Article pubs.acs.org/JPCA
Water Effect on the OH + HCl Reaction Robert J. Buszek,†,§ John R. Barker,‡ and Joseph S. Francisco*,† †
Department of Chemistry, Purdue University, West Lafayette, Indiana 47907-2084, United States Department of Atmospheric, Oceanic and Space Sciences, University of Michigan, Ann Arbor, Michigan 48109-2143, United States
‡
S Supporting Information *
ABSTRACT: Hydrochloric acid is a major reservoir for chlorine radicals in the atmosphere. Chlorine radicals are chemically reactivated by the relatively slow attack of OH radical on HCl. Through the formation of hydrogen-bonded complexes, water has a dramatic effect on the rate of this reaction. The introduction of water opens several new reaction pathways with rate coefficients that are faster than the “bare” reaction. Accounting for the low fraction of hydrogen bonded water complexes in the atmosphere, the present results suggest that these new mechanisms involving water can contribute, although modestly, to the total chemical reactivation of chlorine from HCl in the lower troposphere. The first reported value for the equilibrium constant for the formation of H2O·HCl complex, which is important in understanding the removal of HCl from the atmosphere by deposition, is presented.
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INTRODUCTION Chlorine radicals are of great atmospheric importance due to their ability to destroy ozone. They also play a major role in the formation of the Antarctic “ozone hole”, through the following catalytic cycle:1 2 × (Cl + O3 → ClO + O2 )
(1)
ClO + ClO + M → ClOOCl + M
(2)
ClOOCl + hν → Cl + ClOO
(3)
ClOO + M → Cl + O2 + M
(4)
Net: 2O3 + hν → 3O2
(5)
(1)
ClO + O → Cl + O2
(6)
Net: O3 + O → 2O2
(7)
(9)
OH + O3 → HO2 + O2
(10)
Net: 2O3 + hν → 3O2
(5)
Cl + CH4 → HCl + CH3
(11)
Cl + HO2 → HCl + O2
(12)
HCl + OH → H 2O + Cl
(13)
The reaction of hydrogen chloride with hydroxyl radical has been studied extensively both experimentally5−18 and theoretically.5,6,19−24 The experimental rate constants fall in the range Received: March 15, 2012 Revised: April 25, 2012 Published: May 7, 2012
(1) © 2012 American Chemical Society
HOCl + hν → Cl + OH
Reservoir species (including HCl) are removed from the stratosphere by transport back down into the troposphere and through the reactivation of chlorine, which is initiated by photolysis or chemical reactions. Hydrochloric acid has a strong absorption band centered at 155 nm,3,4 but solar radiation at this wavelength is essentially completely absorbed by molecular oxygen at higher altitudes. Thus chlorine is reactivated from HCl primarily by its reaction with OH radicals (reaction 13).
