Effects of Ring Strain on Gas-Phase Rate Constants. I. Ozone Reactions with

Cycloalkenes

ROGER ATKINSON,* SARA M. ASCHMANN, WILLIAM P. L. CARTER, and JAMES N. PITTS, JR.

Statewide Air Pollution Research Center, University of California, Riverside, California 92521, U.S.A

Abstract

Rate constants for the gas-phase reactions of 0 3 with a series of cycloalkenes and with cis-2-butene have been determined at 297 f 1 K. The rate constants obtained were (in units of cm3/molecule-s): cis-2-butene, 1.38 f 0.16; cyclopentene, 2.75 f 0.33; cyclohexene, 1.04 f 0.14; cycloheptene, 3.19 f 0.36; 1,3-cyclohexadiene, 19.7 f 2.8; 1,4-cyclohexadiene, 0.639 f 0.074; bicyclo]2.2.1]-2-heptene, 21.4 f 3.5; bicyclo[2.2.1]-2,5-heptadiene, 46.8 f 12.9; and bicyclo[2.2.2]-2-octene, 0.728 f 0.090. These data for cis-2-butene, cyclopentene, and cyclohexene are compared with previous literature data, and the effects of ring strain on the rate constants are discussed.

Introduction

The development and use of a priori predictive techniques for the esti- mation of rate constants for the reactions of ozone and hydroxyl radicals with organics has received much attention as a means of cost-effectively assessing the lifetimes of organics emitted into the atmosphere [l-61. However, the development of such estimation techniques depends on the existence of an accurate kinetic data base for a wide variety of organic classes and structures.

While data are available for the reactions of 0 3 and OH radicals with several classes of organics [1,7,8], the effects of ring strain on these reaction rate constants in cyclic and polycyclic organics have received little attention to date. In a recent study of the reactions of OH radicals with a series of cyclic and polycyclic alkanes, where the reactions proceed via H-atom ab- straction, it was observed [9] that ring strain energies in excess of -5 kcal/mol led to a decrease in the rate constants relative to those expected for the strainfree molecules. For the addition reactions of 0 3 and OH

* Author to whom correspondence should he addressed.

International Journal of Chemical Kinetics, Vol. 15,721-731 (1983) 0 1983 John Wiley & Sons, Inc. CCC 0538-8066/83/080721-11$02.10

122 ATKINSON ET AL.

radicals, however, data are available only for a small number of cycloalkenes [7,8]. The limited data for OH radical addition reactions all concern six- membered low-strain rings [7], and no conclusions can yet be drawn as to the effect of ring strain on these reactions. For O3 reactions, where rate constants have been reported for cyclopentene [10,11], cyclohexene [10,11], and a series of monoterpenes [El , the observation that the room temper- ature rate constant for cyclopentene is a factor of -5 higher that that for cyclohexene [10,11] is the sole evidence indicating that ring strain enhances O3 reaction rates.

In this work, as part of a larger investigation into structural effects on O3 and OH radical reactions, rate constants have been determined for the reaction of O3 with a series of cyclic alkenes at 297 f 1 K.

Experimental

The experimental technique has been described in detail previously [13,14], and hence only the relevant details are given here. The O3 reaction rate constants were determined by monitoring the increased rates of ozone decay in the presence of known excess concentrations of the alkenes. In the presence of an alkene, the processes removing 0 3 are:

(1)

(2)

and hence

O3 + wall - loss of O3

0 3 + alkene - products

~- -d[031 - (kl + k.Jalkene])[O3] dt

where kl and kz are the rate constants for reactions (1) and (2), respectively. With the alkene concentrations being in excess of the initial O3 concen- trations ( [alkene]/[03]initial being always 24, and generally L lo), the reactant concentration remains approximately constant throughout the reaction, and eq. (I) may be rearranged to yield

-d = Izl + kz[alkene] dt

Thus from the dependence of the ozone decay rate -d 1n[O3]/dt on the alkene concentration, and with a knowledge of k 1, the background ozone decay rate, the rate constant k2 may be readily obtained.

