Kinetics of Elementary Steps in the Reactions of Atomic Bromine with

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Kinetics of Elementary Steps in the Reactions of Atomic Bromine with Isoprene and 1,3-Butadiene under Atmospheric Conditions Patrick L. Laine,†,‡ Yoon S. Sohn,§ J. Michael Nicovich,∥ Michael L. McKee,⊥ and Paul H. Wine*,†,∥ †

School of Earth and Atmospheric Sciences, §School of Chemical and Biomolecular Engineering, and ∥School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332, United States ⊥ Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849, United States S Supporting Information *

ABSTRACT: Laser flash photolysis of CF2Br2 has been coupled with time-resolved detection of atomic bromine by resonance fluorescence spectroscopy to investigate the gasphase kinetics of early elementary steps in the Br-initiated oxidations of isoprene (2-methyl-1,3-butadiene, Iso) and 1,3butadiene (Bu) under atmospheric conditions. At T ≥ 526 K, measured rate coefficients for Br + isoprene are independent of pressure, suggesting that hydrogen transfer (1a) is the dominant reaction pathway. The following Arrhenius expression adequately describes all kinetic data at 526 K ≤ T ≤ 673 K: k1a(T) = (1.22 ± 0.57) × 10−11 exp[(−2100 ± 280)/T] cm3 molecule−1 s−1 (uncertainties are 2σ and represent precision of the Arrhenius parameters). At 271 K ≤ T ≤ 357 K, kinetic evidence for the reversible addition reactions Br + Iso ↔ Br−Iso (k1b, k−1b) and Br + Bu ↔ Br−Bu (k3b, k−3b) is observed. Analysis of the approach to equilibrium data allows the temperature- and pressure-dependent rate coefficients k1b, k−1b, k3b, and k−3b to be evaluated. At atmospheric pressure, addition of Br to each conjugated diene occurs with a near-gas-kinetic rate coefficient. Equilibrium constants for the addition/dissociation reactions are obtained from k1b/k−1b and k3b/k−3b, respectively. Combining the experimental equilibrium data with electronic structure calculations allows both second- and third-law analyses of thermochemistry to be carried out. The following thermochemical parameters for the addition reactions 1b and 3b at 0 and 298 K are obtained (units are kJ mol−1 for ΔrH and J mol−1 K−1 for ΔrS; uncertainties are accuracy estimates at the 95% confidence level): ΔrH0(1b) = −66.6 ± 7.1, ΔrH298(1b) = −67.5 ± 6.6, and ΔrS298(3b) = −93 ± 16; ΔrH0(3b) = −62.4 ± 9.0, ΔrH298(3b) = −64.5 ± 8.5, and ΔrS298(3b) = −94 ± 20. Examination of the effect of added O2 on Br kinetics under conditions where reversible adduct formation is observed allows the rate coefficients for the Br−Iso + O2 (k2) and Br−Bu + O2 (k4) reactions to be determined. At 298 K, we find that k2 = (3.2 ± 1.0) × 10−13 cm3 molecule−1 s−1 independent of pressure (uncertainty is 2σ, precision only; pressure range is 25−700 Torr) whereas k4 increases from 3.2 to 4.7 × 10−13 cm3 molecule−1 s−1 as the pressure increases from 25 to 700 Torr. Our results suggest that under atmospheric conditions, Br−Iso and Br−Bu react with O2 to produce peroxy radicals considerably more rapidly than they undergo unimolecular decomposition. Hence, the very fast addition reactions appear to control the rates of Br-initiated formation of Br−Iso−OO and Br−Bu−OO radicals under atmospheric conditions. The peroxy radicals are relatively weakly bound, so conjugated diene regeneration via unimolecular decomposition reactions, though unimportant on the time scale of the reported experiments (milliseconds), is likely to compete effectively with bimolecular reactions of peroxy radicals under relatively warm atmospheric conditions as well as in 298 K competitive kinetics experiments carried out in large chambers.

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INTRODUCTION It is well-established that isoprene (2-methyl-1,3-butadiene, Iso) is the single most important atmospheric biogenic hydrocarbon both in terms of magnitude of emissions from terrestrial sources and in terms of reactivity.1,2 Isoprene emissions from vegetation total ∼500 TgC yr−1, whereas anthropogenic emissions of all non-methane hydrocarbons (NMHC) total ∼100 TgC yr−1.3,4 The isoprene flux into the atmosphere is larger than that of any NMHC.4 There have been numerous studies in the literature focusing on the atmospheric oxidation of isoprene initiated by OH radicals, NO3 radicals, Cl atoms, and ozone.5 OH radicals are thought to be the dominant initiator of isoprene oxidation during daytime hours, whereas © 2012 American Chemical Society

NO3 radicals are thought to play a significant role at night in polluted environments and O3 is thought to dominate at night in unpolluted environments.6 Recent work suggesting a potentially significant marine source of isoprene has received considerable attention,7−12 and because marine atmospheric environments contain elevated levels of halogen atoms,13−15 Special Issue: A. R. Ravishankara Festschrift Received: December 15, 2011 Revised: March 21, 2012 Published: March 21, 2012 6341

dx.doi.org/10.1021/jp212127v | J. Phys. Chem. A 2012, 116, 6341−6357

The Journal of Physical Chemistry A

Article

carcinogen.31 We are interested in the Br + 1,3-butadiene reaction for two reasons. First, 1,3-butadiene is the simplest alkene containing conjugated double bonds and, therefore, represents a benchmark for understanding the kinetics and thermochemistry of Br + conjugated diene reactions. Second, the only Br + isoprene study reported in the literature was conducted by Bierbach et al.17 using a relative rate technique where isoprene loss was measured relative to 1,3-butadiene loss at T = 298 K and P = 1 bar air. The overall rate coefficient for loss of isoprene via a multireaction sequence (at least as complex as reactions 1b, −1b, and 2) was measured relative to the overall rate coefficient for loss of 1,3-butadiene via a similar multireaction sequence. Hence, in comparing our Br + isoprene results with those of Bierbach et al., it is useful to examine differences in both reported absolute rate coefficients and reported relative rate coefficients. To study reactions 1−4 over a wide range of temperature, pressure, and [O2], we couple Br generation via laser flash photolysis (LFP) of CF2Br2 with time-resolved monitoring of Br kinetics using atomic resonance fluorescence (RF) spectroscopy. The results allow the kinetics of the first few elementary steps in the overall mechanism for the Br-initiated oxidation of each diene to be evaluated more directly than in earlier studies. Electronic structure calculations are employed to evaluate structures and energetics of key Br−diene radicals, Br− diene−OO radicals, and H-transfer product radicals. As a check on the electronic structure calculations, experimental C−Br bond strengths in the Br−diene adducts are obtained from direct measurements of kib and k−ib (i = 1 and 3) as a function of temperature. Our results are compared with literature data,17 and the potential importance of Br-initiated oxidations as atmospheric sinks for isoprene and 1,3-butadiene is assessed.

