2790
J, Phys. Chem. 1983, 87,2790-2795
Deuterium-Hydrogen Exchange and Scrambling Reactions in the Pyrolysis of Labeled Cyclopentene. A Radical Mechanism Kenneth G. Kosnlk and Sidney W. Benson‘ Department of Chemistry, Hydrocarbon Research Institute, University Park-MC 166 1, Universlty of Southern California, Los Angeles, California 90089- 166 1 (Received: February 8, 1983)
Inter- and intraradical mechanisms that promote deuterium-hydrogen scrambling in labeled cyclopentene-d, are investigated at 800 and 1200 K. Rate constants are estimated for each step and for possible competing side reactions. The fast radical bimolecular exchange at 800 K and unimolecular scrambling at 1200 K of labeled cyclopentene are shown to be faster than the Woodward-Hoffman allowed 1,4 concerted molecular elimination of hydrogen. The low-energy estimate of 8.0 kcal/mol by Lewis of the difference between the allowed 1,4 and disallowed 1,2 channels can thus be explained. No conclusions can be drawn concerning the 1,2 channel. The estimated rates of radical reactions are in agreement with experiments on the addition of D2 to cyclopentadiene at 300 “C which shows only cis, 3-5 addition and with pyrolysis experiments at 500 f 20 OC which show about 5% contribution of a higher than first-order radical reaction. The mechanism of this radical decomposition is given and its steps are explicitly evaluated.
Introduction There has been theoretical interest in the energy difference between the 1,4 allowed and 1,2 disallowed concerted molecular elimination channels for many Baldwin reported the ratio of H2 1,4 elimination to 1,2 elimination from cyclopentene-4-d, a t 823 K to be approximately 6.2 Lewis reported the ratio of 1,4 elimination to 1,2 elimination from cyclopentene-3,3,4,4-d4 a t 1200 K to be approximately 2, and also that vinylic deuterium in cyclpentene-1 -dl a t 1200 K is not eliminated subsequent to a 1,3 u-tropic shifL3r4 Lewis estimated the activation energy difference between the 1,4 and 1,2 process, by incorporating his results with Baldwins, to be -8.0 kcal/mol by using the following A factor e ~ t i m a t e s : ~ = 1014,1s-l = 1012.8 s-l However, structural considerations 6 suggest that A1,2/A1,4 5 3 which would bring AE*(1,2-1,4) to about 4.5 kcal/mol. Recent work on the cyclobutene-butadiene potential surfaces have indicated about 15 kcal/mol activation energy difference between the symmetry allowed and disallowed proce~ses.~The purpose of this research is to probe the possibility of a radical mechanism that exchanges or scrambles the deuterium labels on respective cyclopentenes to account for the apparently low-energy difference between the allowed 1,4 and the disallowed 1,2 elimination of hydrogen. We shall show that a bimolecular radical step can scramble H and D atoms in cyclopentene under the conditions used in the study at 800 K while an intramolecular isomerization can scramble H and D atom positions at 1200 K under the conditions used in the shock tube experiments. In the Appendix we will list all of the steps, radical and molecular, which we have evaluated in analyzing the cy(1) Roald Hoffmann, Trans. N . Y . Acad. Sci., 475 (1966).
clopentene pyrolysis. In the main text we will discuss for purposes of clarity only the important steps occurring under the experimental conditions. We shall in the text use the following abbreviations for the various species: molecules: cyclopentane (CH); cyclopentene (CpH); cyclopentadiene (Cpd); radicals: cyclopentyl ( C ) ; cyclopenten-3-yl (Cp). Scrambling Mechanisms. Scrambling may occur via bimolecular radical processes as follows:
At 800 K we shall show that only process E2 is important while a t 1200 K neither process can complete with the intramolecular process. Scrambling can also occur via intramolecular processes.
?
