2450
The Journal of Physical Chemistry, Vol. 82, No. 23, 1978
(14) Modified procedure B of (13); details will be published elsewhere. (15) S. L. Olsen, L. P. Holmes, and E. M. Eyring, Rev. Sci. Instrum., 45, 859 (1974). (16) M. Eigen and L. DeMaeyer in "Techniques of Organic Chemistry" Vol. VIII, Part 2, Wiley, New York, N.Y., 1963, p 895 ff. (17) P. Debye, Trans. Am. Nectrochem. Soc., 82, 265 (1942). (18) C. H. Springer, J. F. Coetzee, and R. L. Kay, J . Phys. Chem., 73, 471 (1969). (19) H. Eyring and E. M. Eyring, "Modern Chemlcal Kinetics", Reinhold, New York, N.Y., 1963, p 84. (20) N. C. Fawcett and R. D. Caton, Anal. Chem., 48, 600 (1976). (21) G.D. Burfoot, E. F. Caklin, and H. Goodman, J. Chem. Soc., Faraday Trans. 1 , 70, 105 (1974). (22) F. Strohbusch, F. A. Vazquez, A. L. Cummings, D. B. Marshall, and E. M. Eyring, to be published. (23) The sltuation is quite different for methyl red in acetonitrile from the one in water. In water the carboxyl group of methyl red is dissociated under the conditions for the protonationof the azo group and therefore
B. E. Holmes and D. W. Setser
(24) (25) (26) (27) (28) (29)
the solvation shell Is favorably oriented for solvent mediated proton transfer. The anion of methyl orange, whlch is structurally very simibr to the indicators studied here, is protonated exceptionally slowly in water.24 Unfortunately, its protonation kinetics cannot be measured in acetonitrile because the protonated methyl orange Is extremely insoluble in acetonitrile. The dissociation constant of methyl orange was determined by Kolthoff et el. by measurlng absorbances immediately after mixing solutionsSz6 L. P. Holmes, A. Silizars, D. L. Cole, L. D. Rich, and E. M. Eyring, J . Phys. Chem., 73, 737 (1969); R. G. Sandberg, G. H. Henderson, R. D. White, and E. M. Eyring, bid., 76, 4023 (1972). I. M. Kolthoff, prlvate communlcation. Reference 4, p 217. E. J. King in "Physical Chemistry of Organic Solvent Systems", Covington and Dickinson, Ed., Plenum Press, New York, 1973. S. A. Chaudrl and K.-D. Asmus, J. Chem. Soc., Faraday Trans. 7 , 68, 385 (1972). W. R. Davidson and P. Kebarle, J. Am. Chem. Soc., 98, 8125 (1976).
Unimolecular Rate Constants for Ring Rupture and HCI Elimination from Chemically 2-, and 3-Methylchlorocyclobutane and Chloromethylcyclobutane Activated I-, B. E. Holmes" and D. W. Setser Department of Chemistry, Kansas State Universlty, Manhattan, Kansas 66506 (Recelved April 17, 1978)
-
Chemically activated I-, 2-, and 3-methylchlorocyclobutane were prepared with 110 kcal mol-' of internal energy by the insertion of singlet methylene into the C-H bonds of chlorocyclobutane. Total decomposition rate constants for these molecules were measured as 7.6 f 3.8 X lo8, 3.9 f 0.8 X lo8 and 3.9 f 0.8 X lo8 s-l, respectively. Both HCI elimination and ring rupture are unimolecular reaction pathways for these vibrationally excited molecules and the rate constants for individual HC1-elimination and ring-rupture channels were extracted from the pressure dependence of the product yield ratios. These rate constants were interpreted according to RRKM theory and threshold energies for various unimolecular reaction channels were assigned. Chloromethylcyclobutane was prepared with 90 kcal mol-l by the combination of cyclobutyl and chloromethyl radicals, which were formed by methylene abstraction of chlorine from chlorocyclobutane. The unimolecular ring-rupture and HC1-elimination rate constants for chloromethylcyclobutane were 4.7 f 0.2 X lo6 and 4.8 f 4 X lo5 s-l, respectively. RRKM theory also was applied to the chloromethylcyclobutane reactions to assign threshold energies. The transition state models developed for the ring-rupture and HC1-elimination reactions fitted the experimental observation at both energies of activation. The methylchlorocyclobutane chemical activation rate constants are best fitted if A",o(CH2,1Al) = 101 kcal mol-l is used to calculate the energy of activation.
Introduction The H X (X = F, Cl and Br) elimination reactions from thermally and chemically activated halohydrocarbons have been extensively ~tudied.l-~ Both a three-centered and the more common four-centered decomposition pathways have been observed. The chemical and thermal activation studies include the hydrogen-deuterium isotope effects, temperature dependence of the rate constants, and variation of the rate constants with the length of the carbon chain and with position and extent of halogen substitution. Recently the chlorine isotope4and thermal fall-off effects5 have been studied via thermal activation. In addition chemical activation has been used to study intramolecular competitive H X eliminatione and the energy dependence of the rate ons st ants.^^^^ In the present work the chemical activation technique has been extended to study the competitive intramolecular HC1-elimination and ringrupture pathways of methylchlorocyclobutane (MCCB) *Address correspondence t o this author at the Department of Chemistry, Ohio Northern University, Ada, Ohio 45810.
0022-3654/78/2082-2450$0 1.OO/O
and chloromethylcyclobutane (CMCB). The chemical activation results for HX elimination from alkyl halides from this laboratory have been fitted to a common four-centered transition state model using the RRKM theory. The bond orders for the best model were 1.5, 0.9, 0.1, and 0.1 for C-C, C-X, C-H, and H-X, respectively. This model suggests that the hydrogen is only weakly bound to both the halogen and the carbon in the transition state. The sum of the bond orders is less than 3.0, which implies a polar transition state, in agreement with Maccolls' interpretationg of the lowering o f Eowith an a- or @-methyl substitution. The question of the stereochemistry of the elimination process, Le., do the hydrogen and halogen originate from the same or opposite sides of the C-C bond, has not been answered experimentally; however, theoretical s t u d i e favor ~ ~ ~elimination ~~ via a syn transition-state geometry. Since the transition-state model for HC1 elimination is well characterized, the present work offers the opportunity to compare the HC1-elimination channel to the less well understood ring-rupture channel in the 90-110-kcal mol-l range. Our 0 1978 Amerlcan Chemical Society
Elimination Reactions from Activated Hydrocarbons
chemical activation results for the ring-rupture channels of MCCB can be compared to recent studies of methylcyclobutane activated by CH2 insertional1 The main purpose of this study was to elucidate the energy disposal of the elimination channel by measuring the fraction of the energy released to the olefin product from HX elimination (see following paper).1° Before the energy disposal data could be obtained, an understanding of the unimolecular reaction pathways for chemically activated 1-,2-, and 3-MCCB and CMCB was necessary. Activation was by the insertion of the CH2('A1) into the C-H bonds of chlorocyclobutane and the abstraction of chlorine from chlorocyclobutane followed by the recombination of CH2C1 and cyclobutyl radicals. Thus, the magnitudes and rate constant ratios for HC1 elimination and cyclobutane ring rupture were obtained at two levels of excitation. The HC1-elimination and ring-rupture rate constants have different dependencies on energy and provide an interesting contrast. During the course of this work, the value for the AHfoo(CH2,1A1)was seriously questioned.12 The thermochemistry for radical-radical combination giving CMCB is firmly established and the rate constant data for CMCB in conjunction with RRKM theory can be used to deduce threshold energies and models for transition states. These models then can be used to discuss the level of activation provided to MCCB by the insertion reactions. The goals of the work were to (1)measure the chemical activation rate constants for MCCB and CMCB, ( 2 ) determine the threshold energies for the HC1-elimination reactions which are needed for energy disposal analysis (following paper), (3) refine the transition state model describing ring rupture of cyclobutanes, and (4) assign the energy from singlet methylene insertion into C-H bonds of chlorocyclobutane. Three sets of experiments were done. For one set of experiments ketene was photolyzed with chlorocyclobutane. The chlorine abstraction reaction by methylene gives cyclobutyl and chloromethyl radicals, which subsequently combined to produce chloromethylcyclobutane with -90 kcal mol-' of energy. Both HC1elimination and ring-rupture rate constants were determined. In the second set of experiments ketene was photolyzed with chlorocyclobutane with added oxygen to suppress the abstraction reaction. Under these conditions 1-,2-, and 3-MCCB are formed with an energy that depends upon C\Hfoo(CH2,1A1). The ratios of rate constants were measured for most HC1-eliminationand ring-rupture channels. (3) In the final set of experiments oxygen also was employed but cyclooctane was added as an internal standard. Total unimolecular rate constants for 2- and 3-MCCB were measured.
