Kinetics and Products of the Reaction SO3+ NH3+ N2

The kinetics of the gas phase reaction SO3 + NH3 + M were measured in N2 at 295 K over ... the mechanism for SO3 loss in the presence of H2O is uncert...
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J. Phys. Chem. 1996, 100, 4459-4465

4459

Kinetics and Products of the Reaction SO3 + NH3 + N2 Edward R. Lovejoy* and David R. Hanson† NOAA Aeronomy Laboratory, 325 Broadway, Boulder, Colorado 80303 ReceiVed: August 16, 1995; In Final Form: December 13, 1995X

The kinetics of the gas phase reaction SO3 + NH3 + M were measured in N2 at 295 K over the pressure range 10-400 Torr with laminar flow reactors coupled to a chemical ionization mass spectrometer. The pressure dependence of the second-order rate coefficient is fit well by the generalized Troe formalism giving k0 ) (3.9 ( 0.8) × 10-30 cm6 molecule-2 s-1 and k∞ ) (4.7 ( 1.3) × 10-11 cm3 molecule-1 s-1. The association product of the SO3 + NH3 reaction and secondary acid cluster products were detected by chemical ionization mass spectrometry. Models of the temporal behavior of SO3, sulfamic acid, and sulfamic acid dimer show that sulfamic acid dimerizes at near the hard sphere gas kinetic limit (k > 5 × 10-11 cm3 molecule-1 s-1, 20 Torr N2, 295 K) and the dimer is relatively stable with respect to decomposition to monomers (∆G°298 e -9 kcal mol-1).

Introduction Sulfur trioxide is formed in the atmosphere by the gas phase oxidation of SO2.1-3

OH + SO2 + M f HOSO2 + M

(1)

HOSO2 + O2 f HO2 + SO3

(2)

The gas phase reaction of SO3 with water is probably the dominant loss process for SO3 in the atmosphere. However, the mechanism for SO3 loss in the presence of H2O is uncertain. Reiner and Arnold4 reported that the SO3 + H2O reaction (3) has 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. They also provided evidence that H2SO4 is the major product of this reaction, although their chemical ionization detection scheme was unable to distinguish between H2SO4 and the adduct H2O‚SO3.

SO3 + H2O + M f H2SO4 + M f H2O‚SO3 + M

(3a) (3b)

In contrast, Kolb et al.5 observed a second-order dependence of the SO3 loss rate on [H2O] and concluded that the dominant reaction of SO3 in the presence of water is not reaction 3 but a reaction with the water dimer:

SO3 + (H2O)2 f H2SO4 + H2O

(4)

Another possible atmospheric loss process for SO3 is the gas phase reaction with NH3:

SO3 + NH3 + M f H2NSO3H + M f H3N‚SO3 + M

(5a) (5b)

Shen et al.6 studied the SO3 + NH3 reaction in a low-pressure flow reactor with photofragmentation-emission detection of SO3. These workers reported a rate coefficient of (6.9 ( 1.5) × 10-11 cm3 molecule-1 s-1 in 1-2 Torr of He. White powder * Corresponding author. † Also affiliated with the Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, CO. X Abstract published in AdVance ACS Abstracts, February 15, 1996.