In the lower stratosphere, where atomic oxygen is not abundant, chlorine radicals are produced primarily through photolysis of HOCl: Cl + O3 → ClO + O2
(8)
These cycles are slowed by the removal of Cl-atoms and ClO radical through the formation of temporary reservoirs such as HCl. Stratospheric hydrogen chloride is formed primarily by the reaction of Cl-atoms with methane (reaction 11) and hydroperoxyl radicals (reaction 12):
This cycle is estimated to be responsible for ∼70% of the ozone destruction in the Antarctic.2 In this cycle, chlorine radicals are regenerated via photolysis of ClOOCl (the “ClO dimer”). At lower latitudes, where temperatures are higher, this cycle is insignificant because the ClO dimer is not present in sufficient concentrations. Instead, other reactions regenerate chlorine radicals. The dominant catalytic cycle in the mid to upper stratosphere at lower latitudes involves atomic oxygen (reaction 6): Cl + O3 → ClO + O2
ClO + HO2 → HOCl + O2
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from 6.8 × 10−13 to 8.5 × 10−13 cm3 molecule−1 s−1 at room temperature. The value recommended by the NASA Panel for Data Evaluation25 is 7.8 × 10−13 cm3 molecule−1 s−1 at 298 K with an uncertainty factor of 1.1. Theoretical studies6,19 using high level ab initio methods have predicted this reaction to have an energy barrier of 2.43−2.58 kcal mol−1, including zero-point energy (ZPE). Rate constants at 298 K have been predicted using conventional6 and variational transition state theory,19 yielding values of 7.93 × 10−13 cm3 molecule−1 s−1 and 7.78 × 10−13 cm3 molecule−1 s−1, respectively, which are in good agreement with the recommended value. The most important reactions producing and removing HCl in the troposphere are different from those in the stratosphere. Tropospheric HCl is primarily generated from the volatilization of sea salt aerosols through acidification (reactions 14 and 15), but also to some extent from biomass burning, waste incineration, and fossil fuel combustion:26 HNO3(g) + NaCl(aq) → HCl(g) + NaNO3(aq)
(14)
H 2SO4 (g) + NaCl(aq) → 2HCl(g) + Na 2SO4 (aq)
(15)
In this paper, we report on the effects of water vapor on the reaction of HCl with OH radical (reaction 19) under tropospheric and stratospheric conditions.
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(16)
Since then, both experimental27−33 and theoretical33−37 studies have shown that this reaction involving H2O proceeds first by the formation of the HO2·H2O complex, and the subsequent reaction of this complex with HO2 radical is enhanced, compared to the bare reaction. HO2 + H 2O → HO2 ·H 2O
(17)
HO2 ·H 2O + HO2 → HOOH + O2 + H 2O
(18)
(19)
MATERIALS AND METHODS The geometries and frequencies of all points of interest, including reactants, products, transition states, and complexes have been optimized using the quadratic configuration interaction with single and double excitations (QCISD)77 level of theory utilizing Dunning’s augmented, correlation consistent double-ζ basis set (aug-cc-pVDZ).78−80 In a fairly recent benchmark study,81 the QCISD and CCSD geometries were compared in hydrogen-bonded complexes and were in good agreement with one another. For example, the H2O·OH complex that is a part of this study found that the hydrogen bond distance differed by 0.00035 Å, and the angle of the hydrogen bond differed by 0.002 degrees. The QCISD geometries are sufficiently accurate for the present study, especially in view of the high computational cost of some of the larger structures. In order to obtain accurate energies of these species, further single point energies have been calculated using coupled cluster theory including single double and perturbative triple excitations (CCSD(T))82−84 with larger basis sets up to the augmented correlation consistent quad zeta basis set (augcc-pVQZ).78−80 It has been shown that to accurately describe the energetics of hydrogen bonded complexes, larger basis sets are needed, including diffuse functions and large polar valence. Again looking at the H2O·OH complex, a change of 1.6 kcal mol−1 can be seen when going from the CCSD(T)/6-31G(d) level of theory to the CCSD(T)/6-311++G(2df,2p) level of theory. Thus it was important to use a high level of theory with a large basis set to obtain the accurate energetics needed for estimating the rate constants. All of the transition states have been confirmed to be first-order saddle points by the presence of a single imaginary frequency corresponding to the translation along the reaction coordinate. All open-shell structures are calculated utilizing a unrestricted Hartree−Fock (UHF) wave function.85−87 The ab initio calculations were carried out using the Gaussian 0388 or Gaussian 0989 suite of programs. The rates of reaction are calculated using statistical rate theory methods and the master equation code available in the Multiwell suite of programs.90−93