Experimental Section S a m p l e Photolysis and Analysis Procedure. All gas handling was done on greaseless vacuum racks using standard vacuum techniques; a spiral gauge was used for pressure measurements. The vapor pressure of chlorocyclobutane is 75 f 5 Torr at 25 "C, which establishes the high pressure limit without the addition of inert gas. The desired amount of 02 was obtained by expansion from a reservoir into the sample vessel that already contained the other compounds. The samples were prepared in 20-5450 cm3 Pyrex vessels, mixed thoroughly, and then photolyzed at room temperature using a GE AH-6-1B high-pressure mercury lamp. The effective wavelength for ketene photolysis with Pyrex vessels is 3200 f 200 A. After photolysis the condensible products were transferred by vacuum technique into the inlet system of a gas chromatograph equipped with a thermal conductivity detector.
The Journal of Physical Chemktty, Vol. 82,No. 23, 1978 2451
Since the number of products is quite large and the yield for a given product in the oxygen scavenged experiments was small, a dual-pass analysis employing a flame ionization detector for the second pass was necessary. In the initial separation, specific components were trapped from the helium effluent and then transferred to the inlet system of the second gas chromatograph. The initial separation used either a 12-ft Octoil-S or a 12-ft Apiezon-L column; the second employed a combination column of AgN03-saturated ethylene glycol and hexamethylphosphoric triamide (HMPA) or just an Octoil-S column. The gas chromatographic response (peak areas) was calibrated using prepared mixtures approximating the composition of the actual samples. The calibration sample was handled with the identical procedure used for the photolyzed samples. To ensure that the trapping process did not preferentially retain any one component, the calibration mixtures also were analyzed in a single pass on the flame ionization gas chromatograph. Since many of the products are strained ring systems or cis and trans isomers that may undergo catalytic isomerization, the column and detector were maintained at the lowest operable temperature and the carrier gas a t maximum flow rate for the first analysis. Photolytic-induced isomerization was not important as shown by analysis of pure samples which were photolyzed. For study of chemically activated CMCB, samples (CH2CO:chlorocyclobutane= 1.0:3.0) were prepared to give a total volume (STP) of 2.3 cm3. The first analysis used the Apiezon-L column with temperature programming to separate the stabilized chloromethylcyclobutane product from the other reaction products. The HC1-elimination and ring-rupture decomposition products were trapped from the He effluent and subsequently analyzed on a 3-in. HMPA plus 30-ft AgN03 combination column operated at ambient temperatures. The reactant ratios for the study of 1-, 2-, and 3methylchlorocyclobutane reactions were CH2CO:chlorocyclobutane:02 = 1.0:3.0:0.4; all samples were made to a constant total volume (STP) of 2.7 cm3. Either the Octoil-S or Apiezon-L column was used with temperature programming for the first separation. After trapping the HC1-elimination and ring-rupture products from the He effluent, the second analysis was done with a 41-50-ft AgN03 column in combination with a 2.5-3.5-ft HMPA column. For the internal standard experiments the reactant proportions were CH2COchlorocyclobutane:02:cyclooctane = 1.0:3.0:0.3:0.2; the total volume (STP) was 2.8 cm3. For a few experiments SFe was added to increase the pressure above the chlorocyclobutanevapor pressure. The products trapped from the initial analysis, using the Apiezon-L column, were methlcyclooctane and 2- and 3-methylchlorocyclobutane along with a portion of chlorocyclobutane and cyclooctane to facilitate gas transfer. The second analysis employed a temperature programmed Octoil-S column. Purification of Reagents and Identification of Products. Chlorocyclobutane was purified by gas chromatography. Since 3-chloropropene is formed by catalytic decomposition of chlorocyclobutaneduring the gas chromatographic purification, complete removal was impossible. However, the 3-chloropropene(which also is a decomposition product from ring rupture) was reduced sufficiently so that it was not a serious problem. Ketene was prepared by the hot wire pyrolysis of acetic anhydride and purified by trapto-trap distillation. l-Methylchlorocyclobutane was prepared by passing dry hydrogen chloride into a solution
2452
The Journal of Physical Chemistry, Vol. 82, No. 23, 1978
of methylenecyclobutane maintained a t -5 "C; after distillation, mass spectrometric analysis confirmed its identity and purity. Photochemical electrocyclic addition13 of 2-methyl-1,3-butadiene and trans-1,3-pentadiene was used to prepare 1-and 3-methylcyclobutene, respectively. The NMR spectra confirmed the identity and purity of each isomer. Chloromethylcyclobutane and the methylchlorocyclobutane isomers, which have not been previously reported in the literature, were prepared by high pressure photolysis of chlorocyclobutane and ketene. The desired products were obtained after extensive gas chromatographic separations. The compound eluted first, a shoulder on the tail of chlorocyclobutane, wa9 identified as the 1met,hylchlorocyclobutane from the retention time of the known compound. The next four compounds eluted from the Apiezon-L column were separated and purified. Prom the mass spectra these four compounds were identified as MCCB isomers. Since the major fragmentation process for cyclobutane ions14 is ring rupture, the mass spectral cracking pattern can be used to tentatively identify the methyl and chlorine positions. For example, ring rupture of 1-MCCB ion gave an m/e of 76 corresponding to C3H5C1+but no 62 or 42 mass peaks corresponding to C2H3C1+or C3H6+,respectively. Conversely, 2-MCCB gave strong 62 and 42 mass peaks and a much weaker peak at m / e 76; in addition 3-MCCB gave mass peaks of 62 and 42 but none a t 76. Thus, the mass spectra cracking patterns were used to identify the four compounds as cis-2-, cis-3-, trans-2-, and trans-3-methylchlorocyclobutane. The identification of the cis-trans isomers is only tentative and is based upon the characteristics of the Apiezon-L column for cis- and trans-1-chloropropene. A sixth gas chromatographic peak found in the preparative photolysis mixture was absent in photolyzed samples containing added oxygen; whereas, the O2only reduced the first five peaks. The sixth peak, which had an area of approximately 1/6 the sum of the areas of the first five, was identified as CMCB based upon its pressure dependence, mass spectrum, and the fact that O2 prevented its formation. Other components of the reaction mixture were identified by comparison to the retention times and mass spectra of known compounds. To eliminate the possibility that a gas chromatographic peak of the photolyzed sample contained two compounds, a variety of columns was used for both the first and second steps of the analyges. Positive identification of cis- and trans-1,3-pentadiene, 1- and 3-methylcyclobutene, methylenecyclobutane, vinyl chloride, cis- and trans-1-chloropropene, 2-chloropropene, 3-chloropropene, 1,2-dichloroethane, and propene were made by matching mass spectral cracking patterns of separated components with real samples.
Experimental Results Unimolecular Reactions of Chloromethylcyclobutane. Photolysis of ketene produces both singlet and triplet methylene. Singlet methylene reactions are C-H insertion and chlorine abstraction;15 triplet methylene abstracts hydrogen and chlorine atoms: CH,
+d
CI
+ 0'
(la) (Ib)
g c i
(IC)
+.
-+
-+
.CH,Cl *CH, +
Radical-radical combination and disproportionation reactions from (lb) and (IC)lead to many products. The radicals present in highest concentration are from (lb), and
B. E. Holmes and D. W. Setser 14
12
IIPRESSURE ( t o r r ) Figure 1. DiSvs. I/Pplot for ring rupture of chloromethylcyclobutane activated by radical combination. The data were corrected for the 3-chloropropene (the decomposition product) impurity in the chlorocyclobutane; the correction actually was insignificant except at the highest pressure.
combination of chloromethyl and cyclobutyl radicals gives CMCB with -90 kcal mol-l of internal energy:
* CH,C1
+ 0'' dCHzC' +.
Vibrationally excited CMCB may decompose by HC1 elimination and ring rupture or may be collisionally stabilized: (3)
-k 4*
----j
CH,=CH, t CH,=CHCH,Cl
k~vl[M]
d
(4)
CHZCI
(5)
The individual chemical activation rate constants are defined as ha, = kM[M]Di/S;kM[M] is the collision frequency and is directly proportional to the pressure, P; D i is the yield of decomposition product for the ith channel and S the yield of collisionally stabilized product. The single asterisk denotes an energy of -90 kcal mol-I. In the absence of complicating reactions that might affect the D iand S yield ratios, the average rate constant with efficient bath gases is obtained from the slope, in the high pressure region, of a D,/S vs. 1/P plot. The plot, Figure 1,for the ring-rupture process, reaction 4, is linear with an intercept of zero; thus, the effects of side reactions are negligible, and k4* = 0.39 Torr can be obtained. Unfortunately measurement of h3* is complicated by the presence of two additional unimolecular pathways that produce the same decomposition product as (3):
The double asterisk denotes an energy of -110 kcal mol-l. Because of the higher energy, k6d** is a factor of 20-50 larger than hsd*. The yield of 1-methylchlorocyclobutane via (6b) is much smaller than for (6a); thus, the contribution from (6b) to the yield of methylenecyclobutane is negligible. Using the steady state method for (2), (3), (4), (5), and (6a), the following expression can be derived: [methylenecyclobutane] k3* =-+ [CMCB] P
The Journal of Physical Chemistry, Vol. 82, No. 23, 1978 2453
Elimination Reactions from Activated Hydrocarbons
s
I
I
I
10
0
2.0
I 3.0
0'
J
I/PRESSURE (torr) Figure 2. The experimental yield [methylenecyclobutane]/[chloromethylcyclobutane] vs. reciprocal pressure for the CH2 plus chlorocyclobutane system. Two separate unimolecular processes contribute significantly to the methylenecyclobutane yield which is responsible for the pronounced curvature (see text). The solid line was calculated from ea I. I
1
'
4
008
006
004
I 010
IIPRESSURE ( t o r r )
oxygen scavenges all radical reactions except the insertion reactions of singlet methylene:
+
CI
d
I
k,
+l-MCCB** k
Zkd**
-% cis-2-MCCB**
,N 8 . 0
products
Zk,d**
___f
products
k8 Zked** + trans-2-MCCB** -?. k* --f
k 10
I
I
10
0
I
I
20
30
J
I/PRESSURE (torr) Figure 3. The experimental yield of [methylenecyciobutane]/[3chloropropene] vs. reciprocal pressure for the methylene plus chlorocyclobutane system. The solid line was calculated from eq I1 using the same rate constant values which gave the solid line of Figure 2 (see text).