0022-3654/96/20100-4459$12.00/0

collected from the walls of the reactor was tentatively identified as sulfamic acid by IR analysis. High-level theoretical calculations7 predict that the zwitterionic H3N‚SO3 complex has a significant dipole moment (6.6 D) and is quite stable (∆H°298(5b) ≈ -18 kcal mol-1), reflecting the substantial Lewis acid-base interaction between SO3 and NH3. Wong et al.7 also calculate that there is a significant barrier (29 kcal mol-1) separating the zwitterionic form and the nearly isothermal neutral acid form (H2NSO3H). The neutral form has a much smaller dipole moment (3.6 D).7 These calculations suggest that the product of the room temperature gas phase reaction between SO3 and NH3 is the zwitterionic complex (reaction 5b). Spectroscopic studies of codeposited SO3 and NH3 on N2 matrices identified IR bands of the H3N‚SO3 complex.8 The features assigned to the complex disappeared when the temperature of the matrix was increased to 20 K. New features that appeared at the higher temperature were tentatively assigned to sulfamic acid, and the authors postulated that the complex readily rearranged to sulfamic acid in the matrix. Canagaratna et al.9 have studied the microwave spectroscopy of the zwitterionic H3NSO3 complex. They find that the N-S bond is about 0.2 Å longer in the complex than in solid sulfamic acid. Analysis of the nitrogen quadrupole coupling constant suggest that about 0.4 electrons are transferred upon complexation. These results are in very good agreement with theory7 and demonstrate that there are significant differences between the gas phase zwitterionic form and the zwitterionic solid. On the basis of the present understanding of the relative rates for the NH3 and H2O reactions, the water reaction will consume SO3 at least 100 times faster than the ammonia reaction for tropospheric boundary layer mixing ratios of ∼10-2 for H2O and 10-11 to 10-9 for NH3.10,11 However, a small amount of sulfamic acid production may be significant with respect to particle formation because sulfamic acid probably has a much lower vapor pressure than H2SO4. Sulfamic acid has not been considered a precursor for atmospheric aerosol. Sulfamic acid is a nonvolatile solid that decomposes upon melting at 205 °C.12 The vapor pressure over solid sulfamic acid and the heat of formation of gas phase sulfamic acid are not known, but a comparison of the thermodynamics of the following processes © 1996 American Chemical Society

4460 J. Phys. Chem., Vol. 100, No. 11, 1996

Lovejoy and Hanson

SO3(g) + H2O(g) f H2SO4(liquid) -1

∆G°298 ) -22 kcal mol

(6)

SO3(g) + NH3(g) f H2NSO3H(solid) ∆G°298 ) -35 kcal mol-1 (7) illustrates the enhanced driving force for gas-to-particle formation in the SO3 + NH3 system relative to SO3 + H2O. The Gibbs free energy change for process 6 was calculated from tabulated data.13 The enthalpy change for process 7 was evaluated from tabulated data,12,13 and the entropy change for process 7 was assumed to be equivalent to that for the analogous process involving H2SO4 (∆S°298 ) -43 cal mol-1 K-1).13 Understanding and predicting particle nucleation requires knowledge of the kinetics and thermodynamics of the elementary reactions that lead to cluster formation and growth. Presently, particle nucleation is not understood at this level, and theoretical predictions of nucleation rates are not in accord with experiments (see e.g., ref 14). Theoretical studies by Coffman and Hegg15 have shown that ammonia has the potential to significantly enhance particle nucleation in the H2SO4/H2O system, and they conclude that ternary nucleation via H2SO4/ NH3/H2O could represent an important source of particles in the atmosphere. Weber et al.16 observed a strong correlation between gas phase H2SO4 and ultrafine aerosol at the Mauna Loa Observatory, Hawaii, supporting the hypothesis that H2SO4 is an important precursor for atmospheric aerosol. They also note that the atmospheric nucleation rates were significantly higher than predicted by theory for the H2SO4/H2O system and suggest that NH3 may be involved in the nucleation mechanism. In this work, the pressure dependence of the rate coefficient for the three-body association reaction SO3 + NH3 + N2 is reported. The primary association product and acid clusters formed by subsequent reactions of sulfamic acid are detected. The potential implications of these results with respect to particle formation in the atmosphere are discussed. Experimental Section SO3 + NH3 + N2 rate coefficients were measured by monitoring the concentration of SO3 at the exit of a cylindrical flow reactor as a function of the position of SO3 addition to a flow of N2 doped with NH3. SO3 was introduced to the reactor by flowing N2 over solid SO3 held in a temperature-regulated trap (-78 to -95 °C). The SO3/N2 mixture entered the reactor through a moveable 0.25 in. o.d. Pyrex inlet equipped with a Teflon cap with radial holes to help disperse the SO3 into the carrier gas. The main N2 carrier flow was doped with NH3 by metering NH3 mixtures ((1.1 and 0.052) × 10-3 NH3 in ultrahigh purity N2) into the main carrier gas flow. Two Pyrex cylindrical reactors 50 cm long and with internal diameters of 1.64 and 3.10 cm were used in this work. Teflon orifices (diameters of 0.01 to 0.10 in.) separated the flow reactors (10-400 Torr) from the flowing afterglow section (∼0.7 Torr) of the chemical ionization mass spectrometer. Gas flow rates ranged from 10 to 35 STP cm3 s-1 (STP ) 760 Torr and 273 K), giving average linear flow velocities ranging from 20 to 400 cm s-1. The reactor flow was laminar with Reynolds numbers ranging from about 10 to 130. The flow was visualized by adding sulfuric acid aerosol through the movable inlet and illuminating the aerosol with a HeNe laser. For the conditions of the present study, the flow was absent of visible turbulence. The distance along the reactor required to develop the laminar velocity and

