Experimental and Theoretical Analysis of the Kinetics of the Reaction

Oct 22, 2009 - Department of Chemistry, Acadia, UniVersity, WolfVille, NoVa Scotia B4P 2R6, Canada. Núria González-Garcıa and Matthias Olzmann...
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J. Phys. Chem. A 2010, 114, 291–298

291

Experimental and Theoretical Analysis of the Kinetics of the Reaction of Atomic Bromine with 1,4-Dioxane Binod Raj Giri† and John M. Roscoe* Department of Chemistry, Acadia, UniVersity, WolfVille, NoVa Scotia B4P 2R6, Canada

Nu´ria Gonza´lez-Garcı´a and Matthias Olzmann Institut fu¨r Physikalische Chemie, Karlsruher Institut fu¨r Technologie (KIT), Kaiserstr. 12, 76128 Karlsruhe, Germany ReceiVed: August 24, 2009; ReVised Manuscript ReceiVed: September 28, 2009

The rate coefficient for the reaction of atomic bromine with 1,4-dioxane was measured from ∼300 to 340 K using the relative rate method. Iso-octane and iso-butane were used as reference compounds, and the experiments were made in a bath of argon containing up to 210 Torr of O2 at total pressures between 200 and 820 Torr. The rate coefficients were not affected by changes in pressure or O2 concentration over our range of experimental conditions. The ratios of rate coefficients for the reaction of dioxane relative to the reference compound were put on an absolute basis by using the published absolute rate coefficients for the reference reactions. The variation of the experimentally determined rate coefficients with temperature for the reaction of Br with 1,4-dioxane can be given by k1exp(T) ) (1.4 ( 1.0) × 10-11exp[-23.0 ( 1.8) kJ mol-1/(RT)] cm3 molecule-1 s-1. We rationalized our experimental results in terms of transition state theory with molecular data from quantum chemical calculations. Molecular geometries and frequencies were obtained from MP2/ aug-cc-pVDZ calculations, and single-point energies of the stationary points were obtained at CCSD(T)/CBS level of theory. The calculations indicate that the 1,4-dioxane + Br reaction proceeds in an overall endothermic addition-elimination mechanism via a number of intermediates. The rate-determining step is a chair-to-boat conformational change of the Br-dioxane adduct. The calculated rate coefficients, given by k1calc(T) ) 5.6 × 10-11exp[-26.6 kJ mol-1/(RT)] cm3 molecule-1 s-1, are in very good agreement with the experimental values. Comparison with results reported for the reactions of Br with other ethers suggests that this multistep mechanism differs significantly from that for abstraction of hydrogen from other ethers by atomic bromine. Introduction Atomic bromine is formed in the atmosphere by photolysis of Br2 and organobromine compounds which are produced both naturally and by human activity. The reactions of atomic bromine with organic compounds are often fairly slow compared to the corresponding reactions of atomic chlorine. This leads to important differences in the roles of Cl and Br in determining the concentration of atmospheric ozone. It also leads to large differences in the atmospheric concentrations of bromine and chlorine compounds, such as HCl and HBr, that are formed in part by hydrogen abstraction from volatile organic compounds. The rate coefficients for the reactions of Br with saturated organic compounds show much greater dependence on structure than those for the corresponding reactions of Cl. Consequently, rate coefficients for the reactions of atomic bromine with organic compounds are needed as a function of temperature in order to understand the origins of their greater dependence on structure compared to those for atomic chlorine. This should aid in evaluating their contribution to the chemistry of both the troposphere and the stratosphere.1–3 Such information is particularly important in the marine boundary layer2 where the concentration of atomic bromine can be comparatively large. * To whom correspondence should be addressed. Tel: (902) 585-1353. Fax: (902)585-1114. E-mail: [email protected]; [email protected]. † Currrent Address: Alberta Sulfur Research Ltd., #6, 3535 Research Road NW, Calgary, Alberta T2L 2K8, Canada.

While correlations of the rate coefficients for reactions of organic compounds with Br with respect to such species as OH, NO3, and O(3P) exist,4 these are for a fixed temperature near 300 K. Such correlations do not distinguish between the entropic and enthalpic contributions to the chemical reactivity of Br with organic compounds and so do not permit reliable evaluation of rate coefficients at other temperatures that might be of interest in atmospheric chemistry. We have been engaged in a program to systematically examine the relative importance of the entropic and enthalpic contributions to the rate coefficients of reactions of atomic bromine, recently focusing on the reactions of Br with a series of ethers.5–7 A striking difference was found between the reactivity of hydrogen atoms adjacent to the ether oxygen and those on carbon atoms that are more distant from the ether oxygen. We have selected the reaction of Br with 1,4-dioxane for closer scrutiny for several reasons. It is an industrially important organic compound and might be expected to be emitted to the atmosphere. It is also a good choice as a model compound because all of the C-H bonds are adjacent to an ether oxygen. It provides a good comparison with other cyclic ethers which we have studied7 in that it can provide information about the effects of adding a second ether oxygen and possible complications due to conformational changes. Finally, it serves as a good structural model for theoretical studies to examine the role of the ether oxygen in complex formation with Br. Such calculations can also provide information about the transition state structures available for the reaction of Br with ethers in