The ratio of formation rates of 1-MCCB to CMCB by (6a) and (2) is r1 and CkGd** is the sum of all the decomposition rate constants for 1-MCCB. From the high pressure product yield ratio, r1 was estimated to be unity. The plot of (methylenecyclobutane/chloromethylcyclobutane)vs. P-l, Figure 2, is curved as expected. The solid curve of Figure 2 was calculated from eq I using &d** = 15 Torr, k3* = 0.04 Torr, h4* = 0.39 Torr, x h B d * * = 63 Torr, and r1 = 1.0. Another approach is to examine the product ratio. The steady state ratio for methylenecyclobutane and 2-chloropropene is given by [methylenecyclobutane]
-
k3*
I-
[2-chloropropene]
+
h4*
-4 h6d**rI
kq*
P + h3* + k4* P -k Ckp,d**
]
(11)
TLc. yolid curve of Figure 3 was calculated from (11) using the same values for rl and the rate constants that gave the solid line of Figure 2. While the agreement with the experimental data is good, the calculated values are not very sensitive to small (f25%) variation of h3* or ked**. However, no reasonable combination of values for r1 and ha** would fit the experimental data if h3* were less than 0.01 or larger than 0.07 Torr. The unimolecular rate constants for CMCB, activated to -90 kcal mol-I, are summarized in Table I, the k3*:h4*is 0.10 f 0.09. Total Unimolecular Rate Constants for the Methylchlorocyclobutane Isomers. The addition of 10-15%
012
Figure 4. Plot of the left-hand side of eq 111 vs. reciprocal pressure: MCOT = methylcyclooctane, COT = cyclooctane, CCB = chlorocyclobutane, S i = cis-2-MCCB.
CH, I
002
cis-3-MCCB**
xk,d** ___f
k,od
(7 1
(8)
products
products
(9)
**
(10)
trans-3-MCCB** - - - + p r o d u c t s
Total decomposition rate constants, h7d**-klod**, were measured by the internal standard method using cyclooctane as the standard: CH2
+ cyclooctane
hl**
methylcyclooctane (11)
The decomposition rate constant for chemically activated methylcyclooctane with 110 kcal mol-l of energy is T o r P and it will be completely stabilized for all conditions of these experiments. A steady state treatment gives [methylcyclooctane] [chlorocyclobutane] hll** =[Si][cyclooctane] hi N
+
kll**Chid**
(111) Phi where Siis the stabilized MCCB isomer of interest, hiis the rate constant for methylene insertion, and Chid** is the total decomposition rate constants for the MCCB isomers. A plot of [methylcyclooctane]/ [Si]X [chlorocyclobutane]/ [cyclooctane] vs. 1/P should give an intercept of kll**/hi and a slope of k l l * * x h , d * * / k i . The analytical procedure separated the cis-1,2- and the trans-l,3- isomer but the cis-l,3- and the trans-1,2- isomers were measured together. Even a dual analysis did not resolve the 1-MCCB from the chlorocyclobutane. Fortunately %6d** was estimated from the chloromethylcyclobutane experiments, vide supra. The plots of eq I11 are shown in Figures 4 and 5. A least-squares analysis (solid lines of Figures 4 and 5) gave the rate constants in Table I. The methylene relative C-H insertion rates, r, at the 1, 2, and 3 position of chlorocyclobutane are given by the formation ratios for 1-MCCB, 2-MCCB, and 3-MCCB; r2 = (h7 + hs)/ks,, r3 = (k7 + h s ) / ( h g+ hlo). The intercepts of Figures 4 and 5 give h7/k10= 1.9 f 0.4 and (h, + h9)/klo = 2.5 f 0.5. Assuming that CH2 insertion at the 2 or 3 positions gives equal amounts of the cis or trans isomer (Le., k 7 / k I 0= hs/hg),then r3 = 1.9 f 0.4 which is close to the statistical value of 2.0. Since the 1,l isomer was not
2454
The Journal of Physjcal Chernjstry, Vol, 82, No. 23, 1978
B. E.Holmes and D. W. Setser
I
1
.CH>
1401
d-9J
CHsCH2
+
t-
\I3
HCI
CH3CH=CHCI t--
CHsCHCI
I 0
I 002
004
006
008
012
010
I/PRESSURE ( t o r r )
Flgure 5. Plots of the left-hand side of eq 111vs. inverse of pressure. The S, are trans-3-methylchlorocyclobutane ( 0 )and cis-3- plus trans-2-methylchlorocyclobutane (0).
CI
Flgure 6. Reaction scheme for unimolecular decompositionof 1-, cisand trans-2-methylchlorocyclobutane,and cis- and trans-3-methylchlorocyclobutane. HCI-elimination and ring-rupture processes are shown to the right and left of the activated molecules, respectively.
TABLE I: Experimental Rate Constants rate constanta
pressure,b Torr
0.04t 0.03 0.39 f 0.04 15 63 322 6 32t 6 32i.6 rod** 13 k,*** 7.5 k13** 21 kl4** 28 kl,** 35 kI,** 1.2 k,l** 2.0 18** 4.0 k,9** a The asterisk denotes an energy of k,* k'l* kgd** Ck,d** E k7d* * Ck8d** t Ekgd**
'
s - ~b,c
4.8 f 4.7 & 1.9 x 7.6 x 3.9 f 3.9 f 3.9 t 1.6 x 9.0 x 2.5 x 3.4 x 4.2 x 1.4 x
4 x lo5 0.2 x lo6
lo8
10' 0.8 x 10' 0.8 x lo8 0.8 x 10' lo8
I
I
01
107
10'
lo8 lo8 107
x 107 4.8 x 10' 2.4
,
,
I
,
,
,, I
~
0 2 0 3 0 4 0 5 0 6 ' 10 I/PRESSURE ( t o r r )
11
Flgure 7. Experimental product yleld ratlos for [2-chloropropene] / [ cisplus trans-l-chloropropene]).( and [3-methylcyclobutene plus cisand trslns-l,3-pentadiene]/[methylenecyclobutene] (0) vs. reciprocal pressure the solld line is the calculated best flt.
$90 kcal mol-' and the double asterisk denotes an energy of ~ 1 1 kcal 0 mol-1. ColThe uncertainty is t 50% unless otherwise noted. lision diameters of 3.6,4.5, 6.5,and 6.0 A. were utilized for oxygen, ketene, chlorocyclobutane, and the methylcyclobutyl halides, respectively, in computation of kM.
measured, r2 could not be assigned. If the yield of the 1,l isomer is assumed to equal one-half that of the trans-1,3isomer (Le., the insertion is statistical), then r2 = 4.0 and CH2(lA1)reacts by insertion with cyclooctane 4.2 times faster than with chlorocyclobutane which is comparable to reactions of singlet methylene with other hydrocarbon~.~~ Individual Decomposition Rate Constants of MCCB. Figure 6 shows the competitive unimolecular pathways for the methylchlorocyclobutanes. Rate constants are mean values for the cis and trans isomers for 2- or 3-MCCB. All decomposition products were measured except ethene and propene, which also was formed via reactions of CH2 with ketene and are of no value for measuring rate constants of Figure 6. Steady-state expressions for product-yield ratios were utilized to determine ratios of rate constants. These steady-state expressions are straightforwardls but tedious; they involve the rate constant ratios and r2 and r3. The cyclobutenes retain sufficient energy to isomerize so to evaluate the HC1-eliminationunimolecular pathways that gives l-methylcyclobutene; the 2-methylbutadiene yield was added to the l-methylcyclobutene yield. Likewise the cis- and trans-1,3-pentadiene yield was added to that of 3-methylcyclobutene. Some of the experimental product yield ratios and the calculated best fit from the appropriate steady-state expressions are displayed in Figures 7 and 8.
I
0
01
~
.
.
~
02 0 3 0 4 0 5 O B
'
~
26 2 7
.
