. (15) J. P. Chesick, J . Am. Chem. SOC.,8 2 , 3277 (1960). (16) J. G. Larson, Ph.D. Thesis, University of Illinois, Urbana, Ill., 1962. (17) Details of the apparatus and procedure can be found in the Ph.D. Thesis of L. B. Sims, University of Illinois, Urbana, Ill., 1967. (18) Procedure described in Ph.D. Thesis of W. G. Koch, University of Illinois, Urbana, Ill., 1963. (19) P. E.Yankwich and R. L. Belford, J . Am. Chem. SOC.,7 5 , 4178 (1953). (20) P. E.Yankwich and R. L. Belford, ibid., 76, 3067 (1954). (21) P. E.Yankwich and J. L. Copeland, ibid., 79, 2081 (1957).
STRUCTURAL ISOMERIZATION OF CYCLOPROPANE
3461
1.0
0'8
(5)
Equation 5 is much less sensitive to errors in f than related expressions employing (R,) t o among the input data; a 1% error in f generates less than 0.1% error Values of k,/lc,' as functions of temperature in I%&,'. and pressure are shown in Figure 2. Extrapolation a
1.0
10
102
PRESSURE,
103
mm
Figure 1. Effects of temperature and pressure on the first-order rate constant k , for structural isomerization of cyclopropane. Tilted squares are d a t a of Pritchard, Sowden, and Trotrnan-Dickenson,26 corrected by Johnston and Whitez7and replotted.
the same range of pressures (approximately 1-760 mm) employed in the isotope fractionation runs. High-pressure limit values of k, were obtained by extrapolation to p-'12 = o of plots of ks-l vs. p-'".22 At high pressures log (k,") = (15.39
f
I
1
I
1.008
1.006
0.01) -
[(65679 i 308)/2.303RT] (2) The falloff curve, log (Ic,/k,m) vs. log p , shifted23+0.40 log p unit between 450.3 and 513.8'. The effects of temperature and pressure on k,/kSm are shown in Figure 1 ; to avoid crowding, only the data for the extrema1 temperatures were plotted. The isotopic rate constant ratio k,/k,', whose elements are defined as cyclopropane (C1'3H6)
-%
propylene (CI23H6)
ks'
cyclopropane (C122C13H6) + propylene (C122C13H~) (3) is obtained for each experiment from the isotopic ratios (C122C13H6)/(C)12~H~) for propylene and unreacted cyclopropane and the fraction of reaction f. The isotopic ratio Ri = (C1301*2/C120162) obtained from measurements on carbon dioxide derived from combustion of one of the hydrocarbons is related to the hydrocarbon isotopic ratio by
Combination of two expressions like eq 4 with eq IV of Tong and YankwichZ4yields
1.0
10
103
102
PRESSURE, mm Figure 2. Effects of temperature and pressure on the C1a isotopic rate constant ratio ks/ks'.
to high pressures is less satisfactory for the isotopic rate constant ratio than for the rate constant k , itself; the apparent high-pressure limit values, obtained by extrapolation to p-'" = 0 of plots of k,/k,' vs. p-'") are 1.0080 (513.8') and 1,0090 (450.3'). The results for pressures near 1 atm are represented adequately by
k,/k,' = (0.995 i 0,001) exp[(l9.1
f
2.O)/RT] (6)
Discussion The high-pressure rate constant obtained in these experiments, eq 2, agrees well with earlier results reported by Schlag and Rabinovitch8 log (k,")
=
15.26
-
(65,900/2.303RT)
(7)
(22) B. 8. Rabinovitch and K. W. Michel, J. Am. Chem. Soc., 81, 5005 (1959). (23) N.B. Slater, PTOC. Roy. SOC.(London), A218, 224 (1954). (24) J. Tong and P. E. Yankwich, J.Phys. Chem., 61,640 (1967).