As described previously [13,14], reactions were carried out in a -175-L Teflon bag constructed out of a 2-mil-thick, 180 X 140-cm FEP Teflon sheet, heat-sealed around the edges, and fitted with Teflon injection and sampling ports a t each end of the reaction bag. The reaction bag was ini- tially divided into two subchambers with 0 3 being injected into one sub-

RING STRAIN AND GAS-PHASE CONSTANTS 723

chamber and the alkene into the other, with ultrahigh purity air as the diluent gas. The reactions were initiated by removing the bag divider and rapidly mixing the contents by pushing down on alternate sides of the entire bag for -30 s. Initial 0 3 concentrations after mixing were in the range of (0.12-1.2) X 1013 molecules/cm3, and the 0 3 concentrations were monitored as a function of time, after mixing of the reactants, by a Monitor Labs model 8410 chemiluminescence ozone analyzer.

Background ozone decay rates in the absence of the alkenes were de- termined periodically during these rate constant determinations, and were in the range of (0.5-1.8) X s-l. These background 0 3 decay rates were totally negligible compared to the decay rates observed in the presence of the alkenes. The alkene concentrations in the entire reaction bag were quantitatively monitored during and/or after the reaction was complete by gas chromatography with flame ionization detection using a 20-ft X l/&in. stainless-steel column of 5% DC703/C20M on 100/120 mesh AW, DMCS Chromosorb G, operated a t 333 K. The alkenes used were of stated purity levels of >98%, and gas chromatographic analyses showed no observable impurities. All rate constant determinations were carried out a t 297 f 1 K and -735 torr total pressure.

Results

Ozone decays were determined in the presence of known concentrations of the alkenes cis -2-butene, cyclopentene, cyclohexene, cycloheptene, 1,3-cyclohexadiene, 1,4-cyclohexadiene, bicyclo[2.2.1]-2-heptene, bicy-

- - 'i CIS-2- BUTENE

[ALKENE] molecule ~ r n - ~

Figure 1. cyclohexene, and 1,4-cyclohexadiene.

Plot of the ozone decay rates against the alkene concentrrtion for cis-2-butene,

724 ATKINSON ET AL.

P/ B I C Y C L O ~ Z z Z ~ - Z - O C T E N E

0 0.5 1.0 1.5 2.0 2.5 3 . 0 ~ 1 0 ' ~

[ALKENE] molecule ~ r n - ~

Figure 2. pentene, cycloheptene, and bicyclo[2.2.2]-2-octene.

Plot of the ozone decay rates against the cycloalkene concentrations for cyclo-

clo[2.2.1] -2,5-heptadiene, and bicyclo[2.2.2] -2-octene. In all cases plots of ln([0~]~, / [0&) against time ( t - t o ) were linear, indicating exponential ozone decays. (Here [O&, and [O& are the 0 3 concentrations at times t o and t , t o being the time after mixing of the reactants was complete.) Plots of the ozone decay rates against the alkene concentrations are shown in Figures 1-3 for the alkenes studied. The larger scatter in the plots given in Figure 3 is due to the fact that for the cycloalkenes 1,3-cyclohexadiene, bicyclo[2.2.1]-2-heptene, and bicyclo[2.2.1]-2,5-heptadiene the decay rates

0'25 r BICYCLO[ 2 . 2 . I] -2,5-HEPTADIENE

[ALKENE] molecule cm-3

Figure 3. clohexadiene, bicyclo[2.2.1]-2-heptene, and bicyclo[2.2.1] -2,5-heptadiene.

Plot of the ozone decay rates against the cycloalkene concentrations for 1,3-cy-

RING STRAIN AN11 GAS-PHASE CONSTANTS 725

TABLE I. K, together with room temperature literature data.