I/PRESSURE ( t o r r )
Flgure 8. Experimental product yield ratios, HCI ellmlnation/rlng rupture vs, reciprocal pressure. The are for [methylenecyclobutane]/[2chloropropene] and glve a mean value of 1,19, The solid line, wlth a value of 1.15, is the calculated fit of the appropriate analytlcal rate constant expression. The 0 are for [3-methylcyclobutene plus clsand trans-1,3-pentadiene]/ [ cls- plus trans-l-chloropropene]and glve a mean value of 0.54. The solid line with a value of 0.53 is the calculated best fit.
Assignment of the unimolecular rate constants were subjected to the following constraints, which must be simultaneously satisfied. (1)The calculated product ratios from the steady-state expression18 must adequately fit experimental data such as shown in Figures 7 and 8. (2) The total rate constant for both 2- or 3-MCCB must equal 32 Torr, the values obtained by the internal standard method. (3) The value for r3 must agree with the experimental value (1.9). Rate constants that best fit the data are shown in Table I. It was impossible to fit the data if either or both the
.
The Journal of Physical Chemistry, Vol. 82, No. 23, 1978 2455
Elimination Reactions from Activated Hydrocarbons
TABLE 11: Summary of Molecular and Transition State Models for Chloromethylcyclobutane ring rupture transition state vibrational frequencies (cm-I) and degeneracies
moments of inertia, amu A 2
torsional
free rotor
2966 ( 9 ) 1449 ( 4 ) 1210 ( 9 ) 964 ( 6 ) 801 ( 5 ) 648 (1) 479 ( 1 ) 268 ( 2 ) 159 (1) 125 (1)
2975 ( 9 ) 1397 ( 7 ) 1219 ( 7 ) 972 ( 7 ) 648 (1) 419 (1) 305 (1) 374 ( 2 ) 220 ( 2 ) 137 ( 2 ) 75 (1) 354.3 256.8 132.8
2975 (9) 1458 (6) 1230 ( 8 ) 972 ( 5 ) 676 ( 3 ) 419 (1) 305 (1) 220 ( 2 ) 137 (2)
2960 ( 8 ) 1449 ( 4 ) 1188 ( 9 ) 944 (5) 575 (1) 479 (1) 400 (1) 268 ( 2 ) 159 (1)
354.3 256.8 132.8 Z,= 17.0
392.8 369.3 64.5
389.6 349.0 65.3
( I t /Z)L
1.17
a
2.02 4
4
Ua
calcd preexponentiala factor, s-l est preexponentiaP factor, s-'
HC1 transition state
molecule
0.46 x i o i 5 2.8 x i o i 5 2.8 x 1015
1.1 x 1015 2.1 x 1015 2.8 x 1 0 ' 5
1.03
1 0.82 x 1013 2.2 x 10" 0.9 0.1 x 1013
See footnotes to Table 111.
k or r values were changed by more than &50%, thus, the overall fit to the data for these rate constants was judged to be satisfactory. Calculated RRKM Rate Constants. The RRKM rate constant, hE, a t specific energy, E , is givenlJ by
where CP(Et)is the total number of vibrational quantum states of the transition state, N*(E*) is the density of vibrational states of the molecule a t an energy of E*, and u is the reaction path degeneracy. For calculation of hE the reaction path degeneracy, the vibrational frequencies, and moments of inertia for the activated complex and the molecule are needed. All transition state models were calibrated by comparison to known or estimated thermal preexponential factors. Normal mode frequencies of 1-, 2-, and 3-MCCB have not been reported; thus, the frequencies were estimated by removing frequencies corresponding to one C-H stretch and two C-H bends from chlorocyclobutanelg and replacing them by a C-CH3 stretch, two C-C-CH, bends, and six characteristic internal frequencies of the methyl group. Finally, three additional frequencies (a torsion and two rocks) corresponding to motion of CH3 relative to the cyclobutane ring were added. These twelve frequencies were refined via comparison to the normal mode frequencies of similar disubstituted cycloalkanes.20 The CMCB frequencies were obtained by combining characteristic frequencies of the cyclobutyl radical (constructed by removing a C-C1 stretch and two C-C1 bends from chlorocyclobutanelg)with those of a chloromethyl groupaZ0 Three additional frequencies, a C-CH&l stretch and two C-CHZCl bends, were assigned by analogy to several fourand five-carbon chloroalkanes.20 The resulting grouped frequencies for these molecules are shown in Tables 11-V. Moments of inertia for MCCB and CMCB, see Tables 11-V, were calculated from the bond angles and bond lengths, which were estimated from analogy to chlorocyclobutane.21 The structure of the CH, and CHzCl groups were derived from bond angles and lengths of 2-methyl-
propene22and chloroalkanes.20 The transition state for HC1 elimination was based upon the model previously developed6 (Le., a nearly planar ring with bond orders of 1.5,0.9,0.1, and 0.1 for the C-C, C-C1, C-H, and H-C1 bonds, respectively). For the transition state of CMCB the normal mode frequencies of the C-C-H-C1 ring were assigned by analogy to frequencies calculated for the CHzCICHClz transition state.' The reaction coordinate was the C-C-H bend; the C--C-H-C1 ring-puckering frequency was treated as an adjustable parameter to best fit the estimated thermal preexponential factor. The grouped frequencies are given in Table 11. The frequencies for the HC1-elimination transition state for 1-, 2-, and 3-MCCB were assigned as just described for CMCB. The differences between the MCCB transition states and that for CMCB (which is not unlike that for an alkyl halide) arises from the presence of the fused rings which would hinder the C-C-H-C1 ring puckering, the cyclobutane ring puckering, and the C-C-H-Cl ring-deformation motions. The grouped frequencies and moments of inertia for the HC1-elimination transition states for I-, 2-, and 3-MCCB are summarized in Tables 111-V. The only significant change in the geometry of the transition state, relative to the molecules, was the formation of the C-C-H-C1 rings; these bond lengths were computed from the bond orders and Pauling's rule. The transition states for ring rupture were based upon a biradical mechanism with the transition state geometry selected to be between the biradical and the olefin geometry; i.e., complete rupture of one and partial rupture of the opposite C-C bond. For this mechanism the reaction coordinate becomes the ring-puckering mode. Such a process is in accord with a recent ab initio studyz3of the non-least-motion decomposition of cyclobutane. The vibrational frequencies of the transition state were selected from analogy to frequencies of c y ~ l o b u t a n eand ~ ~ the estimated frequencies for 1,4 biradicals. The cyclobutane vibrations that differ from those of 1,4 biradicals involve carbon-carbon skeletal motions. Two basic types of models were tested. For the simplest one, the motion of the two olefinic groups about the breaking C- - -C bond was treated as a torsional vibration. For comparison a free-
2456
The Journal of Physical Chemistry, Vol. 82,No. 23, 1978
B. E. Holmes and D. W. Setser
TABLE 111: Summary of Molecular and Transition State Models for 1-Methylchlorocyclobutane transition states
If
molecule frequencies (cm-' ) and degeneracies
2924 ( 9 ) 1308 (12) 973 ( 6 ) 801 ( 5 ) 530 (1) 370 (3) 286 (1) 179 ( 2 )
moments of inertia, amu A z
t HC1
HClt
2942 ( 8 ) 1449 ( 5 ) 1198 (6) 973 ( 6 ) 806 ( 6 ) 536 ( 2 ) 369 ( 3 ) 210 ( 2 )
2942 ( 8 ) 1293 (12) 911 ( 8 ) 770 ( 3 ) 575 (1) 388 ( 4 ) 286 (1) 159 (1)
2 62 234 93.6
255 233 105
2 54 239 105
0.96
(lf/I)l/Z
1.02
4
Ua
2
0.94 x 1013 2.4 x 1013 1.0 0.1 x 1013
calcdb preexponential factor, s-' estC preexponential factor, s-l
6
1.0 x l o L 3 2.5 x 1 0 1 ~ 0.9 0.1 x 1013
ring rupture 2924 ( 9 ) 1419 (8) 1220 ( 4 ) 980 ( 6 ) 851 (1) 530 (1) 376 ( 5 ) 286 ( 1 ) 219 ( 3 ) 75 (1) 42 1 348 112 1.62 4 0.51 x i o i 5 4.5 x 1015 2.5 ?: 1.5 X 1015
Calculated at 800 K for unit reaction path. The first entry is for the partition function a Reaction path degeneracy. form, while the second entry is for the Arrhenius A factor. Estimated (unit reaction path degeneracy) from analogy to experimental values for similar molecules. The HC1 transition state is for the partition function form, while the ring rupture transition state is for the Arrhenius A factor. TABLE IV: Summary of Molecular and Transition State Models for 3-Methylchlorocyclobutane transition states
H C1
molecule
ring rupture
frequencies 2952 ( 9 ) 2947 ( 8 ) 1361 ( 8 ) 1364 ( 7 ) (cm-') and degeneracies 1118 ( 4 ) 1118 ( 4 ) 964 (6) 947 (6) 801 ( 5 ) 807 ( 6 ) 537 ( 2 ) 539 ( 3 ) 373 ( 2 ) 372 ( 2 ) 286 ( 1 ) 213 ( 2 ) 179 ( 2 ) moments 350 359 of inertia, 336 332 69.7 amu A z 69.4
2952 (9) 1388 (11) 985 ( 7 ) 851 ( 1 ) 537 ( 2 ) 374 ( 4 ) 286 (1) 219 ( 3 ) 75 (1) 508 47 6 76.2
(It/I)l/Z
1.50 4 0.35 x l o t 5 3.4 x 1015
Ua
1.01 4 1.0 x 1013 2.7 x 1013
calcd" preexDonential factor, s-l esta preexponential factor, s-' a See footnotes t o Table 111.
