J. Phys. Chem. 1996, 100, 19911-19916
19911
Kinetics and Products of the Gas-Phase Reaction of SO3 with Water Edward R. Lovejoy,* David R. Hanson,† and L. Gregory Huey† NOAA Aeronomy Laboratory, 325 Broadway, Boulder, Colorado 80303 ReceiVed: August 8, 1996; In Final Form: October 7, 1996X
The kinetics of the gas-phase reactions of SO3 with H2O and D2O were studied over the temperature range 250-360 K in N2 with a laminar flow reactor coupled to a chemical ionization mass spectrometer. The SO3 loss is second order in the water concentration, is independent of pressure (20-80 Torr N2, 300 K), and has a strong negative temperature dependence and a significant H/D isotope effect (kH2O ≈ 2kD2O). The yield of sulfuric acid is 1.0 ( 0.5 per SO3 consumed. These observations are consistent with the rapid association of SO3 and H2O to form the adduct H2OSO3 which reacts with water to produce sulfuric acid. The first-order rate coefficients for loss of SO3 by reaction with H2O and D2O are given by kI(s-1) ) (2.26 ( 0.85) × 10-43T exp((6544 ( 106)/T)[H2O]2 and (9.45 ( 2.68) × 10-44T exp((6573 ( 82)/T)[D2O]2, where T ≡ K and [H2O, D2O] ≡ molecule cm-3. The errors are the uncertainty at the 95% confidence level for precision only. Analysis of the temperature dependence of the SO3 loss yields an upper limit for the H2O-SO3 bond enthalpy of 13 kcal mol-1.
Introduction The gas-phase atmospheric oxidation of sulfur dioxide produces sulfur trioxide:1-3
OH + SO2 + M f HOSO2 + M
(1)
HOSO2 + O2 f HO2 + SO3
(2)
The dominant atmospheric loss process for SO3 is reaction with gas-phase water:
SO3 + H2O ff H2SO4
(3)
Sulfuric acid is an important precursor for atmospheric aerosol.4 SO3 also reacts efficiently with ammonia, producing a stable adduct:5,6
SO3 + NH3 + M f H3NSO3 + M
(4)
It is possible that despite the low atmospheric NH3 concentrations, H3NSO3 may play a role in particle formation because of its very low vapor pressure and strong affinity for sulfuric acid.5 The reaction of SO3 with water has been studied extensively. Castleman et al.7 performed fast-flow experiments with mass spectrometric detection of SO3 and reported a second-order rate coefficient of 9 × 10-13 cm3 molecule-1 s-1. Subsequent calculations by Holland and Castleman8 suggested that SO3 forms an adduct with water:
SO3 + H2O + M f H2OSO3 + M
(5)
which isomerizes efficiently to H2SO4:
H2OSO3 + M f H2SO4 + M
(6)
Chen and Plummer9 applied a higher level of theory to the SO3/H2O system and also concluded that the reaction of SO3 and water forms a relatively stable adduct H2OSO3, but found that the isomerization of the adduct to H2SO4 is inhibited by a * To whom correspondence should be addressed. † Also affiliated with Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, CO 80309. X Abstract published in AdVance ACS Abstracts, November 15, 1996.