10.1021/jp908168u  2010 American Chemical Society Published on Web 10/22/2009

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which all of the C-H bonds are adjacent to an oxygen atom. In that respect, such calculations complement work reported previously for the reaction of atomic bromine with methanol,8 serving to identify various structures on the potential energy surface that might be general to reactions of Br with oxygencontaining organic compounds and could eventually be helpful in obtaining an overall picture of the reaction kinetics involving the Br atom and ethers. Experimental Section The experimental approach has been previously described in detail5–7 and is summarized briefly here. The reactions to be studied took place in a 70-L Pyrex reaction vessel enclosed in an insulated housing through which hot or cold air could be circulated to control the reaction temperature. Atomic bromine was generated by photolysis of Br2 using light from a bank of fluorescent lamps surrounding the reaction vessel and producing useful output from ∼350 to 650 nm. The temperature in the reaction vessel was measured with three iron-constantan thermocouples arranged along its long axis, and the pressures were measured with a 10 Torr Baratron pressure gauge or a 1000 Torr piezoelectric pressure gauge. Reaction mixtures were prepared from dilute mixtures of known composition of Br2, the reference reactant (iso-octane or iso-butane), and dioxane in argon which were stored in separate Pyrex bulbs. The gas handling system was constructed of Pyrex, was mercury free, and used Teflon stopcocks. Typical reaction mixtures contained ∼1 × 1016 molecules cm-3 of Br2 with much smaller concentrations of the organic reactants. The concentrations of atomic bromine produced by photolysis were typically much smaller than those of the organic reactants and remained effectively constant during an experiment. The concentrations of the organic reactants remaining after a known duration of irradiation were determined by gas chromatography using a flame ionization detector with sample separation on an 8 ft × 1/8 in. column packed with 1% SP 1000 on 60/80 mesh Carbopak B. Gas samples of known pressure were injected for analysis directly from a sample loop connected to the inlet of the gas chromatograph. The loss of the organic reactants under these conditions was pseudofirst order, as illustrated in Figure 1, with a first order rate coefficient given by the product k[Br] where k is the second order rate coefficient for the reaction. These first order plots could be used to estimate the concentration of atomic bromine once the second order rate coefficient had been determined at the relevant temperature, either in our experiments or by using the reported values of the rate coefficients for the reactions of the reference compounds.6,9 The concentration of atomic bromine estimated in this way was of the order of 1011 to 1012 molecules cm-3, which is roughly 2 to 3 orders of magnitude smaller than the concentrations of the organic reactants used in the experiments. The good linearity of these plots is also consistent with a nearly constant Br concentration throughout the course of the reaction. In a typical experiment, small, known pressures of Br2, the reference reactant and dioxane were first added to the evacuated reaction chamber and a desired final pressure of usually 1 atm was attained by adding argon and oxygen. After the mixture had equilibrated for at least half an hour, a known amount of the reaction mixture was removed to the sampling loop and injected into the gas chromatograph to provide an indication of the signals for the reference reactant and dioxane before reaction. After exposing the reaction mixture to irradiation from the fluorescent lamps for a known length of time, a second sample

Figure 1. Pseudofirst order decays of the organic reactants (open symbols: reference reactant, closed symbols: 1,4-dioxane). All experiments were done in argon with no added O2. Concentrations are given in molecules cm-3. (O,b) [Br2] ) 1.97 × 1016, [C4H8O2] ) 6.91 × 1015, [C4H10] ) 2.41 × 1015, Total Pressure ) 774 Torr, Temperature ) 321.7 K; (0,9) [Br2] ) 9.91 × 1015, [C4H8O2] ) 2.05 × 1015, [C8H18] ) 2.26 × 1015, Total Pressure ) 761 Torr, Temperature ) 319.6 K; (4,2) [Br2] ) 9.04 × 1015, [C4H8O2] ) 2.26 × 1015, [C8H18] ) 2.13 × 1015, Total Pressure ) 758 Torr, Temperature ) 337.8 K.

was removed from the reaction chamber in the same way and was injected into the gas chromatograph to determine the extent of reaction for each organic reactant. Additional irradiations and analyses were done until the desired extent of reaction had been attained. Comparison of the peak areas for dioxane and the reference reactant after each successive irradiation, after adjustment for small variations in the pressure of the sample removed to the sample loop, permitted calculation of the ratio of rate coefficients for the reaction of Br with dioxane relative to the reference reactant. The samples removed from the reaction chamber for analysis were sufficiently small that several successive irradiations could be done on a reaction mixture without significantly altering its total pressure. The maximum extent of reaction was kept as small as practical to minimize the effects of secondary reactions. The kinetic analysis assumes that loss of dioxane and of the reference reactant occurs only by the following reactions:

Br + C4H8O2 f HBr + C4H7O2

(1)

Br + RHref f HBr + Rref ·

(2)

where RHref is the reference reactant, either iso-butane or isooctane. The rate constant ratio is then given by the expression:

{

ln

[C4H8O2]t0 [C4H8O2]t

}

)

{

k1 [RHref]t0 ln k2 [RHref]t

}

(3)

