J. Phys. Chem. 1996, 100, 10269-10276
10269
Laser-Spectroscopic Measurements of Uptake Coefficients of SO2 on Aqueous Surfaces Akio Shimono and Seiichiro Koda* Department of Chemical System Engineering, School of Engineering, The UniVersity of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113 ReceiVed: December 19, 1995; In Final Form: April 17, 1996X
The uptake of SO2 on aqueous surfaces was studied by directly measuring SO2 concentration distribution above the surface by means of laser-induced fluorescence method in an impinging flow field with a 10-100 ms order contact time between the gas flow containing SO2 and the water flow. The uptake coefficient was determined by using the eq which describes the boundary condition at the surface. The uptake coefficient increased with pH of the aqueous phase and reached the limiting value of 0.028 ( 0.010 at pH ) 13.2 at 293.5 K. Its temperature dependence was slightly negative. The present uptake coefficients could be understood satisfactorily by taking into account the rapid acid-dissociation reaction of dissolved SO2 with the reported bulk reaction rate constant.
Introduction Heterogeneous reactions are significant in the existence of atmospheric aerosols.1,2 In order for the reactions to proceed on and/or in liquid aerosols, the uptake of species by the surface from the air is an essential step. Schwartz3 treated the uptake of atmospheric species by liquids with introducing characteristic times for individual elementary processes relevant to the overall transport such as diffusion in the gas phase, interfacial mass transport, and diffusion in the liquid phase. He emphasized the importance of estimation of the rate for interfacial mass transport. Concerning the interfacial mass transport, the accommodation coefficient, R, is defined as the fraction of collisions of a gas-phase species with a surface that results in dissolution. The uptake coefficient, γ, on the other hand, is defined as the fraction of collisions that removes the species from the gas phase, corresponding to the net transport of the species to the liquid phase. The accommodation coefficient is a rate parameter corresponding to the mass transfer at the moment when the surface has been newly contacted with the objective species. This is not measurable actually because any experiment has an inherent contact time before the measurement is accomplished. The uptake coefficient is the real measurable quantity, from which the accommodation coefficient might be obtained from extrapolation. In any previous experimental methods for determination of γ, stopped flow method,4,5 droplet gas flow method,6-11 wetted wall flow tube method,12,13 Knudsen cell flow method,14 liquid jet method,15 and bubble column reactor method,16 the uptake of the species has been estimated from the average loss of these species in the bulk gas phase or from the average accumulation in the liquid phase. Therefore reliability of the methods depends on how the idealized flow fields are realized in the presence of high concentration of water vapor under lower pressures necessary for minimizing the gas phase diffusion limitation, which is not always easy to prove. We have developed a novel laser-spectroscopic measurement method of the relevant species distribution above the air-water interface which is settled between the opposing air and water flow. The uptake coefficient is determined from the slope of the distribution curve and the value of surface concentration as described later. The advantages of the present method are the X
Abstract published in AdVance ACS Abstracts, June 1, 1996.
S0022-3654(95)03767-1 CCC: $12.00
following: (1) species always contact with the fresh aqueous surface; (2) the gas-phase concentration distribution near the surface which reflects interfacial mass transport can be observed directly; (3) the γ value is simply determined by using the eq which describes the boundary condition at the surface; and (4) necessary parameters for determination of γ values have little uncertainty. The present method can be applied to γ values ranging from 10-1 through 10-5. The sensitivity is quite high, particularly in the γ range from 10-2 through 10-3, where the value has a significant meaning in order to judge whether interfacial mass transport is rate-determining or not. Sulfur dioxide is the trace gaseous species which plays a most important role in the formation of acid rain. About 50% fraction of the SO2 oxidation which results in the acidification of rainfalls or fogs is attributed to heterogeneous pathways.1 According to Schwartz,3 if γ for SO2 is less than 10-2, interfacial mass transport becomes more restrictive to the rate of overall process than the gas-phase diffusion, and the dependence of the overall mass transfer rate is linear on γ at smaller γ values less than 10-3. Recently several measurements of γ were reported for SO2. Tang and Lee obtained the γ value of 2 × 10-2 on an aqueous surface, employing a stopped-flow technique with adding NaClO, a very effective reagent for SO2 oxidation, into the aqueous phase.4 Worsnop et al. measured γ values for various trace gases.6-9 The value for SO2 was 0.11 at 292 K,8 which was determined by extrapolating a set of experimental data to the zero pressure condition. Ponche et al.11 also obtained a value of about 0.13 at 298 K by employing the same method. Based on the obtained γ values and their contact time dependence, Jayne et al.9 proposed the idea of a surface SO2 complex. This is because they could not explain the larger value than 0.03, which should be the upper limit of γ in ms order measurements if the forward rate constant of 3.4 × 106 s-1 in the first acid dissociation of dissolved SO2 is adopted after Eigen et al.17 Putting these results together, the interfacial mass transport of SO2 might be considered not to be a controlling process in actual atmospheric processes. However the interpretation of uptake kinetics of SO2 still requires investigation by direct measurement method. In this paper we report measurements of the uptake of SO2 on aqueous surfaces by employing the novel impinging flow method. The obtained γ value has been found to be smaller than 0.03, which will be critically compared with the reported values by previous researchers.4,6-9,11 © 1996 American Chemical Society
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Shimono and Koda
Experimental Section The principle of the impinging flow method and how to determine the uptake coefficients will be briefly explained in the following (a) and (b) sections. A more detailed description is available elsewhere.18 The experimental setup and procedure are shown in (c) and (d). The contact time between the gasphase species and the aqueous surface will be considered in section (e). (a) Impinging Flow Field. The present impinging flow field is the field where a gas flow is impinging on a water flow coaxially as shown in Figure 1. This configuration offers an intrinsically stable flow field and an always renewed aqueous surface. The species in the gas phase is transferred to the aqueous phase through the interface with an uptake coefficient γ. The governing eq of the species concentration in the gas phase above the aqueous surface is modeled by the diffusion eq 1, taking the cylindrical coordinate where the origin is fixed on the central axis on the aqueous surface
∂C(r,z) ∂C(r,z) ∂2C(r,z) u(r) )0 + ν(z) -D ∂r ∂z ∂z2
(1) Figure 1. Impinging flow field and apparatus.