the SO3 radial concentration profiles (“entrance” and “mixing” lengths)17 were comparable and ranged from about 3 to 10 cm. The NH3 concentration in the flow reactor was determined by measuring the reactor pressure and the flow rates of the NH3/ N2 calibrated mixture and N2 carrier gas. The NH3 mixture flow rate was determined by measuring the change in pressure in the reactor with the mixture flow on and off. This method was preferred over more standard methods (e.g., using a mass flow meter) because it minimized the plumbing between the NH3 mixture and the reactor. The NH3/N2 flow rate was determined by using calibrations of the reactor pressure change as a function of a calibrated flow rate of added N2. The N2 flow rate was calibrated by measuring the rate of pressure change in a calibrated volume. The main N2 flow rate was measured with a mass flow meter that was calibrated with a wet test meter. The reactor pressure was measured either in the center or at the upstream end of the reactor with a capacitance manometer. The pressure drop between the center and end of the reactors was less than 1% of the total pressure.18 The NH3/N2 mixing ratio in the ammonia mixtures was measured by absorption relative to that of pure NH3 at 214 (Zn) and 185 (Hg) nm in a 50 cm cell. The relative concentration of the two NH3 mixtures was also measured with the mass spectrometer by employing the O2+ reagent ion (reaction 10) and comparing the NH3+ signal for the two mixtures as a function of flow rates into the mass spectrometer. Ultrahigh purity N2 (99.9995%) was used for all the flows and was passed through a molecular sieve trap at -78 °C before use. The N2, which passed through the SO3 trap, was dried further by flowing it through P2O5 powder fixed in the inlet of the SO3 trap with glass wool. The chemical ionization mass spectrometer (CIMS) is described in detail elsewhere.2,19 SO3 was detected as FSO3- by reaction with SiF5-:

SO3 + SiF5- f FSO3- + SiF4

(8)

The SiF5- detection scheme had about the same sensitivity for SO3 as the analogous SF6- scheme.5,20 (The rate coefficient for reaction 8 appears to be within 50% of the rate coefficient for the analogous SF6- reaction.) The SiF5- detection scheme was used for most of the kinetic experiments because it had less background interference at mass 99 (FSO3-). SiF5- was generated by reacting SF6- with SF4 in the flowing afterglow reactor, upstream of the SO3 reactor inlet:

SiF4 + SF6- f SiF5- + SF5

(9)

NH3 in the reactor effluent was monitored with O2+:

NH3 + O2+ f NH3+ + O2

(10)

(k10 ) (1-2) × 10-9 cm3 molecule-1 s-1).21 NH3 concentrations in the flow reactor ranged up to 2 × 1013 molecule cm-3. All kinetic measurements were made after the NH3 concentration, measured by charge transfer with O2+, had stabilized (less than 15 min). The concentration of a species X in the flow reactor [X]r is related to the CIMS signal Sx for species X by

[X]r )

MSxprFfaTfa Sy-pfaFrktTr

(11)

where M is the mass discrimination between the parent ion Yand the product ion of X, Sy- is the parent ion signal, k is the

Reaction of SO3 + NH3 + N2

J. Phys. Chem., Vol. 100, No. 11, 1996 4461

Figure 1. Variation of the SO3 signal as a function of reaction distance for various concentrations of NH3: (O) [NH3] ) 0; (3) [NH3] ) 2.3 × 1012; (1) [NH3] ) 4.3 × 1012; (b) [NH3] ) 7.4 × 1012. A background signal of 21 Hz was subtracted from all the points. Experimental conditions were p ) 41 Torr, T ) 295 K, V ) 47 cm s-1, r ) 1.55 cm, and [SO3]0 ≈ 1 × 1010 molecule cm-3.

second-order rate coefficient for X + Y-, t is the average flowing afterglow reaction time, p is the pressure, F is the flow rate at standard temperature and pressure, T is the temperature, and r refers to the neutral flow reactor and fa indicates the flowing afterglow reactor. The concentration of SO3 was estimated by using a rate constant of 1 × 10-9 cm3 molecule-1 s-1 for the SiF5- reaction (Langevin k ) 7 × 10-10 cm3 molecule-1 s-1). We estimate that the uncertainty in the SO3 concentration derived from eq 11 is about a factor of 2. Initial SO3 concentrations in the reactor were in the range (0.2-4) × 1010 molecule cm-3.