The major removal processes of HCl in the troposphere are deposition and rain-out. Surprisingly, previous studies have never examined the possible catalytic effects of water vapor on reactions involving HCl in the planetary boundary layer, where deposition occurs. In the late 1970s, Hamilton was the first to show that water vapor significantly affects the rate of the HO2 self-reaction, which produces hydrogen peroxide in the gas phase.27 HO2 + HO2 → HOOH + O2
HCl + OH( +H 2O) → Cl + H 2O( +H 2O)
Further studies have shown that the equilibrium constant for forming the HO2·H2O complex is 2.4 × 10−25 e(4350)/T cm3 molecule−1 at 298 K with an uncertainty factor of 2.0.25 It has been suggested that up to ∼30% of atmospheric HO2 summed over all altitudes is complexed with water,38 and that near sea level ∼10% of HO2 is bound in the complex.39 Not only is the formation of the HO2·H2O complex important in the catalytic response seen for this gas phase reaction, but the complex has also been implicated in the heterogeneous removal of HO2.40 Interest in the reaction of water complexes with atmospheric species has been increasing. The effects of water vapor have also been studied in relation to other radical−radical reactions,41−45 radical−molecule reactions,46−59 molecule−molecule reactions,60,61 hydrolysis reactions,62−66 as well as unimolecular isomerization67−70 and decomposition reactions.71−76 Recently, several studies have investigated the potential catalytic effects of water vapor on hydrogen abstraction reactions involving OH radicals. These include the reactions of OH with formic acid,48,57 nitric acid,49,51 acetaldehyde,47,56 acetone,53 HOCl,59 methane,50 glyoxal,52,58 dimethyl sulfide (DMS),54 and propionaldehyde.55
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RESULTS AND DISCUSSION To determine the effects of water vapor in the reactivation of chlorine via the atmospheric oxidation of hydrogen chloride, the potential energy surface (PES) of the reaction in the absence of water (the “bare reaction”) is compared to the PES when water vapor is present. In the bare reaction, a prereactive complex with a binding energy of 2.3 kcal mol−1 is formed in which the oxygen of the hydroxyl radical forms a hydrogen bond with the hydrogen in HCl (Table 1 and Figure 1). The minimum energy path on the PES passes through a first-order saddle point where the hydrogen of the HCl is abstracted by the OH radical. In the present work, this transition state is 2.1 kcal mol−1 higher in energy than the reactants, in good agreement with previously reported barriers6,19 of ∼2.5 kcal mol−1. As the reaction proceeds beyond the transition state, it generates a halogen-bonded adduct (Figure 1), which subsequently dissociates into Cl + H2O. In the halogen-bonded adduct, the H2O rotates to allow the oxygen atom to interact 4713
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are that the activation barrier is reduced from 2.1 kcal mol−1 to 1.8 kcal mol−1, and two new reaction channels open up at even lower energies: 4.2 and 4.4 kcal mol−1 below the energy of the reactants. In these new channels, the key difference is the orientation of the pendant hydrogen of the H2O. The dramatic lowering of the reaction barrier suggests that the presence of water vapor will enhance the reaction rate significantly. To assess the possible enhancement of the reaction, the rate constant for the bare reaction is compared to the effective rate constant when water vapor is present. Under atmospheric conditions, the rates of pure termolecular reactions are insignificant compared to the rates of sequential bimolecular reactions. This consideration leads to three distinct bimolecular reaction sequences in which a complex is first formed by reaction of H2O with OH or HCl, followed by the bimolecular reaction of the complex with the third species. In other words, the OH·H2O complex (a) reacts with HCl (Sequence A); OH·HCl complex (b) reacts with water (Sequence B); and the H2O·HCl complex (c) reacts with OH radical (Sequence C):
Table 1. Relative Energies Including ZPE (kcal mol−1) with Respect to the Separated Reactants (2H2O + HCl)
[OH·HCl] + H2O [OH·H2O] + H2O [H2O·HCl] + H2O [OH·HCl·H2O] (d) [OH·HCl·H2O] (g) [OH·HCl]‡ + H2O [OH·HCl·H2O]‡ (e) [OH·HCl·H2O]‡ (e′) [OH·HCl·H2O]‡ (h) [Cl·H2O·H2O] (f) [H2O·Cl] + H2O [H2O·H2O] + HCl
QCISD/ aug-cc-pVDZ
CCSD(T)/ aug-cc-pVTZa
CCSD(T)/ aug-cc-pVQZa
−2.3 −3.6 −3.5 −8.1 −7.5 3.5 −3.2 −3.2 5.4 −22.1 −16.8 −17.7
−2.3 −3.8 −3.7 −8.7 −8.1 2.2 −4.2 −4.4 2.1 −23.0 −17.0 −18.0
−2.3 −3.8 −3.6 −8.6 −8.0 2.1 −4.2 −4.4 1.8 −23.1 −17.0 −17.8
a
CCSD(T) single point energy results using the QCISD/aug-ccpVDZ optimized geometries and ZPE.