where C(r,z) is concentration of the species; z, height above the surface; r, distance from the origin along the surface (the surface is assumed to be flat); u(r), velocity component in r direction; ν(z), velocity component in z direction; D, diffusion coefficient of the given species. u(r) is assumed to be a function of r and ν(z), a function of z. The flux into the aqueous phase at the surface (z ) 0) is equated to the number of collisions on the surface multiplied by the uptake coefficient as shown in eq 2. This eq is used as the boundary condition at the surface
∂C(r,z) γνmCs(r) ) ∂z 4
D
(2)
where Cs(r) is the concentration of the species just on the surface in the gas phase and νm, the molecular velocity. Applying the boundary layer theory, u(r) and ν(z) are derived from the governing eqs for continuity and momentum with introducing the boundary layer function and the stream function in the usual manner.19,20 Then eq 1 is switched to a onedimensional problem on the central z axis by substituting r ) 0 and is solved by a finite deference method by employing the value of ν(z) at each point. Detailed procedure is found elsewhere.18 (b) Determination of γ from the Spatial Distribution of SO2. Simulations were executed in order to understand the effect of γ value on the spatial distribution, using the same conditions as employed in experiments. The diffusion coefficient of SO2 in the gaseous mixture of He and water vapor, D, was calculated in terms of the following approximate method21
PH2O PHe 1 + ) D DSO2-H2O DSO2-He
(3)
by employing the data of binary diffusion coefficient for SO2 in the water vapor, DSO2-H2O, and in He, DSO2-He. The values of DSO2-H2O and DSO2-He were respectively calculated from the value at 298 K (0.124 atm cm2 s-1) with a temperature dependence of T2.0 and the value at 298 K (0.534 atm cm2 s-1) with a temperature dependence of T1.7 which were reported by Van Doren et al.10 Figure 2 shows some examples of the simulated distributions with several assumed γ, under the condition that total pressure, P is 90.0 Torr; temperature, T, 293.2 K; the gas flow velocity at the discharge νg0, 90.0 cm/s;
and the distance between the surface and the gas discharge, 20.95 mm. The distribution is normalized against C0, which is the concentration at the gas discharge (z ) l) at the edge of the upper pipe. In the γ range smaller than 0.01, the intercept values change widely dependent on γ. By comparing the initially assumed γ value with the γ value which has been obtained by applying eq 2 to the simulated result, the estimation of γ using the averaged slope in the height of 0-2 mm above the surface is proven to produce an error within -20% (- means that the estimated γ is smaller than the true γ), over the entire range of conditions employed. The accuracy is much more satisfactory within -2% for the γ of ∼10-2-10-5, which is negligible. In conclusion, the determination procedure by applying eq 2 is not affected by the flow field at a distance from the surface, as far as the region of a linear distribution above the surface is adopted. Therefore we have determined γ in every experiment by applying eq 2 to the experimentally obtained distribution of SO2 above the surface. (c) Experimental Setup. As illustrated in Figure 1, an impinging flow apparatus consisted of a double-cylinder, temperature-adjustable vessel. The opposed pipes were placed in the center of the cylinder 24.95 mm distant from each other. The gaseous flow containing a very small amount of SO2 was discharged from the upper vertical pipe and then collided on the aqueous surface. The pH-adjusted, doubly-distilled water (Wako Pure Chemical) was flowed coaxially from the lower vertical pipe. The distance between the aqueous surface and the edge of the gas-discharge pipe, which was weakly dependent on the water flow rate, was 20.95 mm under a typical condition. The linear velocity along the center of the pipes of gas and water (νg0 and νa0, respectively) was calculated from the total flow rate, assuming Poiseulle flows. The vessel was kept at a given reduced pressure (P, 28-99 Torr) and temperature (T, 275.8-304.5 K). As for the gaseous flow, SO2 diluted in He (Takachiho Chemical) and humidified He through a humidifier were supplied by the individual mass flow controller and then mixed in the pipe system. The ratio of the former gas flow rate to the latter was regulated to be less than 0.17 so that the partial pressure of water vapor in the observation region reached almost the saturated condition. The inlet line of gaseous flow was kept at the same temperature as the observation vessel. The temperature-controlled water was supplied to the lower vertical