Rate constants k2 for the reaction of 0 3 with a series of alkenes a t 297 f 1

10l6 x k2(crn 3 molecule-' sec-l)

Alkene T h i s Worka) Literature Values

cis-2-butene 1.38 i 0.16 0.49 [151; 3.32 [16]; 1.41 (171; 1.61 f 0.07 [lo]; 1.26 [I81

cyclopentene 2.75 f 0.33 8.13 f 0.79 1101; 9.69 (111

cyclohexene 1.04 f 0.14 0.59 [191; 1.69 ? 0.15 [lo]; 2.04 [ll]

cycloheptene 3.19 f 0.36

1,3-cyclohexadiene 19.7 5 2.8

1,4-~yclohexadiene 0.639 f 0.074

bicyclo[2.2.1]-2-heptene 21.4 lr 3.5

bicyclo[2.2.1]-2,5-heptadiene 46.8 f 12.9

bicyclo[2.2.2]-2-octene 0.728 f 0.090

a At 297 f 1 K. Indicated errors include two least-squares standard deviations of the slopes of the plots shown in Figures 1-3 together with a 10% estimated overall uncertainty in the alkene concentrations.

were rapid, being close to the limit of the experimental system, and the rate constant data obtained are subject to significant uncertainties. cis -2- Butene was included among the alkenes studied in order to validate the present experimental system since cis-2-butene has been the subject of numerous previous studies [10,15-181, and since the present rate constants for cyclohexene and cyclopentene are significantly lower than those ob- tained in other recent studies [10,11] (see Discussion).

Discussion

The rate constants k2 obtained by least-squares analyses of the plots of eq. (11) shown in Figures 1-3 are given in Table I together with the available literature data for cis-2-butene7 cyclopentene, and cyclohexene. (No data have been reported for the other cycloalkenes studied here.) It can be seen from Table I that the present rate constants for cyclopentene and cyclo- hexene are significantly lower, by factors of 1.6-3.5, than the recent values obtained by Japar et al. [lo] and Adeniji et al. [ l l ] using techniques similar to that used here. However, the present rate constant for cis-2-butene is in excellent agreement with the most recent values obtained by Japar et al. [lo], Cox and Penkett [17], and Huie and Herron [18]. Since the rate constant for cis-2-butene is of a magnitude similar to those for cyclohexene and cyclopentene, it thus does not appear likely that the present experi- mental technique leads to systematically low rate constants. Reasons for the discrepancies between the present work and that of Japar et al. [lo] and

726 ATKINSON E T AL.

TABLE 11. energies.

Rate constants k z ratioed to that for cis-2-butene, together with ring strain

Relative Strain Energybsc) Strain

Cycloalkene k 2 2 lk (cis-2-butene)a) (kcal mole-‘) Lkkcal mole-‘)

cyciopentene 2.0 f 0.3 -0.3 5.3

Cycloheptene 2.3 t 0.4 -0.8 5.3

Cyclohexene 0.75 f 0.14 1.5 1.4

1,3-Cyclohaxadiene 7.1 f 1.3 3.3e) 4 . 7 e )

1,4-Cyclohexadiene 0.23 t 0.04 -0.3 0.5 bicycla[2.2.1]-2-hept~”~ 16 f 3 6.0 15.8 bicyclo[2.2.11-2,5-heptadiene 17 ? 5 3.0 25.2 bicyclo[2.2.21-2-octene 0.53 f 0.03 0.8-2.2 10.3-11.7

__ a Per double bond, that is, the rate constants for the cyclohexadienes and bicyclo[2.2.1]-

2,5-heptadiene have been divided by a factor of 2. The indicated error limits are two standard deviations.

Ring strain energy difference between the cycloalkene and the corresponding hydrocarbon with one less double bond (see text).

