J. Phys. Chem. A 1999, 103, 7017-7025
7017
Kinetic Study of OH + OH and OD + OD Reactions Y. Bedjanian,* G. Le Bras, and G. Poulet Laboratoire de Combustion et Syste` mes Re´ actifs, CNRS and UniVersite´ d’Orle´ ans, 45071 Orle´ ans Cedex 2, France ReceiVed: April 6, 1999; In Final Form: June 14, 1999
The kinetics of the disproportionation reactions of OH and OD radicals, OH + OH f O + H2O (1), OD + OD f O + D2O (3), have been studied by the mass spectrometric discharge-flow method at temperatures between 233 and 360 K and at total pressure of 1 Torr of helium. The following Arrhenius expressions were obtained: k1 ) (7.1 ( 1.0) × 10-13exp[(210 ( 40)/T] and k3 ) (2.5 ( 0.5) × 10-13exp[(170 ( 60)/T] cm3 molecule-1 s-1. Reaction 4 between OH and OD radicals was also investigated and the same rate constant as for reaction 1 was measured. Both the observed temperature dependence of k1 and the measured kinetic isotopic effect (k1/k3) are compatible with the mechanism proposed in a previous theoretical study (Harding, L. B.; Wagner, A. F. 22nd International Symposium on Combustion, 1988). In addition, a temperatureindependent rate coefficient of (1.20 ( 0.25) × 10-10 cm3 molecule-1 s-1 was measured for the reaction D + NO2 f OD + NO in the temperature range 230-365 K.
Introduction OH radicals are important intermediate species in gas-phase combustion and atmospheric processes. It is not surprising that the kinetics of OH reactions have been studied very extensively in the past. For example, there are about 800 reactions of OH compiled in the NIST data base.1 The disproportionation reaction of OH radicals has been also studied in many laboratories:2-18
OH + OH f O + H2O
(1)
OH + OH (+M) f H2O2 (+M)
(1′)
The kinetics of these reactions have been investigated at high temperature (T ) 1050-2380 K)2-4 and at room temperature,5-13 and a temperature dependence study14 has been carried out at T ) 250-580 K. The pressure dependence of the rate constant of the reaction, which possesses one pressure-dependent channel (reaction 1′), has been also investigated.12,15-18 Besides, the temperature dependence of the rate constant of reaction 1 calculated in an ab initio study19 is in good agreement with all experimental data between 300 and 2000 K. However, some uncertainties still remain. First, the value of k1 even at room temperature lies between 1.4 × 10-12 and 2.3 × 10-12 cm3 molecule-1 s-1 (e.g., ref 20). Second, the temperature dependence of the rate constant in the low-temperature range has been measured in only one study.14 Such uncertainties are revealed by recent compilations of kinetic data for atmospheric chemistry,20,21 which propose different recommendations for the temperature dependence of k1: E/R ) (240 ( 240) K,20 based on the results of ref 14 and a negative temperature dependence of k1 (at low temperatures)21 based on the theoretical calculations.19 Accurate kinetic information on reaction 1 at high temperatures is important for modeling of combustion processes, where high OH concentrations may make this reaction significant. Although the OH + OH reaction is negligible in atmospheric processes (because of the low OH concentrations), lowtemperature data are important for laboratory studies of OH
reactions of atmospheric relevance. For example, the present study has been triggered by that of the reaction of OH with BrO radicals:
OH + BrO f HO2 + Br
(2a)
f HBr + O2
(2b)
The potential occurrence of channel 2b is of great importance for the stratospheric bromine partitioning.22,23 Hence, the experimental determination of the branching ratio for channel 2b is required. From the unique study of reaction 2,24 and considering that the branching ratio of channel 2b is likely to be as low as a few percentages, it appears that one cannot neglect the side and secondary processes involved in the reactive system used to produce OH and BrO radicals. Thus, accurate kinetic data for all these reactions are needed. In a preliminary study,25 the kinetic parameters for the reactions of OH and OD with Br2 have been measured. In the present paper, the temperature dependence of the OH disproportionation reaction has been measured at low pressure:
OH + OH f O + H2O
∆H ) -16.8 kcal mol-1 (1)
Unless specified, the heats of formation of species used are from ref 20. The isotopic substitution is known to be adapted in kinetic studies, especially for the determination of reaction products. Isotopic labeling experiments have been performed in a recent study of the OH and OD + ClO reactions26 for the determination of the branching ratio of the minor HCl- or DCl-forming channel. In relation with these OD reactions, reaction 3 has been also investigated:
OD + OD f O + D2O
∆H ) -17.5 kcal mol-1 (3)
(The heats of formation for deuterium-containing species are from ref 27.)