Uptake Coefficients of SO2 pipe by a magnet pump after removal of the internal gas-bubbles. The back-pressure of the system was controlled at a balanced pressure within 0.1 Torr against the observation vessel. (d) Measurement of the Concentration Distribution of SO2. The direct measurement of the spatial distribution of SO2 along z axis was performed by means of laser-induced fluorescence method. As an excitation source, a XeCl excimer-laser pumped pulsed-dye laser (Lambda Physik LPX 100/FL3002) was operated at 20 Hz and the frequency-doubled light by a BBO crystal was used. The laser beam was introduced through a Brewster-angle side window and focused at the position to be monitored in the observation vessel using a quartz lens (f ) 200 mm). Both the incident and the transmitted laser light were monitored by photodiodes. The fluorescence was detected at right angles to the incident laser beam. The detection optics system and the observation vessel were placed on individual XYZ-stages adjustable with 0.05 mm accuracy. The fluorescence intensity along z axis was measured, changing the height of the observation vessel, without moving the laser beam nor the detection optics system. Spatial resolution in vertical (z) and depth direction were dependent on the waist radius of the laser beam; and were estimated to be both 0.1 mm. On the other hand, the resolution in horizontal (r) direction was mainly determined by the size of the aperture on the optical axis of the lens system for collecting the fluorescence and was estimated to be 0.3 mm. The position of the aqueous surface was determined by moving the vessel in z direction and finding the position where the intensity of the transmitted laser light through the observation vessel decreased to the half of the original value. The accuracy of allocation of the aqueous surface was within 0.05 mm under a typical condition. Measured excitation spectra from 222 to 227 nm at several different z positions ascertained that SO2 was indeed monitored at any height. The excitation wavelength of 224.34 nm was employed for the distribution measurements, which was corre˜ -X ˜ sponding to the head of (112)-(000) band of the SO2 C transition. The fluorescence emitted in the wavelength range longer than 260 nm was detected by a photomultiplier tube. The signal was accumulated using a boxcar averager (PAR 4121B), and the output was recorded by a personal computer through an AD converter. The fluorescence intensity was proven to be linear against the concentration of SO2 over the entire concentration range of 3.3 × 1011-1.7 × 1014 molecules/ cm3 adopted in the experiments. The laser pulse energy was kept smaller than 0.26 mJ/pulse, and the linear relationship of the fluorescence intensity against the laser pulse energy was also confirmed. At the SO2 concentration of 3.3 × 1011 molecules/cm3, S/N ratio was about 25. (e) Estimation of the Contact Time of the Gas Flow with the Aqueous Surface. The contact time of the gas flow with the aqueous surface is an essential parameter in the interpretation of the obtained γ value. The detection region by laser-induced fluorescence method expanded from r ) -0.15 mm to r ) 0.15 mm, considering the spatial resolution of 0.3 mm in r direction. The average contact time between the gas flow and the aqueous surface can be evaluated from the velocity of the aqueous surface provided that the gas flow did not slip from the aqueous surface movement. Because we could not determine the surface velocity by calculation, its measurement was required. For this purpose, TiO2 particles of 10-100 µm diameter were premixed in the gas flow, and the movement of the particles fallen on the aqueous surface was photographed with a high speed camera (Nac Ltd. 16HD) of 0.25 ms time resolution, being illuminated by the light sheet from an Ar+ laser (50 mW). The particle on the surface was stationary when νa0 ) 0. Then the measure-