The experimental heats of formation AH, (in kcal/mol) of the cycloalkenes and cycloal- kanes used were: cyclopentane, -18.46 [24]; cyclopentene, 8.56 [25]; cyclohexane, -29.43 [24]; cyclohexene, -0.84 [25]; cycloheptane, -28.41 [24]; cycloheptene, -1.8 [25]; 1,3-cyclo- hexadiene, 25.9 [23]; 1,4-cyclohexadiene, 26.3 [25]; bicyclo[2.2.l]heptane, -12.42 (26,271; bi- cyclo[2.2.1]-2-heptene, 21.4 [27], bicyclo[2.2.1]-2,5-heptadiene, 57.4 [27]; bicyclo[2.2.2]octane, -23.75 [26]; bicyclo[2.2.2]-2-octene, 4.9-6.3 [28-301. The strain energies were calculated from [AH,(experimental) - AH,(calculated)], the latter being calculated using the group addi- tivities of Benson [23].

Strain energy (SE) released in breakage of double bond. For bicyclic alkenes this is the difference between the strain energy for the bicycloalkene and the remaining cycloalkene or cycloalkane; that is, for bicyclo[2.2.1]-2-heptene, it is SE (bicyclo[2.2.1]-2-heptene) - SE (cyclopentane) j .

Since there is some resonance energy (-3.6 kcal/mol[23] included in the observed ring interaction energy, i.e., AH, ,,bs - AHf talc), this offsets the ring strain energy.

Adeniji et al. [ll] for cyclopentene and cyclohexene are thus unfortunately not known.

The variations in the 0 3 reaction rate constants observed for the cyclic and polycyclic alkenes studied here could be attributed to a number of factors, including entropy and steric effects as well as differences in the ring strain energies. In the absence of any knowledge of the temperature dependencies of these rate constants, an unambiguous determination of the relative importance of these effects is not possible at present. In the following discussion it is assumed that differences in the ring strain energies are the major factor in causing the variations in the room temperature rate constants measured in this work. The quality of the correlations obtained will indicate the extent to which this assumption is valid. cis-2-Butene serves as an unstrained “reference” alkene since all the double bonds in the cycloalkenes studied here are disubstituted with a cis conformation. Table I1 gives the ratios of the rate constants k 2 for the cycloalkenes studied, relative to that for cis -2-butene, along with two measurements of the ring

RING STRAIN AND GAS-PHASE CONSTANTS 727

strain energy of the cycloalkenes: (1) the strain energy released when the double bond is broken by the ozone reaction (this being, for the bicyclic alkenes, the total strain energy of the bicycloalkene minus that of the ring which remains after the double bond is broken), and (2) the ring strain energy difference between the cycloalkene and the corresponding hydro- carbon with one less double bond (the “relative” ring strain). The possible correlations of these thermochemical quantities with the ozone reaction rate constants are discussed below. (For the three dialkenes studied the observed rate constant ratios have been divided by a factor of 2 to obtain the rate constant ratios per double bond. This approach is supported by kinetic data for the reaction of OH radicals with dialkenes [20]. While this introduces some uncertainties into the rate constant ratios, it does not affect in any way the discussion and conclusions presented below.)

The gas phase reactions of 0 3 with alkenes [21,22] are believed to proceed via the initial formation of a highly energetic (-58 kcal/mol [all) 1,2,3- trioxide ring compound which rapidly decomposes via a concerted process to the aldehyde and a biradical. For example, for the reaction of bicyclo- [2.2.1]-2,5-heptadiene (I) with 0 3 , the overall process involves initial for- mation of the primary ozonide (II), with subsequent decomposition to (111):

(I\’) (V)

If the transition state determining the rate of the overall reaction is similar in structure to that of the primary ozonide (II), then the rate constant would be expected to correlate with the difference in the ring strain energy (SE) between the cycloalkene and the corresponding 1,2,3-trioxide ring structure, that is, SE(1) - SE(I1) for the example above. Since the strain energies of polycyclic ring compounds are approximately the sum of the strain energies of the individual rings [23], the difference between the ring strain in the primary ozonide (11) and that of the corresponding hydrocarbon (IV) should be approximately independent of the cycloalkene being studied. Thus the 0 3 rate constant may be expected to correlate with the “relative” strain energy [SE(I) - SE(1V) for the bicyclo[2.2.1]-2,5-heptadiene system above], which is tabulated for each cycloalkene in Table 11.