S0022-3654(96)02414-8 CCC: $12.00
barrier. They postulated that the simple reaction of SO3 and one water molecule to form H2SO4 is unlikely. Molecular beam experiments by Hofmann-Sievert and Castleman10 demonstrated that H2SO4 is a product of the reaction of SO3 with water clusters. Wang et al.11 studied the gas-phase kinetics of SO3 + H2O by using a flow reactor with photofragment emission detection of SO3. They measured an upper limit of 6 × 10-15 cm3 molecule-1 s-1 for the bimolecular rate coefficient in 1-10 Torr of He at room temperature and concluded that the earlier kinetic studies were influenced by heterogeneous chemistry. A smaller upper limit of 2.4 × 10-15 cm3 molecule-1 s-1 was measured in 85 Torr of air subsequently by Reiner and Arnold12 using a flow reactor coupled to a chemical ionization mass spectrometer. In a more detailed study, Reiner and Arnold13 report a pressure independent (23-195 Torr air) bimolecular rate coefficient of (1.2 ( 0.2) × 10-15 cm3 molecule-1 s-1 at room temperature. Recent high level theoretical studies by Hofmann and Schleyer14 and Morokuma and Muruguma15 indicate that H2OSO3 is bound by about 8 kcal mol-1 relative to SO3 + H2O, and the isomerization of the H2OSO3 adduct to sulfuric acid is inhibited by a very large barrier (19 (ref 14) and 24 kcal mol-1 (ref 15) above SO3 + H2O). Morokuma and Muruguma15 find that more facile paths to sulfuric acid exist when SO3 interacts with two water molecules:
SO3 + (H2O)2 f H2SO4 + H2O
(7)
H2OSO3 + H2O f H2SO4 + H2O
(8)
Their calculations suggest that the reaction with the water dimer (7) proceeds without a barrier, and the reaction of H2OSO3 with water (8) is inhibited by a small barrier of about 5 kcal mol-1. Morokuma and Muguruma15 also predict that the (H2O)2SO3 species is bound by about 6 kcal mol-1 relative to H2OSO3 + H2O but is separated from H2SO4 + H2O by a barrier of about 10 kcal mol-1. Recently Kolb et al.16 studied the SO3 + H2O reaction with an atmospheric pressure turbulent flow reactor coupled to a chemical ionization mass spectrometer. They report that the loss of SO3 is second order in the water concentration and © 1996 American Chemical Society
19912 J. Phys. Chem., Vol. 100, No. 51, 1996 increases significantly (>10 times) as the temperature is lowered from 333 to 243 K. Kolb et al.16 postulate that a significant fraction of the SO3 loss likely involves reaction with the water dimer (reaction 7). Matrix isolation studies have identified IR absorptions due to the H2OSO3 complex.17-19 Bondybey and English18 report that the complex is stable with respect to isomerization to H2SO4 at 5 K in a Ne matrix. From observed isotope shifts, Schriver et al.19 conclude that the complexation involves charge transfer with an O-S interaction. Phillips et al.20 have recently measured the microwave spectrum of the H2OSO3 species in the gas phase and obtained accurate stuctural information which is in good agreement with the predictions of ab initio theory.14 Despite considerable theoretical and experimental effort, the details of the mechanism of the reaction of SO3 and water are still not resolved. In this work, measurements of the first-order rate coefficient for the loss of SO3 in excess H2O and D2O as a function of temperature (250-360 K, 50 Torr N2) and pressure (20-80 Torr of N2 at 300 K) are presented. The SO3 loss is second order in water concentration and has a strong negative temperature dependence, little pressure dependence, and a significant H/D isotope effect. These results are consistent with the rapid formation of an H2OSO3 adduct (reaction 5) followed by a slower reaction of the adduct with water (reaction 8) to produce sulfuric acid. The implications of these results to the understanding of the atmospheric chemistry of SO3 are discussed. Experimental Section The kinetics of the SO3 + H2O reaction were studied by measuring the concentration of SO3 at the exit of a high-pressure laminar flow reactor as a function of the contact distance with water vapor. SO3 was detected in the reactor effluent by chemical ionization mass spectrometry (CIMS). The flow reactor was a jacketed Pyrex cylinder with an internal diameter of 3.1 cm and a length of 50 cm. Temperatureregulated methanol (T < 270 K) or ethylene glycol (T > 270 K) was circulated through the jacket to regulate the reactor temperature. The main carrier gas N2 was added with water at the upstream end of the reactor. Typical N2 flows were about 