the gas phase reactions with atomic Cl and Br could represent significant atmospheric oxidation processes for isoprene. In comparison with other radical species, such as Cl, OH, O3, and NO3, the kinetic database for the reactions of Br atoms with hydrocarbons is rather sparse.16−20 Reactions of atomic bromine with alkenes are thought to play a significant role in the chemistry of marine atmospheric environments, particularly in polar regions during ozone depletion events.21,22 During these events Br atom concentrations as high as 5 × 107 atoms cm−3 have been inferred on the basis of differential optical absorption spectroscopy (DOAS) and chemical ionization mass spectrometry (CIMS) measurements of BrO in conjunction with model simulations.23−27 If Br + alkene reactions occur with rate coefficients as fast as the analogous OH + alkene reactions, then the Br reaction could compete with the OH reaction under some atmospheric conditions. The bromoalkyl radicals formed via Br + alkene addition reactions typically have relatively weak C−Br bonds such that under atmospheric conditions radical unimolecular decomposition occurs in competition with radical + O2 reaction. As a result, the rates of Br-initiated oxidations of alkenes under atmospheric conditions display complex temperature and pressure dependences.16,18,28−30 In this study, we focus on the expected early elementary steps of the Br-initiated oxidations of atmospheric isoprene and 1,3butadiene (Bu), that is, H-transfer reactions, reversible addition reactions, and potentially reversible reactions of the radical adducts with O2: Br(2 P3/2) + H 2CC(CH3)CHCH 2 → HBr + H 2CC(CH 2)CHCH 2

(1a)

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Br(2 P3/2) + H 2CC(CH3)CHCH 2 + M ↔ BrH 2CC(CH3)CHCH 2 + M

EXPERIMENTAL SECTION The experimental apparatus used in this study is similar to that employed in previous studies carried out in our laboratory where loss or production of atomic bromine was monitored using the RF technique.32−39 The experimental approach involves coupling the time-resolved RF detection scheme with production of Br by LFP of CF2Br2. A schematic diagram of the LFP−RF apparatus is published elsewhere.40 The two reaction cells used in this study are different from the one shown in the published apparatus diagram.40 The cell used for all experiments at temperatures below 440 K is specially designed to minimize the throughput path of resonance radiation, thus allowing vacuum UV Br fluorescence to be excited and detected in reaction mixtures containing significant levels of O2; a diagram of this cell is published elsewhere.41 The cell used for a small number of experiments at T > 440 K is described below along with other important features of the apparatus and experimental details specific to this study. A jacketed Pyrex reaction cell with an internal volume of 150 cm3 was used in all experiments at T < 440 K; as mentioned above, this cell was specially designed to minimize the throughput path of resonance radiation. The cell was maintained at constant temperature by circulating ethylene glycol (for T > 298 K) or an ethanol−methanol mixture (for T < 298 K) from a thermostatically controlled bath through the outer jacket. A chromel−alumel thermocouple was inserted into the reaction zone through a vacuum seal, thus allowing for measurement of the gas temperature under the precise pressure and flow rate conditions of the experiment. The temperature variation in the reaction volume (i.e., the volume from which

(1b,−1b)

BrH 2CC(CH3)CHCH 2 + O2 + M ↔ BrH 2CC(OO)(CH3)CHCH 2 + M

(2,−2)

Br(2 P3/2) + H 2CCHCHCH 2 → HBr + H 2CCCHCH 2

(3a)

Br(2 P3/2) + H 2CCHCHCH 2 + M ↔ H 2CCHCHCH 2Br + M

(3b,−3b)

H 2CCHCHCH 2Br + O2 + M ↔ H 2CCHCH(OO)CH 2Br + M

(4,−4)

There are multiple possible pathways for each H-transfer, addition, and adduct + O2 reaction; the reactions shown above are the ones with the energetically most favorable product(s) but are not necessarily the only ones of importance under either laboratory or atmospheric conditions. Although identifying reaction products is not a focus of this study, the impact of potentially complex product branching on interpretation of kinetic and thermochemical data is addressed as appropriate throughout the paper. Like isoprene, 1,3-butadiene has also been found in the atmosphere, primarily as a result of the processing of petroleum;31 this conjugated diene is known to be a human 6342



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fluorescence could be detected) was less than ±2 K at the temperature extremes of the study. For all experiments at T > 440 K, a Pyrex reaction cell with an internal volume of approximately 200 cm3 was employed. This cell was resistively heated using electrically insulated nichrome wire windings wrapped around the outer surface. The wire heaters were covered with ceramic felt and a stainless steel radiation shield. Air-cooled jackets on the arms of the reaction cell allowed the O-ring joints to be kept near 298 K. The temperature of the gas mixture inside the reaction zone was measured using a chromel-alumel thermocouple inserted through a vacuum seal. The temperature variation in the reaction volume was less than ±3 K at the highest temperature employed to obtain kinetic data (673 K). In most experiments bromine atoms were generated using fourth harmonic radiation (266 nm) from a Quanta Ray model DCR-3 Nd:YAG laser as the photolytic light source. In a few experiments, 248 nm radiation from a GAM model 50 KrF excimer laser was employed as the light source: CF2Br2 + hν (248 or 266 nm) → Br + CF2Br

excited state (2P1/2) bromine atoms. Approximately 0.5 Torr of CO2 was added to the reaction mixture to rapidly deactivate any photolytically generated spin−orbit excited bromine atoms. The rate coefficient for electronic-to-vibrational energy transfer from Br(2P1/2) to yield ground state Br(2P3/2) via collision with CO2 is known to be 1.5 × 10−11 cm3 molecule−1 s−1.43 This rapid deactivation of excited state bromine atoms avoided any problems associated with the difference in detection sensitivities for the two atomic bromine electronic states. To avoid accumulation of photolysis or reaction products in the detection zone, all experiments were carried out under “slow flow” conditions. The linear flow rate through the reactor was typically in the range 2−4 cm s−1, and the laser repetition rate was varied over the range 2−10 Hz. Hence, no volume element of the reaction mixture was subjected to more than a few laser shots. The diene and CF2Br2 flowed into the reaction cell from 12 L bulbs containing dilute mixtures in N2, whereas carbon dioxide, methane, helium, and additional nitrogen flowed directly from their storage cylinders. The fractions of diene in each diene/N2 mixture were checked frequently by UV photometry at 228.8 nm using a Cd Penray lamp as the light source. The absorption cross sections needed to convert absorbances to concentrations were measured during the course of this study and found to be 9.36 × 10−18 cm2 for isoprene and 1.30 × 10−18 cm2 for 1,3-butadiene; the estimated accuracy of these cross sections is ±5% at the 95% confidence level. The gases used in this study were obtained from AirGas and had the following stated minimum purities: N2 (99.999%), He (99.999%), and CO2 (99.99%). For CO2, the stated purity refers to the liquid phase in the high-pressure gas cylinder. The liquids used in this study had the following stated minimum purities and suppliers: CF2Br2 (97%, Aldrich), isoprene (99%, TCI America, stabilized with tert-butyl catechol (TBC)), and 1,3-butadiene (99%, Aldrich, stabilized with TBC). N2, He, and CO2 were used as supplied, whereas isoprene, 1,3-butadiene, and CF2Br2 were degassed repeatedly at 77 K and then diluted in N2 or He and stored in 12 L Pyrex bulbs.