Sequence A: H 2O + OH ⇌ H 2O ·OH
(20)
H 2O·OH + HCl → Cl + 2H 2O
(21)
Sequence B: OH + HCl ⇌ OH ·HCl
(22)
OH·HCl + H 2O → Cl + 2H 2O
(23)
Sequence C: H 2O + HCl ⇌ H 2O ·HCl
(24)
H 2O·HCl + OH → Cl + 2H 2O
(25)
Thus reactions including bimolecular complexes a, b, and c must be investigated. The OH·HCl complex (b) was discussed above in the context of the bare reaction. At the energy minimum of the H2O·HCl complex (c), a hydrogen bond with a binding energy of 3.6 kcal mol−1 exists between the hydrogen of the HCl and the oxygen in the water (Figure 3). The H2O·OH complex (a), which has a hydrogen bond between the hydrogen of the OH radical and the oxygen in water, has the largest binding energy of the three at 3.8 kcal mol−1 (Figure 2 and Table 1). This is in good agreement with the literature, which reports a binding energy of 3.6 kcal mol−1 at the CCSD(T)/CBS//B3LYP/augcc-pVTZ level of theory.94 It should be noted that the H2O·OH complex has been well studied previously.94−108 It has been suggested that the vibrational deactivation of OH(v) by H2O proceeds by the formation of hydrogen bonds, which facilitate rapid intramolecular vibrational energy redistribution prior to redissociation. In the study of vibrational deactivation,108 the equilibrium constant for formation of complex a was estimated to be 1.72 × 10−22 cm3 molecule−1. The three complexes give rise to two major reaction pathways. The first pathway begins with the formation of complex d via the H2O·OH complex (b) reacting with HCl (Sequence A) or via the OH·HCl complex reacting with H2O (Sequence B). Complex d forms a hydrogen bonded six member cyclic structure with a binding energy of 4.8 kcal mol−1 relative to complex a or 6.6 kcal mol−1 relative to complex b, respectively, as shown in Figure 2. The geometry of complex d resembles the prereactive complex of the bare reaction where the oxygen of the OH radical is hydrogen bonded to the hydrogen in HCl. However, with the addition of a single water molecule, a cyclic structure is formed (Figure 3) in which the hydrogen of the OH radical is hydrogen-bonded to the oxygen
Figure 1. The PES of the bare reaction, in kcal mol−1 calculated at the CCSD(T)/aug-cc-pVQZ//QCISD/aug-cc-pVDZ level of theory. Along with the geometries of the stationary points calculated at the QCISD/aug-cc-pVDZ level of theory, all angles are in degrees, and lengths are in angstroms. Figure is not to scale.
weakly with the chlorine atom yielding a binding energy of 17.0 kcal mol−1 with respect to the reactants; the overall reaction enthalpy is −14.8 kcal mol−1. When water vapor is present, the PES is significantly more complex, as seen in Figures 2 and 3. The most notable changes
Figure 2. The PES with the addition of water in kcal mol−1 calculated at the CCSD(T)/aug-cc-pVQZ//QCISD/aug-cc-pVDZ level of theory. Figure is not to scale. It should be noted that the top surface is the same as in Figure 1. 4714
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Figure 3. The optimized geometries of all complexes and transition states involving water calculated at the QCISD/aug-cc-pVDZ level of theory. Bond lengths are in angstroms, and bond angles are in degrees.