10.1021/jp991146r CCC: $18.00 © 1999 American Chemical Society Published on Web 08/18/1999
7018 J. Phys. Chem. A, Vol. 103, No. 35, 1999
Bedjanian et al.
Figure 1. Diagram of the apparatus used.
Only one kinetic determination at room temperature is available for this reaction.28 In fact, the kinetic database for reactions of isotopically substituted species is rather scarce. Finally, to provide a complete data set the cross-reaction between OH and OD radicals has been also studied:
OH + OD f O + HDO
∆H ) -17.1 kcal mol-1 (4)
OH + Br2 f Br + HOBr
(7)
k7 ) (1.8 ( 0.3) × 10-11exp[(235 ( 50)/T] cm3 molecule-1 s-1 (ref 25) k7 ) (1.97 ( 0.32) × 10-11exp[(240 ( 62)/T] cm3 molecule-1 s-1 (ref 29) OD + Br2 f Br + DOBr
In addition, kinetic data for the reaction of D atoms with NO2, used as a source of OD radicals, have been obtained for the first time:
D + NO2 f OD + NO
∆H ) -30.6 kcal mol-1 (5)
Experimental Section Experiments were carried out in a discharge flow reactor using a modulated molecular beam mass spectrometer as a detection method. The main reactor, shown in Figure 1 along with the movable injector for the reactants, consisted of a Pyrex tube (45 cm length and 2.4 cm i.d.) with a jacket for the thermostated liquid circulation (water or ethanol). The walls of the reactor as well as of the injector were coated with halocarbon wax to minimize the heterogeneous loss of active species. All experiments were conducted at 1 Torr total pressure, with helium being used as the carrier gas. The fast reaction of hydrogen atoms with NO2 was used as a source of OH radicals, H atoms being produced in a microwave discharge of H2/He mixture:
H + NO2 f OH + NO -11
k6 ) 4.0 × 10
3
exp(-340/T)cm molecule
s
(ref 20)
Similarly, the reaction of D atoms with NO2 was used to produce OD radicals:
D + NO2 f OD + NO
k8 ) (1.9 ( 0.2) × 10-11exp[(220 ( 25)/T] cm3 molecule-1 s-1 (ref 25) This method of OH and OD detection was preferred to the direct detection of these radicals at m/e ) 17 (OH+) and m/e ) 18 (OD+) because of significant contributions of traces of water vapor. The same procedure of OH(OD) chemical conversion to HOBr(DOBr) was used for the measurements of the absolute radical concentrations: [OH] ) [HOBr] ) ∆[Br2] (or [OD] ) [DOBr] ) ∆[Br2]). Thus, OH(OD) concentrations were determined from the consumed fraction of [Br2]. [Br2] was determined from the flow rate of known Br2/He mixtures. The method used for this HOBr(DOBr) detection and their absolute calibrations requires that secondary reactions be negligible. For example, in the case of OH radicals, possible secondary reactions following reaction 7 are:
OH + HOBr f products
(5)
k5 ) (1.20 ( 0.25) × 10-11 cm3 molecule-1 s-1 (T ) 230-365 K) (this study) NO2 was always used in excess over H and D atoms. OH and OD radicals were detected as HOBr+(m/e ) 96/98) and DOBr+(m/e ) 97/99) respectively, after scavenging by an excess of Br2 (added at the end of the reactor through inlet 4, located 5 cm upstream of the sampling cone) via reactions 7 and 8, respectively:
(9)
OH + Br f O + HBr ∆H ) 14.9 kcal mol-1 -1
(10a)
f H + BrO ∆H ) 44.7 kcal mol
(10b)
f HOBr (+M) ∆H ) -50 kcal mol-1
(10c)
Br + HOBr f OH + Br2
(6) -1 -1
(8)
(11a) ∆H ) (4.0 ( 2.0) kcal mol-1
f BrO + HBr
(11b) ∆H ) (4.2 ( 3.4) kcal mol-1
(The heat of formation of BrO radicals, ∆Hf(BrO) ) (28.6 ( 1.4) kcal mol-1, is from ref 30.) It has been shown that reaction 9 is slow, the upper limit for the rate constant being: k9 e 5 × 10-13 cm3 molecule-1 s-1 (at T ) 300 K).31 Considering this value and the fact that OH is rapidly consumed in reaction 1 (at the high Br2 concentrations used), reaction 9 was negligible in the present experiments. The bimolecular channels of reaction 10 are too endothermic to proceed with a significant rate, and the association channel (10c) could also be considered as negligible at the low pressure (1 Torr) used. Finally, both channels of reaction 11 are endothermic and are likely of minor importance. The same conclusions apply for the case of OD radicals. Because relatively high concentrations of OH and OD were used in the calibration experiments, the O atoms produced in reactions 1 and 3 could react with Br2, and the possible
Kinetics of OH + OH and OD + OD Reactions
J. Phys. Chem. A, Vol. 103, No. 35, 1999 7019
O + NO2 f NO + O2
(14)
k14 ) 6.5 × 10-12exp(120/T) cm3 molecule-1 s-1 (ref 20)
Figure 2. Example of calibration curve for DOBr (see text): DOBr formed in the OD + Br2 reaction as a function of Br2 consumed (in relative units).