(5)

In all figures and tables where data are presented, the photolysis wavelength was 266 nm unless otherwise indicated. The maximum laser repetition rates were both 10 Hz and the pulse widths were ∼20 ns (248 nm) and ∼6 ns (266 nm). Laser fluences in units of mJ cm−2 pulse−1 ranged from 0.3 to 3 at 248 nm and 3 to 20 at 266 nm. The laser energy was measured by a thermopile calorimeter energy meter upon exit of the laser beam from the reaction cell. Bromine atom concentrations produced by the laser flash were typically in the range of (1−6) × 1011 atoms cm−3. The absorption cross sections for CF2Br2 at the photolysis wavelengths are 7.3 × 10−19 cm2 at 248 nm and 7.5 × 10−20 cm2 at 266 nm,5 whereas the quantum yield for Br production at these wavelengths is unity.42 An atomic resonance lamp situated perpendicular to the photolysis laser excited resonance fluorescence in the photolytically produced bromine atoms. The resonance lamp consisted of an electrodeless microwave discharge through ∼1 Torr of a flowing mixture containing a trace of Br2 in helium. The flow of a 0.2% Br2 in He mixture and pure He into the lamp were controlled by separate needle valves, thus allowing the total pressure and Br2 concentration to be adjusted for optimum signal-to-noise. Radiation was coupled out of the lamp through a MgF2 window and into the reaction cell through a MgF2 lens. Before entering the reaction cell, the lamp output passed through a flowing gas filter containing dry N2. Fluorescence was collected by a CaF2 lens on an axis orthogonal to both the photolysis laser and the resonance lamp beams and was imaged onto the photocathode of a solar blind photomultiplier (PMT). The region between the reaction cell and the photomultiplier was purged with a gas filter containing 200 Torr−cm of methane. The methane filter prevented radiation at wavelengths shorter than 140 nm (including impurity emissions from excited oxygen, hydrogen, and nitrogen atoms) from reaching the PMT but transmitted the strong bromine lines in the 140−160 nm region. Signals were processed using photon counting techniques in conjunction with multichannel scaling. A large number of laser shots were typically averaged to obtain a bromine atom temporal profile with signal-to-noise ratio sufficient for quantitative kinetic analysis. It is worth noting that the resonance fluorescence detection scheme is sensitive to both ground state (2P3/2) and spin−orbit

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COMPUTATIONAL METHODOLOGY Structures and energetics of dienes, Br−diene radicals, Br− diene−OO radicals, and H-abstraction product radicals were determined by the G4 method44 using the Gaussian09 program.45 The G4 method is a composite of several calculations and includes an extrapolation procedure and a spin−orbit correction for the bromine atom (−14.7 kJ mol−1). The average absolute deviation from experiment for the G3/05 test set (454 experimental energies, 34 of which are for radicals) is 3.5 kJ mol−1.

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RESULTS AND DISCUSSION All experiments were carried out under pseudo-first-order conditions with the diene in large excess over [Br]0. Thus, in the absence of secondary reactions that enhance or deplete [Br], the Br temporal profile following the laser flash would be described by the relationship ln{[Br]0 /[Br]t } = ln{S0/St } = (ki[diene] + k6)t = k′t (I)

In eq I, S0 is the Br fluorescence signal at a time immediately after the laser fires, St is the Br fluorescence signal at a later time t, ki (i = 1 or 3) is the overall rate coefficient for loss of Br by all Br + diene reaction channels that are irreversible on the 6343



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experimental time scale, and k6 is the rate coefficient for the following reaction Br(2 P3/2 ) → loss by diffusion from detector field of view and/or reaction with background impurities (6)

The bimolecular rate coefficients of interest, ki(P,T), are determined from the slopes of k′ versus [diene] plots obtained at constant T and P. Kinetics at T > 436 K. Br + Isoprene. Well-behaved pseudo-first-order kinetics were observed in Br + isoprene studies carried out at 526 K ≤ T ≤ 673 K; that is, Br temporal profiles were exponential and the observed first-order decay rates were found to increase linearly with increasing [Iso] but were independent of laser photon fluence and [CF2Br2]. The above kinetic observations are consistent with the behavior predicted by eq I. Furthermore, bimolecular rate coefficients obtained from the slopes of k′ versus [Iso] plots were found to be independent of pressure over the range 25−150 Torr. The observational evidence strongly supports the contentions that the dominant pathway for Br + isoprene at 526 K ≤ T ≤ 673 K is H-transfer and that reactions 1a and 6 are the only processes that significantly affect the post-laser-flash Br time history in this high temperature regime. Typical data are shown in Figures 1 and 2 and measured bimolecular rate coefficients, k1a(P,T),

Figure 2. Plots of k′, the pseudo-first-order Br atom decay rate vs [Iso] for data obtained at three different temperatures. For all data shown, P = 50 Torr. Solid lines are obtained from linear least-squares analyses; their slopes give the bimolecular rate coefficients listed in Table 1.

Table 1. Kinetic Data for Reaction 1a a T

P

# expb

[CF2Br2]

[Br]0

[Iso]max

k′max

526 555 582 610 646 650 673

50 50 50 50 25 150 50

5 5 5 5 5 5 6

4500 5400 4300 6000 6200 6800 6300

8.5 4.7 3.9 6.1 5.1 5.9 6.9

38200 40300 34700 33500 37000 41000 33600

910 1120 1250 1220 1850 1970 1880

k1ac 2.32 2.65 3.49 3.61 4.83 4.75 5.55

± ± ± ± ± ± ±

0.12 0.13 0.23 0.19 0.16 0.26 0.46

Units are T (K); P (Torr); concentrations (1011 molecules cm−3); k′ (s−1); k1a (10−13 cm3 molecule−1 s−1). b# exp ≡ no. of pseudo-firstorder Br decays measured. cUncertainties are 2σ, precision only.

a

Figure 1. Typical resonance fluorescence temporal profiles observed in kinetic studies of reaction 1a: T = 610 K and P = 50 Torr; Concentrations (1011 per cm3): [CF2Br2] = 6000; [Br]0 ∼ 6; [Iso] = (A) 0, (B) 12500, (C) 33500. Number of laser shots averaged = (A) 50, (B) 500, (C) 1500. Data were collected for 2000 channels with the multichannel scalar dwell time set to (A) 500, (B) 50, and (C) 20 μs. Solid lines are obtained from linear least-squares analyses and give the following pseudo-first-order decay rates in units of s−1: (A) 35, (B) 480, and (C) 1220. For clarity, trace (C) is scaled by a factor of 0.75.

Figure 3. Arrhenius plot for the Br + isoprene H-transfer reaction. The solid line is obtained from an unweighted linear least-squares analysis and gives the Arrhenius expression reported in the text (eq II). P = 25 (filled circle), 50 Torr (open circles), 150 Torr (filled square). Uncertainties are 2σ, precision only.

are summarized in Table 1. An Arrhenius plot for reaction 1a is shown in Figure 3. The following best fit Arrhenius expression is derived from a linear least-squares analysis of the ln k1a versus T−1 data:

this uncertainty to be ±10% independent of pressure and temperature. Because the precision of the k1a(P,T) values tabulated in Table 1 is quite good (2σ < 9% in all cases), we conservatively estimate the accuracy of each reported value for k1a(T) to be ±15%. Br + 1,3-Butadiene. Extrapolation of reversible Br addition data (discussed below) to T = 437 K suggests the Br−Bu adduct is extremely short-lived at this temperature. This would allow for investigation of a potential H-transfer channel (k3a). An experiment was conducted at T = 437 K and P = 25 Torr

k1a(T ) = (1.22 ± 0.57) × 10−11 exp{(− 2100 ± 280)/T } cm 3 molecule−1 s−1

(II)