A plot of ln {[C4H8O2]t0/[C4H8O2]t} against ln {[RHref]t0/[RHref]t} is predicted to be linear with slope k1/k2 and with an intercept of zero. The peak areas in the gas chromatograms are proportional to the concentrations of dioxane and the reference reactant so the peak areas can be substituted for the concentrations in eq 3 after the peak areas are normalized to a constant sample loop pressure. The absolute rate coefficient for the reaction with dioxane can then be calculated from the measured values of k1/k2 using the known value of the absolute rate coefficient k2

Reaction Kinetics of Atomic Bromine with 1,4-Dioxane

J. Phys. Chem. A, Vol. 114, No. 1, 2010 293 rapidly with OH. The rate coefficients obtained for the reaction of Br with dioxane were independent of the concentration of oxygen, suggesting that the effects of secondary reactions of OH and organic free radicals have been largely avoided.

Figure 2. Plots of reduced concentrations according to eq 3. All experiments were done in argon with no added O2. Concentrations are given in molecules cm-3. (O) [Br2] ) 1.91 × 1016, [C4H8O2] ) 5.80 × 1015, [C4H10] ) 3.04 × 1015, Total Pressure ) 774 Torr, Temperature ) 321.8 K; (0) [Br2] ) 3.99 × 1016, [C4H8O2] ) 5.56 × 1015, [C4H10] ) 3.13 × 1015, Total Pressure ) 757 Torr, Temperature ) 311.2 K; (b) [Br2] ) 1.03 × 1016, [C4H8O2] ) 1.95 × 1015, [C8H18] ) 2.03 × 1015, Total Pressure ) 762 Torr, Temperature ) 296.5 K; (9) [Br2] ) 9.88 × 1015, [C4H8O2] ) 2.53 × 1015, [C8H18] ) 2.33 × 1015, Total Pressure ) 760 Torr, Temperature ) 330.1 K.

for the reference reaction at the same temperature. These plots were linear, suggesting that the assumptions upon which the kinetic analysis is based were valid and that secondary reactions did not affect the values calculated for the rate coefficients. Typical plots are found in Figure 2. Although eq 3 suggests that the intercepts of these plots should be zero, the intercepts were not forced to be zero because a small systematic error in the initial value of the chromatographic peak area for either dioxane or the reference reactant would result in a positive or negative intercept. Such an error would not influence the slope, but forcing the plots to pass through the origin would bias the slope leading to inaccurate rate coefficients. However, 0,0 is a valid experimental data point and was included in the leastsquares analysis of the data for each rate constant measurement. The intercepts of our experimental plots were smaller than the standard deviation of the regression fit. Experiments such as ours are often done in synthetic air, both to simulate the Earth’s atmosphere and in the hope that the oxygen present will scavenge free radicals generated in the initiation reactions, preventing them from initiating secondary reactions that might complicate the kinetic analysis. However, organic free radicals such as those generated in reactions 1 and 2 usually react with O2 to generate peroxy radicals and an analysis of the potential effects of this intervention by O2 was discussed in earlier publications.6,7 In summary, the concern is that formation of organic peroxy radicals leads to formation of HO2 which can react rapidly with Br forming OH. Since OH tends to react with organic compounds much more rapidly than Br does, formation of OH would then increase the rate of consumption of the organic reactants, leading to either upward or downward curvature of the relative rate plots depending on its relative reactivity toward dioxane and the reference compound. In an earlier publication,5 we have indeed observed such curvature at large extents of reaction and in the presence of large concentrations of O2 but we found that this effect could be avoided by keeping the extent of reaction sufficiently small. All our experiments used a large excess of Br2, which not only is an effective scavenger of organic free radicals but also reacts

The liquid organic reactants used in this work were iso-octane (Aldrich, 99+%) and 1,4-dioxane (Aldrich, 99.8%, inhibitor free). These were thoroughly degassed followed by distillation of the desired amount into its storage bulb. Bromine (ACP, 99.5%) and iso-butane (Aldrich, 99.995%) were purified by freeze-pump-thaw cycles followed by distillation of the desired amounts into their storage bulbs. The other gases, He (Praxair, 99.9995%), Ar (Praxair, 99.9995%), and O2 (Praxair, 99.9995%), were used without further purification. As in our previous work,5–7 the organic reactants were tested for possible interference due to photolysis or from dark reaction with bromine. Each organic reactant was used to prepare a reaction mixture with a composition similar to that used in the kinetic experiments except that bromine was not added to the mixture. Irradiation by the fluorescent lamps for as long as 1 h produced no appreciable change in the concentration of the organic reactant as determined by gas chromatography, leading to the conclusion that photolysis of the organic reactants did not influence the values obtained for the rate coefficients. To test for a dark reaction, reaction mixtures were prepared with concentrations typical of those used in the kinetic experiments. The reaction mixtures were allowed to stand in the reaction chamber for several hours with the lamps turned off. Again, no appreciable change in the concentrations of the organic reactants was found upon chromatographic analysis leading us to conclude that our kinetic calculations were not influenced by dark reactions between the organic reactants and Br2. Calculations The experimental results were rationalized in terms of equilibrium constants from statistical thermodynamics and rate coefficients from transition-state theory (TST) using the molecular and transition-state parameters from quantum chemical calculations. The methods used in our calculations are first briefly outlined. Structures and Energies. Geometries and vibrational frequencies of the stationary points were calculated using secondorder Møller-Plesset perturbation theory (MP2),10,11 with Dunning’s augmented correlation-consistent polarized valence double-zeta basis set (aug-cc-pVDZ).12,13 In order to improve the energetic description, we additionally performed single-point coupled cluster calculations14,15 with single and double excitations including triples corrections (CCSD(T)).16 In these calculations, Dunning’s correlation consistent polarized valence doublezeta (cc-pVDZ) or triple-zeta (cc-pVTZ) basis sets were used.12,13 The CCSD(T) energies at the complete basis set (CBS) limit were obtained by employing the extrapolation scheme developed by Helgaker et al.17,18 We calculated zero-point corrections from the frequencies obtained at the MP2/aug-ccpVDZ level of theory, using a scaling factor of 0.9615.19 All computations were performed with the Gaussian03 program package20 employing the spin-unrestricted formalism.11 Equilibrium Constants and Rate Coefficients. For the calculation of equilibrium constants, K(T), and rate coefficients, k(T), the standard expressions from statistical thermodynamics21 and statistical rate theory,22,23 respectively, were used:

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K(T) )

∏

(qi /V)

∏

(qi /V)

products

(

exp -

∆H0K RT

Giri et al.

)

(4)

reactants

k(T) ) L

kBT h

qTS /V

∏

( )

exp -

(qi /V)

E0 RT

(5)

reactants

Here, qi denotes the molecular partition function of the species i, where TS stands for transition state, V is the volume, ∆H0K is the enthalpy of reaction at T ) 0 K, and E0 is the threshold energy at T ) 0 K. The quantities kB and h denote Boltzmann’s constant and Planck’s constant, respectively. The rovibrational partition functions were calculated in the rigid rotor/harmonic oscillator approximation, and the electronic partition functions were set equal to 2 for the polyatomic radical species and equal to 4 for the bromine atom. In eq 5 external symmetry numbers, σi, of reactants and transition states were omitted from the rotational partition functions and combined together with the number of optical isomers, mi, in the reaction path degeneracy L ) mTSσreactant/(mreactantσTS).24 Results and Discussion We begin by describing the results of the experimental work. This is followed by a description of the computational results. Experiments. Examination of the reaction mixtures by FTIR spectroscopy after irradiation indicated that a large amount of HBr was formed. This is consistent with the results of our earlier work5–7 and confirms that the chemical reactions upon which our kinetic analysis was based provide a good description of our experiments. The rate of reaction of dioxane with atomic bromine proved to be roughly comparable to the rates of reaction of Br with iso-octane and with iso-butane, making these useful reference reactants as in previous work.6,7 The rate coefficients for the reaction of Br with iso-octane were calculated from results which we reported earlier6 and are traceable to the

Figure 3. Temperature dependence of the rate coefficient k1; (O) measured relative to iso-butane; (b) measured relative to iso-octane. The solid line represents the linear fit to the experimental data while the dashed line represents the results calculated from theory.

absolute rate coefficients for the reaction of Br with iso-butane reported by Seakins et al.9 When the reaction of Br with isobutane was used as the reference reaction, the rate constant reported by Seakins et al. was also used. The equations relating these reference rate coefficients to temperature were, for isobutane, k(T) ) (1.61 ( 0.60) × 10-10 exp[-(3.46 ( 0.17) × 103/T] cm3 molecule-1 s-1 and for iso-octane, k(T) ) (3.34 ( 0.59) × 10-12exp[-(1.80 ( 0.11) × 103/T] cm3 molecule-1 s-1. Typical relative rate plots are provided in Figure 2 and the temperature dependence of the rate coefficients is presented in Figure 3. The results are summarized in Table 1. The presence of O2 was found to have no perceptible effect on the numerical values of the rate coefficients within the experimental uncertainty limits. The temperature dependence of the experimentally determined rate coefficients for the reaction of Br with dioxane was given by the following:

TABLE 1: Summary of Kinetic Data for the Reaction of Br with 1,4-Dioxane Measured Relative to the Reactions of Br with Iso-Octane and with Iso-Butanea absolute temperature

[REF]0 × 10-15 (molec. cm-3)

296.5 297.8 298.9 299.2 299.2 301.1 319.6 321.2 331.6 337.4 337.8

2.03 2.37 2.02 2.03 2.03 2.06 2.26 1.99 2.33 2.21 2.13

305.0 305.4 311.2 313.7 315.8 321.7 321.8

2.79 3.03 3.13 3.26 2.47 2.41 3.04

a

[C4H8O2]0 × 10-15 (molec. cm-3)

The uncertainties represent one standard deviation.