Under the typical conditions of the calibration experiments ([OH]max = 1013 molecules cm-3 and [NO2] = 5 × 1013 molecules cm-3), the steady-state concentration of O atoms was lower than 0.02 × [OH]. Therefore the contribution of O + Br2 reaction in the consumption of Br2 was negligible. The same conclusion can be driven for the OD calibration, because the O-forming reaction OD + OD has a rate constant around three times lower than that of the OH + OH reaction (this study). An example of calibration plot for [DOBr] is shown in Figure 2. The linear dependence observed for the signal of DOBr on the fraction of Br2 consumed in reaction 3 (∆[Br2] being changed by more than one order of magnitude) demonstrates the negligible role of secondary chemistry. The same procedure as above was used for the detection and measurements of the absolute concentrations of H and D atoms. Br2 was added at the end of the reactor (inlet 4) to convert H and D atoms into HBr and DBr, respectively via reactions 15 and 16:
H + Br2 f Br + HBr
(15)
k15 ) 6.7 × 10-10exp(-673/T) cm3 molecule-1 s-1 (ref 33) D + Br2 f Br + DBr
(16)
k16 ) 6.0 × 10-10exp(-709/T) cm3 molecule-1 s-1 (ref 33) Absolute concentrations of H and D atoms were determined as: [H] ) [HBr] ) ∆[Br2] or [D] ) [DBr] ) ∆[Br2]. The purities of the gases used were as follows: He > 99.9995% (Alphagaz), was passed through liquid nitrogen traps; H2 > 99.998% (Alphagaz); D2 > 99.7% (Alphagaz); Br2 > 99.99% (Aldrich); NO2 > 99% (Alphagaz). Results
Figure 3. Reaction OH + OH f O + H2O (1): example of experimental (points) and simulated (solid lines) decays of OH for different initial concentrations (T ) 299 K): [OH]0 ) 34.3 (9), 16.1 (b), 6.4 (+), and 0.34 ([) × 1012 molecules cm-3.
contribution of this O + Br2 reaction should be considered:
O + Br2 f BrO + Br
(12)
k12 ) 1.76 × 10-11exp(40/T) cm3 molecule-1 s-1 (ref 32) In fact, O atoms, formed in reaction 1 (in the case of OH + Br2 reaction) and consumed mainly in reactions with OH (13) and NO2 (14), reach steady-state concentration: [O]ss ) k1[OH]2/(k13[OH] + k14[NO2]):
O + OH f H + O2
(13)
k13 ) 2.2 × 10-11exp(120/T) cm3 molecule-1 s-1 (ref 20)
Reaction OH + OH f O + H2O. Reaction 1 was studied in the temperature range 233-360 K. OH radicals were produced directly in the main reactor through reaction 6, H atoms and NO2 being introduced through the movable inlet 1 and the fixed inlet 3, respectively. High initial concentrations of NO2 were used {[NO2]0 ) (3-20) × 1013 molecules cm-3}, leading to a fast disappearance of H atoms, as verified by the detection of HBr (Br2 being added at the end of the reactor: see previous section). OH decay kinetics were measured for different initial concentrations of the radicals. To derive the rate constant k1, these kinetic runs were simulated using a simplified two-step mechanism:
OH + OH f O + H2O
(1)
OH f loss
(17)
The possible secondary reaction 13 between O atoms and OH radicals did not contribute to the OH consumption, because the H atoms formed in this reaction were rapidly converted back to OH by the NO2 used in excess: [NO2] ) (2.5-5) × 1013 molecules cm-3. The rate of reaction 17 was measured directly in independent experiments using low initial concentrations of OH: [OH] ) (2-4) × 1011 molecules cm-3. After a small
7020 J. Phys. Chem. A, Vol. 103, No. 35, 1999
Bedjanian et al.