D
-0 D
D
(2) John E. Baldwin, Tetrahedron Lett., 26, 2953 (1966). (3) David K. Lewis, Mark A. Greaney, and Edwin L. Libert, J . Phys. Chem., 85, 1783 (1981). (4) David K. Lewis, Mark A. Greaney, and Edwin L. Lilbert, J . Phys. Chem., 85, 1787 (1981). (5) Leonard M. Stephenson, Jr., and John I. Brauman, Acc. Chem. Res., 7, 65 (1974). (6) S . W. Benson. “Thermochemical Kinetics”, 2nd ed. Wiley, New York, 1976.
0022-3654/83/2087-2790$01.50/00 1983 American Chemical Society
D
The Journal of Physical Chemistv, Vol. 87, No. 15, 1983 2791
Pyrolysis of Labeled Cyclopentene
The pyrolyses of vinylcyclopropane and of bicyclo[2.1.0]pentane have both been investigated and from the measured rate constanta reported in the literature and the known thermochemistry it is possible to evaluate rate constants for (Sl) and (S2). We shall show that neither of these high activation energy rates are of importance at 800 K but that process S1, effectively scrambles the positions of H and D atoms in the aliphatic (3,4,5) positions under the conditions of the shock experiments at 1200 K. The net result of these scrambling processes will be to make impossible any conclusions about the unallowed 1,2 process from labeling experiments that have been done. Radical Chains a t BOOK. From the more extensive rate data listed in the Appendix we abstract the following steps as the steps of importance in the region from 600 to 900 K. initiation
+ Cp
C
2CpH termination
+ Cpd
2Cp -4, CpH chain decomposition
C
2.6
C. allyl
H
~
-3
2
+ allyl ~ 4
CpH
+H
7 + CpH e C3H6 + Cp Cp+Cpd + H
+ CpH -!+ H2 + Cp ~ A H cp.
+C
~ H
Applying steady-state methods to the radicals H, C,and Cp we can evaluate the following: (H)ss/(CP)Bs= kd/[k-r(Cpd)
+ ~-~(CPH)I
(Cp)ss = (kil/kt)'/2(CPH) Using the.rate data presented in the Appendix we can show that (C)s, is negligibly small and that (H)ss/(Cp)ss a t 800 K. Also a t 800 K it will turn out that since k4 k-, and (CpH) (Cpd) N (CPH)~,this ratio does not change much as the reaction proceeds. With these steady-state concentrations we can evaluate explicity the rate of Hz + Cpd production via the radical chain and also the rate of scrambling (d(S)/dt):
--
N
k5K4(ki/kt)"2[(CpH)/(CpH),I10'4.8-79.5/s
The ratio of this to the concerted 1,4 path rate constant is given by
kU,i/kO
N
+
-d(HJ - dt
= k2.6(C)
Using the steady-state expression evaluated for (C)and the rate constants from the Appendix we find about 4% of C2H4 in excellent agreement with the observations. About 12% of this is contributed by the initiation reaction and 88% by the chain itself. We note that the production of C2H4is not quite second order in (CpH) [see steady-state concentration of (C)] in agreement with the observation that it is of higher than first order. Knecht also observed that (C2H4)exceeded (C3H6)by some 15-2070. This is expected since C3H6is more reactive than C2H4 in radical reactions because the allyl radical can be formed and participate in both termination and polymerization processes. Radical Chains a t 1200 K. The radical chain we have been considering for H2 production is negligible relative to the first-order, concerted process at 800 K and if we extrapolate to 1200 K it is still negligible. However, at 1200 K, the initiation by unimolecular fission (step i2) of cyclopentene to Cp + H is 15 times faster than the bimolecular path (step il) effective at 800 K when (CpHIo M. This raises the steady-state radical concentrations by a factor of about 4 which is still not sufficient to make radical chain production of H2 competitive with the concerted reaction. The overall mechanism at 1200 K is as follows: initiation
