Pressure and temperature dependence of the gas ... - ACS Publications

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4184

J. Phys. Chem. 1988, 92, 4184-4190

a direct consequence of the fact that both C-H bond lengths are also very similar. For insight into the description of the electronic structure of the transition state, Figure 5 presents the spin density map. Obviously, in the reactants the spin density differs from zero only on triplet methylene, since ethylene is a closed-shell molecule. Figure 5 shows that the a spin density of triplet methylene has been delocalized over the whole system at the transition state. In ethylene the a spin density is concentrated on the carbon atom that is closest to methylene. Another interesting fact is the existence of a noticeable @ spin density at the hydrogen atom that is being transferred. This is due to an important phenomenon of spin polarization in the linear fragment C-H-C. Let us now compare the results obtained for the two studied processes. Undoubtedly, the most important difference between them lies in the values of the energy barriers. Thus, the energy barrier for the insertion reaction of singlet methylene is much smaller than the one corresponding to hydrogen abstraction by triplet methylene. This occurs at all levels of calculation considered by us. At the MP3/6-31G*//3-21G level, for instance, the hydrogen abstraction by triplet methylene requires a barrier of 24.4 kcal/mol while no energy barrier is found for the insertion reaction of singlet methylene. In fact this great difference between both energy barriers mainly arises from the energy gap between singlet and triplet methylene, this gap being 18.5 kcal/mol at the MP3/6-31G*//3-21G level of calculation. Regarding, the mechanism, it is generally accepted that the insertion of singlet methylene takes place in one step via formation of a cyclic tricentric bond, while triplet methylene abstracts one hydrogen atom in a first step, the subsequent formation of a C-C bond between the two generated radicals requiring a previous intersystem crossing. Our results seem to indicate that both processes are not very different at the beginning, since the structure of the transition state for the insertion of singlet methylene does not present such a cyclic tricentric bond, and the main component of the transition vector corresponds to the transfer of one hydrogen atom from ethylene to methylene. Finally, another aspect that is interesting to discuss is the competition between the studied processes and the addition of singlet and triplet methylene to the ethylenic double bond. It is well-known that the insertion of singlet methylene into vinylic C-H

bonds can compete with the addition process, although the latter is f a ~ t e r . ~On , ~the ~ contrary, the hydrogen abstraction by triplet methylene is never observed when addition to a double bond is also possible.50 All these facts can be understood if one compares the energy barriers obtained in this work with those previously calculated for the addition of ~ i n g l e t ~and l . ~triplet4* ~ methylene to ethylene. Thus, the competition in the case of singlet methylene can be explained by the facts that no energy barrier is found for the addition process at all levels of calculation and the same occurs for insertion when electron correlation is introduced. On the contrary, the addition of triplet methylene has a much smaller energy barrier than the one corresponding to the hydrogen abstraction process. For instance, the energy barriers are 11.2 and 25.7 kcal/mol, respectively, at the MP2/3-21G//3-21G level of calculation. This large difference is the responsible for the fact that the hydrogen abstraction reaction is not observed when addition to a double bond is possible. In conclusion, we believe that this work has permitted us to gain insight into the different reactivity patterns that present singlet and triplet methylene when they react in front of a vinylic double bond. In the first stage both processes imply the transfer of a hydrogen atom from ethylene to methylene, this transfer being already important at the transition state. Given this similarity between the structures of both transition states, the difference in the energy barriers mainly arises from the energy gap between singlet and triplet methylene. Finally, the results obtained in this work have also permitted us to understand the different competitivity of the two studied processes when compared with the well-known addition reactions to olefinic double bonds.

Acknowledgment. This work has been supported by the U. S.-Spain Joint Committee for Scientific and Technological Cooperation under Contract No. CCB-8509/016. Registry No. Methylene, 2465-56-7;ethylene, 74-85-1, (49) Tomioka, H.; Tabayashi, K.; Ozaki, Y.; Izawa, Y . Tetrahedron 1985, 41, 1435. (50) Ring, D. F.; Rabinovitch, B. S. Can. J . Chem. 1968, 46, 2435. (51) Zurawski, B.; Kutzelnigg, W. J . Am. Chem. SOC.1978, ZOO, 2654. (52) Rondan, N. G.; Houk, K. N.; Moss, R. A. J . Am. Chem. SOC.1980, 102, 1770.