Table 2. Equilibrium Constants and Expressions at Temperatures Relevant to the Atmosphere T (K) 200 225 250 275 298
Keq[OH·HCl] 1.52 7.55 4.36 2.81 2.02
× × × × ×
10−21 10−22 10−22 10−22 10−22
2.62 2.92 3.28 3.69 4.11
× × × × ×
10−24 10−24 10−24 10−24 10−24
Keq[H2O·HCl] exp(1273/T) exp(1250/T) exp(1222/T) exp(1191/T) exp(1161/T)
4.91 × 10−20 1.66 × 10−20 7.07 × 10−21 3.55x 10−21 2.11 × 10−21
2.68 3.02 3.43 3.92 4.43
× × × × ×
10−24 10−24 10−24 10−24 10−24
Keq[H2O·OH] exp(1963/T) exp(1938/T) exp(1907/T) exp(1873/T) exp(1837/T)
4.24 1.34 5.42 2.61 1.49
× × × × ×
10−20 10−20 10−21 10−21 10−21
1.31 1.45 1.62 1.83 2.05
× × × × ×
10−24 10−24 10−24 10−24 10−24
exp(2077/T) exp(2056/T) exp(2029/T) exp(1997/T) exp(1964/T)
transition state h is 1.8 kcal mol−1 above the separated reactants. This barrier inhibits Sequence C from proceeding beyond the formation of complex g. From the above description, it is apparent that the introduction of water vapor catalyzes the reactivation of chlorine radicals by lowering the reaction energy barriers and opening new low-energy pathways. However, the atmospheric significance of the reactions involving water is dependent on the concentrations of the bimolecular complexes formed in reactions 20, 22, and 24. To determine the atmospheric importance of the reaction sequences, the equilibrium constants for formation of the complexes are calculated at tropospheric temperatures and are presented in Table 2. The equilibrium constant for formation of HCl·OH (complex b) is approximately an order of magnitude smaller than those for the other two complexes. In contrast, H2O·HCl (complex c) is predicted to have the largest concentration of the three, based on typical atmospheric concentrations for HCl, OH, and H2O (∼109, ∼106, and ∼1017 to ∼1018 molecules cm−1, respectively). However, as discussed earlier, the subsequent reaction of complex c is energetically unfavorable due to its barrier of 5.4 kcal mol−1 with respect to the reactants. (It should be noted that this is the first reported value for the equilibrium constant for the formation of complex c, which is important in understanding the removal of HCl from the atmosphere by deposition.) The equilibrium constant for forming H2O·OH (complex a), 1.21 × 10−21, is roughly an order of magnitude larger than the estimated value discussed earlier. This value is large compared to the other complexes discussed, and its subsequent reactions are energetically favorable, compared to
of the water, and a hydrogen of the water forms a weak interaction with the chlorine in HCl. Complex d then reacts via transition states e and e′, which are similar in structure to the transition state of the bare reaction where the hydrogen is abstracted by the OH radical. The energies of these transition states are more than 4 kcal mol−1 below the energy of OH + HCl + H2O. Following transition states e and e′, a post reactive complex f is formed. The structure of complex f is similar to the postreactive complex of the bare reaction, as shown in Figure 3; the oxygen of the newly formed water interacts with the chlorine atom. In complex f, the additional water molecule is hydrogen bonded to the hydrogen of the newly formed water and has a weak interaction with the chlorine atom product. Complex f dissociates quickly to produce