20 STP cm3 s-1 (STP ) 273 K and 760 Torr) and the pressure ranged from 20 to 80 Torr, giving, for example, an average flow velocity of about 45 cm s-1 at 50 Torr and 300 K. The entrance and mixing lengths21 were about 10 cm, and the Reynolds number was about 40. Water was introduced into the reactor by flowing N2 through a bubbler containing liquid H2O or D2O. The bubbler was immersed in a water bath to stabilize the temperature. The pressure was measured at the exit of the bubbler with a capacitance manometer. The water flow rate was calculated by assuming that the N2 leaving the bubbler was saturated with water. Saturation was confirmed by observing that the CIMS H2O signal was proportional to the calculated water flow rate. The water-saturated N2 stream passed through a Teflon membrane filter to remove particles and mixed with the main N2 flow before entering the reactor. The reactor pressure and temperature were measured in the middle of the reaction zone with a capacitance manometer and glass encased thermocouple, respectively. All of the flow reactor effluent entered the CIMS through a Teflon fitting equipped with a variable orifice to control the reactor pressure. SO3 was added to the reactor through a movable inlet (0.25 in. o.d. Pyrex) which entered the upstream end of the reactor on axis. SO3 was generated at the end of the inlet by passing
Lovejoy et al. SO2 and O2 over a red-hot Nichrome filament (0.004 in. diameter) fixed about 0.5 cm from the exit of the inlet. Typical inlet flow rates were about 0.003 STP cm3 s-1 of SO2 and 0.10.5 STP cm3 s-1 of O2. An aluminum cylinder (about 3 cm long by 3 cm diameter) with a series of longitudinal passages for gas transit was attached to the end of the inlet to enhance the conduction of heat from the filament to the reactor walls. Typically, 0.5-1 W was dissipated by the filament. With the Al radiator in place, the hot filament caused < 3 °C temperature drop along the length of the reaction zone. The largest temperature drops occurred for the lowest reaction temperatures. The formation of aerosol in the reactor was examined by measuring aerosol in the reactor effluent with an expansion counter.22 For the conditions used in the present study no aerosol was detected in the reactor effluent (90%.
Figure 1. FSO3- signal as a function of the reaction distance for a range of [H2O] in 50 Torr of N2 at 330 K. [H2O] ) 0.0, 0.51, 1.03, 1.75, and 2.36 × 1016 molecules cm-3. A background signal of 18 Hz was subtracted from the data.
Results and Discussion The variation of the SO3 signal as a function of reaction distance and water concentration at 330 K is shown in Figure 1. The first-order rate coefficient for loss of SO3 was derived from the measured decays by employing the Brown27 algorithm and using an SO3/N2 diffusion coefficient5 of 87(T/295 K)1.9 cm2 Torr s-1. The first-order decay of SO3 was independent ( -11 kcal mol-1, which indicates that for the conditions of the present study only a small fraction of the SO3 is tied up as H2OSO3 (i.e., Ka[H2O] , 1). In this case eq 22 reduces to kI ≈ k8Ka[H2O]2, and the temperature dependence is given by the exponential of the sum ∆H + Ea. Fits of the data to this simplified expression gave kI(s-1) ) (2.26 ( 0.85) × 10-43T exp((6544 ( 106)/T)[H2O]2 and (9.45 ( 2.68) × 10-44T exp((6573 ( 82)/T)[D2O]2 where T ≡ K and [H2O, D2O] ≡ molecules cm-3. The errors are the uncertainty at the 95% confidence level for precision only. The fits are the solid lines in Figure 2. These observations suggest an upper limit for the H2O-SO3 bond enthalpy of about 13 kcal mol-1 which is consistent with the recent ab initio values from Hofmann and Schleyer14 and Morokuma and Muguruma15 (about 8 kcal mol-1). It should be noted that the Morokuma and Muguruma calculation underestimates the stability of H2SO4 by 8 kcal mol-1 whereas Hofmann and Schleyer are within 2 kcal mol-1 of the accepted experimental value. In the context of the proposed mechanism, the -13 kcal mol-1 “activation” energy is the sum of the enthalpy of H2OSO3 formation from SO3 + H2O and the activation energy of the H2OSO3 + H2O reaction. The limit on the H2O-SO3 bond enthalpy then also implies a limit on the activation energy for the reaction of the H2OSO3 adduct with water of Ea < 0 kcal mol-1. This value contradicts the theoretical results of Moro-
Figure 4. k8Ka/T as a function of 1/T. H2O (filled circles), D2O (filled squares), Kolb et al.16 (open circle).