Pressure and Temperature Dependence of the Gas-Phase Recombination of Hydroxyl Radicals R. Zellner,* F. Ewig, R. Paschke, and G. Wagner Institut fur Physikalische Chemie, Universitat Gottingen, Tammannstrasse 6, 3400 Gottingen, FRG (Received: August 28, 1987)

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Rate constants for the reaction OH + OH + M H202+ M (M = N2,H20) have been determined by using flash photolysis of H 2 0vapor in combination with quantitative OH resonance spectrometry. For M = N2 experiments were performed at 253,298, and 353 K and at pressures between 26 and 1100 mbar. Under these conditions the reaction is found to be primarily in the low-pressure limit with kl,N: ( T = 298 K) = (6.9!;,$) X low3'cm6/s and a temperature dependence of p , *Both . the absolute value of kl,N: and its temperature variation are in very satisfactory agreement with theoretical predictions and extrapolations from high-temperaturedissociation data. A pressure falloff of kl,Nzis also observed. On the basis of a theoretical analysis of the falloff behavior, a high-pressure limiting rate coefficient of k," = 1.5 X lo-" cm3/s, independent of temperature, is predicted. From experiments in N2/H20mixtures with xHZo= 0.11 at pressures up to 140 mbar a low-pressure limiting X rate coefficient for H 2 0 as a third body of kl,H200( T = 298 K) = (40.);: cm6/s is obtained.

I. Introduction Due to their importance in the chemistry of combustion proCeSSeS and in the atmosphere, reactions of O H radicals have received considerable attention. The range of interest covers the temperature region from around 250 K up to 2000 K and the 0022-3654/88/2092-4184$01.50/0

pressure scale from a few millibars to 1 bar. Although considerable progress has been made in recent years in measuring the rate coefficients for bimolecular reactions of the O H radical, comparatively little work has been devoted to a study of the -"t 1eCUlar process 0 1988 American Chemical Society

Gas-Phase Recombination of Hydroxyl Radicals

+ O H (+M)

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The Journal of Physical Chemistry, Vol. 92, No. 14, 1988 4185

= -215 kJ/mol (1) This recombination of OH radicals is in competition with the corresponding disproportionation, viz. OH O H H 2 0+ 0 AH, = -71 kJ/mol (2) OH

+

H202

(+M)

AHR

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In fact reaction 2 is sufficiently exothermic to create a dominantly bimolecular flux and hence to suppress recombination provided both reactions occurred via a common intermediate on the same electronic potential surface. This, however, is not the case since the interaction of two OH(21T) radicals gives rise to both singlet and triplet surfaces which keep the product channels (1) and (2) separated. Despite their molecular separation, reactions 1 and 2 always occur simultaneously, and formidable difficulties arise in their experimental isolation. Whereas this has been achieved for reaction 2 by use of low-pressure studies’” or corresponding ext r a p o l a t i o n ~ the , ~ ~same ~ is not the case for reaction 2. The recombination of OH radicals was first studied by Black and Porter9 using absorption spectrometry in the flash photolysis of H20vapor and up to 1 bar of various third bodies. In similar flash mixtures Caldwell and Backio subsequently monitored the yields of H2 and O2and obtained estimates for the relative rates of reactions 1 and 2. Together with the relative third-body efficiencies as determined by Black and Porter9 and the absolute value of k2 as obtained by Del Greco and Kaufman,’ this provided the first indirect information on the rate coefficient kl. The only direct study of reaction 1 was performed by Trainor and von Rosenberg’ using flash photolysis in combination with quantitative line spectrometry. From measurements in up to 520 mbar of N 2 these authors obtained a rate coefficient in the low-pressure limit of kI0(M = N2) = (2.5 0.3) X cm6/s; a pressure falloff, however, was not observed. The present work is both a refinement and extension of the work of ref 7 using essentially the same experimental technique. Moreover, since we have observed the falloff behavior of reaction 1, our data are being analyzed in terms of current unimolecular rate theory. A comparison with high-temperature dissociation data is also provided.

