464
NOTES
K4
Chemically Activated Pentene-2 from the
DMC* * 2MB2*, 2MB1*
4358 and 3660-A Photolyses of
(IV)
K6
Diazomethane-cis-2-Butene-Oxygen Mixturesla
* P2*
(VI
W
DMC
--f
by G. W. Taylorlb and J. W. Simons
-
P2* +CH3 3. CH3CH = CHCHz
Chemistry Department, New Mexico State University, Las Cruces, New Mexico 88001 (Receized April BY, 1969)
Quantitative kinetic studies of the unimolecular primary decomposition step for ground electronic state olefins have been limited t o two shock-tube studies2 and two chemical activation s t u d i e ~ . ~Chemical .~ activation studies of unimolecular decompositions having known energetics are of particular interest since comparisons of experimental rate constants to RRKM5 theory rate calculations give information about activat,ed complex structures for the reactions. This information is similar to that which can be obtained from reliable experimental thermal A factors. Olefins that decompose by either C-H or C-C rupture to give allylic resonance stabilized radicals are expected to decompose with enhanced rates due to lowered critical energies. Recent values of the allylic and methallylic resonance energye along with the appropriate alkane C-C bond dissociation energy' can be used to give reliable estimates of the critical energies for these olefin decompositions. A study of the decomposition kinetics of the chemically activated 2-pentene produced in the photolysis of diazomethane-cis-2-butene mixtures at 4358 and 3660 b is reported here. Experimental Section The materials and analytical procedures employed in this study have been described previously.8 Results and Discussion The following reactionss~g represent the important steps leading to "hot" 2-pentene decomposition in this system.
-
4358 A; 3660 .i
CHs('A1)
+ N%
(1)
Ka
CHz('A1) $- CB2 +P2*
(11)
Ks ---f
The Journal of Physical Chemistry
DMC*
(VII)
W
P2
CH2N2
(VI)
XI
(111)
(VIII)
where DMC = cis and truns-1,2-dimethylcyclopropane, P2 = cis and truns-2-pentene, W = collisional stabilization rate constant, and (*) = excess vibrational and internal rotational energy. Only the reactions of singlet methylene [CH2 AI) 3 are considered here since all photolysis runs were performed in the presence of a t least 10% oxygen which scavenges triplet methylene radical p r o d u ~ t s ~as~ ~ well ' ~ as the doublet radicals produced by decomposition in this system. Vibrationally energized cis-2-pentene is produced by direct C-H insertion (reaction 11) as well as by the structural isomerization of excited cis- and trans-l,2-dimethylcyclopropane (reaction V). Experimental Rate Constants. I n order to determine experimentally the unimolecular decomposition rate constants for the excited 2-pentene, mixtures of CB2DM-02 in the approximate ratios of 8: 1: 1 were photo(1) (a) The National Science Foundation is gratefully acknowledged for financial support. (b) NDEA Predoctoral Fellow. (2) (a) W. Tsang, J. Chem. Phys., 46, 2817 (1967). (b) G. A. Chappell and A. Shaw, J . Phys. Chem., 72,4672 (1968). (3) F. H. Dorer and B. S. Rabinovitch, ibid., 69, 1952 (1965). (4) J. W. Simons, B. S. Rabinovitch, and F. H. Dorer, ibid., 70, 1076 (1966). (5) R. A. Marcus and 0. K. Rice, J. Phys. Colloid Chem., 5 5 , 894 (1951); R. A. Marcus, J. Chem. Phys., 20, 359 (1952); B. 8. Rabinovitch and D. W. Setser, Advan. Photochem., 3 , l (1964). (6) S. W. Benson, A. N. Bose, and P. Nangia, J . Amer. Chem. Soc., 85,1388 (1963) ; D. M. Golden, K. W. Egger, and 8. W. Benson, ibid., 86, 5416, 5420 (1964); J. A. Kerr, R. Spencer, and A. F. TrotmanDickenson, J . Chem. SOC.,6652 (1965); R. J. Ellis and H. M. Frey, ibid., Suppl. No. 1, 5578 (1964). (7) J. A. Kerr, Chem. Rev., 66,465 (1966), and references therein. (8) J. W. Sinions and G. W. Taylor, J. Phys. Chem., 73, 1274 (1969). (9) (a) H. M. Frey, Proc. Roy. Soc., A250, 409 (1959); ibid., 251, 575 (1954). (b) P. S. Skell and R. C. Woodword, J. Amer. Chem. Soc., 78, 4486 (1956); ibid., 81, 3383 (1959), and references therein. (c) D. W. Setser and B. 5. Rabinovitch, Can. J . Chem., 40, 1425 (1962). (d) J. W. Simons and B. S. Rabinovitch, J. Phys. Chem., 68, 1322 (1964). (10) (a) F. H. Dorer and B. S. Rabinovitch, ibid., 69, 1952 (1965). (b) S. Ho, I. Unger, and W. A. Noyes, Jr., J. Amer. Chem. SOC.,87, 2297 (1965). (c) H. M. Frey, Chem. Cowmun., 260, (1965). (d) R. W. Cam, Jr., and G. B. Kistiakowsky, J . Phys. Chem., 70, 118 (1966). (e) B. 9. Rabinovitch, K. W. Watkins, and D. F. Ring, J. Amer. Chem. SOC.,87, 4960 (1965). (f) R. L. Russell and F. S. Rowland, ibid., 90,1671 (1968).