either H2O + H2O·Cl or (H2O)2 + Cl, which respectively lie 17.0 kcal mol−1 and 17.8 kcal mol−1 below the energy of the separated reactants. The second major pathway involves the H2O·HCl complex c reacting with OH radical (Sequence C). As discussed earlier, the H2O·HCl complex c has the oxygen on water hydrogen bonded with the hydrogen on HCl. Introduction of OH radical produces prereactive complex g, which is similar to complex d, except that the OH radical and the water molecule have exchanged positions. In complex g, a hydrogen from the water molecule is hydrogen-bonded to the oxygen in the OH radical, and the hydrogen of the OH radical forms a weak interaction with the chlorine to complete the cyclic structure, as shown in Figure 3. Complex g reacts via transition state h in which the water acts as a bridge for the hydrogen transfer from the hydrogen chloride to the OH radical. As the water molecule accepts the hydrogen from HCl, it simultaneously donates another hydrogen atom to the OH radical. The energy of 4715
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Table 3. Bimolecular Rate Constants (in cm3 molecule−1 s−1) without water T (K) 298 260 255 250 245 240 235 230 225 220 215
with water k19a
k13 8.49 6.74 6.57 6.33 6.12 5.95 5.75 5.53 5.35 5.19 4.99
× × × × × × × × × × ×
10−13 10−13 10−13 10−13 10−13 10−13 10−13 10−13 10−13 10−13 10−13
9.05 9.61 9.70 9.80 9.91 1.00 1.01 1.02 1.04 1.05 1.07
× × × × × × × × × × ×
10−13 10−13 10−13 10−13 10−13 10−12 10−12 10−12 10−12 10−12 10−12
k19b 9.91 1.06 1.07 1.08 1.09 1.11 1.12 1.13 1.15 1.16 1.18
× × × × × × × × × × ×
10−13 10−12 10−12 10−12 10−12 10−12 10−12 10−12 10−12 10−12 10−12
[H2O]c
k19 1.90 2.02 2.04 2.06 2.08 2.11 2.13 2.15 2.18 2.22 2.25
× × × × × × × × × × ×
10−12 10−12 10−12 10−12 10−12 10−12 10−12 10−12 10−12 10−12 10−12
7.70 5.45 3.50 2.21 1.37 8.29 4.92 2.85 1.61 8.86 4.74
× × × × × × × × × × ×
1017 1016 1016 1016 1016 1015 1015 1015 1015 1014 1014
ktotd 8.51 6.75 6.57 6.34 6.12 5.95 5.75 5.53 5.35 5.19 4.99
× × × × × × × × × × ×
10−13 10−13 10−13 10−13 10−13 10−13 10−13 10−13 10−13 10−13 10−13
enhancement factore (%) 0.26 0.065 0.050 0.039 0.030 0.022 0.017 0.012 0.0088 0.0063 0.0044
Going through transition state e. bGoing through transition state e′. cAll values in molecules cm−3 at 100% relative humidity, value at 298 taken form reference 114, values at 260 and 255 taken from reference 115, and renaming values taken from reference 116. dCalculated using the Keq[H2O·OH] value from Table 2. eEnhancement factor calculated as (k19·Keq[H2O·OH]·[H2O]]/ktot) × 100. a
200 and 298 K, giving A28 = 3.8 × 10−12 cm3 molecule−1 s−1. This value is close to the high pressure rate constants for recombination reactions involving species of roughly the same size: OH + SO2 and HO2 + NO2, which have recommended values of 1.6 × 10−12 and 2.9 × 10−12 cm3 molecule−1 s−1, respectively.109 These values are significantly lower than the recommended high pressure rate constants for OH + OH, OH +NO, and OH + NO2, each of which is found near 3 × 10−11 cm3 molecule−1 s−1.109 This would suggest that the magnitude is reasonable, but near the low end of the range. In order to obtain agreement with the experimental rate constant for the bare reaction, the energy barrier for reaction 13 was decreased by −0.8 kcal mol−1, an amount