J. Phys. Chem., Vol. 100, No. 24, 1996 10271 ments were performed under various νa0 values smaller than 20 cm/s. Any stagnant point larger than 0.01 mm in diameter was not observed on the surface. The measured surface movement was plotted against r. It was found that the surface velocity, νs, was proportional to r (νs ) ar). Then the averaged surface velocity, νsm, at r ) 0.075 mm, a half distance of 0.15 mm, was determined. The measured γ by employing the present method is not equal to the γ at one specific time t. We have actually measured a certain average of γ(t). However, in order to treat the data simply, we have defined the time dependent γ(t) as the γ at the time calculated from 0.15 mm/νsm, viz., the average contact time. Figure 3 shows the relationship of the estimated contact time against νa0. The dots in the figure denote the average value. The bars reflect the (1σ deviation of measured νs. For example, the estimated contact time at νa0 ) 19.4 cm/s scattered in the range from 25 through 52 ms and the average value was 37 ms. This scatter mainly arose from the meandering of the streamline on the aqueous surface, probably caused by the Coriolis force. Results Spatial Distribution of SO2 and the Estimation of γ. A typical experimental distribution of SO2 above the aqueous surface is shown in Figure 4, together with simulated distributions at γ ) 0.001, 0.01, and 0.1. The data in the region below the height of 0.15 mm above the surface were omitted because they were contaminated by the scattered light from the surface. In the present example, γ was determined to be 0.013 by inserting the intercept and the slope of the distribution curve in the 0.15-2 mm region to eq 2. The intercept value in this case was obtained by extrapolation of the line fitted to the data in the 0.15-2 region to 0 mm. The necessary diffusion coefficient, D, was estimated as described in the simulation part (b) in Experimental Section. The distribution curve which was experimentally obtained fits quite well to the simulated curve. Strictly a slight difference exists between them. This is because the actual flow field in the gas phase was a little different from the modeled flow field which was simplified for the calculation. Irrespective of this small difference, we could determine the γ from eq 2, judging from the fact that the obtained profiles near the interface were observed to be linear. Therefore the γ values were determined directly from eq 2 in all the experiments. It is certain that the uncertainty in the determined position of the surface (the 0 mm position), which corresponds directly to the uncertainty in the intercept value, exists in each experiment. In the worst case where γ ) 0.028, +0.05 mm uncertainty and -0.05 mm uncertainty in the allocation of the 0 mm position lead to +46% uncertainty and -24% uncertainty in γ, respectively. However we conducted more than nine independent experimental runs under the individual condition. The uncertainty in the allocation of the surface is not a systematic one and is considered to be included in the standard deviation in the experimental results. Effect of Water Vapor on the Fluorescence Measurements. It is important to judge whether the fluorescence intensity is affected by the quenching effect of water vapor, because water vapor might distribute inhomogeneously in the gas phase. It is, however, difficult to measure the distribution of water vapor, and also there is no reliable quenching data of H2O for SO2 in its C ˜ state. Hence another approach was taken. According to the simulation results shown in Figure 2, the concentration distribution is flat when γ is smaller than 10-5, which is realized under the surface saturation. The aqueous surface is readily saturated when water is acidic as stated by Worsnop et al.8 and has been also confirmed by us. The fluorescence intensity obtained under the condition of surface saturation should be
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Figure 2. Concentration profiles of SO2 above the surface in simulation for various γ values. C0 ) 8.3 × 1013 molecules/cm3, P ) 90.0 Torr, T ) 293.2 K, νg0 ) 92.7 cm/s.
Figure 3. Relationship of the measured contact time against νa0. Symbols denote averages of experimental data and error bars are (1σ deviation. P ) 90.1 Torr, T ) 293.2 K, νg0 ) 92.6 cm/s.
Shimono and Koda
Figure 5. Observed fluorescence intensity along z axis under the surface saturated condition. C0 ) 8.1 × 1013 molecules/cm3, P ) 90.0 Torr, T ) 293.2 K, νg0 ) 92.7 cm/s, νa0 ) 0 cm/s, pH of water ) 3.0.
Figure 6. Effect of the gas flow velocity on γ at two different pH values. Error bars show (1σ deviation. C0 ) 6.5 × 1013 molecules/ cm3 (pH ) 5.6) or 4.3 × 1013 molecules/cm3 (pH ) 13.2), P ) 89.890.3 Torr, T ) 293.2 K, νa0 ) 19.4 cm/s (pH ) 5.6) or 2.1 cm/s (pH ) 13.2).
Figure 4. Experimental and simulated distribution curves of SO2 on the water surface. b: experimental result. Experiments were performed under conditions that C0 ) 7.8 × 1012 molecules/cm3, P ) 89.3 Torr, T ) 293.2 K, νg0 ) 93.5 cm/s, νa0 ) 2.1 cm/s, pH of water ) 10.0. 1: simulation result with γ ) 0.001, 2: simulation result with γ ) 0.01, 3: simulation result with γ ) 0.1.