Figure 2. First-order SO3 loss rate coefficient kIz as a function of NH3 concentration. Experimental conditions are the same as in Figure 1.

TABLE 1: SO3 + NH3 + N2 Experimental Conditions and Kinetic Results reactor k radius [SO3]0 (10-12 N2 V number [NH3]max (torr) (cm s-1) (cm) (109 cm-3) of expt (1012 cm-3) cm3 s-1)a 12.7 20.5 21.4 41.0 80 80 150 250 250 400 a

40 393 44 47 90 23 50 54 24 27

1.55 0.82 1.55 1.55 0.82 1.55 0.82 0.82 0.82 0.82

2 4 2-8 6-20 4-40 2-12 4 4-20 20 8-20

6 6 10 11 10 14 6 12 5 6

9 20 15 7 8 15 2.3 2.4 1.2 1.2

1.5(0.2) 2.1(0.1) 2.1(0.1) 3.6(0.2) 5.2(0.5) 6.1(0.4) 9.6(1.4) 11.4(15) 10.9(1.0) 15.0(1.2)

95% confidence levels for precision are indicated in parentheses.

Results and Discussion SO3 + NH3 Kinetics. The kinetics of the SO3 + NH3 + N2 reaction were studied by monitoring the SO3 signal as a function of the SO3/NH3 reaction distance. Plots of the decay of the SO3 signal vs reaction distance for a range of NH3 concentrations in 41 Torr of N2 are shown in Figure 1. The slopes of the lines are the observed first-order loss rate coefficients (kIz (cm-1)). The observed decay is the sum of diffusion-limited loss to the reactor wall and gas phase reaction:

kIz )

3.6Dp pVr2

+

kI 1.7V

(12)

where Dp is the diffusion coefficient (cm2 Torr s-1), p is the pressure (Torr), V is the average flow velocity (cm s-1), r is the radius of the reactor (cm), and kI is the first-order rate coefficient (s-1) for the gas phase reaction of the SO3. The coefficients in eq 12 were calculated by numerically solving the continuity equation for the conditions of the present work.22 Equation 12 is accurate to better than 4% for the conditions of the present study. The NH3 concentration was typically at least 10 times greater than the SO3 concentration so that kI is given to a good approximation as the product of the second-order rate coefficient and the concentration of NH3: kI ) kII [NH3]. The secondorder rate coefficient kII was determined by measuring kIz as a function of the concentration of NH3. Then kII is equal to the product of the slope of kIz vs [NH3] times 1.7V. The variation of kIz vs [NH3] in 41 Torr N2 is shown in Figure 2. Experimental conditions and rate coefficients are summarized in Table 1, and the second-order rate coefficients are plotted as a function of N2 concentration in Figure 3. The uncertainties for the second-order rate coefficients are the 95% confidence intervals for precision based on the fits to the slopes of the first-

Figure 3. Second-order SO3 + NH3 rate coefficient as a function of N2 concentration. Error bars represent the precision at the 95% confidence level. The solid line is a fit to eq 13.

order rate coefficients vs [NH3]. The difficulty in measuring the rate coefficients increased with pressure because of enhanced secondary chemistry and deviations from pseudo-first-order conditions. Higher SO3 concentrations were needed in the higher pressure experiments because of the increased dilution from the flow reactor into the mass spectrometer. Also, the reaction rate coefficient and reaction time increased as the pressure increased, which necessitated lower NH3 concentrations. The higher SO3 concentrations enhanced secondary chemistry (vide infra) and, coupled with reduced NH3 concentrations, also compromised pseudo-first-order conditions. The solid line in Figure 3 is a fit of the variation of the second-order rate coefficient with [N2] to the Troe formula employed in the JPL data evaluation:23

4462 J. Phys. Chem., Vol. 100, No. 11, 1996

kII(M) )

k0[M]