rotor model (the two olefinic groups rotate freely) also was developed for chloromethylcyclobutane. The reduced moment of the free rotor was calculated by the method of PitzernZ5For both models the vibrational frequencies were adjusted so that the calculated thermal Arrhenius A factors were equal to the estimated preexponential factor. Although both models have the same Arrhenius preexponential factor and activation energy, the threshold energies are not identical. Threshold energies are related to activation energies by Eo = Eact+ (E,) - (E?) - RT (1/2RT)(N,t- N,).The average vibrational energy of the molecule and transition state are (E,) and (E:), respectively; the last term is the difference in thermal energy of the free rotors of the transition state and the molecule. The additional free rotor in the transition state lowers Eo
by lIZRT;but, the loss of a low frequency torsional vibration raises (for a classical vibration) Eo by RT. The net result is that for the rotor model Eo is RT/2 larger than for the torsional model. The effects of slight differences in frequencies, adjusted to reproduce the same preexponential factor, give a net difference in Eo values of 1kcal mol-'. The k E values for the torsional model (Eo= 60 kcal mol-') and the free rotor model (E, = 61 kcal mol-') are shown in Figure 9 and are almost identical at all energies. However, for the same threshold energy the free rotor kE values would be larger by approximately a factor of 2. Since the computations are much simpler for the torsional model and since both give nearly the same kE, all comparisons with experimental rate constants were done using the torsional models. Since thermal activation studies for MCCB and CMCB have not been done, the preexponential factors were estimated by analogy to other substituted cyclobutanes. Recent thermal activation studies26for cyclobutanes give Arrhenius preexponential factors that are a factor of 2-10 larger (cyclobutane = 1016.5; trans-1,3-dimethylcyclobutane - 1016.89;cis-1,3-dimethylcyclobutane= 1016.96;methylcyclobutane = 10l6.O2)than earlier data.27 A recent chemical activation study of methylcyclobutanel'b also favored the larger preexponential factor. The experimental preexponential factors for 1-,2-, and 3-MCCB, therefore, were taken to be 1016.0*o.2.A recent thermal pyrolysis study26cwith chlorocyclobutane reported k = 1014.76* exp(-60 070 cal mol-'/RT) s-l. We believe that systematic error must exist in this work and these data were not included in the reference set. After the reaction path degeneracy is properly considered, the preexponential factors for HC1 elimination vary little with chain length and methyl sub~titution.'~~ Therefore, methylenecyclobutane formation from 1-MCCB was assigned the standard value for chloroalkanes (-0.8 X 1013 s-' in partition function form) and then multiplied by the appropriate reaction path degeneracy. The preexponential factors for HC1-elimination reactions of MCCB giving cyclobutenes are expected to be somewhat, larger than for linear alkyl chlorides since the entropy of activation will be somewhat
The Journal of Physical Chemistry, Vol. 82,No. 23, 1978 2457
Elimination Reactions from Activated Hydrocarbons
TABLE V: Summary of Molecular and Transition State Models for 2-Methylchlorocyclobutane transition states frequencies (cm-*)and degeneracies
moments of inertia, amu A 2
(IT /
molecule
d
2957 ( 9 ) 1440 ( 5 ) 1174 ( 7 ) 964 ( 6 ) 801 (5) 537 (2) 373 ( 2 ) 286 (1) 179 ( 2 )
2953 (8) 1371 ( 7 ) 1118 ( 4 ) 944 ( 6 ) 806 ( 6 ) 538 (3) 372 ( 2 ) 213 ( 2 )
287 220 110
Ip
ua
calcda preexponential factor, s-l esta preexponential factor, s-l a
d 2953 (8) 1371 ( 7 ) 1118 ( 4 ) 944 ( 6 ) 806 ( 6 ) 538 (3) 372 (2) 213 ( 2 )
288 217 102
288 217 102
0.96
0.96 1 0.94 x 1013 2.5 x 10’3 L O * 0.1x 1013
2 0.94 x 1013 2.5 x 10i3 L O + 0.1x 10i3
CH,CH=CHCl 2957 (9) 1411 ( 7 ) 1231 ( 4 ) 985 ( 7 ) 851 (1) 537 ( 2 ) 374 ( 4 ) 286 (1) 219 (3) 75 (1) 379 349 111
CH,=CHCl 2957 (9) 1411 (7) 1231 (4) 985 ( 7 ) 8 5 1 (1) 537 (2) 374 ( 4 ) 286 (1) 219 ( 3 ) 75 (1) 540 48 7 89.3
1.45
1.84
2
2
0.37 x 1015 5.2 x i o i 5 2.5 * 1.5 X 1015
0.47 x 1015 4.2 x i o i 5 2.5 P 1.5 x 1015
See footnotes to Table 111.
smaller for the ring than for open chain alkyl halides. The entropy change associated with the stiffening of the methyl internal rotation in the HC1 elimination from CzH5C1is 1eu. Since MCCB does not lose a methyl torsion, the entropy loss in forming the transition state will be less than for ethyl chloride. Hence, A S would be somewhat smaller and the preexponential factor was estimated at 1.0 f 0.1 X 1013s-l, per reaction path. Tables 11-V summarize the estimated and calculated preexponential factors (partition function form) and Arrhenius A factors. The method given by Schlag and HallerZs for enumeration of all equivalent reaction paths was adopted for assignment of reaction path degeneracies. For HC1 elimination it was assumed that both “syn” and “anti” elimination can occur, Le., the hydrogen and chlorine can originate from the same or opposite sides of the cyclobutane ring. This leads to optically active transition states. The transition state model for ring rupture has complete fission of the first bond and partial fission of the second C-C bond. The number of transition state complexes is equivalent to the number of different C-C bonds that can be initially broken to yield the same product. For cyclobutane the reaction-path degeneracy would be four. The average energy (see Appendix) is the sum of Emin, the minimum energy of the activated molecule, the threshold energy for the activation reaction, and the average thermal energy of the activated molecule, Since the wavelength used for photolysis is close to the threshold energy for CH2 formation, the excess energy of CH2 need not be considered30 and the CH2 (or CHzC1)was assumed to have a Boltzmann energy. The value of (&h) for CMCB was obtained from the thermal energy distribution, f(E) dE, which was computed for a CHzCl plus cyclobutyl radical combination reaction in the usual way.l The distribution for CMCB is shown in Figure 9; this energy distribution also was used for the MCCB formed by insertion. To verify that the strong energy dependence of kE(ring rupture)/kE(HC1 elimination) did not lead to a significant pressure dependence of the experimental rate constant ratios, the unit deactivation chemical activation rate constant values for chloromethylcyclobutane were calculated by averaging the hE’s over the distribution function. Calculations were done over the 0.1-1000 Torr to range, which corresponded to an SID range of 3 X
-
(&)e
ENERGY (kcal/mole)
Figure 9. Calculated specific rate constants, for the models of Table 11, as a function of energy for chloromethylcyclobutane. The type of unimolecular process (shown in parentheses) and the E, values are identified. The FRM and TM are for free rotor and torsional model, respectively.
3 X lo3. The calculated HC1-elimination rate constants changed by 15% and the ring-rupture rate constants changed by 20%. However, the rate constant ratio varied only 6%. If cascade deactivation was used, with a moderate size for the energy loss per collision, rather than unit deactivation, the same conclusion is reached. Therefore, for simplicity, the experimental rate constants will be compared with ko, values rather than ha” calculated from the average of k E over f(E). Another important consequence of the invariance of the calculated rate constant ratios with pressure pertains to the assumption used in the analysis of Figures 7 and 8. That is, the experimental variation of the product ratios with pressure is a result of two or more unimolecular processes with significantly different rates yielding a common decomposition product and not from an intrinsic variation of the rate constant ratio with pressure.
Discussion Comparison with Other Data. Four studies’l have been reported recently for chemically activated methylcyclo-
2458
The Journal of Physical Chemistry, Vol. 82, No. 23, 1978
6.E. Holmes and D. W. Setser
0 02
70 80 90 100 110 120 ENERGY (kcal/mole)
Flgure I O . Calculated specific rate constants, for the models of Table 111, as a function of energy for 1-methylchlorocyclobutane. The (--) curve is for ring rupture: while for dehydrohalogenation the (. .) curve is for formation of methylene cyclobutane and the (-) curve is for 1-methylcyclobutene formation. Note the inversion of the HCI and ring-rupture rates relative to the 2- and 3-MCCE.