that is well within the expected uncertainty of our electronic structure calculations. The inverse Laplace transform method110−112 (an option in the Multiwell master equation code) is used to obtain k−28(E), the microcanonical rate constant. The rate constant k29(E) for the forward reaction was obtained from RRKM theory, including tunneling through an asymmetrical Eckart barrier. The simulation was run for Nitrogen collider gas, based on literature values for the Lennard-Jones (LJ) parameters.113 The conventional exponential model is used to simulate the energy transfer by assuming the average energy transferred in deactivating collisions is ⟨ΔE⟩down = 500 cm−1. Because the hydrogen-bonded complexes have low binding energies, their lifetimes are too short for many energy transfer collisions to occur. The LJ parameters for complex CX are assumed to be the same as those for methyl chloride, which is somewhat analogous; methyl ether was assumed to be analogous to CXw. During each simulation, 106 stochastic trials were computed for a simulated time corresponding to 200 collisions in each trial. Each trial was initiated for a newly formed prereactive complex with energy selected randomly from a chemical activation energy distribution. In each trial, the prereactive complex reacted by returning to separated reactants, or by proceeding on to products. Collisional deactivation of the prereactive complex was negligible, as expected. From the predicted relative yields of reactants and products, a product branching ratio (γ) is obtained: ηprod γ= ηreact + ηprod (35)
the bare reaction. Thus, only the reaction sequence involving complex a is included in the following kinetic mechanism: OH + HCl ⇌ CX
(26)
CX → H 2O + Cl
(27)
OH· H 2O + HCl ⇌ CX w
(28)
CX w → H 2O· H 2O + Cl
(29)
where CX and CXw are the prereactive complexes for the bare and water-assisted reactions, respectively. To evaluate the rate constant of the forward reaction, several assumptions and empirical parameters are used. The first assumption is that the rate constants for the recombination reactions 26 and 28 to form CX and CXw, respectively, are independent of temperature, which is justified because barrierless recombination reactions generally have a very weak temperature dependence.16,17 It is also assumed that the reverse reactions follow Arrhenius behavior. Thus we obtain the following expression for the equilibrium constant for reaction 28: K 28 =
A 28 A −28e−E−28 / RT
(30)
where A28 is the pre-exponential factor for the formation of CX, A−28 is the pre-exponential factor for the reverse reaction,17,19 E−28 is the energy barrier for exiting the CX well, R is the gas constant, and T is the temperature. The equilibrium constant can be written as
K 28 = Ae−B / T
(31)
Then A −28e−E−28 / RT =
A 28 −B / T e A
(32)
A −28 = A 28 /Aeq
(33)
E−28 = R ·Beq
(34)
Aeq and Beq are obtained when calculating the equilibrium constant with the Thermo program, which uses standard statistical mechanics methods. The pre-exponential factor for the recombination reaction 28, A28, was varied in order to fit the recommended rate constant for the bare reaction between
k1 = A 28 × γ 4716
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Figure 4. Arrhenius plot for k13, k19, ktot, and the suggested NASA/JPL(3) data for k13.