465
NOTES lyzed at 4358 and 3660 over a pressure range from 0.05 cm to 150 cm. It was found that the ratio of 2-pentene to the total dimethylcyclopropanes was constant above about 10 cm total pressure; consequently the ratios were averaged for all data above this pressure to obtain the ordinate intercepts of the curves in Figure 1. Appljcation of the steady-state approximation to the reactions 11-VI11 leads to eq 1.
+
where K s = Kd K5. The collisional deactivation rate constant, W , is assumed to be equal to the collision frequency. The ratio of K z / K 3in eq 1was taken from the ordinate intercepts of the appropriate experimental curves in Figure 1. Averages over many runs indicate the best value for K z / K 3is 0.77 a t both wavelengths. The value of K5 for each wavelength investigated was taken to be half of the value of K , the total dimethylcyclopropane structural isomerization rate constant as previously determined.8 This procedure is supported by RRKM theory calculations and also by the experimental ther~ " the mal A factors and energies of a c t i ~ a t i o n . ~ ~Using appropriate values of K I , where K7 is the decomposition rate constant for the 2-pentene1 for each wavelength eq 1 was fitted to the experimental points as shown in Figure 1 at 4358 and 3660 A. The values of K , that best fit the experimental points at 4358 and 3660 A in Figure 1 are (4.05 f 0.4) X lo7 sec-' and (5.5 f 0.6) X lo7sec-', respectively. It may be seen from eq 1 that if W >> K7 i.e., either high total pressures or greater olefin stability, then eq 1 reduces to eq 2.
The dark lines in Figure 1 represent this linear relationship between [P2]/[DMC] and 1/W. A comparison of these lines with the data in Figure 1 clearly indicates the extent of 2-pentene decomposition in this system.
Theoretical Rate Calculations The RRKM theory expression for k ~ the , unimolecular rate constant at the energy, E , is given by eq 3. (3) where Q+/Q* is the ratio of the partition functions for adiabatic degrees of freedom including reaction path degeneracy, Z:P(E+vr)is the sum of energy eigenstates for t,he activated complex up to the energy, E+, and N(E*,,) is the density of energy eigenstates for th.e active degrees of freedom (vibrations and internal rotations) of the energized molecule a t the energy,
Figure 1. Variation of the ratio of pentene-2 to dimethylcyclopropanes with inverse pressure. Dark lines represent the plot of eq 2 (the upper and lower lines are for 3660 and 4368 A, respectively). The dashed curv!s represent the plots of eq 1 a t 3660 A (upper curve) and 4358 A (lower curve) using the K? values giving the best fit to the data.
E*. The evaluation of the sum and density terms for 2-pentene and the various activated complexes at the appropriate energies were carried out on a CDC-3300 computer using the accurate approximation of Whitten and Rabinovitch.12 Energies. The average energy contents, E*, of the chemically activated dimethylcyclopropanes produced in this system have been previously determined.8z13 The structural isomerization of cis-1,2-dimethylcyclopropane to cis-Zpentene is exothermic by 4.9 kcal/mol thus the E* values for excited cis-2-pentene in the 3660 and 4358-A systems are 124.2 kcal/mol and 120.7 kcal/mol, respectively. la It was assumed that these same energies apply for the cis-2-pentene and trans-2pentene mixture, called 2-pentene in this work. This assumption introduces a negligible error. The critical energy for 2-pentene decomposition is determined by the dissociation energy for an equivalent alkane C-C bond, the allylic resonance energy from the formation of a methallyl radical, and the critical energy for recombination of a methyl and methallyl radical. The energy required to break an alkane primarysecondary C-C single bond is 83 kcal/mol at 298.16"K with an uncertainty of about 1 kcal/mol. Recent determinations of the allylic resonance energy are in agreement with a value of 12 f 1 kcal/mol. The methallylic resonance energy is probably also 12 kcal/ mol. The critical energy, Eo, for the decomposition of cis-2-pentene is then 70 f 2 kcal/mol if a 2-3 kcal/mol critical energy for recombination is assumed. The excess energies, E+ = E* - EO,for 2-pentene decomposition are 54.2 kcal/mol at 3660 A and 50.7 kcal/mol a t 4358 8. (11) M. C. Flowers and H. M. Frey, PTOC.Roy. SOC.,A260, 424 (1961). (12) G. Z.Whitten and B. 8. Rabinovitch, J . Chem. Phys., 38, 2466 (1963);41, 1883 (1964). (13) Energies derived for [AHroo(CH)z f E*(CHz)] in ref 8 have been adjusted downward by 0.4and 0.7 kcal/mol for 4358 and 3660-H photolyses, respectively. These adjustments result from
more exact RRKM calculations. Volume 74, Number 2 January 28, 1070
NOTES