-
butane formed by CHz insertion. For photolysis of ketene between 335 and 320 nm, each reported the same (within the experimental uncertainty) chemical activation rate constants of 32 f 6 Torr for the methylcyclobutane. For 2-MCCB and 3-MCCB the insertion reactions give the same energy as for methylcyclobutane and, since the dominant (>go%) decomposition pathways are ring rupture, the rate constants of Table I can be compared with those for methylcyclobutane, The rate constants for and for trans-3-MCCB are 32 f 6 cis-2-MCCB, CkYd**, Torr which is excellent agreement with those for methylcyclobutane. For 1-MCCB the dominant reaction (>80%) is HC1 elimination because the threshold energy for HC1 elimination is lower than for 2- or 3-MCCB; the rate constant, therefore, increased to 63 Torr. Three sets of thermal Arrhenius parameters have been reportedz6 for methylcyclobutane; the A factors, s-l, (activation energy, kcal mol-') are 2.4 X 1015(61.2), 4.4 X 1015(62.0), and 1.1 X 10l6 (63.1). As noted in the preceding section, our calculations are based upon a loose transition state model (the A factor was N 10l6 s-l) for ring rupture. Simonsllb developed models for each set of Arrhenius parameters and found that the model based upon the largest preexponential factor best matched the chemical activation rate constant. Carr and McCluskeyllC showed that cascade deactivation must be included in comparing the calculated and experimental rate constants. Based upon their views of the acceptable range for the average energy of methylcyclobutane, the collision diameters, and the average energy lost per collision, Carr and McCluskey could not decide in favor of a specific transition state model. Before proceeding further, we must consider the importance of cascade deactivation for MCCB and CMCB. Richardson and SimonsZ9have investigated methylcyclobutane formed by methylene generated from photolysis of diazomethane a t different wavelengths. The results were interpreted as evidence for a broad vibrational energy distribution of singlet CH, and the loss of 6 f 2 kcal mol-' from methylcyclobutane per collision with cyclobutane. Studies30 of' ethylcyclobutane activated by CH2(lA1)plus methylcyclobutane favor step sizes of -4 kcal mol-l. Similar studies31 with spiropentane activated by singlet CH2 with methylenecyclopropane favor step sizes of -7 kcal mol-l. A comprehensive energy transfer using chemically activated CH3CF3with a variety
Flgure 11. Calculated specific rate constants, for the models of Table V, as a function of energy for 2-methylchlorocyclobutane. The (. * -) curve is for ring rupture to give CH2=CH, f CH,CH=CHCI, while the (---) curve is for ring opening to give CH3CH===CH, f CH,=CHCI. For HCI elimination the (-) and (--) curves are for 3- and I-methylcyclobutene formation, respectively.
ENERGY (kcal/mole)
Figure 12. Calculated specific rate constants, for the models of Table IV, as a function of energy for 3-methylchlorocyclobutane.
of bath gases suggests that a step size of 6-10 kcal mole1 would be likely for bath gases such as cyclobutane. For MCCB and CMCB only high pressure ( D / S < 0.2) measurements were done and the effect of cascade would be to increase the magnitude of the rate constants relative to unit deactivation values. For a step size of 6 kcal mol-' the calculated high pressure rate constant would be increased by about a factor of 1.6. This, however, is balanced integral from the collision by our omission of the Q(T)2>z . comparing diameters used for calculating k ~ Therefore, unit deactivation calculated rate constants with experimental values using hard sphere collision diameters is adequate considering the reliability of the rate constants obtained in this complex chemical system. At low pressure cascade deactivation would have a more serious effect32on the chemical activation rate constants, but that is not of concern here. Assignment of Threshold Energies. One of our main goals was to assign the threshold energies by matching the calculated rate constants, k(E),to the experimental values of Table I. In addition to the absolute magnitude, the ratios of the rate constants for the intramolecularly competing channels are of interest. According to the calculated rate constants in Figures 9-12, the energy
Elimination Reactions from Activated Hydrocarbons
The Journal of Physical Chemistry, Vol. 82, No. 23, 1978 2459
TABLE VI: Comparison of Calculated and dependence of the HC1-elimination channel is much Experimental Results different than that for ring rupture. For thermal activation, HC1 elimination is favored because of the lower Emd ha( expt),a k,( calcd),b kcal threshold energy, but at higher energy the ring-rupture molecule product ss-' mol-' channel is dominant. For example the calculated ring4.8 X lo5 5.0 X l o 5 52.5 rupture:HCl-elimination rate constant ratio for 3-MCCB is 0.40, 1.4, 3.0, 5.0, 7.2, and 13.0 for a 420 K thermal experiment and ( E ) = 80,90,100,110, and 120 kcal mol-l, ( E ) = 89.8 CH,=CHCH,Cl 4.7 X lo6 3.8 X lo6 60.0 kcal mol-' 4.0 x 61.0 respectively. This contrasting energy dependence is a consequence of the faster increase of the sums of states 1.9 x 10' 1.7 x 10' 47.5 for the transition state for the ring-rupture process relative 4.2 X lo8 3.8 X 10' 47.0 to that of the HC1-elimination process with increasing energy. The uncertainty in the difference in Eo values for ( E ) = 112.5 CH,=C(CH,)Cl 1.6X loa 1.3 X loa 61.0 the intramolecularly competitive channels is estimated to kcal mol-' be f l kcal mol-l. The error in the absolute Eo values may 4.8 x 107 4.7 x i o 7 52.5 be considerably larger, perhaps f2-3 kcal mol-l, because of experimental error in the absolute values of ha, uncertainty in the calculated kfE)values, and uncertainty in (4)=109.5 CH,=CHCl 3.4 X loa 3.3 X 10' 59.0 ( E ) ,vide infra. kcal mol-' The average energy for CMCB* formed by radical 3 1.4 X l o 7 1.4 x 10' 51.5 combinations is well established (see Appendix). Also, the experimental CMCB* rate constants were more directly 2 . 4 X 10' 2.3 x lo7 52.5 measured than for some of the MCCB** processes. ( E )= 109.5 CH,=CHCl 2.5 X 10' 2.4 X 10' 59.0 Therefore, the threshold energies assigned by varying Eo kcal mol-' CH,CH=CHCl 9.0 X 10' 8.8 X l o 7 61.0 until the calculated k(E)values match the experimental k, values can be viewed with greater confidence. The results All calculations of ring-rupture rate a See Table I. are Eo = 52.5 and 60 kcal mol-l for HC1 elimination and constants are for the torsional model except where specified, Free rotor model. E,, value may be converted t o ring rupture. The threshold energy for ring rupture should Ea by adding 1.5 kcal mol-' for HCl elimination and 3.0 be similar to that for methylcyclobutaneZ6(60 kcal mol-l) kcal mol-' for ring rupture. and this expectation is fulfilled. This assignment of Eo supports the higher range of Eo values for methylcyclopreexponential for chlorocyclobutane is an order of butanes but, of course, the large preexponential factor magnitude lower than the other cyclobutane reactions and models were used to calculate kE, The HC1-elimination the accompanying low E , may be the result of some threshold energy is consistent with other alkyl halides systematic experimental error. The Eo(HC1)values from having P-methyl s u b ~ t i t u t i o n . ~ Table I are a few kcal mol-l lower than Eo(HC1)reported The procedure for assigning the threshold energies for from the thermal activation study of chlorocyclobutane.zk the 1-,2-, and 3-MCCB** reactions is complicated by the As for the ring rupture channel, error is suspected because uncertainty of AH,O(CH2,lA1). We have used (see Apthe preexponential factor for HC1 elimination appears to pendix) AHfOo(CHz)= 101 kcal mol-l which is a concensus be higher than expected. value based upon a variety of kinetic and thermochemical Energy Dependence of the Unimolecular Rate Confor ~ ~ r This kleads to , (E)~= 109.5 ~ kcal mol-l ~ ~ 2- ~ stants ~ and~ PH,0(CH2,1A1). ~ ~ The ~ correct ~ value ~ of AH?and 3-MCCB** and 112.5 kcal mol-l for 1-MCCB**. (CH2,1A1)is of crucial importance for the assignment of Matching calculated k ( ~to) experimental rate constants the average energy for chemically activated studies inusing the (E) value gives threshold energies of Table VI. volving cyclopropanes and cyc1obutanes.l A value near 100 The ring-rupture Eo for 1-,2-, and 3-MCCB** (See Table kcal mol-l is required to obtain sensible match between VI) should be, and are, similar to those