TABLE 1: Experimental Conditions and Results of the Reaction OH + OH f O + H2O (1) T ) 360 K
T ) 340 K
T ) 320 K
T ) 299 K
T ) 273 K
T ) 253 K
[OH]0a
k1b
[OH]0
k1
[OH]0
k1
[OH]0
k1
[OH]0
k1
[OH]0
k1
9.1 11.7 18.5 30.8 40.5 49.3 66.4
1.29 1.26 1.26 1.39 1.22 1.29 1.26
7.0 9.4 11.8 17.9 24.8 34.0 40.6 50.3
1.31 1.33 1.26 1.31 1.31 1.31 1.27 1.25
4.5 8.2 11.2 12.1 15.1 18.2 24.2 30.6 37.5
1.37 1.27 1.31 1.30 1.37 1.40 1.37 1.35 1.33
3.5 6.4 11.3 14.7 16.1 23.1 25.3 28.9 34.3
1.42 1.30 1.45 1.41 1.44 1.44 1.37 1.38 1.36
2.2 5.0 8.8 13.2 16.3 20.6 23.6 29.8
1.54 1.54 1.63 1.54 1.59 1.58 1.67 1.60
4.4 6.7 9.8 13.0 16.6 19.5 25.0 31.6
1.54 1.47 1.58 1.62 1.54 1.54 1.63 1.59
k1c ) 1.28 ( 0.18
k1 ) 1.29 ( 0.16
a
k1 ) 1.34 ( 0.17 -3
12
k1 ) 1.40 ( 0.19 -12
b
k1 ) 1.59 ( 0.21 3
-1
k1 ) 1.56 ( 0.21
T ) 233 K [OH]0
k1
2.9 1.77 5.2 1.53 8.2 1.78 9.5 1.60 12.1 1.74 14.8 1.67 17.8 1.88 20.7 1.75 24.6 1.84 33.7 1.77 37.4 1.76 k1 ) 1.74 ( 0.27
-1
Concentrations are in 10 molecule cm units. Rate constants are in 10 cm molecule s units. c Mean values of the rate constants in 10-12 cm3 molecule-1 s-1 units; the error is the statistical uncertainty with addition of 10% for systematic errors.
correction due to the contribution of reaction 1, the measured values of k17 were in the range 4-16 s-1 and increased with increasing [NO2] and decreasing temperature. Typical examples of experimental and simulated decays of OH are shown in Figure 3. All the conditions and results for the measurements of k1 are summarized in Table 1. The temperature dependence of k1 is shown in Figure 4. The Arrhenius expression for k1 derived from a least-squares fit to the experimental data is:
k1 ) (7.1 ( 1.0) × 10-13exp[(210 ( 40)/T] cm3 molecule-1 s-1 Quoted uncertainties represent two standard deviations. In the determination of k1, the rate of reaction 17 measured at low initial concentrations of OH was considered as constant for the entire range of [OH]0 used. In fact, reaction 17 is a combination of several processes: the heterogeneous OH loss, the reaction of OH with NO2 (18), and the possible secondary reaction between OH and HNO3 (19):
OH + NO2 (+M) f HNO3 (+M) -30
k18 ) 2.5 × 10
-4.4
(T/300)
(18) 6
-2 -1
cm molecule s (for M ) N2) (ref 20)
OH + HNO3 (+M) f H2O + NO3 (+M)
(19)
k19 ) 7.2 × 10-15exp(785/T) cm3 molecule-1 s-1 (ref 20) k19 is pressure dependent, and the expression given here is the low-pressure (bimolecular) limit of the rate constant.20 In the present study, k19 lies between 6.4 × 10-14 (T ) 360 K) and 2.1 × 10-13 cm3 molecule-1 s-1 (T ) 233 K). To estimate the contribution of reaction 19 in the OH loss rate, numerical simulations have been performed. It was observed that, even at the lowest temperature of this study (T ) 233 K), that is, for the maximum values of the rate constants of reactions 18 and 19, the contribution of reaction 19 to OH loss rate was negligible (