kuma and Muguruma,15 which predict a 5 kcal mol-1 barrier. A small negative activation energy would suggest that the reaction H2OSO3 + H2O f H2SO4 + H2O is not a simple elementary bimolecular reaction but may involve a weakly bound intermediate such as (H2O)2SO3 (see Figure 3). It is possible that there is significant tunneling involved in this reaction which may explain why the experimental barrier is significantly lower than that predicted by ab initio methods. Preexponential factors (A, eq 23) of 1.3 × 10-15 cm3 molecule-1 s-1 for the H2OSO3 + H2O reaction and 5.5 × 10-16 cm3 molecule-1 s-1 for the D2OSO3 + D2O reaction are calculated from the fit results and the entropy changes for H2OSO3 and D2OSO3 formation (-0.027 kcal mol-1 K-1, see discussion above). The preexponential factors are small, which is consistent with the highly constrained six-center transition state predicted by Morokuma and Muguruma.15 The kI vs [H2O,D2O] data (Figure 2) were also analyzed by fitting the individual temperature curves to the expression kI ) B[H2O,D2O]2, and then plotting the logarithm of B/T vs 1/T to determine ∆H + Ea from the slope. The dashed lines in Figure 2a and b are the individual fits to kI ) B[H2O,D2O]2, and log(B/T) are plotted vs 1/T in Figure 4. This analysis yields kI(s-1) ) 3.95 × 10-43T exp(6397/T)[H2O]2 and 8.15 × 10-44T exp(6619/T)[D2O]2 where T ≡ K and [H2O,D2O] ≡ molecules cm-3. To quantify the possible contribution of the water dimer reaction 7, the data were also fit to the expression kI ) (a1T exp(c/T) + a2T exp(2013/T))[H2O]2 , which assumes that there are two parallel reaction channels, one with an effective “activation” energy of -4 kcal mol-1 (the H2O dimerization enthalpy28,29). This expression fit the data as well as the one
Gas-Phase Reaction of SO3 with Water
Figure 5. First-order rate coefficient for SO3 loss as a function of [H2O] at 300 K in 20 (squares), 40 (triangles), and 80 Torr N2 (circles).
channel expression, and indicated that a -4 kcal mol-1 channel could contribute 0.2% at 250 K, 4% at 300 K, and 30% at 360 K. The variation of the first-order loss of SO3 due to H2O at 300 K as a function of pressure is shown in Figure 5. The first-order SO3 loss at 300 K changed by less than 10% over the pressure range 20-80 Torr N2. Reiner and Arnold13 also reported no significant pressure dependence for the SO3 loss over the range 23-195 Torr of air. The lack of pressure dependence is consistent with the assumption that the SO3 + H2O T H2OSO3 equilibration is rapid relative to the H2OSO3 loss by reaction with water, so that the rate-limiting step is a pressure-independent reaction of H2OSO3 with water. On the basis of the lack of a pressure dependence, a lower limit of 1 × 10-14 cm3 molecule-1 s-1 can be assigned to the rate coefficient for the association reaction of SO3 and H2O in 20 Torr N2 at 300 K (reaction 5). This is consistent with the rapid association observed for SO3 and NH3 (k ) 2 × 10-12 cm3 molecule-1 s-1 in 20 Torr of N2 at 295 K).5 The present measurements of the first-order rate coefficient for loss of SO3 due to reaction with H2O in 50 Torr of N2 interpolated to 295 K are about 5 times smaller than the values measured by Kolb et al.16 at 295 K and atmospheric pressure (see Figure 4). This discrepancy is probably not due to a pressure effect since in the present work the first-order loss increased by less than 10% for a factor of 4 increase in pressure. This weak pressure dependence has also been documented by Reiner and Arnold.13 The first-order SO3 rate coefficients measured in the present work are in good agreement with the Reiner and Arnold13 data. For example, at 298 K with [H2O] ) (1-10) × 1015 molecules cm-3, the present work predicts effective bimolecular rate coefficients of (0.2-2) × 10-15 cm3 molecule-1 s-1 which encompass the value measured by Reiner and Arnold13 for similar water concentrations ((1.2 ( 0.2) × 10-15 cm3 molecule-1 s-1 ). The quadratic dependence of the SO3 loss on [H2O] first reported by Kolb et al.16 is reproduced in the present study. In contrast, Reiner and Arnold13 fit their data to a linear [H2O] dependence. The source of this discrepancy is unknown. The variation of SO3 and H2SO4 as a function of reaction distance and [H2O] are shown in Figure 6. The chemical ionization schemes used in the present work probably do not distinguish between the isomers H2SO4 and H2OSO3. However, on the basis of the interpretation of the present measurements, the fraction of SO3 in the form of the adduct is small ([H2OSO3] < 0.25[SO3] at 253 K,