Lovejoy and Hanson 2 -1

0.6[1+(log(k0[M]/k∞)) ] k0[M] 1+ k∞

(13)

where [M] is the concentration of the bath gas, k0 is the thirdorder rate coefficient as [M] f 0, and k∞ is the second-order rate coefficient at [M] ) ∞. The fit yields the parameters k0 ) (3.9 ( 0.8) × 10-30 cm6 molecule-2 s-1 and k∞ ) (4.7 ( 1.4) × 10-11 cm3 molecule-1 s-1. The uncertainties are the 95% confidence levels for precision only. This work yields a rate coefficient in 2 Torr N2, which is about 300 times smaller than that reported by Shen et al.6 for 1-2 Torr He. The high rate coefficient measured by Shen et al. may be a result of secondary chemistry between SO3 and sulfamic acid clusters (vide infra) and/or heterogeneous chemistry on the reactor walls. Shen et al. used SO3 concentrations that were 10-100 times higher than in the present study and measured first-order rate coefficients that were comparable to the diffusion-limited wall loss rate coefficient. The intercept of the measured first-order loss rate coefficient vs [NH3] (see, e.g., Figure 2) is the rate coefficient for loss to the reactor wall (first term of the rhs of eq 12). Diffusion coefficients were extracted from the intercepts by using eq 12. The diffusion coefficients are plotted vs 1/p in Figure 4. The slope of this plot yields an SO3 diffusion coefficient of (87 ( 8) cm2 Torr s-1 in N2 at 295 K. The quoted uncertainty is the 95% confidence level for precision. The measured SO3 diffusion coefficient is in good agreement with an estimate calculated using the method of Hirschfelder et al.24 with the potential parameters for HSO325 (83 cm2 Torr s-1 in N2 at 295 K). On the basis of the observed linear decay of SO3 in the presence of NH3 at 295 K and 150 Torr N2, an upper limit of 4 s-1 is assigned to the decomposition rate constant for the SO3/ NH3 association product (reverse of reaction 5), yielding an upper limit for the Gibbs free energy change for reaction 5 of -10 kcal mol-1 at 295 K. Assuming that the entropy of gas phase sulfamic acid is the same as that of sulfuric acid (the entropies of the isoelectronic species FSO3H and HOSO3H are 71.1 and 71.4 cal K-1 mol-1, respectively13), this gives an entropy change of -36 cal mol-1 K-1 for reaction 5 and a limit of e-20 kcal mol-1 for the enthalpy change. This upper limit for the reaction enthalpy is comparable to the theoretical value7 of about -18 kcal mol-1 for reaction 5b. Products. The mass spectrometer is sensitive only to the mass of the ions that are detected and does not distinguish between isomers. In the discussion that follows, the terms “sulfuric acid” and “sulfamic acid” refer to the isomers with masses of 98 and 97 and atomic compositions H2SO4 and H3NSO3, respectively. Sulfuric and sulfamic acid were detected with Cl- and SF6-:

Figure 5. Variation of SO3 (3: FSO3-), H3NSO3 (O: H2NSO3-‚HF), and H2SO4 (b: HSO4-) as a function of reaction distance. Experimental conditions are p ) 21 Torr N2, T ) 294 K, r ) 0.82 cm, V ) 388 cm s-1, [NH3] ) 8 × 1012 molecule cm-3, and [SO3]0 ≈ 1 × 1010 molecule cm-3. The solid lines are from model calculations (see text).

SO3 was also detected by association with Cl-:

SO3 + Cl- + M f Cl-‚SO3 + M

(18)

H2SO4 + Cl- f HSO4- + HCl

(14)

This scheme was not used in the SO3 kinetic studies because of its poor sensitivity (k18 ) 7 × 10-27 cm6 molecule-2 s-1)2 relative to the schemes employing SiF5- and SF6-. The product of the reaction of SO3 and NH3 reacted rapidly with F-, Cl-, and Br- and reacted about 100 times slower with I- to give H2NSO3-. Exothermic proton transfer reactions generally proceed near the collision frequency.26 Hence, we conclude that the reaction

H3NSO3 + Cl- f H2NSO3- + HCl

(15)

I- + H3NSO3 f H2NSO3- + HI

H2SO4 + SF6- f HSO4- + HF + SF5

(16a)

f HSO4-‚HF + SF5 H3NSO3 + SF6- f H2NSO3- + HF + SF5 f H2NSO3-‚HF + SF5 -

Figure 4. Variation of the SO3 diffusion coefficient with pressure of N2. Error bars represent the precision at the 95% confidence level. The line is a fit to the data yielding a pressure independent diffusion coefficient for SO3 in N2 at 295 K of 87 ( 8 cm2 Torr s-1. The uncertainty is the 95% confidence level for precision.