466 2-Pentene Molecular Frequencies. The vibrational frequencies for 2-pentene were deduced from the known frequencies for propylene and ethane.14 The C=C torsional frequency was derived from substituted ethylene torsional freq.uencies14by allowing proportionally for mass changes. Skeletal bending frequencies were estimated from similar alkane vibrations.'* Activated Complex Models. The activated complex for 2-pentene decomposition may be schematically represented as
This complex representation is consistent with those previously postulated for l-olefin decompositions. Since RRKM theory rate calculations are not very sensitive t o the detailed activated complex model employed, the molecular parameters adjusted here were those most reasonably believed to be involved in the reaction coordinate. The C(4)-C(5) stretchingfrequency was taken as the translation along the reaction coordinate in the activated complex. The C(4)-C(5) bond length in the activated complex was set a t twice its value in the molecule. 2-Pentene has three internal rotations which were treated as free rotors in the molecule. The tightening in the activated complex due to the allylic resonance will cause a barrier to rotation about the C(3)-C(4) bond and, therefore, one internal free rotor becomes a low-frequency torsional vibration. The magnitude of this torsional frequency wag used as the adjustable parameter to best fit theory and experiment (complex 11) and to fit our best estimates of the limits (complexes I and 111) of the combined uncertainties in the experimental rates and EOvalues used in the theoretical calculations. A 10% uncertainty in the experimental rates was combined with a 2 kcal/mol uncertainty in Eo. The magnitudes of other frequency adjustments were the same in all of the activated complexes and were such as to bring theory and experiment into only approximate agreement in hopefully a reasonable fashion. Comparison of Theory and Experiment. The theoretical rates of 2-pentene decomposition a t 3660 and 4358 A are presented in Table I for three EO values. The experimental rate constants are also given in Table I. It is seen from Table I that E* = 124.2 kcal/mol and 120.7 kcal/mol gives k~ = 6.21 X lo7sec-' and 3.60 X lo7 sec-', respectively, a t EO= 70 kcal/mol, which are within experimental error of the 3660 and 4358-b experimental rates, respectively. The experimental rates could be fitted better by independent adjustments of about 1 kcal/mol in the 4358 and 3660-b E* values; however, since these energies are based on more reliable results8 such adjustments seem unjustified. The Journal of Physical Chemistry
Table I lists the A factors calculated from absolute rate theory for all three complex models employed. An A factor of 1015.8*0.3for the decomposition of 4,4-dimethylpentene-l into t-butyl plus allyl radicals has been determined in a shock-tube study by Tsang.S This experimental A factor for a similar reaction is similar to the theoretical A factor of 1018-'5calculated for complex model 11. It might be expected that the -4 factor for 4,4-dimethyl-l-pentene would be slightly larger than the A factor for 2-pentene decomposition because of an increase in the activation entropy for producing a t-butyl radical as compared t,o that for producing a methyl radical; however, the two values are well withing the limits of uncertainty in the two studies as seen from Table I.
Table I : Theoretical kE, sec-1, for 2-Pentene Decomposition
EO, kcrtl/mol
I
Complex Model I1 -Log A
16.5
16.15
c
E* 68 70 72
=
--I11
--
15.8
120.7 kcal/mol
1 . 5 6 X 108 7 . 7 1 x 107 3 . 7 6 x 107
7 . 2 6 x 107 3 . 6 0 x 107 1 . 7 6 X 10'
3.43 x 107 1 . 7 0 x 107 8 . 3 3 X lo8
K7 = (4.05 f 0.4) X lo7 sec-' at 4358 E* = 124.2 kcal/mol 68 70 72
2 . 6 1 X lo8 1 . 3 3 X lo8 6 . 6 7 x 107 K7 = (5.5 f 0.6)
1 . 2 2 x 108 5 . 7 3 x 107 6 . 2 1 x 107 2 . 9 3 x 107 3 . 1 2 x 107 1.47 X 10' X lo7 sec-' at 3660 A
Rabinovitch and Dorer3 have determined the experimental decomposition rate constant for 2-pentene from the photolysis at 4358 b of diazomethane-l-butene mixtures in the absence of radical scavengers. The average excitation energy is 122.2 kcal/mol using the energetics from our previous ~ o r k . ~This J ~ value is slightly larger than the excitation energy used in the present 4358-A study because of the difference in the heats of formation at 0°K of cis-&butene and l-butene. Using a critical energy of 70 kcal/mol, a theoretical decomposition rate constant of 4.57 X lo7 sec-' is predicted from complex model 11. The experimental value found by Rabinovitch and Dorer is 0.9 X 10' sec-l. Part of this difference may be due to the presence of a significant quantity of ground triplet state methylene radical reaction and part may be due to radical recombination giving extra stabilized 2-pentene a t all pressures. (14) G. Herzberg, "Infrared and Raman Spectra, of Polyatomic Molecules," D. Van Nostrand and Co., Princeton, N. J., 1945.