for 1,2- and 1,3the calculated RRKM rate constants (including step size dimethylcyclobutane26e since the steric hindrance for deactivation) and the experimental rate constants. This methyl and chlorine are similar. The ring rupture of value for AHf0(CH2,lA1)has been placed in question by 2-MCCB** gives two sets of products and, as expected the report12of the singlet-triplet separation (19.5 f 0.7 kcal the Eo from comparison with 1,2-dimethylcyclobutane,26e mol-l) and the accepted33AHfo(CH2,3Bl)value of 92 f 2 values for the two pathways differ by 2 kcal mol-l. kcal mol-l, which gives AHfo(CH2,1A1)= 112 kcal mol-l. Substituent effects can be used to partly test the reliability In the current work the unimolecular reactions of of the derived Eo for HC1 eliminations. The a-methyl structural isomers of chlorine-substituted methylcyclosubstituent lowered the Eo€or HC1 elimination from 1butane were investigated at two energies. The energy for MCCB by -5.5 kcal mol-l relative to elimination from chloromethylcyclobutane is well defined as (E) = 90 kcal 3-MCCB, as would be expected. Both 1- and 3-methylmol-l. For 1-,2-, and 3-MCCB** activated by CH2 incyclobutene are formed by HC1 elimination from 2-MCCB; sertion the ( E )is -122 kcal mol-l, if AH,0(CH2,1A1)= 112 the lower threshold energy for l-methylcyclobutene (1kcal kcal mol-l is used. The experimental rate constants can mol-l) is a consequence of the methyl group on the p be compared to the calculated RRKM values at 122 and carbon. The Eo(HCl) for 3-MCCB** (52.5 kcal mol-l) is 109.5 kcal mol-l to see which energy assignment the 2-4 kcal mol-' higher than the value for similar chloromethylchlorocyclobutane data favor. In comparing total a l k a n e ~ ~ (2-chloropropane ~-~l = 50.0, 3-chloropentane = rate constants, one should note that ring rupture is the 49.5, and chlorocyclohexane = 48.7 kcal mol-l). This dominant contribution except for 1-MCCB**. The exprobably is a consequence of the ring strain energy in perimental rate constants for 2- or 3-MCCB** are 70-80 cyclobutene, which is 2.7 kcal mol-l larger for cyclobutene times larger than for CMCB*, The same energy depenthan for cyclobutane. The derived Eo values in Table VI dence holds for ring rupture with CMCB* and MCCB**, for ring rupture of MCCB are 2-4 kcal mol-1 higher than since the same transition state models were used and since for chlorocyclobutane.26C However, the Arrhenius the Eo values are nearly identical. A 70-fold increase in
yj"H2c'
&L3
e pCH qCH
2480
The Journal of Physjcal Chemjstry, Vol. 82, No. 23, 1978
B. E. Holmes and D. W. Setser
the calculated ring-rupture rate constants requires a -20 difference in the experimental rate constants a t the two kcal mol-l increase in energy above ( E ) = 90 or a final levels of activation with the calculated difference supported energy of -110 kcal mol-'. If ( E ) was increased to 120 AHf0(CH2,'A1)= -100 kcal mol-I, rather than the higher value suggested by recent CH2- photodetachment work. kcal mol-l, the calculated rate constants would be increased For 1-methylchlorocyclobutane the HCI-elimination by a factor of -300 rather than 70; a clear-cut discrepancy relative to experimental data. The argument presented process is dominant but for 2- and 3-methylchlorocycloin this paragraph is independent of the absolute magnitude butane and chloromethylcyclobutane the ring-rupture of the rate constants. The effect of cascade collisional pathway is favored by a factor of 8-10. Fortunately, the deactivation is not explicitly included in the argument; yields of the olefin products from the HC1-elimination step however, the step size would have to change dramatically were sufficient so that the subsequent isomerization of the olefin could be measured. The isomerization rate constants for the two levels of activation and there is no evidence of the olefins were used to determine the fraction of energy in the literature to support this.32 The comparison made above for the chlorine-substituted released to the olefin from HC1 elimination (following isomers of methylcyclobutane activated to two levels of paper). energy also can be made for two other cases of chemically Acknowledgment. This work was supported by the activated fluoroalkanes. In these instances the same National Science Foundation (MPS 75-02793),and by the molecule was activated by radical combination and by Phillips Petroleum Company through a fellowship to methylene C-H insertion reactions. For both fluoroB.E.H. ethane35ps and 2-fluorobutane@ the experimental rate constants for activation by CH2 insertion was 15-20-fold Appendix larger than for genesis by radical combination. Such an s ~ ~ ~ to ~ ~ ~ ~In ~order to determine the average internal energy of increase in the calculated k E v a l ~ e corresponds -20 kcal mol-l increase in ( E ) ,Le., from (E) = 90 to ( E ) chloromethylcyclobutane (CMCB) the enthalpy of the = 110 kcal mol-'. Adjustment of the transition state radical combination reaction at 0 K is needed. The AH,0B8 models can alter the magnitude of the calculated k E values is 28.1 and 51.1 kcal mol-' for CH2C17*and cyclobutyP8 but the effect on the calculated energy dependence is small. radicals, respectively. Benson's group additivity method39 In conclusion, AHf"(CH2,1A1) of -100 kcal mol-' is was utilized to estimate AH?298(CMCB)= -6.2 kcal mol-'. required to match the RRKM calculated energy depenThus, the enthalpy of reaction equals -84.4 kcal mol-' at dence of the rate constant to the chemical activation rate 298 K and -84.1 kcal mol-l at 0 K. Combining this value constants for either H F elimination of alkyl fluorides or with a 1.0 kcal mol-' barrier for radical combination and ring rupture of cyclobutanes. Simonsllb and others31have 4.8 kcal mol-' thermal energy gives the average internal reached a similar conclusion based upon matching the energy as 89.9 kcal mol-' at 298 K, which was rounded to absolute values of the chemical activation rate constants 90 kcal mol-'. As stated in the text, the thermal energy by RRKM calculations for a number of cyclopropane and was calculated from the CMCB distribution function. cyclobutane systems. The new experimental d u e l 2 of the The average energy of the methylchlorocyclobutanes singlet-triplet energy separation of CH2 also sparked a formed by the methylene insertion reaction (generated by surge of interest among theoreticians. The recent theophotolysis of ketene) was assigned from the Eminvalue, retical studies36 report the singlet-triplet energy level 104.7 kcal mol-', recommended by Simons1lb for mesplitting to be 10.5 f 2, 11.0 f 2, and 11.3 f 2 kcal mol-' thylcyclobutane that was activated by CH2 insertion. This rather than 19.5 kcal mol-'. One of these investigation^^^ Eminvalue, which includes any energy retained from the suggested that the CH2- photodetachment spectra may photodissociation of ketene, corresponds to a AH?have involved transitions to excited vibrational states and (CH2,IA1)of 101 kcal mol-'. This AHfo(CH2)gives good thus does not give the minimum energy separation between agreement between RRKM calculated and experimental the states. Direct experimental evidence for a chemical activation rate constants for decomposition, and (CH2,'A1) of -100 kcal mol-' was provided by Welge and structural and geometrical isomerization of methylc o - w o r k e r ~ .Laser ~ ~ ~ induced fluorescence was used to substituted cyclopropanes and cyclobutanes (also see text detect CH2('A1) from the 337-nm laser photodissociation for discussion of alkyl fluorides). Since 2- and 3-MCCB of ketene. The photon energy of 337 nm together with the are formed by insertion into secondary C-H bonds, known thermochemistry for CH2(3B1)formation gave a whereas 1-MCCB is formed by insertion into tertiary C-H singlet-triplet energy separation of 6.3 f 0.8 kcal mol-'. bonds, the levels of activation will differ by the difference The confirmation of a AHf"(CH2,lA1)value near to that The AHf' values4' in AH:', which is -3.0 kcal assigned by S i m ~ supports n ~ the~ claim ~ that ~ ~ for~1,2-dimethylcyclopentanes ~ ~ ~ ~ ~and ~-cyclohexanes ~ ~ show that RRKM calculated rat,e constants can be routinely used the trans isomer is the more stable by -1.0 kcal mol-'. with confidence to match experimental rate constants. However, cis-1,3-dimethylcycloalkanehas the lower heat The chemical activation studies with alkyl halides' have of formation by -0.5 kcal mol-l. The presence of the cis used radical combination, with known ( E ) ,as the actiand trans isomers add a f l kcal mol-' uncertainty to AH: vation reaction. These data,' as well as the alkyl radical for 2- and 3-methylchlorocyclobutane. The thermal energy studies of R a b i n ~ v i t c hprovide ,~~ an independent set of of MCCB was taken to be the same as that for CMCB, chemical activation data for which RRKM calculations do Thus, the average energies for 2- and 3-MCCB and 1match experimental rate constants. MCCB were 109.5 and 112.5 kcal mol-', respectively. Conclusion References and Notes The unimolecular rate constants for HC1 elimination and (1) D. W. Setser, MTPInt. Rev. Scl.: fhys. Chem., Ser. One, 9, 1 ring rupture of 1-,2-, and 3-methylchlorocyclobutane and 119721 chloromethylcyclobutane has been measured. The me(2) M.