Cl-

(16b) (17a) (17b)

SF6 and were generated by electron attachment to SF6 and CCl4, respectively.

(19)

is nearly thermoneutral, and the gas phase acidity of H3NSO3 is comparable to the gas phase acidity of HI27 (∆Hacid(H3NSO3) ) 314 ( 5 kcal mol-1). The variations of SO3, sulfuric acid, and sulfamic acid in the presence of NH3 as a function of reaction distance are shown in Figure 5. Sulfuric acid is an impurity from the SO3 source. The mass 96 sulfamic acid signal (H2NSO3-) is not shown but exhibited identical behavior to the mass 116 signal (H2NSO3-‚HF) at a level 2.6 times lower than that of the mass 116 signal. The solid lines in Figure 5 are calculated with a simple model that included the following processes:

Reaction of SO3 + NH3 + N2

J. Phys. Chem., Vol. 100, No. 11, 1996 4463

SO3 + NH3 + M f H3NSO3 + M

(5b)

SO3 f wall

(20)

H3NSO3 f wall

(21)

H2SO4 f wall

(22)

Note that the first experimental points (z < 5 cm) are in the “mixing” region and the reaction time may not be given simply by t ) z/(1.7V) (eq 12). The first-order rate coefficient for SO3 wall loss was calculated with eq 12 and the measured diffusion coefficient. The first-order rate coefficients for sulfamic acid wall loss were equated to the observed first-order H2SO4 wall loss. This model describes the loss of SO3 and production of sulfamic acid very well. The calculated sulfamic acid profile has been multiplied by a factor of 1.7 relative to the SO3 profile, indicating that the CIMS SF6- sensitivity for sulfamic acid is about 1.7 times greater than it is for SO3. Note that in this analysis it is assumed that the yield of sulfamic acid from the SO3 + NH3 reaction is unity. It was generally observed that after SO3 had been consumed, sulfamic acid and sulfuric acid decayed with the same firstorder rate coefficient. At low [SO3], secondary chemistry was minimized, and the acids were lost at the diffusion-limited wall loss rate. Analysis of the acid decays yields a diffusion coefficient of 85 ( 15 cm2 Torr s-1 for sulfuric and sulfamic acids in N2 at 295 K. The acid decays were not influenced (90% of clusters had less than 10 monomer units at the longest reaction time with the highest [SO3]0. The model data in Figure 6 have been scaled by the following factors: 1.1 × 10-8 Hz cm3 molecule-1 for SO3, 6.3 × 10-7 for sulfamic acid, and 4.7 × 10-8 for the sulfamic acid dimer. The SO3 scale factor was calculated with eq 11. The other scale factors were chosen to best fit the data. Conclusions

∆G1,n ) (∆Gc - ∆G1,1)(1 - e

) + ∆G1,1

(1-n)/b

(33)

where ∆Gc is the Gibbs free energy change for condensation of gas phase sulfamic acid to solid sulfamic acid (i.e., in the limit n f ∞) and ∆G1,1 is the Gibbs free energy change for the dimerization reaction 25. ∆Gc was estimated to be -20 kcal mol-1 at 295 K by using the Gibbs free energy change for the conversion of SO3 and NH3 to solid sulfamic acid (eq 7) and an estimate of -15 kcal mol-1 for the Gibbs free energy change for reaction 5. ∆G1,1 was a model parameter. It was assumed that SFAn were lost to the reactor walls at the diffusion-limited rates, similar to SO3 and SFA. The firstorder wall loss rate coefficients for the clusters were calculated from eq 12 with estimates for the diffusion coefficients

Dp(SFAn) )

Dp(SFA) nc

(34)