Uncertainties in the above expression are 2σ and represent the precision of the Arrhenius parameters. We believe that the largest systematic uncertainty in the determination of each bimolecular rate coefficient lies in the determination of the reagent concentration in the reaction mixture, and we estimate 6344



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N2, in an effort to evaluate k3a. As expected, only an upper limit could be deduced, as no reaction was observed: k3a(437 K) < 5 × 10−14 cm3 molecule−1 s−1. Thermochemistry of H-Transfer Reactions. The 298 K bond dissociation enthalpies (BDEs) obtained from electronic structure calculations for all C−H bonds in isoprene and 1,3butadiene are tabulated and compared with the limited literature in Table 2. Comparison of the theoretical C−H

Table 3. Summary of Kinetic Data Obtained at T = 227 K with No O2 Added to the Reaction Mixturea

Table 2. C−H and Br−H Bond Dissociation Enthalpies (BDEs) at 298 Ka bond

BDE (kJ mol−1)

H2CCHCHCH2 H2CCHCHCH2 H2CC(CH3)CHCH2 H2CC(CH3)CHCH2 H2CC(CH3)CHCH2 H2CC(CH3)CHCH2 HBr

465.7, 478.866 420.4, 427.766 467.2 377.5 424.8 461.2 366.25

# expb

20 50 100 200 400 700 P

4 6 6 5 4 6 # expb

960 1200 1200 900 1300 1600 [CF2Br2]

20 50 100 200 400 700

5 5 4 5 5 4

7900 5900 7000 8200 8100 9600

[CF2Br2]

[Br]0

[Bu]max

0.9 250 1.5 246 1.3−3.6 252 0.8 236 1.2 182 1.5−4.0 228 [Br]0 [Iso]max 2.6 1.8 2.2 2.5 2.5 2.9

334 434 253 250 269 436

k′max

k3bc

2580 2870 4010 4320 3760 5040 k′max

1.02 ± 0.04 1.19 ± 0.13 1.58 ± 0.03 1.86 ± 0.08 2.08 ± 0.10 2.14 ± 0.23 k1bc

6760 8350 6010 6100 7170 11600

1.99 1.98 2.39 2.51 2.67 2.73

± ± ± ± ± ±

0.07 0.12 0.08 0.20 0.16 0.17

Units are P (Torr); concentration (1011 molecules cm−3); k′ (s−1); kib (10−10 cm3 molecule−1 s−1). Photolysis wavelength was 248 nm. b# exp ≡ no. of pseudo-first-order Br decays measured. cUncertainties are 2σ, precision only. a

a

BDEs without reference numbers are theoretical values obtained as part of this study.

The rate equations for the above reaction schemes can be solved analytically and predict a double exponential functional form for the Br decay.

BDEs with the well-established H−Br BDE5 suggests that all possible H-transfer reactions are endothermic and only the methyl C−H bonds in isoprene are sufficiently weak for Htransfer to Br to occur at a non-negligible rate at the temperatures investigated in this study. In later sections of the paper we estimate k1a at T < 360 K using eq II, that is, by linear extrapolation of the ln k1a versus T−1 data to lower temperatures. The C−H BDEs in 1,3-butadiene are so large that the H-transfer rate coefficient must be negligibly slow at all temperatures of relevance in this study. Kinetics at T = 227 K. As for the case of the hightemperature studies described above, well-behaved pseudo-firstorder kinetics were observed in Br + diene studies carried out at T = 227 K; that is, Br temporal profiles were exponential and observed first-order decay rates were found to increase linearly with increasing [diene] but were independent of laser photon fluence and [CF2Br2]. The above kinetic observations are consistent with the behavior predicted by eq I. Unlike the high temperature results, however, bimolecular rate coefficients obtained from the slopes of k′ versus [diene] plots at 227 K were found to increase with increasing pressure over the range 20−700 Torr. The results, which are summarized in Table 3, strongly suggest that the dominant observed pathways for Br + isoprene and Br + 1,3-butadiene at T = 227 K are the addition reactions 1b and 3b, respectively, and that reactions ib and 6 (i = 1 or 3) are the only processes that significantly affect the post-laser-flash Br time history at this relatively low temperature. Kinetics at 271 K ≤ T ≤ 357 K. Over the temperature range 271 K ≤ T ≤ 357 K, kinetic evidence for reversible addition of Br to isoprene and 1,3-butadiene was observed. The relevant kinetic scheme for analysis of this adduct formation/ dissociation equilibration data includes reactions 1a, 1b, −1b, 6, and 7 for Br + isoprene and 3a, 3b, −3b, 6, and 7 for Br + 1,3butadiene.

St /S0 = {(Q + λ1) exp(λ1t ) − (Q + λ 2) exp(λ 2t )} /(λ1 − λ 2)

(III)

In eq III, S0 and St are the same as in eq I and Q = k −ib + k 7

(IV)

−(λ1 + λ 2) = Q + k6 + (kia + ki b)[diene]

(V)

λ1λ 2 = Q (k6 + kia[diene]) + k 7ki b[diene]

(VI)

where i = 1 for Br + isoprene and i = 3 for Br + 1,3-butadiene. Typical observed Br temporal profiles are shown in Figure 4. The temporal profiles were fit to the double exponential eq III using a nonlinear least-squares method to obtain values for the fit parameters S0, Q, λ1, and λ2. Rearrangement of eqs IV−VI

Figure 4. Typical resonance fluorescence temporal profiles observed over the temperature range 273 ≤ T (K) ≤ 357: T = 346 K and P = 50 Torr. Concentrations (1011 per cm3): [CF2Br2] = 3600; [Br]0 ∼ 3; [Iso] = (A) 517 and (B) 1810. Solid lines through data at t > 0 are obtained from nonlinear least-squares fits to eq III. Best fit parameters are (A) S0 = 4780, Q = 5880 s−1, λ1 = −8480 s−1, λ2 = −170 s−1; (B) S0 = 4783, Q = 7090 s−1, λ1 = −18400 s−1, λ2 = −227 s−1. For clarity, trace A is scaled upward by a factor of 1.6.

Br− diene → loss by processes that do not regenerate Br atoms

P

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Table 4. Results of the Br + Isoprene + N2 ↔ Br−Isoprene + N2 Equilibration Kinetics Experimentsa T

P

S0

Q

−λ1

−λ2

[Iso]

[CF2Br2]

[Br]0

k1b

k7

k−1b

Kp

273

50

284

50

298

20

3857 3566 3548 3152 3231 2777 3090 3093 4582 4921 4912 3285 3416 5268 3491 3326 3635 4155 2675 3918 4272 3673 3741 3587 2588 2663 4730 3715 4800 4537 4339 2620 4153 3704 5597 5497 4935 5399 3026 2926 2719 2927 3180 3512 4780 5232 5434 4783 2319 2373 4732 4717 4638

138 −115 −61 245 354 271 488 623 522 664 453 592 578 752 788 760 771 681 699 819 823 1350 1380 600 852 887 803 916 909 1000 1420 1550 1680 1690 2860 2890 3010 3040 4200 4480 4410 4400 4490 6470 5880 6030 6980 7090 7530 7310 7690 8160 8350

6450 11200 22200 3450 4890 9400 14300 17900 15600 26000 5270 6390 6440 9260 11300 12700 14100 13600 6650 6740 11700 22700 39900 4590 8340 11700 7000 9400 16700 22700 5930 8310 17100 22500 7250 10200 14300 17000 12100 17900 17600 21500 22100 9290 8480 9480 14800 18400 11900 12800 14300 17500 19800