[Br2]0 × 10-15 (molec. cm-3)

Measured relative to iso-octane 1.95 10.3 1.97 9.49 2.56 10.8 1.92 10.7 2.55 13.9 1.86 7.79 2.05 9.91 2.33 9.10 2.53 9.87 2.19 9.94 2.26 9.04 Measured relative to iso-butane 5.96 21.4 6.32 20.7 5.56 31.3 5.33 21.5 6.00 13.4 6.91 19.7 5.80 19.1

kC4H8O2/kREF

kC4H8O2 × 1015 (cm3 molec.-1 s-1)

0.167 ( 0.017 0.141 ( 0.013 0.148 ( 0.033 0.157 ( 0.015 0.173 ( 0.010 0.209 ( 0.022 0.151 ( 0.010 0.221 ( 0.010 0.207 ( 0.010 0.250 ( 0.018 0.253 ( 0.015

1.29 ( 0.13 1.11 ( 0.10 1.20 ( 0.27 1.28 ( 0.12 1.41 ( 0.08 1.77 ( 0.19 1.80 ( 0.12 2.71 ( 0.12 3.03 ( 0.15 4.02 ( 0.29 4.10 ( 0.24

0.804 ( 0.055 0.908 ( 0.070 0.899 ( 0.056 0.954 ( 0.081 0.777 ( 0.039 0.720 ( 0.008 0.821 ( 0.024

1.62 ( 0.11 1.93 ( 0.15 2.15 ( 0.13 2.24 ( 0.19 2.32 ( 0.12 2.47 ( 0.03 2.83 ( 0.08

Reaction Kinetics of Atomic Bromine with 1,4-Dioxane

J. Phys. Chem. A, Vol. 114, No. 1, 2010 295

-11 kexp × 1 (T) ) (1.4 ( 1.0) × 10 -1

-1 -1

exp[-(23.0 ( 1.8)kJ mol /(RT)]cm molecule s 3

(6)

in which the uncertainties represent one standard deviation. While the uncertainty in the pre-exponential factor is large, this is a result of the long extrapolation to the axis of data obtained over the rather small temperature range accessible in our apparatus. The experimental precision of the rate coefficients obtained at a given temperature was approximately (10%, which is much smaller than would be suggested by the standard deviation in the pre-exponential factor. Calculations. The energy diagram of the reaction with the electronic energies obtained at the CCSD(T)/CBS level of theory is shown in Figure 4. The geometrical parameters are given in Table IS, and the structures are displayed in Figures IS and IIS of the Supporting Information.

Figure 4. Energy profile obtained at the CCSD(T)/CBS level of theory for the C4H8O2 + Br reaction system (including scaled zero-point energies, see text); the prefixes c- and b- denote the chair and boat conformer, respectively.

It is important to note that 1,4-dioxane can occur in two stable structures, a chair and a boat conformation. At the CCSD(T)/ CBS level of theory, the chair conformer was found to be 27.4 kJ/mol more stable than the boat conformer, and the transition state connecting these isomers lies 45.5 kJ/mol above the chair conformer. In the temperature regime of our experiments, it follows that the relative fraction of the boat conformer under equilibrium conditions is below 10-4. Consequently, the 1,4dioxane + Br reaction is completely governed by the chair conformer. The overall reaction 1 was calculated to be endothermic by 23.1 kJ/mol at T ) 0 K, a value which is in reasonable agreement with our experimentally determined activation energy of 23.0 ( 1.8 kJ/mol. However, in our calculations, the H-abstraction reaction was found not to occur directly but through an addition-elimination mechanism proceeding via a sequence of isomerization steps involving different intermediates. The initial step is the formation of an association complex, c-C4H8O2-Br, which is essentially stabilized by the interaction between the bromine atom and one of the oxygen atoms in the ether moiety. This is analogous to the adduct previously described for the reaction of Br with methanol.8 The association complex is lower in energy by 24.7 kJ/mol with respect to the reactants and represents the most stable intermediate along the entire reaction pathway. Although we performed extensive calculations, we were not able to find a transition state connecting this complex directly

to the reaction products, C4H7O2 + HBr. Obviously, the hydrogen abstraction itself does not happen from this structure but requires a ring inversion. The 1,4-dioxane ring in the c-C4H8O2-Br adduct was found to flip at first to a more unstable boat conformation, b-C4H8O2-Br, from which the H-transfer from the carbon to the bromine atom occurs. It appears that the ring inversion is necessary before the hydrogen-transfer step itself can happen. A transition-state for the interconversion of the two dioxane-bromine adduct conformers was found and is located 22.4 kJ/mol above the bimolecular reactants and 47.1 kJ/mol above the c-C4H8O2-Br complex; it represents the highest barrier along the reaction pathway. The isomerization product, b-C4H8O2-Br, lies 1.1 kJ/mol above the bimolecular reactants. The intramolecular H abstraction in this conformation has a threshold energy of only 17.4 kJ/mol, and the transition state is product-like, where both the forming (H-Br) and breaking (C-H) bonds are already very close to their final values. This transition state, however, does not directly lead to the final products either but to a predissociative complex, which finally decomposes into the separate fragments C4H7O2 + HBr. This predissociative complex is stabilized by long-range interactions between the abstracted hydrogen and the oxygen in the 1,4-dioxanyl radical. Again, this type of behavior is similar to that found for the predissociative complex in the reaction of Br with methanol.8 Our kinetic analysis is based on the energy profile displayed in Figure 4. Accordingly, the mechanism of reaction 1 can be written as a sequence of four elementary steps:

c-C4H8O2 + Br a c-C4H8O2-Br

(1a)

c-C4H8O2-Br a b-C4H8O2-Br

(1b)

b-C4H8O2-Br a C4H7O2-HBr

(1c)