A set of experimental and calculated SO3, SFA, and SFA2 profiles are shown in Figure 6. Solid lines are the profiles calculated with the following parameters: [SO3]0 ) (2.3, 0.8, 0.4) × 1011 molecule cm-3, kf1,1 ) 3 × 10-10 cm3 molecule-1 s-1, kr1,1 ) 30 s-1 (∆G1,1 ) -11.4 kcal mol-1), a ) 0.8, b ) 4, ∆Gc ) -20 kcal mol-1, and c ) 0.67. The dimerization rate constant corresponds to a hard sphere radius of 2.6 × 10-8 cm. The collision radius exponent (a ) 0.8) is significantly larger than would be expected by assuming that the clusters are spherical (0.33). The model results were very sensitive to the value of the radius exponent a. The large value of a was

SO3 and NH3 react by an efficient three-body mechanism in the gas phase with an effective second-order rate coefficient k(SO3 + NH3) ) 2 × 10-11 cm3 molecule-1 s-1 in 1 atm N2 at 295 K. The association product is stable (∆G°295 e -10 kcal mol-1) and clusters efficiently with itself and with sulfuric acid. The sulfamic acid dimerization reaction occurs with nearly every gas kinetic collision (k > 5 × 10-11 cm3 molecule-1 s-1, 20 Torr N2) and has a Gibbs free energy change of e-9 kcal mol-1 at 295 K. The association reactions between sulfamic acid and higher clusters also appear to be very efficient and to have significant negative Gibbs free energy changes. The sulfamic acid + sulfuric acid reaction may represent an important step in the mechanism for new particle formation in the atmosphere because it appears to be a barrierless pathway to cluster formation. Additional studies of the SO3/NH3/H2O system are needed to evaluate the role of water in the cluster growth mechanism. Acknowledgment. The authors are grateful to L. G. Huey for suggesting the SiF5- detection scheme for SO3 and to A. O. Langford and E. Williams for the loan of an NH3 mixture. The authors are also grateful to M. Canagaratna, J. A. Phillips, H. Goodfriend, and K. R. Leopold for a preprint of ref 9. This work was supported in part by the NOAA Climate and Global Change Program. References and Notes (1) Stockwell, W. R.; Calvert, J. G. Atmos. EnViron. 1983, 17, 2231.

Reaction of SO3 + NH3 + N2 (2) Gleason, J. F.; Sinha, A.; Howard, C. J. J. Phys. Chem. 1987, 91, 719. (3) Wine, P. H.; Thompson, R. J.; Ravishankara, A. R.; Semmes, D. H.; Gump, C. A.; Torabi, A.; Nicovich, J. M. J. Phys. Chem. 1984, 88, 2095. (4) Reiner, T.; Arnold, F. J. Chem. Phys. 1994, 101, 7399. (5) Kolb, C. E.; Jayne, J. T.; Worsnop, D. R.; Molina, M. J.; Meads, R. F.; Viggiano, A. A. J. Am. Chem. Soc. 1994, 116, 10314. (6) Shen, G.; Suto, M.; Lee, L. C. J. Geophys. Res. 1990, 95, 13981. (7) Wong, W. M.; Wiberg, K. B.; Frisch, M. J. J. Am. Chem. Soc. 1992, 114, 523. (8) Sass, C.; Ault, B. S. J. Phys. Chem. 1986, 90, 1547. (9) Canagaratna, M.; Phillips, J. A.; Goodfriend, H.; Leopold, K. R. J. Am. Chem. Soc., submitted. (10) Langford, A. O.; Fehsenfeld, F. C.; Zachariassen, J.; Schimel, D. S. Global Biogeochem. Cycles 1992, 6, 459. (11) Dentener, F. J.; Crutzen, P. J. J. Atmos. Chem. 1994, 19, 331. (12) Encyclopedia of Chemical Technology, 3rd ed.; John Wiley: New York, 1983; Vol. 21, p 949. (13) Chase, M. W., Jr.; Davies, C. A.; Downey, J. R., Jr.; Frurip, D. J.; McDonald, R. A.; Syverud, A. N. JANAF Thermochemical Tables. J. Phys. Chem. Ref. Data Suppl. 1 1985, 14. (14) Wyslouzil, B. E.; Seinfeld, J. H.; Flagan, R. C.; Okuyama, K. J. Chem. Phys. 1991, 94, 6842. (15) Coffman, D. J.; Hegg, D. A. J. Geophys. Res. 1995, 100, 7147. (16) Weber, R. J.; McMurry, P. H.; Eisle, F. L.; Tanner, D. J. J. Atmos. Sci. 1995, 52, 2242. (17) Keyser, L. F. J. Phys. Chem. 1984, 88, 4750.

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