Volume 71, A'umber 11
October 1087
L. B. SIMSAND PETERE. YANKWICH
3462
ka
and by Falconer, Hunter, and Trotman-Dickensonz5 log (k,") = 15.45 - (65,600/2.303RT)
(8)
For comparison of our falloff curves to earlier work, the data of Pritchard, Sowden, and Trotman-DickensonZ6 (P. S. & T.), corrected to 500" by Johnston and White,27 are replotted in Figure 1; since the shape of the falloff curve is relatively insensitive to temperature, the agreement is excellent. Comparison of our results with those of Blades6 shows that the C13 isotope effect exhibits qualitatively the same behavior as the deuterium isotope effect: at high pressures the isotope effects are relatively pressure independent, but below about 100 mm they decrease (within experimental error) approximately linearly with log p . Preliminary RRKM calculations for 500" indicate, however, that the C13 isotope effect may invert near 0.1 mm, whereas the deuterium isotope effect inverts a t somewhat lower pressures. l 2 % l 3 (Experiments to extend measurements of the C13 isotope effects to lower pressures are in progress.) The C13isotope effect, though small, nevertheless can be determined precisely as a function of pressure and temperature, and the magnitudes of those dependences suggest that the reaction coordinate is more complex than proposed o rig in ally;^ in addition to hydrogen bridging, the reaction coordinate includes considerable ring relaxation. If one reduces the C13 isotope effect to 25" using eq 6, a value for k,/k,' a t 1 atm of 1.0251.030 results; this is surprisingly large for isotopy at only one of the carbons in cyclopropane. The statistical effect of isotopy at but one of the three positions in the cyclopropane ring complicates any interpretation of the C13 isotope effect and must be taken correctly into account in any theoretical calculations and comparisons. It is worthwhile to attempt a statistical correction by the method introduced by Weston.6 Consider the possible reactions of the isotopic cyclopropanes with skeletons C123 and C122C13
Cl2LC12
rupture
C12H3C13H=C12H2
=
k*
=
(11)
k12
and if it is further assumed that the C13 isotope effect arises principally in C-C bond rupture, as compared with hydrogen transfer, then
kz
= k3 =
k13
(12)
These assumptions lead to the expression for the statistically corrected isotopic rate constant ratio in the isomerization of cyclopropane
Recalculation yields the following for 1 atm k12/k13 = 0.995 exp[(27
f
2)/RT]
= 1.012 a t 513.8" = 1.014 a t 450.3"
(14)
= 1.041 a t 25.0"
These are large C13 isotope effects, consistent with a transition state involving considerable ring relaxation. Detailed comparison of the C13 isotope effect with theory is much more difficult than in the cases of the kinetics results or the deuterium isotope effect, because much smaller computation errors (e.g., in the calculation of the RRKRI rate integral) can be tolerated. Our analysis is not yet complete, but preliminary results indicate that a model for the activated complex such as that proposed by Rabinovitch and his coworkers"S'2 does account qualitatively for the shape of the isotope effect falloff curves (Figure 2 ) . However, certain changes in the vibrational frequency pattern of the complex are necessary to account for the magnitude of the C13 isotope effect, particularly at high pressures. Specifically, changes in the ring deformation frequencies (which are strongly affected by carbon isotope substitution) are suggested. At the same time, both the isomerization rate constant k, and the deuterium isotope effect calculated are very insensitive to these frequencies of the complex, hence the C13 isotope effect can provide important new information on the vibrational frequency pattern of the activated complex. A full account of the theoretical investigation will be published subsequently.
Then (25) W. E. Falconer, T. F. Hunter, and A. F. Trotman-Dickenson,
J. Chem. SOC.,609 (1961). (26) H. 0. Pritchard, R. G . Sowden, and A. F. Trotman-Dickenson,
If it is assumed that C12-C1* bond rupture is equally probable in these two isotopic cyclopropanes The Journal of Physical Chemistry
Proc. Roy. SOC.(London), A217, 563 (1953). (27) H. 5. Johnston and J. R. White, J . Chem. Phys., 22, 1969 (1954).
MICROWAVE MEASUREMENTS OF NONEQUILIBRIUM AIR PLASMAS
Acknowledgments. We are indebted to Dr. Donald Barton (Memorial University of Newfoundland) for invaluable assistance in the early stages of this work and to Professor R. A. Marcus for helpful discussions.
3463
Fellowship support of L. B. S. by the National Science Foundation and Sun Oil Co. is gratefully acknowledged. This research was supported by the U. S. Atomic Energy Commission, COO-1142-74.
Microwave Measurements of Nonequilibrium Air Plasmas behind Shock Waves Containing Electrophilic Gases
by A. P. Modica Avco Corporation, Space Systems Division, Wilmington, Masaachusetts
(Received March 13, 1967)
The kinetic behavior of electrons in underdensed air plasmas seeded with sulfur hexafluoride (SFs), trichlorofluoromethane (CFCb), and dichlorodifluoromethane (CF2C12)was studied with 3.14-cm microwaves (X-band) behind reflected shock waves. According to electron-attachment cross sections, electron attachment in plasmas with SFB should be 6.2 times faster than with CFC13 and 10.5 times faster than with CF2C12. I n the temperature range of the study, 3400-4200°K, measured electron relaxation rates instead are found to be similar for the three electrophilic gases. Analyses of the thermal decomposition rates of these halomolecules indicate that the lifetimes are extremely short compared to the air ionization reactions for electron quenching to be effective. At high temperatures, a common mechanism for electron removal is explained in terms of attachment by the halogen atom products. Experimental nonequilibrium electron density profiles are compared to those calculated from chemical rate constants. The agreement between the laboratory results and theory is demonstrated.
1. Introduction The property of fluids t o attach electrons in a plasma has immediate applications in aerospace engineering, for example, in atmosphere research of the ionosphere and communications with space craft during reentry. Experimental studies of electron attachment have been accomplished usually by mass spectrometer, ionization chamber, and microwave3 techniques. Attachment cross sections have been determined by these methods for a number of electrophilic gases a t room temperature. However, the performance of such gases to attach electrons a t high temperatures is little understood and may- be markedly reduced by thermal de-
composition and instability of the molecular ion complex. In the present investigation, three highly electrophilic gases, sulfur hexafluoride (SFe), Freon 11 (CFC18), and Freon 12 (CF2C12)were chosen to study their effect on electron formation in high-temperature air plasmas generated by shock waves. These gases were considered for study on the basis of their relatively high electron-attachment cross sections, chemical inertness, (1) R. E.Fox, Phys. Rev., 109, 2008 (1958). (2) J. D. Craggs and B. A. Tozer, Proc. Roy. SOC.(London), A254, 229 (1960). (3) AM.A. Biondi, Phys. Rev., 109, 2005 (1958).
vo'olume 71, Number 11
October 1967