C4H8O2-HBr a C4H7O2 · + HBr

(1d)

where the prefixes c- and b- denote the chair and boat conformers, respectively. The overall endothermicity, the low temperature, and the fact that we did not observe any discernible pressure dependence of the overall rate coefficient in our experiments strongly indicate that the rate coefficients of all elementary steps involved are at their high-pressure limits. This ensures that pressure-dependent chemical activation effects need not be considered, and in such a case, canonical transition state theory (TST) and equilibrium statistical thermodynamics can be used for kinetic analyses. At first we note that the simple association reaction 1a occurs without a transition state and, hence, with a rate coefficient near the collision limit. Since reaction 1b has a considerably higher threshold energy than the reverse of reaction 1a and, moreover, a comparatively tight transition state, the equilibrium (1a) is rapidly established and virtually not affected by reaction 1b. Furthermore, reaction 1c is faster than reaction (-1b) due to the lower threshold energy, and reaction 1d is faster than reaction (-1c) due to the much higher entropy of the loose dissociation pathway (1d). The latter was verified by comparing the rate coefficient of reaction (-1c) from TST with the rate coefficient of reaction 1d obtained from the rate coefficient of reaction (-1d) and the equilibrium constant K1d. With k-1d ≈ 10-10 cm3 molecule-1 s-1 (collision limit, no barrier) and an equilibrium constant K1d ≈ 2 × 1022 molecules cm-3 (eq 4 with data from

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TABLE 2: Enthalpies of Reaction, Enthalpies of Activation and Entropies of Activation for the Reactions of Atomic Bromine with 1,4-Dioxane Compared to Dimethyl Ether, Diethyl Ether, Tetrahydrofuran, Tetrahydropyran, and Methanola enthalpy of reaction at 298 K (kJ mol-1)

enthalpy of activation (kJ mol-1)

entropy of activationb (J K-1 mol-1)

ref

22.2c

21.3c

-86.5c

this work

Br + C4H8O f HBr + C4H7O

19 ( 6 19 ( 6

18 ( 2 16 ( 2

-99 +10/-5 -94 ( 6

this work 7

Br + C5H10O f HBr + C5H9O

19 ( 6

17 ( 1

-94 ( 4

7

Br + (C2H5)2O f HBr + C2H5OCHCH3

23 ( 4

18 ( 3

-96 ( 8

7

Br + (CH3)2O f HBr + CH2OCH3

36 ( 4

27 ( 2

-96 ( 6

7

Br + CH3OH f HBr + CH2OH

36 ( 1

33 ( 1

-98 ( 2

8

reaction Br + C4H8O2 f HBr + C4H7O2

a The thermodynamic data are estimated using enthalpies of formation of the stable species from ref 25 and bond dissociation energies from ref 26. The results of our quantum chemical calculations are also shown. The uncertainties represent one standard deviation. b Standard state 1 atm, T ) 298 K. c From our quantum chemical calculations (see text).

our quantum chemical calculations), one obtains k1d ≈ 2 × 1012 s-1, which is more than 1 order of magnitude higher than k-1c ≈ 1 × 1011 s-1 (T ) 300 K). Accordingly, the overall reaction 1 can be described in a reasonable approximation by the rate determining step (1b) with a pre-equilibrium (1a). Accordingly, for the overall rate coefficient, it follows that,

k1(T) ) K1a(T)k1b(T)

(7)

With K1a(T) from eq 4 and k1b(T) from eq 5 (with L ) 2), one obtains rate coefficients, which can be represented in the range T ) 300-340 K by the following Arrhenius equation.

kcalc 1 (T) ) 5.6 10-11exp[-26.6 kJ mol-1 /(RT)]cm3molecule-1s-1

(8)

The excellent agreement between this result and our experimental values is indicated in Figure 3. The temperature dependence of the rate coefficients for the reaction of atomic bromine with 1,4-dioxane measured in this work is compared in Table 2 with the corresponding results for dimethyl ether, diethyl ether, tetrahydrofuran, and tetrahydropyran reported previously,6,7 as well as for the reaction of Br with methanol.8 The reaction of dioxane has an enthalpy of activation that is similar to those of all the ethers except dimethyl ether. The data in Table 2 suggest that when Br abstracts hydrogen from CH2 groups adjacent to an ether oxygen the enthalpy of activation is ∼20 kJ mol-1. However, the results for dimethyl ether and methanol indicate that abstraction of hydrogen from CH3 groups adjacent to an oxygen atom has a significantly larger enthalpy of activation of roughly 30 kJ mol-1. This behavior mirrors that observed in the reactions of Br with small alkanes.7,9 The difference in behavior of the abstraction reactions at CH3 and CH2 hydrogens has been attributed to the increased stability of a secondary free radical relative to that of a primary free radical. It is also anticipated that the activating effect of the ether oxygen will decrease significantly at carbon atoms that are not adjacent to the oxygen atom. From Table 2, it is also obvious that there is a pronounced correlation between the enthalpies of activation and the enthalpies of reaction for these endothermic reactions.