-
d(S)/dt = ks(ki/kJ'/2(CpH)2 Using the data in the Appendix we can estimate an effective first-order rate constant for Hzproduction via the radical chain:
10'."2'/8
and we see that at 800 K the radical H2 production is less than 0.01% of the concerted rate and thus negligible. A t 800 K, k,(ki/kt)1/2 = 109.36-35/8 M-' s-' so that, at 100 torr of CpH, the rate of scrambling and the rate of the concerted reaction are equal. At 700 K scrambling is about 12 times faster. At 900 K the concerted reaction is 5 times faster than scrambling but we would have to go to 5 torr initial pressure of cyclopentene to reduce scrambling to less than 1% of the concerted process. It appears that postional labeling experiments may not be useful in examining the 1,2 process at temperatures below 1000 K. Anet and Leyendecker22have measured the addition of D2 to cyclopentadiene a t 300 "C (573 K) using 40 atm of D2 and a radical inhibitor to prevent chain processes. By NMR they observed only 3,5 cis addition to the diene. If we assume that the 3,4 and 3.5 processes differ in A factor by a factor of 3 favoring the disallowed 3,4 reaction then the NMR observations (assuming 19'0 sensitivity for the 3,4 adduct) fixes a minimum difference of 7.0 kcal between the two processes. KnechtZ3 has studied the pyrolysis of both cyclopentene-do and CyClOpentene-d8 a t 750-800 K and measured the small amounts of ethylene and propylene formed in the system. The processes responsible for these products appear to be radical processes with a higher than first order in CpH and amount to about 5% of the first-order concerted process. We can use these observations to check our estimated rate constants for the radical processes. The rate of production of ethylene is given by d(C&J/dt
scrambling
cp + C
ku,i(H2)
CpH
i2
Cp
+H
termination 2Cp
CpH'+ Cpd
2792
The Journal of Physical Chemistry, Vol. 87, No. 15, 1983
chain decomposition
-
Kosnik and Benson
+ allyl ~ 4 C '-3 L CpH + H
C
~
2
H allyl
Cpd
+H
+ CpH -!.,
H2 + Cp
+ CpH
C3H6+ Cp
7
(C) /(H) = k-,(CPH) /k2.6
2cp
The rate of chain H2 production is given by Cp
d(C2H4)/dt = 1016.s-ss/e(CpH)'/2 d(H2)/dt = 1016.5-96/0(CpH)1/2 Chain C2H, production is about 80 times faster than chain Hz production at 1200 K and nearly competitive with the concerted 3,5 H2 elimination. Radical scrambling via exchange is given by d(S)/dt = ks(Cp)(CpH) = ks(ki2/kt)1/2(CpH)3/2
A t 1200 K this becomes d(S)/dt = 1012.0-53/8(CpH)3/2 and comparing it with the four-center process it amounts M to about 3% of the rate of the latter a t (CpH) = which was approximately the concentration used by Lewis in his shock experiments. Argon was the inert gas carrier. To apply the above estimates to his data, small corrections should be made for the isotope effect since Lewis used cy~lopentene-3,3,4,4-d,.~~~,~~ Appendix A . Overall Mechanism. In the following we list all of the elementary reactions that we have considered in evaluating radical chain processes in cyclopentene:
a ~l l y l
+H H + C p H e C p + H2 7 allyl + CPH eC3H6 + Cp t2 2 allyl ebiallyl t3 2 allyl eC3H6+ allene 2Cp CpH + Cpd
+ k-dCpH)I
a t low conversions. It is to be noted that a t both 800 and 1000 K the slow step in the pyrolysis of CpH is step 4, the relatively high activation energy decomposition of the allylic-stabilized cyclopentene-3-yl radical. This gives, to ethylene formation, an effective activation energy of about 88 kcal. Employing the numbers from the Appendix we obtain the following rates a t 1200 K:
+H
5
(Cp) = (ki2/kt)1/2(CpH)1/2
and a t less than 30% overall decomposition
~
4
The steady-state concentrations are [k-,(Cpd)
C
Cp=Cpd
cp + C ~ 5 H cp + CPH
k4/
+
S.H~CH~CH~CH=CH~
C&C~H+H
scrambling
(H)/(CP),, =
Cp
i2
S. Cp
l i
+ C. CpHeCp+H
2CpH
t4
(CP)2
+ CpH 5 exchange of H atoms (scrambling)
Numerical values for these reactions listed in Tables I and I1 together with their Arrhenius parameters at 800 and 1200 K. B. Discussion of Elementary Steps. The initiation reaction il was chosen for chain mechanism 1 because this channel is faster than i2 at 800 K. The situation is reversed when considering chain mechanism 2 a t 1200 K. The back reaction -il is an exothermic (-46.4 kcal/mol) radical disproportionation for which activation energies are normally zero and A factors are in the range of 108.8*0.5 L/(mol.s).6 The back reaction, -il, is also endentropic at 800 K by -7.5 eu and at 1200 K by -8.5 eu. The A factors were estimated by using Benson's thermochemical methods.6 The unimolecular initiation reaction i2 is endothermic by the amount of the bond dissociation energy.12 It produces the cyclopentene-3-yl radical which is stabilized by allylic conjugation. When judged from the rate constant for recombination, an A factor for i2 can be expected to be in the range of 1014.9*0.5 s-'.~ The back reaction -i2 has been neglected in chain mechanisms because alternate termination paths involving radicals can be shown to be much more significant. Reaction step 2 has never been observed, but the overall process 2 + 6 leading to ethylene + allyl has been. The rate constant kz.6 = Kzk6 used in the text is product of the equilibrium constant K 2 and kg. The Arrhenius parameters for reactions 2 and -2 are still contr~versial.~-" Gordon studied the cyclopentyl ring opening reaction in the range of 160-440 "C and obtained the following parameters -42.6 = 1014.5s-l and Ez.6 = 37.7 kcal/mola8 These results are in agreement with an earlier determination obtained by Gunning and Stock.7 Walsh stated that Benson and O'Neal suggested that reaction 6 rather than 2 may be rate determining such that A2 = 1013.5 s-l and E2I32.5 kcal/mol.8 Several years later Carter and Tardy reported A2 = 1014.0s-l and E 2 = 34.6 kcal/mol at 300 K.l' Since ring closure involves a radical adding to a double bond the A factor should be much smaller than (7) Harry E. Gunning and Richard L. Stock, Can. J . Chem., 42,357 (1964). (8)Alvin S. Gordon, Can. J. Chem., 43, 570 (1965). (9) Robin Walah, Znt. J. Chem. Kinet., 2, 74 (1970). (IO) Alvin S. Gordon, Znt. J . Chem. Kinet., 2, 75 (1970). (11) W. P. L. Carter and D. C. Tardy, J . Phys. Chem., 78,1573 (1974).
The Journal of Physical Chemistry, Vol. 87, No. 75, 1983 2793
Pyrolysis of Labeled Cyclopentene
TABLE I: Kinetic Data for Unimolecular Reactions no.
reaction
log huni,aca K, s - '
log hini,imc K , s-'
log kuni,wnK log k u n i , i m K
0
13.0 - 58.8/ea
13.2 - (59.5)/e
-3.02
2.34
i2
14.9 t 0.04 - (82.1 t i . 5 ) / e
14.9
-7.56
- 0.10
2
14.4
i
0.4 - (34.0
i
1.5)/0
14.47
5.10
8.21
-2
11.3
i
0.4 - (15.9
i
La)/@
11.4
6.97
8.51
3
13.6
i
0.3 - (37.7
i
1.5)~
13.6 - (37.2 i 1.5)/0
3.30
6.80
4
13.5 i 0.3 - (48.2 i 1.5)/S
13.6 - (48.0 * 1.5)/0
0.4
4.9
6
13.7
t
0.4 - (24.3
13.6
0.4 - (23.8 ~t 2.0)/e
7.08
9.29
-tt4
16.4
i
0.4 - (51.4 t 1 . 5 ) / 0
16.7 f 0.4 - (50.5 i 1 . 5 ) / s
2.79
7.47
SI
15.4
t
0.4 - (72.5 t l . S ) / e
15.4
i
0.4 - (73.2 t 1.5)ie
-4.44
2.05
S- 1
13.6 t 0.4 - (49.8 i 1.6)/0
13.7
i
0.4 - (50.0 i 1.5)/e
S.