68.7 −162 −102 137 226 149 333 461 302 391 168 254 237 380 378 381 404 297 317 391 378 801 774 236 376 422 174 237 218 270 180 172 213 195 236 219 209 213 297 304 254 294 292 166 170 212 216 227 196 203 274 277 282

362 634 1320 222 315 628 958 1200 1370 2260 387 501 502 696 908 1040 1130 1130 361 380 656 1310 2270 223 404 601 585 830 1480 2000 437 646 1470 1990 578 945 1460 1800 549 887 899 1170 1200 517 517 649 1250 1810 610 803 2000 2560 3290

3500 3500 3400 3600 3500 3200 3500 3400 5200 5200 5200 4200 4200 5500 4100 4100 4300 4300 3700 3800 3800 3800 3700 5800 5800 5700 3500 3500 3500 3500 3300 3300 3300 3300 3300 3400 3200 3300 4000 4100 4200 4000 4000 3600 3600 3600 3700 3600 1700 1700 3300 3400 3400

3.7 3.7 2.9 3.3 3.2 2.7 3.3 3.1 5.5 5.5 5.2 4.4 4.9 5.5 4.3 4.8 4.8 4.6 3.7 3.8 3.9 4.3 3.9 6.0 6.8 5.9 3.4 2.9 3.4 3.2 3.0 3.1 3.1 2.8 3.0 3.0 3.0 2.9 4.2 4.5 4.1 4.2 4.2 3.4 3.4 3.3 3.4 3.3 1.4 1.4 2.9 2.9 2.9

1.76 1.76 1.68 1.50 1.50 1.47 1.47 1.47 1.12 1.14 1.29 1.20 1.21 1.28 1.19 1.19 1.21 1.17 1.73 1.66 1.71 1.69 1.73 1.89 1.94 1.86 1.09 1.05 1.08 1.10 1.07 1.07 1.07 1.06 0.797 0.799 0.786 0.785 1.49 1.55 1.49 1.49 1.49 0.572 0.529 0.560 0.640 0.634 0.751 0.711 0.344 0.373 0.356

69 −163 −102 141 231 151 336 465 305 395 177 266 249 395 391 392 414 305 336 417 392 821 786 255 398 439 188 253 226 279 219 200 229 206 354 286 253 250 432 392 328 359 357 466 470 511 377 347 468 423 538 480 456

69 48 41 104 123 120 152 158 216 270 276 326 330 357 397 368 357 376 364 402 430 531 598 345 454 447 615 663 683 723 1200 1350 1450 1480 2500 2600 2750 2790 3770 4080 4090 4040 4130 6000 5410 5520 6610 6750 7060 6890 7150 7680 7890

68.4 98.8 111 37.1 31.7 31.7 25.1 24.2 12.8 10.4 11.5 9.07 9.01 8.80 7.40 7.94 8.32 7.67 11.7 10.1 9.77 7.85 7.12 13.5 10.6 10.2 4.21 3.76 3.77 3.62 2.05 1.83 1.70 1.65 0.708 0.684 0.635 0.627 0.879 0.841 0.813 0.819 0.804 0.202 0.207 0.216 0.206 0.200 0.224 0.218 0.0987 0.0999 0.0928

50

200

297

700

308

50

319

50

330

50

700

a

346

50

348

50

357

20

Units: T (K); P (Torr); S0 (counts); Q, λ1, λ2, k7, k−1b (s−1); concentrations (1011 molecules cm−3); k1b (10−10 cm3 molecule−1 s−1); KP (106 atm−1).

k −ib = Q − k 7

gives the following relationships for the rate coefficients of interest: ki b = −(Q + k6 + kia[diene] + λ1 + λ 2)/[diene]

k 7 = {λ1λ 2 − Q (k6 + kia[diene])}/(ki b[diene])

(IX)

The background Br atom loss rate (k6) was directly measured by observing the RF decay in the absence of added diene at each temperature and pressure. At 298 K, k6 varied from 35 s−1 at P = 25 Torr to 12 s−1 at P = 700 Torr. As mentioned above,

(VII) (VIII) 6346



Article

Table 5. Results of the Br + 1,3-Butadiene + N2 ↔ Br−1,3-Butadiene + N2 Equilibration Kinetics Experimentsa T

P

S0

Q

−λ1

−λ2

[Bu]

[CF2Br2]

[Br]0

k3b

k7

k−3b

Kp

271

700

283

100

295

20

297

50

3393 3391 4032 2758 3119 3159 2935 3853 4277 3191 3299 4014 3129 3184 3014 5567 3850 2959 1758 6533 4701 3560 2532 2854 2478 2179 2323 2375 2575 3237 3671 2159 2843 2869 3104 2648 2688 2560 2724 2323 2862 2488 3344 3938 2858 2449 3136 3049 4006 3626 3665 3642 4313 3873 3727 3753 3579 7961 7576 3798 3903

270 358 360 205 297 354 416 518 547 554 422 709 811 979 724 1130 1200 1110 1100 1470 1530 1480 1510 1540 1700 1840 1870 1970 1950 1890 1900 2140 2070 1160 1170 2320 2280 2280 3430 3560 4260 4610 2190 2110 2190 2320 2390 2450 5660 5910 6030 6140 5310 5570 6160 6490 6350 9780 9990 10800 11200

3550 4980 6690 8490 4560 6060 7140 1560 2330 2870 4090 1420 2720 3680 5210 3280 4070 4870 5920 3970 4650 5690 6570 8060 4700 7510 7620 8880 10400 5150 6100 10400 12700 9050 9290 9400 16800 17200 19600 20700 31000 37200 4650 5680 6400 7130 8160 10100 10600 13400 16700 18000 9450 10700 14800 19400 20700 15500 17500 19100 22300

111 180 192 55 58 104 141 182 211 178 81 218 196 283 91 147 147 109 89 238 171 176 200 168 177 182 188 217 206 195 201 300 215 182 145 263 188 180 105 129 144 208 228 197 209 230 236 232 267 262 258 272 150 175 190 200 205 163 163 190 207

212 288 376 465 390 522 676 206 365 430 670 130 270 375 592 202 260 339 444 195 214 295 361 451 173 313 315 378 458 169 214 390 531 1760 1750 993 1920 1920 1530 1540 2030 2060 379 508 604 671 771 1010 943 1330 1830 2070 1840 2130 3380 4830 5800 3330 4370 4510 5500

9100 9300 960 9100 2000 1900 2000 1000 1000 1000 1000 1400 1400 1500 1400 1000 990 980 990 990 1000 1100 1100 1100 940 1100 1000 1000 980 1200 1200 1100 1200 2200 2300 2000 1900 1900 2900 2900 3800 4000 950 1100 1100 1100 1120 1100 1500 1600 1400 1500 1100 1100 1100 1100 1100 1400 1300 1300 1300

1.4 1.4 1.8 1.4 0.9 0.9 0.9 1.6 1.9 1.6 1.6 4.3 3.9 4.0 3.4 1.2 0.9 1.2 1.0 1.5 1.3 1.6 1.7 1.6 1.7 2.7 2.5 1.8 1.8 3.0 3.7 3.5 3.6 1.1 1.1 0. 9 0.9 0.9 1.3 1.3 1.9 1.2 0.9 1.0 1.0 1.1 1.0 1.0 1.3 1.6 1.4 1.3 1.0 1.0 1.0 1.0 1.0 1.2 1.2 1.2 1.2