Figure 7. Effect of total pressure on γ. Error bars show (1σ deviation. C0 ) 7.8 × 1012 molecules/cm3, T ) 293.2 K, νg0 ) 89.9-140 cm/s, νa0 ) 19.8 cm/s, pH of water ) 13.0.
constant along z axis, if it is not affected by the quenching effect of H2O even in the case when water vapor is distributed inhomogeneously. Figure 5 shows an experimental result obtained under the condition that the water adjusted to pH ) 3.0 was kept stationary long enough for the surface saturation under a constant gas flow. The observed profile in Figure 5 is flat, which verifies that water vapor is distributed uniformly above the surface or the effect of quenching is negligibly small, if it is distributed inhomogeneously. We cannot judge which is the case. However, we have also observed the distribution of NO2 in the same system and again found that the distribution was flat under the condition of surface saturation. Considering that NO2 should be much more affected by H2O quenching effect, it is plausible that the concentration gradient in water
vapor is negligibly small. Anyhow, it is true that we can forget the effect of water on the SO2 fluorescence intensity measurements, because either water vapor is distributed uniformly or its quenching effect is negligible. Effect of Gas Flow Velocity. The effect of gas flow velocity, νg0, ranging from 35 to 730 cm/s on γ is shown in Figure 6 at two different pH (thus for two different γ ranges). The obtained γ value is independent of the gas flow velocity over the entire range studied, which guarantees that eq 2 is valid independent of the momentum flow in the outer region. Effect of Total Pressure. Figure 7 shows the results with different total pressure, P, ranging from 23.4 to 90.2 Torr. The diffusion coefficient changes from 4.46 to 2.39 cm2/s, dependent on the total pressure. Except for the lowest pressure region,
Uptake Coefficients of SO2
Figure 8. Effect of SO2 concentration on γ at two different pH values. The inserted figure is an enlargement of the range of low SO2 concentrations. O: pH ) 5.6. b: pH ) 12.8. P ) 90.1 Torr, T ) 293.4 K, νg0 ) 71.3-384 cm/s, νa0 ) 2.1 cm/s.
J. Phys. Chem., Vol. 100, No. 24, 1996 10273
Figure 10. Effect of pH on γ. Error bars show (1σ deviation. C0 ) 8.7 × 1013 molecules/cm3, P ) 89.8 Torr, T ) 293.2 K, νg0 ) 92.9 cm/s, νa0 ) 2.1 cm/s.
exceeding pH ) 12. On the other hand, the γ values at smaller pH conditions than 3 are by one magnitude smaller than those in the neutral region. Effect of Temperature. The effect of temperature on γ is very small judging from the data at four different pH conditions shown in Figure 11. Discussion
Figure 9. Effect of the water flow velocity on γ at two different pH values. Error bars show (1σ deviation. C0 ) 3.8 × 1013 molecules/ cm3, P ) 89.8 Torr, T ) 293.5 K, νg0 ) 93.0 cm/s.
the observed γ value is not affected by the change in the total pressure and the resultant change in the diffusion coefficient. The large deviation of γ observed in the lowest pressure region was attributed to the instability of the aqueous surface. Though the dissolved gases were effectively eliminated by the degassing procedure, it was difficult to maintain the steady flow of the water through a pump when the total pressure was low. The low total pressure inevitably led to the vaporization of water at the pump suction. Therefore, in the determination of γ, we have employed experimental conditions where the total pressure was above 45 Torr, which gave no impropriety. Effect of SO2 Concentration. The effect of SO2 concentration in the gas phase was investigated in the range from 8.3 × 1011 to 3.3 × 1014 molecules/cm3 at two different pH conditions (5.6 and 12.8) as shown in Figure 8. The obtained γ value decreases with the increase of SO2 concentration at both pH conditions. It is shown that it converges to a constant value when the SO2 concentration becomes lower than 1 × 1013 molecules/cm3. The extrapolated value to the zero concentration is 0.0077 at pH ) 5.6 and 0.029 at pH ) 12.8. Effect of Water Flow Velocity. Experiments were performed with changing νa0 from 0 to 20.0 cm/s in order to investigate the effect of the contact time on γ. The corresponding contact time ranges from infinity to 27 ms according to Figure 3. Figure 9 shows the results at two different pH conditions, pH ) 5.9 and pH ) 13.2. The obtained γ value is very close to zero when νa0 is zero, but it is not largely dependent on the water flow velocity. Effect of pH. Figure 10 shows the effect of pH ranging from 2.6 through 13.2 at 293.2 K. The obtained γ value varies little in the neutral region between pH ) 4 and pH ) 8. Relatively large γ values are observed under the alkaline condition
Aqueous Phase Reactions of SO2 and Their Contribution to Effective Henry’s Constant and Equilibrium pH. We have proven that the obtained γ value is not affected by gas-phase flow and pressure conditions, which supports the application of the present novel method to direct measurements of uptake coefficients. We have observed a large pH effect on the uptake coefficient. Considering the fact that differences in physical properties of aqueous solutions between the acidic and alkaline condition are very small (for example, only 0.8%, 0.2%, and 1.0% increase in viscosity, density, and surface tension, respectively, is expected from pH ) 5.6 to pH ) 13), the cause of the large pH effect should be searched for in chemistry in the aqueous phase. The uptake coefficient is, as mentioned elsewhere,3 dependent on the degree of saturation in the aqueous phase. The dissolution equilibrium is described by the Henry’s constant H. If the Henry’s constant is so large that the saturation may not be established within the observation time, the uptake coefficient is expected to stay large. Schwartz3 derived an effective Henry’s constant H*, taking into account the following acid-dissociation equilibrium.