14.5 i 0.4 - (75.0 t 1.5)/e
14.5
i
0.4 - (75.1 i 1.5)/e
14.1 t 0.4 - (45.5 * 1.50)/0
14.1 t 0.4 - (45.2
t
2.0)/e
i
t
i
0.4 - (82.4 i 1.5)/S f
0.40
0.4
-
(34.4
- (15.7 i
i
1.5)/e
i
1.5)/e
0.03
4.57
-5.97
1.5)/s
0.79
1.72
5.85
References 20 and 23. TABLE 11: Kinetic Data for Bimolecular Reactions no. i, -11
reaction
log kBi,xw K , L/(mol's)
0 0+0---0 0
Q 0 +
(3,
+
+
10.0
-
(46.4
* 0.4 - (47.2 i 1.5)/0
9.8
9.8
i
0.4
9.82
9.80
10.47
10.84
5
10.4 .+0-(3, 0---0+ 10.9
-6
y,:_+=-
_+
0.4
H2
i
0.5)/e
11.2 t 0.4 - (2.0 i 0.5)le
i
0.5)le
10.5 r 0.4 - (2.0
i
0.5)/e
9.86
10.10
*
2.0)/0
10.9
f
0.4 - (9.7
i
2.0)/e
8.62
9.15
(14.3 5 2.0)/e
9.9
i
0.4 - (15.9
i
2.0)/6
5.56
6.99
0.4 - (9.5 i 2.0)/0
8.9
i
0.4 - (11.4
i
2.0)/0
5.88
6.82
8.45
8.59
i
0.4 - (2.0
i
0.4C
9.5 i 0.4 8.5
F
-
-
(9.7
t,
2()-Q+O
8.5 i 0.4
8.6
*
0.4
-t1
Q + Q - 2 c )
9.4
9.7
i
0.4
t 4
0 0-
t? t3 S
\
k+k+ \'.-...
0
+.
+
allene
- 0 (3, +
i
0.4 - (36.0 t 1.5)/e
-
(36.2 i 1.5)/e
-0.40
3.07
10.1 t 0.4
10.0 t 0.4
10.09
9.99
10.1 t 0.4
10.0
i
0.4
10.09
9.99
9.4
i
0.4
9.04
9.37
8.8
f
0.4 - ( 1 3 i 2)/e
5.26
6.38
9.0
f
0.4
8.5
t
0.4
-
(12.0 f 2.O)le
a ring closure involing two radicals which are about 1015 Since reactions 2 and -2 are not rate determining in either chain mechanism 1 or chain mechanism 2, a rough estimate will be sufficient under these conditions. Median values of k2 = 1013.s34.0/swill be used to model the reaction at 300 K. The Arrhenius parameters corrected to 800 and 1200 K are listed in Table I. The A factor can be readily determined for reactions 3 and -3 by the methods of thermochemical kinetics using
K
1.82 8.56
-4
+
-2.62 8.41
11.0i 0.4 - (2.0
+
10.4
0.4
u+0-(3,
A
1.5)le
i
-3
H +
*
8.6
H+O-O
+
0.4
kBi.12nn
8.4r0.4
-i,
7
i
log kBi,uno K I L/(mol's) log ~ B I , RKO Olog
an estimate for the entropy loss due to the stiffening of ring puckering.6 Because of the tight transition state, small relative mass of the hydrogen atom, and the formation of a "stiffer" radical the A factors involving C-H bond fissions in radicals are in the range of 1013.6 a t 300 K. The activation energy for the addition of a hydrogen atom to ethylene (300-540 K) is about 2.0 kcal/mol.6 If the assumption is made that the E-3 is also 2 kcal/mol then E3 is also known
2794
The Journal of Physical Chemistry, Vol. 87,No. 15, 1983
since AH (35.7 kcal/mol) can be readily calculated from A?If,298(cyclopentyl)= 24.3 kcal/mo1.I3 To be able to determine an A factor for reaction 4, the entropy loss due to the stiffening of ring puckering must be made. Reaction 4 is also the rate-determining step in chain mechanism 1a t 800 K by which the cyclopentene3-yl radicals are depleted. We estimate6 a loss of 2.0 eu which is probably not the maximum stiffening. In cyclopentadiene the ethylenic groups can be puckered relative to each other; however, in the transition state additional conjugative effects probably make ring puckering less prominent. A value of (800 K) was estimated for