1.20 1.26 1.30 1.35 1.10 1.11 1.01 0.436 0.405 0.431 0.418 0.530 0.582 0.596 0.581 0.851 0.868 0.856 0.830 1.05 1.15 1.12 1.09 1.12 1.38 1.41 1.42 1.42 1.42 1.53 1.54 1.64 1.53 0.458 0.472 0.736 0.761 0.785 1.06 1.12 1.32 1.59 0.708 0.740 0.730 0.751 0.778 0.772 0.546 0.579 0.596 0.585 0.232 0.249 0.259 0.271 0.251 0.176 0.174 0.188 0.203

115 186 197 56 61 108 146 225 242 200 86 327 248 345 101 203 193 134 104 339 236 223 247 199 255 229 237 266 244 285 273 362 249 201 159 329 211 201 124 153 161 235 387 291 298 321 317 295 534 445 387 398 287 316 294 279 275 370 324 381 373

155 171 163 149 237 246 270 293 305 353 336 382 562 633 623 930 1010 980 995 1130 1300 1260 1260 1340 1440 1610 1630 1710 1700 1610 1630 1780 1820 963 1010 1990 2070 2080 3300 3410 4100 4380 1800 1820 1890 2000 2070 2150 5130 5460 5650 5740 5020 5260 5870 6210 6070 9410 9660 10400 10900

21.0 19.8 21.6 24.5 12.1 11.7 9.74 3.71 3.30 3.03 3.09 3.43 2.56 2.33 2.30 2.25 2.12 2.15 2.05 2.29 2.19 2.19 2.13 2.05 2.36 2.16 2.13 2.04 2.05 2.34 2.33 2.27 2.07 1.12 1.11 0.871 0.867 0.890 0.758 0.773 0.759 0.855 0.925 0.958 0.908 0.885 0.884 0.843 0.239 0.238 0.237 0.229 0.0987 0.101 0.0945 0.0934 0.0884 0.0385 0.0371 0.0372 0.0386

100

200

400

700

311

25 100

250

312

500 700 100

327

100

343

25

356

25

6347



Article

Table 5. continued T a

P

S0

Q

−λ1

−λ2

[Bu]

[CF2Br2]

[Br]0

k3b

k7

k−3b

Kp

3932

11100

23500

200

6470

1140

1.3

0.195

341

10700

0.0373

Units: T (K); P (Torr); S0 (counts); Q, λ1, λ2, k7, k−3b (s−1); concentrations (1011 molecules cm−3); k3b (10−10 cm3 molecule−1 s−1); KP (106 atm−1).

values for k1a(T) are obtained by extrapolation of the hightemperature (526 K ≤ T ≤ 673 K) kinetic data, assuming Arrhenius behavior, that is, a linear ln k1a versus T −1 dependence from 526 K down to 271 K. Because of the unfavorable thermochemistry for both Br + 1,3-butadiene Htransfer reactions (Table 2) it is assumed that k3a(T) ≈ 0 at all temperatures investigated. Experimental conditions and results of all of the equilibration kinetics experiments are summarized in Tables 4 (Br + isoprene) and 5 (Br + 1,3-butadiene). The values of the equilibrium constants given in these tables are derived from the following relationship: KP = ki b/(k −i bRT ) = K C/(RT )

Br + 1,3‐butadiene:

ln KP (atm−1)

= −(9.8 ± 0.6) + (7270 ± 180)/T (K )

Uncertainties in the above expressions are 2σ and represent the precision of the slopes and intercepts obtained from the van’t Hoff analyses; as discussed below, these slopes and intercepts give ΔrH and ΔrS, respectively, for reactions 1b and 3b. Theoretical Structures and Energetics. The geometries of each diene and Br−diene adduct were determined by the G4 method44 using the Gaussian 09 program.45 The Br adducts with 1,3-butadiene and isoprene are formed via electron promotion in the diene followed by 2-center−2-electron (2c−2e) bonding of the bromine atom to a terminal carbon of the diene. In isoprene, the more stable adduct is formed with Br bonded to C1 (8.3 kJ mol−1 more stable than with Br bonded to C4). Optimizations started with Br bonding to C2 or C3 rearranged without barrier to the C1 and C4 adducts, respectively. The unpaired spin density is distributed over the three carbon atoms of the allylic system. The bromine atom in the adduct has about 0.14 to 0.16 unpaired spin density (B3LYP/6-31G(2df,p) level of theory). The G4 bond enthalpy at 298 K is 6.6 kJ mol−1 larger for isoprene (C1-adduct) compared to 1,3-butadiene. The experimental difference in the energies of the first excited states of butadiene and isoprene is 7.5 kJ mol−1 (217 nm excitation threshold for 1,3-butadiene compared to 220 nm for isoprene). The lower excitation energy for isoprene means that it is easier to promote an electron from the π to the π* orbital. Therefore, the stronger Br−adduct calculated bond dissociation enthalpy in isoprene can be attributed to the lower promotion energy. In the Br−isoprene adduct with C1 symmetry, the G4 transition state for methyl torsion has an enthalpy (298 K) 2.4 kJ mol−1 lower than the G4 minimum, which indicates that the role of minimum and transition state have been reversed and that the best structure of the adduct is actually the methylrotation transition state and the best adduct enthalpy is the G4 minimum plus 2.4 kJ mol−1. Theoretical structures and energetics of potentially important Br−diene and Br−diene− OO species as well as transition states are shown in Figures 6 and 7. Complete xyz structures of all species in Figures 6 and 7 are available as Supporting Information. Br−Diene Thermochemistry. Both second- and third-law methods are employed to evaluate the thermochemistry of the Br−diene adducts. In the second-law approach, the enthalpy and entropy changes associated with Br−diene formation (reactions (ib), i = 1 or 3) are evaluated from the van’t Hoff plots shown in Figure 5. Because

(X)

The results at T = 298 ± 1 K and P = 20−700 Torr show that kib and k−ib are dependent on pressure, whereas KP is not, which is expected for an addition/dissociation reaction. The observed pressure-independence of KP increases confidence that the nonlinear least-squares fitting procedure is relatively free of systematic errors in the extracted rate coefficients. Examination of Tables 4 and 5 shows that the precision of multiple determinations of kib and k−ib at a given temperature and pressure is quite good. We estimate that the absolute accuracies (95% confidence levels) of reported values for kib and k−ib are ±15 and ±35%, respectively. Hence, a reasonable estimate for the accuracies of reported values for Kp is ±40% (95% confidence level) over the full range of temperatures investigated.