The entropy of activation of the Br + dioxane reaction as determined from our experiments is rather uncertain due to the large uncertainty of the pre-exponential factor. From our quantum chemical calculations, we obtain a value of -86.5 J K-1 mol-1, which differs by about +10 J K-1 mol-1 from the results for the other reactants. If we separate this overall value into the contributions from the association step, eq 1a, and the chair-boat conformational change, eq 1b, we obtain values of -94.5 and +8.0 J K-1 mol-1, respectively. If these values are compared with the results for the other reactions of Br with ethers, then it becomes obvious that the entropies of activation for these systems indicate a similar bromine + ether association step with a subsequent hydrogen atom transfer, but which occurs in these cases without a significant entropy change. In this respect, the reaction of Br with dioxane has a significantly different mechanism from that for the reactions of Br with these other ethers. The variation in the reactivity of atomic bromine with cycloalkanes and the cyclic ethers, tetrahydrofuran, tetrahydropyran, and 1,4-dioxane, requires some comment here. An experimental examination of the kinetics of the reaction of Br with cycloalkanes using the relative rate method,27 combined with absolute rate coefficients from the literature,4,9 indicates that the rate coefficient for the reaction of Br with cyclohexane at 298 K is in the range 10-16 to 10-17 cm3 molecule-1 s-1. This makes it roughly an order of magnitude slower than the reaction of Br with 1,4-dioxane. However, the reaction of Br with tetrahydrofuran7 has a rate coefficient at 298 K of 1.8 × 10-13 cm3 molecule-1 s-1 and the reaction of Br with tetrahydropyran7 has a rate coefficient at the same temperature of 1.3 × 10-13 cm3 molecule-1 s-1. At first glance, this would suggest that the incorporation of a second oxygen atom in dioxane produces less, rather than more, activation of the C-H bond. However, the activation of the C-H bond is more appropriately measured by the activation energy. The Arrhenius activation energy reported27 for the reaction of Br with cyclohexane is 48.2 ( 1.3 kJ mol-1, while for the reactions of Br with dioxane, tetrahydrofuran, and tetrahydropyran the Arrhenius activation energies are, respectively, 23.0 ( 1.8 kJ mol-1, 18.2 ( 1.2 kJ mol-1, and 19.5 ( 1.3 kJ mol-1. This comparison makes it clear that incorporation of the first oxygen atom (in tetrahydrofuran and tetrahydropyran) has approximately the same activating effect on the C-H bonds adjacent to it as does incorporation

Reaction Kinetics of Atomic Bromine with 1,4-Dioxane of the second oxygen atom into the ring (in dioxane). In all three cyclic ethers, it is postulated that the C-H bonds adjacent to the ether oxygen are the ones that react with atomic bromine. In all three ethers, the ether oxygen has four C-H bonds adjacent to it. Thus, the three ethers are expected to show approximately the same degree of activation relative to cyclohexane, consistent with the measured activation energies. As indicated earlier, the smaller rate coefficients for the reaction of Br with dioxane, compared with those for the reactions of Br with tetrahydrofuran and tetrahydropyran, are a result of the complex reaction path of the dioxane reaction. Conclusions It is clear that structural considerations, particularly the role of a heteroatom, play an important part in determining the reactivity of organic compounds with atomic bromine. In the case of the reactions of Br with ethers, the reactivity is controlled by variations in both the pre-exponential factor and the enthalpy of activation. While the pre-exponential factors and enthalpies of activation of the reactions of ethers with Br show uniform behavior as long as conformational changes do not occur, the situation with dioxane is unique. Our quantum chemical calculations have shown that for this reaction system, at first a bromine-ether adduct complex is formed from the chair conformer only, which then isomerizes to the boat conformer of the adduct complex followed by an intramolecular H abstraction and subsequent elimination of HBr. In the reaction of Br with dioxane, the c-C4H8O2-Br complex is analogous to the CH3(Br)OH complex formed in the reaction of Br with methanol. Our calculated entropy change for the complex formation has the same order of magnitude as the overall entropies of activation experimentally obtained for the reaction of atomic bromine with dimethyl ether, diethyl ether, tetrahydrofuran, and tetrahydropyran. In our previous work,7 we also noted that complex formation did not appear to affect the measured entropy of activation but evidently led to an increase in the enthalpy of activation. This was based on a comparison of the temperature dependence of the reaction of Br with methanol,8 in which a hydrogen bonded complex is formed, with our experimental results for the reactions of Br with ethers. The methanol reaction had the same entropy of activation as the ether reactions but its enthalpy of activation was significantly larger than the enthalpies of activation of the ether reactions. However, the presence of the ether oxygen decreased the enthalpy of activation relative to the enthalpies of activation of reactions of Br with small alkanes.9 The variation with structure in the enthalpy of activation of the reactions of Br with the ethers was similar to that found for the reactions of the alkanes. Since formation of a complex between Br and an alkane is unlikely, this led us to conclude in our previous work7 that our results did not require the formation of a complex between Br and the ethers, and that the reactions of Br with the ethers proceeded by direct hydrogen abstraction. However, the results of the computational work reported here suggest that a similar computational analysis of the reactions of Br with the other ethers may well indicate that these bromine + ether reactions are also initiated by bromine-ether adduct formation but that subsequent steps, unlike in the case of Br + dioxane, do not significantly contribute to the entropy of activation. The lack of measurable pressure dependence for the reaction of Br with dioxane as well as for the corresponding reactions of the other ethers7 provides experimental evidence that complex formation between Br and the ether is effectively in its high pressure limit. Prediction of the relative reactivity of organic compounds with atomic bromine based only on rate coefficients measured