However, the possibility that the transition state which determines the overall ozone reaction rate constant in the gas phase may have the C-C

728 ATKINSON ET AX>.

t

I I I I I I 0 2 4 6 8 I0

0.1 1 -2

RELATIVE STRAIN ENERGY (kcol mole-1)

Figure 4. Plot of the rate constants 1 ; ~ per double bond, relative to that for cis-2-butene, against the relative strain energy (that is, the strain energy of the cycloalkene minus that of the corresponding cycloalkane or cycloalkene with one less double bond).

bond in the primary ozonide nearly broken must also be considered. In this case, the rate constant would be expected to correlate with the differ- ence between the strain energy of the cycloalkene and the strain energy (if any rings remain) of the species formed after the double bond is broken. For monocycloalkenes this quantity is the total strain energy of the monocycloalkene, while for bicycloalkenes, this quantity is the strain energy of the ring being opened [SE(I) - SE(V) for the example above]. These quantities are also tabulated in Table 111.

Figure 4 shows a plot of the rate constants k2 per double bond for the cycloalkenes studied, relative to that for cis-2-butene, against the relative strain energy, and Figure 5 shows a similar plot of the rate constants per double bond against the strain energy released when the double bond in the cycloalkene is broken. It can be seen from Figure 5 that in the latter case the rate constant for 1,3-cyclohexadiene is considerably higher, and that for bicyclo[2.2.2] -2-octene is considerably lower, than the other data would predict. For 1,3-~yclohexadiene this discrepancy could possibly be attributed to some effect of ring conjunction, though it should be noted that the rate constants for the reactions of 0 3 with 1,3-butadiene [10,31,32] and

RING STRAIN AND GAS-PHASE CONSTANTS 729

/ /

/ 10-

0 / /

/ 5 -

/ /

o /

/ 2 - O /

/ 1: / 143 c

,N 0.5

1

0

/ ' 0

0. I , 0 5 10 15 20 25 30

STRAIN ENERGY (kcol mole-')

Figure 5. Plot of the rate constants k z per double bond, relative to that for cis-2-butene, against the strain energy released when the C-C double bond in the cycloalkene is broken.

isoprene [11,33,34] are lower than may be expected based on the rate con- stant data for other monoalkenes. The discrepancy for bicyclo[2.2.2] -2- octene is more difficult to rationalize, though steric effects hindering ozone attack may be larger in this cycloalkene than in the other cycloalkenes studied. In general, however, the present data do not convincingly dem- onstrate the existence of a significant correlation between ozone reaction rate constants and the total strain energy of the ring being broken.

On the other hand, it can be seen from Figure 4 that although the points are highly scattered, there indeed appears to be a general correlation be- tween the rate constant per double bond and the relative strain energy, with much of the observed scatter of Figure 4 being attributed to the f2-3- kcal/mol uncertainties in the relative ring strain energies. This suggests that the transition state which determines the overall rate constant is probably closer to the 1,2,3-trioxide ring intermediate than to the aldehyde + biradical species subsequently formed, which is as expected for these systems. Additional data, preferably with more strained alkenes and in- cluding the temperature dependencies of the rate constants, are required for the most useful correlation to be more unambiguously established.

730 ATKINSON ET AL.

Acknowledgment

This work was supported by the U.S. Environmental Protection Agency under Cooperative Agreement CR809247-01. Although the research de- scribed in this article has been funded by the Environmental Protection Agency, it has not been subjected to agency review and therefore does not necessarily reflect the views of the agency and no official endorsement should be inferred.

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Received September 28,1982 Accepted February 16,1983