-J.-Perona, J. T. Bryant, and G. 0. Pritchard, J. Am. Chem. Soc., 90, 4782 (1972). thylchlorocyclobutanes and chloromethylcyclobutane were (3) . . P. J. Robinson and K. A. Holbrook, "Unimolecular Reactlons",Wiley, prepared by the insertion of methylene into the C-H bonds New York, N.Y., 1972. of chlorocyclobutane and by the combination of CH2C1 and (4) J. R. Chrieie, W. D. Johnson, A. G. London, A. MacColl, and M. N. Mruzek, J. Chem. Soc., Faraday Trans. 1, 71, 1937 (1975). cyclobutyl radicals, respectively. Comparison of the
Unimolecular Hydrogen Chloride Elimination Reaction H. Heydtmann, B. Dill, and R. Jonar, rnt. J . Chem. Kinet., 7, 973 (1975). (a) R. L. Johnson and D. W. Setser, J. Phys. Chem., 71, 4366 (1967); (b) K. C. Kim and D. W. Setser, ibid., 77, 2021 (1973). (a) K. C. Kim and D. W. Setser, J. Phys. Chem., 78, 2166 (1974); (b) K. C. Kim, D. W. Setser, and B. E. Holmes, ibid., 77, 725 (1973); (c) B. E. Holmes, D. W. Setser, and G. 0. Pritchard, Int. J . Chem. Kinet., 8, 215 (1976). (a) P. Cadman, A. W. Kirk, and A. F. Trotman-Dickenson, J . Chem. Soc., Faraday Trans. 7 , 72, 996, 1426 (1976); (b) A. W. Kirk, A. F. Trotman-Dickenson, and B. L. Trus, J. Chem. Soc.A, 3056 (1966). (a) A. Maccoll, Chem. Rev., 69, 33 (1969); (b) P. C. Hiberty, J. Am. Chem. Soc., 97, 5975 (1975); (c) I. Tvaroska, V. Klimo, and L. Valko, Tetrahedron, 30, 3275 (1974). B. E. Holmes and D. W. Setser, J . Phys. Chem., following paper in this issue. (a) H. M. Frey, G. R. Jackson, M. T. Thompson, and R. Walsh, Trans. Faraday SOC.,6, 2054 (1973); (b) J. W. Simons, W. L. Hase, R. S.Phillips, E. J. Porter, and F. B. Growcock, rnt. J . Chem. Kinet., 7, 679 (1975); (c) R. J. McCluskey and R. W. Carr, Jr., J . Phys. Chem., 80, 1393 (1976); (d) R. L. Russell, Ph.D. Thesis, University of California, Irvine, Calif., 1971. P. F. Zittel, G. B. Ellison, S.V. O'Neil, E. Herbst, W. C. Lineberger, and W. P. Reinhardt, J . Am. Chem. SOC.,98, 3732 (1976). R. Srinivasan, J . Am. Chem. Soc., 84, 4141 (1962). E. F. Brittain, C. H. J. Wells, and H. M. Paislsy, J . Chem. SOC. 6, 304 (1968). W. G. Clark, D. W. Setser, and E. E. Seifert, J . Phys. Chem., 74, 1670 (1970). J. F. Meagher, K. J. Chao, J. R. Baker, and B. S. Rabinovitch, J . Phys. Chem., 78, 2535 (1975). (a) S.E. Stein and B. S. Rabinovitch, Int. J . Chem. Kinet., 7, 531 (1975); (b) W. L. Hase and J. W. Simons, J . Chem. Phys., 54, 1277 (197 1). B. E. Holmes, Ph.D. Thesis, Kansas State University, 1976. J. R. Durig and A. C. Morrissey, J . Chem. Phys., 46, 4654 (1967). R. B. Synder and J. H. Schachtschneider, Spectrochem. Acta, 21, 169 (1965); J . Mol. Spectrosc., 30, 290 (1969). H. Kim and W. D. Guinn, J. Chem. Phys., 44, 865 (1966). L. H. Scharpen and V. W. Laurie, J. Chem. Phys., 39, 1732 (1963). G. A. Segal, J. Am. Chem. SOC.,96, 7692 (1974).
The Journal of Physical Chemistry, Vol. 82, No. 23, 1978 2461 (24) "Table of Molecular Frequencies", National Bureau of Standards, Washington, D.C., NBS, 11, 1967. (25) K. S.Pitzer, J. Chem. Phys., 14, 239 (1946). (26) (a) H. M. Frey and R. Walsh, Chem. Rev., 68, 103 (1966); (b) P. C. Beadle, D. M. Golden, K. D. King, and S. W. Benson, J. Am. Chem. SOC.,94, 2943 (1972); (c) A. T. Cocks and H. M. Frey, ibid., 91, 7583 (1969); (d) T. F. Thomas, P. J. Conn, and D. F. Swinehart, ibid., 91, 761 1 (1969); (e) A. Ramakrishna, R.D. Thesis, Rochester, 1970. (27) (a) S. W. Benson and H. E. O'Neal, "Kinetic Data on Gas Phase Unimolecular Reaction", National Bureau of Standards, Washington, D.C., 1970; (b) N. N. Das and W. D. Walters, J. Phys. Chem., 15, 22 (1956); (c) A. F. Patzracchia and W. D. Walters, ibid., 68, 3894 (1964). (26) E. W. Schlag and G. L. Haller, J . Chem. Phys., 42, 584 (1965). (29) (a) T. H. Richardson and J. W. Simons, Chem. Phys. Left., 41, 166 (1976); (b) T. H. Richardson and J. W. Simons, J. Am. Chem. Soc., 100, 1062 (1976). (30) R. J. McCluskey and R. W. Cam, Jr., J. Phys. Chem., 81, 2045 (1977). (31) (a) H. M. Frey, G. E. Jackson, R. A. Smith, and R. Walsh, J. Chem. SOC.,Faraday Trans. 1 , 71, 1971 (1975); (b) A. D. Clements, H. M. Frey, and R. Walsh, ibid., 73, 1340 (1977). (32) P. J. Marcoux and D. W. Setser, J . Phys. Chem., 82, 97 (1976). (33) K. W. McColloh and V. H. Dibeler, J. Chem. Phys., 64, 4445 (1976). (34) (a) J. W. Simons and R. Curry, Chem. Phys. Left., 38, 171 (1976); (b) J. Danon, S. V. Filseth, D. Feldmann, H. Zacharias, C. H. Dugan, and K. H. Welge, Chem. Phys., 29, 345 (1978). (35) J. A. Kerr, B. V. O'Grady, and A. F. Trotman-Dickenson, J . Chem. SOC.A , 275 (1969). (36) (a) 8.0. Ross and P. M. Siegbahm, J. Am. Chem. Soc., 99, 7716 (1977); (b) R. R. Lucchese and H. F. Schaefer, 111, ibid., 99, 6766 (1977); (c) L. B. Harding and W. A. Goddard, 111, J . Chem. Phys., 67, 1776 (1977). (37) (a) S. E. Stein and B. S.Rabinovtch, J. Phys. Chem., 79, 191 (1975); (b) E. W. Hardwidge, B. S.Rabinovitch, and R. C. Ireton, J. Chem. Phys., 58, 340 (1973). (38) D. F. McMillen, D. M. Golden, and S.W. Benson, Jnt. J. Chem. Kinet., 4, 487 (1972). (39) S.W. Benson, "Thermochemical Klnetics", Wiley, New York, N.Y., 1966. (40) R. M. Joshi, J. Macromol. Sei.-Chem., AB, 595 (1972).
Energy Disposal by the Four-Centered Unimolecular Hydrogen Chloride Elimination Reaction B. E. Holmes" and D. W. Setser Department of Chemistry, Kansas State University, Manhattan, Kansas 66506 (Received April 17, 1978)
The vibrational energy partitioned to 1-and 3-methylcyclobutene by the four-centered HC1 elimination reactions from 1-,2-, and 3-methylchlorocyclobutanes has been investigated by the sequential unimolecular reaction technique. The chemically activated methylchlorocyclobutanes were prepared with 110 kcal mol-' of internal energy by the insertion reaction of singlet methylene into the C-H bonds of chlorocyclobutane. The elimination reactions give 1-and 3-methylcyclobutenewith enough energy to undergo the cyclobutene-butadiene isomerization reaction. The magnitude and pressure dependence of the rate constants for isomerization of 1- and 3methylcyclobutene to 2-methyl-1,3-butadieneand 1,3-pentadiene, respectively, were measured. Matching model calculations to the experimental rate constants gave an assignment of the vibrational energy retained by the methylcyclobutenes. The available energy was divided into statistical and potential energy components in the model calculations. The former is the excess energy above the threshold, (E) - Eo,for HC1 elimination. A Gaussian distribution, which could be altered in both position and width, was used to represent the potential energy. The calculated best fit for both 1-and 3-methylcyclobutene was for an energy distribution that gave (fv (olefin)) = 0.60. This total energy corresponds to 32% of the potential energy plus the statistical component, which is 80% of the excess energy. The effects of cascade collisional deactivation and formation of methylcyclobutene with excess translational energy upon the matching of the experimental and calculated rate constants are discussed. N
Introduction For only a few unimolecular processes has the energy disposal been well characterized.1 When available, such data provide insight into dynamical features and potential *Address correspondence to this author at the Department of Chemistry, Ohio Northern University, Ada, Ohio 45810. 0022-3654/78/2082-2461$01 .OO/O
energy surface for the latter stages of the unimolecular reaction.2 Although the four-centered unimolecular HX elimination reactions have been extensively in~estigated,~ the energy disposal pattern is not completely understood. Translational energy distributions have been determined for the dehydrohalogenation from alkyl halide ions4 and the hydrogen halide vibrational distributions have been 0 1978 American
Chemical Society