Figure 5. van’t Hoff plots for Br + diene ↔ Br−diene reactions. Solid lines are obtained from linear least-squares analyses of the ln KP vs T−1 data and give the second-law thermochemical parameters reported in Table 7. Dashed lines represent the results of the third-law analyses.

ln K p = (Δr S /R ) − (Δr H /RT )

the enthalpy change is obtained from the slope of the van’t Hoff plot, whereas the entropy change is obtained from the intercept. At 309 K, the midpoint of the experimental T−1 range for the Br + isoprene equilibration kinetics experiments, the second-law analysis gives the results ΔrH = −65.3 ± 1.6 kJ mol−1 and ΔrS = −85.9 ± 5.0 J mol−1 K−1, whereas at 308 K, the midpoint of the experimental T−1 range for the Br + 1,3-

Plots of ln KP versus T−1, that is, van’t Hoff plots, are shown in Figure 5. Linear least-squares analyses of the data give the following expressions: Br + isoprene:

(XI)

ln KP (atm−1)

= −(10.3 ± 0.6) + (7850 ± 190)/T (K ) 6348



Article

Figure 6. Reaction coordinate diagram for the Br + isoprene + O2 system. Enthalpies (298 K) in kJ mol−1 are obtained at the G4 level of theory.

Figure 7. Reaction coordinate diagram for the Br + 1,3-butadiene + O2 system. Enthalpies (298 K) in kJ mol−1 are obtained at the G4 level of theory.

−81.3 ± 4.9 J mol−1 K−1. Uncertainties in the above second-law thermodynamic parameters are 2σ and represent precision only.

butadiene equilibration kinetics experiments, the second-law analysis gives the results ΔrH = −60.5 ± 1.5 kJ mol−1 and ΔrS = 6349



6350

g0 and g1 are the degeneracies of the ground and first excited electronic states, respectively, and Δε is the energy difference between the two states; the dienes do not have energetically accessible excited electronic states and it is assumed that the Br−diene adducts also do not. σ ≡ symmetry factor. Rotational constants and vibrational frequencies are calculated at the B3LYP/6-31G(2d,p) level of theory. Vibrational frequencies in bold italics are torsions. bCH3 torsion. cBrCH2 torsion.

79, 152,c 261, 280, 475, 506, 573, 801, 845, 855, 952, 1011, 1078, 1161, 1192, 1234, 1289, 1356, 1475, 1499, 1526, 3116, 3138, 3156, 3166, 3191, 3252 177, 294, 514, 544, 788, 901, 937, 941, 1001, 1011, 1069, 1228, 1318, 1320, 1421, 1477, 1662, 1714, 3134, 3144, 3149, 3150, 3234, 3234

σ rotational constants (GHz) vibrational frequencies (cm−1)

σ rotational constants (GHz) vibrational frequencies (cm−1)

a

1 11.2616, 1.1249, 1.0741 1,3-Butadiene

35,b 66,c 119, 215, 290, 345, 396, 489, 541, 633, 779, 842, 884, 984, 993, 1029, 1048, 1110, 1183, 1259, 1281, 1370, 1408, 1447, 1479, 1491, 1493, 1537, 3022, 3083, 3115, 3117, 3139, 3165, 3191, 3253 164, 209,b 277, 413, 426, 533, 649, 794, 796, 930, 937, 965, 1012, 1041, 1074, 1091, 1328, 1330, 1411, 1435, 1462, 1481, 1503, 1669, 1708, 3029, 3080, 3121, 3140, 3148, 3158, 3230, 3237

Isoprene

2 42.5477, 4.4283, 4.0111

1 4.9426, 1.0021, 0.9319

Br−diene 2 diene 1 Br

4 2 3685.24 g0 g1 Δε (cm−1)

Table 6. Summary of Parameters Used in Calculations of Absolute Entropies and Heat Capacity Corrections for Br + Diene Association/Dissociation Reactionsa

In addition to the second-law analyses, we have carried out third-law analyses where experimental values for KP at the midpoints of the investigated T−1 ranges are employed in conjunction with calculated entropy changes to evaluate ΔrH(309 K) for Br + isoprene and ΔrH(308 K) for Br + 1,3-butadiene. The experimental equilibrium constants used in the third-law analyses, in units of 106 atm−1, are 3.41 ± 1.36 for Br−Iso formation/dissociation and 1.04 ± 0.42 for Br−Bu formation/dissociation. To evaluate ΔrS, absolute entropies as a function of temperature were obtained from the JANAF tables for Br46 and calculated using ab initio vibrational frequencies and moments of inertia for each diene and Br−diene adduct. All torsional frequencies are treated as vibrations in the entropy calculations. Relevant parameters used in the calculations of absolute entropies and heat capacity corrections are summarized in Table 6. Theoretical bond strengths are tabulated in Table 7 and agree reasonably well with the experimental values. The third-law analyses give the following results (units are kJ mol−1 for ΔH and J mol−1 K−1 for ΔS): For reaction 1b, ΔrH309 = −69.6 ± 4.5 and ΔrS309 = −99.7 ± 8.8, whereas for reaction 3b, ΔrH308 = −68.5 ± 4.0 and ΔrS308 = −107.4 ± 6.5. In arriving at the above uncertainties in ΔrS, we assume that the frequencies of the low frequency Br−diene vibrations could differ from the values given in Table 6 by ±25% for frequencies less than 100 cm−1 and ±25 cm−1 for frequencies greater than 100 cm−1. Appropriate heat capacity corrections have been employed to obtain ΔrH values at 298 and 0 K; the results are given in Table 7. The thermochemical parameters determined from the second- and third-law analyses differ significantly, particularly for the Br + 1,3-butadiene reaction. Frequently, in this type of study the third-law results are preferred because the entropy change can be calculated more accurately than it can be evaluated on the basis of a long extrapolation of the ln KP versus T−1 data. In this study, however, the precision of the second-law analysis is unusually good and significant systematic errors are possible for both the second-law and third-law approaches. Important potential sources of systematic error include formation/dissociation of multiple radical adducts as well as improper treatment of torsional modes in the entropy calculations. Interestingly, these potential systematic errors are expected to affect the Br + isoprene results more than the Br + 1,3-butadiene results, yet the difference between second-law and third-law results is significantly larger for Br + 1,3butadiene than it is for Br + isoprene (Table 7). We feel that it is prudent to report thermochemical parameters that are averages of the second- and third-law values and adjust error estimates to include all reasonable possibilities. With this approach, we report the following experimental values for ΔrH (in units of kJ mol−1) and ΔrS (in units of J mol−1 K−1): For reaction 1b, ΔrH0 = −66.6 ± 7.1, ΔrH298 = −67.5 ± 6.6, and ΔrS298 = −93 ± 16, whereas for reaction 3b, ΔrH0 = −62.4 ± 9.0, ΔrH298 = −64.5 ± 8.5, and ΔrS298 = −94 ± 20; uncertainties can be viewed as accuracy estimates at the 95% confidence level. Reaction enthalpies obtained using G4 theory (Table 7) are larger than the experimental values for both reactions 1b and 3b, although experiment and theory agree within the combined uncertainties. Further experimental and theoretical research will be required to reduce the uncertainty limits in the reported thermochemical parameters. Regarding potential systematic errors that could result from improper treatment of torsional modes in entropy calculations, Gaussian 09 has an option called “hinrot” that can be used to calculate entropies treating torsions as hindered rotors rather

1 8.5477, 4.1750, 2.8544

Article



Article

Table 7. Thermochemical Parameters for the Br + Isoprene and Br + 1,3-Butadiene Addition Reactions Forming the Most Stable (C1) Productsa T

method

309

second law third law second law third law G4 theoryd second law third law G4 theoryd second law third law second law third law G4 theoryd second law third law G4 theoryd

diene isoprene

0

298

1,3-butadiene

308 0

298

−ΔrH

−ΔrS

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

85.9 ± 5.0b 99.7 ± 8.8c

65.3 69.6 64.4 68.7 72.6 65.3 69.6 75.6 60.5 68.5 58.4 66.4 66.9 60.5 68.5 69.0

1.6b 4.5c 2.1b 5.0c 3.5e 1.6b 4.5c 3.5e 1.5b 4.5c 2.0b 5.0c 3.5e 1.5b 4.5c 3.5e

ΔfH(Br−diene)