A4. Benson has reported AHf0298= 38.4 kcal/mol.12 Again assuming 2.0 kcal/mol activation energy for the back reaction and computing AH (46.2 kcal/mol) for the reaction, one can estimate the value for E4 to be approximately 48 kcal/mol. It is helpful to consider the model reaction H + C2H6 H2 + C2H5 when considering the Arrhenius parameters for reaction 5. For the model reaction A = lo1'.' L/(mol.s) and E = 9.7 kcal/mol(300-100 K).6 It is important to note only a very small variation in Arrhenius parameters with temperature. If a bent transition state is assumed A5 = 1010.91L/(mol.s) can be estimated. A Cp* for reaction 5 of 0.03 eu implies a rather small temperature variation for the estimated Arrhenius parameters. The activation energy for reaction 5 was roughly estimated to be about the same as the model reaction or approximately 9.7 kcal/mol. __ When +
is used as a model for the transition state, a value of 1013.73"0.43 was obtained for A, at 800 K. According to the model for the ring opening of the cyclopentyl radical proposed by Tardy, if Ez = 34.0 kcal/mol then E4 (allyl + ethylene) should be 14.3 kcal/mol." Tardy remarked that computed activation energy for allyl + ethylene was higher than the usual radical + olefin additions with the excess 6.0 kcal/mol attributed to a partial destruction of allylic resonance in the transition state.ll Along with the computed A?I8W (10.0 kcal/mol) for the reaction, E, can be estimated to be approximately 24.3 kcal/mol at 800 K. Steps 2 6 are in competition as an overall first-order process with step 3, the loss of H atoms. Our parameters for step 3 are probably quite accurate. Step 3 is negligible compared to steps 2 + 6 as estimated. k2.6 can be faster than estimated but not significantly slower, otherwise we would be in serious error in our estimated rate of C2H4 production. The appropriate thermochemical parameters for reaction 7 were obtained by using
+
r
as a model for the transition state. The value for A7 was 108.48*0.40 a t 800 K. Most A factors for radical-molecule abstraction reactions are in the range of 108.5*0.5.Alfassi and Benson have noted that there is a very strong relationship between activation energies and electron affinities of the terminal atoms in a typical metathesis reaction A BC -AB + C6 - 14.8 - 3.641 Ea(intrinsic) 1.0 + AH/40
+
Kosnik and Benson
I is the sum of electron affinities of A and C in electronvolts. Using the values in ref 12 and 14 to estimate the electron affinities of
respectively, one can estimate E7 to be 9.5 kcal/mol. The termination reaction tl was chosen to be the disproportionation of the cyclopentene-3-yl radicals because these radicals have the largest steady-state concentrations a t 800 K and the direct association of these radicals (t4) forms a rather weak bond. The equilibrium constant (107.6 L/mol) at 800 K favors dissociation of the bicyclopentenyl into two cyclopentene-3-yl radicals only at low conversions (