SO2(g) a SO2(aq) H
(4)
SO2(aq) + H2O a H+ + HSO3- Ka1
(5)
HSO3- a H+ + SO32- Ka2
(6)
The effective Henry’s constant is equated as
(
H* ) H 1 +
Ka1 +
[H ]
+
)
Ka1Ka2 [H+]2
(7)
The proton concentration [H+] is derived as shown below from the acid-dissociation equilibrium (eqs 4-6) and taking into account the mass-balance of ionic species
[H+]3 - 2 × H′[H+]2 - (Kw + Ka1[SO2(aq)])[H+] - 2 × Ka1Ka2[SO2(aq)] ) 0 (8)
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Figure 11. Effect of temperature on γ at four different pH values. Error bars show (1σ deviation. C0 ) 8.7 × 1013 molecules/cm3, P ) 89.8 Torr, νg0 ) 92.9 cm/s, νa0 ) 19.4 cm/s.
Figure 13. γ as a function of contact time. Error bars show (1σ deviation. The deviation in the contact time is not taken into account. Data are transferred from Figure 9. Solid (for pH ) 13.2) and dotted (for pH ) 5.9) lines are estimated γ values in terms of eq 9 adopting γ(0) ) 0.028. C0 ) 3.8 × 1013 molecules/cm3, P ) 89.8 Torr, T ) 293.5 K, νg0 ) 93.0 cm/s.
from the value of R with the progress of the dissolution of the gaseous species until the dissolution equilibrium is attained, where γ ) 0. According to the derivation led by Danckwerts23 and also to the similar treatment by Hanson and Ravishankara,24 the time dependence of the uptake is given below.
γ(t) )
Figure 12. γ as a function of pH*. 0: pH ) 5.6 (data from Figure 8). 4: pH ) 12.8 (data from Figure 8). b: C0 ) 8.7 × 1013 molecules/cm3 (data from Figure 10). P ) 89.8-90.1 Torr, T ) 293.2-293.4 K, νg0 ) 71.3-384 cm/s, νa0 ) 2.1 cm/s.
where [H+]0 is the initial value before the contact with SO2containing gases, and H′ is given by
H′ ) ([H+]0 - Kw/[H+]0)/2
(9)
We will designate the pH value calculated by numerically solving eq 8 as equilibrium pH, pH*, in order to discriminate it from the initial pH value before the contact with SO2containing gases. The effective Henry’s constant (and also the equilibrium pH corresponding to it) must be consulted in place of the Henry’s constant H (and initial pH) in the time range longer than the establishment of the acid-dissociation equilibrium, which is the inverse of the pseudo-first-order rate constant of the forward reaction of eq 5. It is 2.9 × 10-7 s, if the rate constant of Eigen et al.17 is adopted. The effective Henry’s constant is calculated from the reported values of H, Ka1, and Ka2.22 Because H* increases with the increase of pH*, the uptake coefficient, which is determined experimentally in a given observation time, is expected to increase with pH and also with the decrease of SO2 concentration. For example, the difference between the data (γ ) 0.013) in Figure 4 and the pH ) 10 data (γ ∼ 0.01) in Figure 11 is attributed to the difference in SO2 concentration in these two data, which affects the γ value by changing pH*. The data in Figures 8 and 10 were altogether plotted against pH* as shown in Figure 12. The dependence of the uptake coefficient both on pH and SO2 concentration is altogether described as a single relationship dependent on pH*. It is understood that the uptake coefficients are controlled by pH* and thus, probably by H*. Time Dependence of the Uptake Coefficient and Its Interpretation. The uptake coefficient is expected to decrease
1 ν 1 m πt + γ(0) 4H*RT Dl
()
1/2
(10)
and
νm 1 1 ) + R γ(0) 4HRT(Dlk1)1/2
(11)
where Dl is the diffusion coefficient of S(IV) species in the aqueous phase and k1 is the pseudo-first-order rate constant of the forward reaction of eq 5. νm is the molecular velocity as in eq 2. The above eqs are derived on the assumption that the acid-dissociation equilibrium is established within a much shorter time than the observation time (or contact time). Indeed, the equilibrium of eq 5 is established within the time corresponding to the inverse of k1 in the aqueous surface. The eq 10 is adequate when the contact time is longer than µs. The uptake coefficient obtained under various νa0 values at two different pH values (the data are from Figure 9; pH ) 5.9 and 13.2: corresponding pH* ) 3.7 and 6.4) is plotted against the contact time in Figure 13. Here, the νa0 value has been converted to the contact time using the relationship drawn in Figure 3. In Figure 13, one standard deviation due to the scattering of the measured values, σ1, is drawn with the bars, which amounts to (0.002 at pH ) 13.2. On the other hand, it is stated by many researchers10,13 that an uncertainty of (1520% ((0.006) cannot be avoided in the estimation of the diffusion coefficient, which is transferred to the uncertainty in γ. Thus the total uncertainty with a 95% confidence is at most 2σ1 plus the uncertainty due to the uncertainty of diffusion coefficient. If we take into account a possible uncertainty of (20% in the diffusion coefficient, the γ(0) value from Figure 13 is 0.028 ( 0.010. On the contrary, the simulated γ(t) value according to eq 10 with γ(0) ) 0.028 is also drawn in Figure 13 as a function of the contact time t. Thus the data at two different pH values seem to be satisfactorily correlated in terms of eq 10. The above treatment allows us to use the uptake coefficients obtained at sufficiently large pH* as γ(0). Eventually, by averaging the data in the region of pH* larger than 6.4,
Uptake Coefficients of SO2
J. Phys. Chem., Vol. 100, No. 24, 1996 10275
Figure 14. γ as a function of pH* at four different temperatures. C0 ) 8.2 × 1011-9.7 × 1013 molecules/cm3, P ) 89.8 Torr, νg0 ) 87.496.0 cm/s, νa0 ) 19.4 cm/s, pH of water ) 13.2.