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11. Experimental Section The reaction has been studied by using a conventional flash photolysis technique to generate OH in a mixture of N 2 / H 2 0 ( H 2 0 hv (A d 185 nm) OH(211) H(2S)) and by observing the time-resolved decay of OH using quantitative resonance absorption in the rotational lines of the A2Z+-X211-(0,0)-band transition. The technique has been described fully,8~’i~12 and only the main features and necessary modifications will be briefly mentioned. The Spectrosil quartz reaction cell (length, 600 mm; inner diameter, 36 mm) and the flash lamp are of annular arrangement. Both together are surrounded by a third tube through which oil-either from a cryostat or from a thermostat-can be circulated. The accessible temperature range is 250-400 K. The end windows of the reaction cell are placed well inside the thermostated and flash-illuminated region at a mutual distance (equal to the absorption path length) of 370 mm. This arrangement not only ensures a homogeneous temperature profile along the reactor, it

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+

(1) Del Greco, F. P.; Kaufman, F. Discuss. Faraday SOC.1962, 33, 128. (2) Dixon-Lewis, G.; Wilson, W. E.; Westenberg, A. A. J . Chem. Phys. 1966, 44, 2877. (3) Breen, J. E.; Glass, J. P. J . Chem. Phys. 1970, 52, 1082. (4) Westenberg, A. A.; de Haas, N. J . Chem. Phys. 1973, 58, 4006. (5) McKenzie, A,; Mulcahy, M. F. R.; Steven, J. R. J. Chem. Phys. 1973, 59, 3244. (6) Clyne, M. A. A,; Down, S. J . Chem. Soc., Faraday Trans. 2 1974, 70, 253. (7) Trainor, D. W.; von Rosenberg, C. W. J . Chem. Phys. 1974,61, 1010. (8) Wagner, G.; Zellner, R. Eer. Bunsen-Ges. Phys. Chem. 1981,85, 1122. (9) Black, G.; Porter, G. Proc. R . Soc. London, A 1962, 266, 185. (10) Caldwell, J.; Back, R. A. Trans. Faraday Soc. 1965, 61, 1939. (11) Zellner, R.; Steinert, W.; Int. J . Chem. Kine?. 1976, 8, 397. (12) Handwerk, V.;Zellner, R. Eer. Bunsen-Ges. Phys. Chem. 1978, 82, 1161.

0.4

0.2p IO

0.5

LO

1.5

2.0

IOHI /cm” Figure 1. Calculated line absorption intensity as a function of OH concentration ( T = 300 K, 1 = 37 cm, Q14 line) for (i) pure Doppler line shape (a = 0) and (ii) combined Doppler- and pressure-broadened lines ( a = 1). The line oscillator strength is taken as 5.2. X lo4; the emitter temperature is assumed to be 650 K.” In each case the dotted line represents the small absorption limit. 3

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TABLE I: Effective Absorption Coefficients of the Q14 Line of the X2n,Y” = 0 Transition of OH for Pure Doppler A2E+, Y’ = 0 .. Profile (eD) and Corresponding Pressure Corrections f(P)

plmbar

0 130 260 390 520 650 780 910 1040 cD/cm2

253 K

298 K

353 K

1.0 0.94 0.83 0.74 0.67 0.66 0.62 0.59 0.57

1 .o 0.95 0.85 0.76 0.69 0.67 0.63 0.60 0.58

1.O 0.95 0.86 0.78 0.72 0.69 0.65 0.62 0.60

9.49 X lo-’’

1.06 X

1.12 X

also avoids larger axial concentration gradients of O H which cannot be accepted in second-order kinetics. The detection of O H is along the axial direction. Moreover, due to the short absorption path length relatively high O H concentrations (>loi4 ~ m - can ~) be used without creating undue large and nonlinear absorptions.8 In experiments with N2 as a third body the H 2 0partial pressure was between 0.5 and 0.8 mbar for all pressures up to 1100 mbar. In experiments to determine the rate coefficient for recombination with H 2 0 as a third body, mixtures of N 2 and H 2 0 with a mole fraction of xH,o = 0.11 at total pressures up to 140 mbar were used. Effective OH Absorption Coefficients for Combined Temperature- and Pressure-Broadened Lines. In order to analyze absorption vs time profiles in second-order kinetics, absolute OH concentrations have to be known. These can be obtained from the observed absorptions by using quantitative line absorption spectrometry. According to theoryI3J4the absorption ( A ) resulting from a resonance transition (A2Z+,u f = 0, J’+ X2n, u“ = 0, J”) of the O H radical will be given by

where:Z is the line intensity distribution of the light source, eo is the absorption coefficient in the center of a Doppler-broadened line eo = ((ln 2 ) / ~ ) i i 2 ( 2 . n e 2 / m c A v ~ J X ,J,,) (2J” + 1) eXp(-EJ,