99.8 ± 8.8c

121.8 ± 6.0c 117.5 ± 7.3c

81.3 ± 4.9b 107.4 ± 6.5c

107.4 ± 6.5

c

161.1 ± 6.0c 153.1 ± 7.3c

Units are T (K); ΔH (kJ mol−1); ΔS (J mol−1 K−1). bUncertainty is 2σ, precision only. cUncertainty is estimated accuracy at the 95% confidence level. dThe level of optimization is B3LYP/6-31G(2df,p). eUncertainty represents average deviation between experiment and theory for a test set of 454 chemical species, 34 of which were radicals. a

than harmonic oscillators. The approach is based on methodology developed by Ayala and Schlegel.47 When the “hinrot” option is used, the 298 K entropy changes associated with Br + Iso → Br−Iso and Br + Bu → Br−Bu increase by 4.1 and 1.6 J K−1 mol−1, respectively; these changes in ΔrS298 are much smaller than the uncertainties that we have adopted (see above). The dashed lines in Figure 5 are generated from eq XI using the third-law values for ΔrS and ΔrH at the midpoint temperature of the experimental T−1 range. The mathematical expressions represented by the dashed lines in Figure 5 are Br + isoprene:

ln K p (atm−1)

= −12.0 + 8370/T (K) Br + 1, 3‐butadiene:

(third‐law analysis)

Figure 8. Typical data showing the dependence of observed resonance fluorescence temporal profiles on [O2]. T = 298 K and P = 700 Torr. Concentrations (1011 molecules cm−3): [CF2Br2] = (A) 2190, (B) 2040, (C) 4290; [Br]0 = (A) 2.8, (B) 2.6, (C) 4.5; [Iso] = (A) 509, (B) 509, (C) 449; [O2] = (A) 0, (B) 45900, (C) 151000. Red lines are obtained from nonlinear least-squares fits to eq III. Best fit parameters are (A) S0 = 2377 counts, Q = 1050 s−1, λ1 = −10500 s−1, λ2 = −368 s−1; (B) S0 = 2308 counts, Q = 2180 s−1, λ1 = −10100 s−1, λ2 = −1690 s−1. Trace C is exponential; the black line is obtained from a linear least-squares analysis of the ln St vs time data, and its slope gives k′ = 7980 s−1. For clarity, traces A and B are scaled upward by factors of 10 and 4, respectively.

ln K p (atm−1)

= −12.9 + 8240/T (K)

(third‐law analysis)

The values for ΔrH reported above can be used in conjunction with literature values for the standard enthalpies of formation of Br,46 isoprene,48 and 1,3-butadiene49,50 to deduce values for the standard enthalpies of formation of Br− Iso (ΔfH298 = 120 ± 9 kJ mol−1) and Br−Bu (ΔfH298 = 157 ± 9 kJ mol−1). Br−Diene + O2 Reactions. Observations of perturbation to “approach to equilibrium” kinetics upon addition of small amounts of O2 to CF2Br2/diene/N2 reaction mixtures allows the Br−diene + O2 rate coefficients, kj(T,P), j = 2 or 4, to be evaluated. The data shown in Figure 8 illustrate how addition of O2 perturbs the Br approach to equilibrium kinetic data. Rate coefficients, kj(T,P), j = 2 or 4, are obtained from the slopes of k7 versus [O2] plots, as shown in Figure 9, where values for k7 are obtained using eq VII in conjunction with the double exponential fit parameters and independently determined values for k6 and kia. Reactions 2 and 4 compete with reactions −1b and −3b, respectively, for removal of Br−diene. Hence, the slow component of the double exponential decay becomes faster as [O2] increases. If O2 is added in sufficient excess, the

Br decay should become exponential and the slope of a plot of the pseudo-first-order Br decay rate versus [diene] should give the sum of the H-abstraction and forward addition rate coefficients. At the temperatures employed in these studies (297 K for Br−Iso + O2 and 311 K for Br−Bu + O2), all Habstraction pathways are negligibly slow. Hence, in experiments where enough O2 is present in the reaction mixture that single exponential decays are observed, plots of k′ versus [diene] should have slopes equal to kib. Table 8 summarizes Br−diene + O2 results obtained under conditions where double exponential decays were observed. The Br−Iso + O2 rate coefficient is found to be independent of pressure over the range 50−700 Torr at T = 297 K with k2 ± 6351



Article

function of [O2] is k7, the rate coefficient for Br−diene loss via reactions that do not regenerate Br atoms. Pressure Dependences of the Br + Diene Association Rate Coefficients. As discussed in previous sections of the paper, values for the association rate coefficients k1b and k3b have been derived from analysis of data obtained from (i) low temperature experiments (227 K) with no added O2 where single exponential decays were observed (Table 3), (ii) experiments over the temperature range 271−357 K with no O2 added where double exponential decays were observed (Tables 4 and 5), and (iii) experiments over the temperature range 210−300 K, where O2 was added to the reaction mixture and single exponential decays were observed (Table 9). Falloff curves, that is, plots of bimolecular rate coefficient versus total gas number density, for reactions 1b and 3b at 298 K are shown in Figure 10. Rate coefficients were found to increase with increasing pressure at all temperatures investigated. To provide a parametrization that is convenient for representing pressure dependent kinetic data in atmospheric models and in Figure 10, the data were fit to the following expression:5

Figure 9. Plots of k7, the pseudo-first-order rate coefficient for loss of Br−diene via processes that do not regenerate Br, vs [O2]. Data shown in black are for Br−Iso + O2, reaction 2, at 298 K. Data shown in red are for Br−Bu + O2, reaction 4, at 311 K; P = 50 Torr (black squares; solid line), 100 Torr (red squares; solid line), or 700 Torr (black and red circles; dashed lines). Bimolecular rate coefficients obtained from the slopes of the lines are (units are 10−13 cm3 molecule−1 s−1): k2(50 Torr) = 2.94 ± 0.68; k2(700 Torr) = 3.09 ± 0.74; k4(100 Torr) = 3.11 ± 0.12; k4(700 Torr) = 4.66 ± 0.96.

k II([M],T ) = Xk∞(T )0.6Y /(1 + X )

2σ = (3.2 ± 1.0) × 10−13 cm3 molecule−1 s−1, whereas the Br− Bu + O2 rate coefficient (k4) increases with increasing pressure at T = 311 K [(3.2−4.7) × 10−13 cm3 molecule−1 s−1 over the pressure range 25−700 Torr]. It is worth noting that the kinetic data used to obtain values for k2 and k4 actually measure removal of either of the equilibrating species (Br or Br−diene). Hence, an inherent assumption in our data analysis is that the change in Br temporal profiles observed upon addition of O2 is entirely due to the influence of O2 on Br−diene chemistry; that is, addition of O2 has no effect on Br chemistry. All evidence points toward this assumption being correct. In the absence of added diene, background Br decay rates are found to be slow (always

Kinetics of Elementary Steps in the Reactions of Atomic Bromine with

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