individual γ(0) values are determined. Figure 14 shows the uptake coefficients obtained at four different temperatures. The R value can be estimated from eq 11 by adopting the determined γ(0) value. The R value corresponding to the average γ(0) value of 0.028 at 293.5 K is calculated to be 0.2, if we adopt the rate constant value by Eigen et al.17 for k1. The R value ranges from 0.04 to 1.0, if the uncertainty limit of the γ(0) value is taken into account. In the above estimation, the liquid phase diffusion coefficient Dl has been taken to be 1.56 × 10-5 cm2/s, being estimated in terms of the Wilke-Chang eq 12, with adopting the adequate temperature dependent viscosity and the reported value25 for Dl at 298 K (1.77 × 10-5 cm2/s)
T Dl ) a η
(12)
where a is a constant and η, viscosity. Temperature Dependence of the Uptake Coefficient. By using the γ(0) values obtained at four different temperatures in Figure 14, the activation energy of γ(0) is determined to be -6.0 kJ/mol. The temperature dependence of R could not be mentioned from these results, because the temperature dependence of k1 remains unknown. A Surface SO2 Complex and Its Contribution to the Interfacial Mass Transport. Very recently, Donaldson et al.,26 evidenced the existence of a surface SO2 complex on the water surface from SHG and surface tension measurements. They showed that SO2 molecules adsorb on the water surface obeying a Langmuir-type relation and that the saturated surface coverage is 5 × 1014 molecules/cm2. They gave the relation between the surface coverage and the concentration of S(IV) species in the aqueous phase. We have obtained the relationship between the surface coverage and the equilibrated gaseous SO2 pressure based on their data, by estimating the latter value by using H* calculated against the S(IV) concentration in the aqueous solution. For example, the surface coverage is estimated to be 2.6 × 1014 molecules/cm2 (coverage ) 0.5) at the gaseous SO2 pressure of 76 Torr or 2.5 × 1018 molecules/ cm3. The pressure range adopted in the present experiment is 8.4 × 1011-3.4 × 1014 molecules/cm3 (at pH ) 13.2), which is much smaller than the above pressure. The corresponding equilibrium concentration of the SO2 complex is 8.1 × 10101.7 × 1012 molecules/cm2 (coverage is 1.5 × 10-4-3.2 × 10-3). The surface coverage is very small, and the contribution of the surface complex formation to the overall uptake coefficient is limited to the fraction of the coverage, that is, less than 1.5 × 10-4-3.2 × 10-3. Thus we conclude that the surface complex of Donaldson’s type does not play a significant role on the mass transport process at the interface under the present experimental
conditions. The above consideration seems to be different from Jayne et al.,9 who tried to explain their larger γ(0) than 0.032 by assuming a certain kind of surface SO2 complex. Comparison of the Uptake Coefficient with Previous Values. It is important to note that the uptake coefficient at high pH changes very slowly with the time progress because of considerably large H* values. Thus the obtained γ values at large pH* is approximately equal to γ(0), even though the contact time in the present experiments are not so short as Worsnop et al.8 The present γ(0) is in the reasonable range predicted if the rate coefficient of k1 from the bulk-phase experiment of Eigen et al.17 is adopted. On the other hand, Worsnop et al.8 and also Jayne et al.9 reported a larger value of 0.11, which is four times larger than the present value. We are not certain what is the possible reason for the difference, but some comments may be made. At first we have paid attention to the difference of the surface curvature between the two works. We have adopted a flat surface, while Worsnop et al., a droplet surface of ca. 100 µm diameter. The surface tension Γ of a liquid drop is dependent on the droplet radius, R. According to Tolman27
(
Γ(R) ) Γ∞ 1 -
2δ + O(R-2) R
)
(13)