is potentially an important catalyst for the reaction. However, to quantitatively assess the impact of water vapor on the reaction between OH and HCl, the total rate constant, ktot, for the reaction must be calculated by taking into account the concentration of the H2O·OH complex, which is proportional to Keq[H2O·OH]·[H2O]:
The overall forward rate constant for the reaction is equal to the product of the branching ratio multiplied by the high pressure limit for reaction, as shown in eq 36. The same approach was used for simulations in both the presence and absence of water. The high pressure limit rate constant (i.e., the pre-exponential factor, since the reaction is barrierless) for the formation of the prereactive complex was assumed to be the same both with and without water, i.e., A13 = A28. Also, no changes were made to any of the energetics, as only a slight change was needed in the case of the bare reaction. Because the pathway has two transition states, through the same complex, the rate going through the lower energy barrier (e) is labeled as ka19, and kb19 for the slightly larger barrier (e′); the total rate constant involving water is then the sum of the two rate constants (reaction 37). a b k19 = k19 + k19
k tot = k13 + k19Keq[H 2O· OH]·[H 2O]
In Figure 4, ktot is plotted alongside k13 and k19, with the water concentration set to the saturated equilibrium vapor pressure.114−116 At first, the total rate constant does not appear to diverge from the rate constant of the bare reaction. Closer examination shows that there is a small water vapor effect, which is larger at higher temperatures (Table 3). While at low temperatures, k19 and Keq[H2O·OH] are larger in magnitude, but H2O has a very low saturation vapor pressure at these temperatures. At high temperatures, k19 and Keq[H2O·OH] are smaller, but the abundance of H2O is much larger, resulting in a ∼0.26% enhancement due to water vapor at 298 K. Under atmospheric conditions, it is estimated that in the upper troposphere, the water vapor reaction contributes only ∼0.005% of the total rate constant (ktot). However, a warmer air mass with a temperature of 298 K and a humidity of 80% (7.7 × 1017 molecules cm−3 of H2O), the contribution increases significantly to ∼0.3% closer to the surface. This is consistent with the previously examined behavior of the water enhancement due to the combined effects of the higher saturation vapor pressure of H2O and smaller equilibrium constant for the complex at higher temperature (i.e., at lower altitude).
(37)
In these reactions, CX and CXw are prereactive complexes HCl·OH and H2O·HCl·OH, respectively. To assess the impact that water will have on this reaction, the rate constants of both the bare, k13 (reactions 26 and27), and the water-assisted reaction, k19 (reactions 28 and 29), were calculated at atmospherically relevant temperatures (see Table 3 and Figure 4) and fitted to Arrhenius expressions: k13 = 3.23 × 10−12e−405/ T
(38)
k19 = 1.22 × 10−12e131/ T
(39)
(40)
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The reaction has no significant dependence on total pressure, as shown in the Supporting Information. An examination of the rate expressions for k13 and k19 reveals that the rates behave differently as functions of temperature. It can be seen in Figure 4 that k13 is in good agreement with the recommended experimental value.25 The rate constant of the water-assisted reaction, k19, is significantly larger in magnitude than k13 and exhibits a negative temperature dependence, as is expected when the reaction energy barriers following formation of a prereactive complex are lower than the energy of the reactants. Moreover, at 220 K, a temperature typically found near the tropopause, the ratio k19/k13 is ∼10, which suggests that water
SUMMARY The OH + HCl reaction produces Cl-atoms throughout the atmosphere, where chlorine can attack ozone, hydrocarbons, and other species. Understanding the effects that atmospheric water has on the OH + HCl reaction is of great interest. Our analysis shows that the presence of water vapor enhances the reaction rate constant significantly. This enhanced reaction rate constant exhibits a negative temperature dependence, and is found to be ∼2−5 times faster than for the bare reaction. Because the enhanced reaction takes place through H2O·OH 4717
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(complex a), which reacts more rapidly than the bare OH reaction with HCl, the concentration of the H2O·OH (complex a) limits the contribution of the water assisted reaction. This work also reports the first estimate of the equilibrium constant of the H2O·HCl complex, which is calculated to be 2.11 × 10−21 cm3 molecule−1 at 298 K.
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ASSOCIATED CONTENT
S Supporting Information *
Information regarding the Cartesian coordinates for optimized structures, total energies, relative energies, vibrational frequencies, and rotational constants for all relevant species, as well as rate and equilibrium constants including pressure dependence and all relevant RRKM parameters can be found in the supporting material. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Present Address §
Space and Missile Propulsion Division, Propulsion Directorate, Air Force Research Laboratory, AFRL/RZSP, Edwards AFB, CA 93524, United States. Notes
The authors declare no competing financial interest.
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REFERENCES
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