J. Phys. Chem. A, Vol. 114, No. 1, 2010 297 at a single temperature should be used with caution when applying these results to significantly different temperatures. Although application of enthalpies and entropies of activation which might be thought to be characteristic of a particular kind of reaction provides some improvement in predictive ability, it is beneficial to have supporting computational studies which can identify distinctive features of the potential energy surface of a reaction. This work represents one of a very few reports of a systematic theoretical analysis of the underlying structural foundations controlling the observed variation in chemical reactivity of atomic bromine toward organic compounds. Acknowledgment. This work was supported by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada. N.G.-G. and M.O. are grateful to the Alexander von Humboldt Foundation for a Research Fellowship to N.G.-G. Supporting Information Available: Figures and tables with geometric parameters and harmonic wave numbers of all relevant species. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Bedjanian, Y.; Poulet, G. Chem. ReV. 2003, 103, 4639. (2) Finlayson-Pitts, B. J. Chem. ReV. 2003, 103, 4801. (3) Finlayson-Pitts, B. J.; Pitts, J. N., Jr. Chemistry of the Upper and Lower Atmosphere Theory, Experiments, and Applications; Academic Press: New York, 2000. (4) Bierbach, A.; Barnes, I.; Becker, K. H. Int. J. Chem. Kinet. 1996, 28, 565. (5) Anthony, L. M.; Roscoe, J. M. J. Phys. Chem. A 2004, 108, 7535. (6) Wheeler, M.; Mills, R.; Roscoe, J. M. J. Phys. Chem. A 2008, 112, 858. (7) Giri, B. R.; Roscoe, J. M. J. Phys. Chem. A 2009, 113, 8001. (8) Jodkowski, J. T.; Rayez, M-T; Rayez, J-C; Be´rces, T.; Do´be´, S. J. Phys. Chem. A 1998, 102, 9230. (9) Seakins, P. W.; Pilling, M. J.; Niiranen, J. T.; Gutman, D.; Krasnoperov, L. N. J. Phys. Chem. 1992, 96, 9847. (10) Møller, C.; Plesset, M. S. Phys. ReV. 1934, 46, 618. (11) Hehre, W. J.; Radom L.; Schleyer, P. v. R.; Pople, J. A. Ab initio Molecular Orbital Theory; Wiley: New York, 1986. (12) Dunning, T. H., Jr. J. Chem. Phys. 1989, 90, 1007. (13) Kendall, R. A.; Dunning, T. H., Jr.; Harrison, R. J. J. Chem. Phys. 1992, 96, 6796. (14) E`´ıek, J. J. Chem. Phys. 1966, 45, 4256. (15) Purvis III, J. D.; Bartlett, R. J. J. Chem. Phys. 1982, 76, 1910. (16) Pople, J. A.; Head-Gordon, M.; Raghavachari, K. J. Chem. Phys. 1987, 87, 5968. (17) Helgaker, T.; Klopper, W.; Koch, H.; Noga, J. J. Chem. Phys. 1997, 106, 9636. (18) Halkier, A.; Helgaker, T.; Jorgensen, P.; Klopper, W.; Koch, H.; Olsen, J.; Wilson, A. K. Chem. Phys. Lett. 1998, 286, 243. (19) Merrick, J. P.; Moran, D.; Radom, L. J. Phys. Chem. A 2007, 111, 11683. (20) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, Jr., J. A.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin; A. J.; Cammi; R.; Pomelli; C.; Ochterski; J. W.; Ayala; P. Y.; Morokuma; K.; Voth; G. A.; Salvador; P.; Dannenberg; J. J.; Zakrzewski; V. G.; Dapprich; S.; Daniels; A. D.; Strain; M. C.; Farkas; O.; Malick; D. K.; Rabuck; A. D.; Raghavachari; K.; Foresman; J. B.; Ortiz; J. V.; Cui; Q.; Baboul; A. G.; Clifford; S.; Cioslowski; J.; Stefanov; B. B.; Liu; G.; Liashenko; A.; Piskorz; P.; Komaromi; I.; Martin; R. L.; Fox; D. J.; Keith; T.; Al-Laham; M. A.; Peng; C. Y.; Nanayakkara; A.; Challacombe; M.; Gill; P. M. W.; Johnson; B.; Chen; W.; Wong; M. W.; Gonzalez; C.; and Pople; J. A. Gaussian 03, reVision C.02; Gaussian, Inc.: Wallingford, CT, 2004. (21) McQuarrie, D. A. Statistical Thermodynamics; University Science Books: Mill Valley, 1973. (22) Glasstone, S.; Laidler, K. J.; Eyring, H. The Theory of Rate Processes; McGraw-Hill: New York, 1941.

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