where Γ∞ is the surface tension of a planar surface, and δ, the Tolman length. The latter value is less than 1.9 σ (σ: the length parameter of the Lennard-Jones potential) according to recent molecular dynamics calculations.28,29 Because the droplet radius of Worsnop et al.8 is much larger beyond comparison than σ, the difference in surface curvature of the droplet cannot explain the difference between our value and that of Worsnop et al.8 In the research of Worsnop et al.,8 the overall mass transfer rate from the surrounding atmosphere to the moving droplet was measured, from which the uptake coefficient was estimated. The typical diameter of the moving droplet, dp, was 1.0 × 10-4 m, and the droplet velocity was in the order of several 10 m/s. The Reynolds number is considerably larger than unity and then the droplet seems to be susceptible to hydrodynamic distortion. It has been shown by a number of investigators30-33 that viscous circulation often occurs within drops. The resultant convective mass transport in the moving droplet is noticed when the droplet diameter is larger than 10 µm.3 According to Levich,30 the order of the internal velocity uir is
3 uir ) ud 2
(14)
where ud is the velocity of the moving droplet. In the case of Worsnop et al.,7 uir is in the order of several 10 m/s. If the aqueous surface is disturbed by this internal flow, the eventual contact time between the gaseous SO2 and the aqueous surface may be estimated from dp/uir, which is in the order of µs in the present estimation. The estimation by eq 14 is stated to be too large than the value by later workers.32 Even if it were so, we may not forget the possible contribution of the internal flow. In other words, we suspect that the real contact time in the experiments of Worsnop et al.8 were much shorter than they expected (several ms or longer). If it were so, their γ(0) value may be different from the value estimated from eq 11, which is applicable in the time region longer than ms order. Their extrapolation procedure might reach a certain value between R and γ(0). This consideration might give us a clue to solve the discrepancy between Worsnop et al.8 and us. Conclusion We have reported the uptake of SO2 on the aqueous surface by employing a laser-spectroscopic direct measurement method.
10276 J. Phys. Chem., Vol. 100, No. 24, 1996 The uptake coefficient was determined in terms of the eq which described the net flux of the uptake. The determined γ value with a 95% confidence is 0.028 ( 0.010 at 293.5 K, which is understandable on the basis of the first-order reaction rate obtained by Eigen et al.17 for the acid-dissociation reaction in the aqueous phase. The surface complex of SO2 of Donaldson’s type may not contribute to the uptake process to a large extent, at least when the gaseous SO2 concentration is quite small as in this research. Acknowledgment. This work is supported by a Grant-inAid for Scientific Research on Priority Area from the Ministry of Education, Science and Culture of Japan (No. 05237106), which is greatly appreciated. References and Notes (1) Barrie, L. A. J. Geophys. Res. 1985, 90, 5789. (2) Moller, D. Atmos. EnViron. 1983, 17, 1603. (3) Schwartz, S. E. In Chemistry of Multiphase Atmospheric Systems; Jaeschke, W., Ed.; Nato ASI Series; Springer-Verlag: Berlin, 1986; Vol. G6, p 415. (4) Tang, I. N.; Lee, J. H. In The Chemistry of Acid Rain: Sources and Atmospheric Processes; Johnson, R. W., Gordon, G. E., Eds.; ACS Symposium Series No. 349; American Chemical Society: Washington, DC; 1987; p 109. (5) Tang, I. N.; Lee, J. H. Atmos. EnViron. 1988, 22, 1147. (6) Gardner, J. A.; Watson, L. R.; Adewuyi, Y. G.; Davidovits, P.; Zahnisher, M. S.; Worsnop, D. R.; Kolb, C. E. J. Geophys. Res. 1987, 92, 10887. (7) Gardner, J. A.; Watson, L. R.; Adewuyi, Y. G.; Van Doren, J. M.; Davidovits, P.; Worsnop, D. R.; Zahniser, M. S.; Kolb, C. E. In Biogenic Sulfur in the EnVironment; Saltzman, E. S., Cooper, W. J., Eds.; ACS Symposium Series No. 393; American Chemical Society: Washington, DC; 1989; p 504. (8) Worsnop, D. R.; Zahniser, M. S.; Kolb, C. E.; Gardner, J. A.; Watson, L. R.; Van Doren, J. M.; Jayne, J. T.; Davidovits, P. J. Phys. Chem. 1989, 93, 1159. (9) Jayne, J. T.; Davidovits, P.; Worsnop, D. R.; Zahniser, M. S.; Kolb, C. E. J. Phys. Chem. 1990, 94, 6041.
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