1684
J . Phys. Chem. 1991,95, 1684-1689
for the linear and Guerbet compounds. It is observed that the greater positive entropy contribution governs the magnitude of the work of transfer in the ethoxy sulfates. This positive entropy contribution is greater for the Guerbet surfactants than the linear ones. The structural features of the Guerbet hydrophobe that can cause steric disfavorability to micellization may be the cause for the large entropy contribution to the positive value of the work of transfer. The thermodynamics of aggregation at the airaqueous solution interface and in bulk were investigated in 0.1 N NaCl solution for the CI6ethoxy sulfates. Results are shown in Table 11. Trends in free energies of adsorption and micellization observed in water (and discussed above) were similar to those in 0.1 N NaCl solution also. Guerbet branching of the hydrophobe results in a decreased thermodynamic favorability for micellization and increased fa-
vorability for adsorption at the air-water interface.
Conclusion Branching the linear hydrophobe to give the Y-branched Guerbet structure results in an increase in thermodynamic favorability for adsorption at the air-water interface compared to micellization in bulk. In Guerbet surfactants steric features tending to disfavor micellization result in entropy being the major thermodynamic factor. Because of the relative thermodynamic favorability for adsorption at the air-water interface, Guerbet surfactants are very effective in reducing the air-water surface tension. Guerbet surfactants would offer unique advantages in surfactant applications such as foaming which depend on surfactant adsorption at the air-water interface and the effectiveness of surface tension reduction.
Uptake of N,05 and HNO, by Aqueous Sulfuric Acid Droplets J. M. Van Doren,t L. R. Watson: P. Davidovits, Department of Chemistry, Boston College, Chestnut Hill, Massachusetts 021 67
D. R. Worsnop,* M. S. Zahniser, and C. E. Kolb Aerodyne Research, Inc., 45 Manning Road, Billerica, Massachusetts 01821 (Received: March 20, 1990; In Final Form: August 24, 1990)
Uptake coefficients for gaseous NzOs and HN03 into liquid 0.33 HzS04mole fraction (73 wt %) droplets at 283 K have been measured. HN03 in the gas phase was directly observed as a product of Nz05uptake. The experimental method employs a monodisperse train of droplets (-200-pm diameter) in a low-pressure flow reactor. Droplet-trace gas interaction times are 1-2 ms. Uptake coefficients are 0.058 f 0.006 for NzOSand 0.1 1 f 0.01 for HN03. These values are 40% larger and smaller than for NzOSand HN03 uptake, respectively, into pure water. The product branching ratio for gaseous evolution of H N 0 3 from N 2 0 5heterogeneous reaction ranged from 0.25 to 0.37 for gas/liquid contact times of (1.1-1.6) X s. Both the reduction in HN03 uptake coefficient (relative to that on water) and the HN03 gaseous evolution from N I O Suptake can be explained by limited H N 0 3 solubility in aqueous sulfuric acid. A value of 4 ( f 2 ) X IO3 M atm-l at 283 K IS derived for the Henry’s law constant based on a time-dependent model of this limitation. Nitric acid production from the heterogeneous reaction of N205with aqueous sulfuric acid may provide an important mechanism for removal of NO, from the stratosphere.
-
Introduction The heterogeneous interactions of gas-phase species with aerosols play an important role in atmospheric chemistry. In the polar stratosphere heterogeneous reactions have been pivotally involved in the ozone destruction process.’-‘ Heterogeneous reactions provide both a mechanism for the removal of gaseous species and a means for chemical transformation of these species. An important process in Antarctic ozone depletion is the removal of nitrogen oxides from the gas phase (denitrification), which inhibits the formation of chlorine nitrate leading to large concentrations of ozone reactive CIO. In this context the heterogeneous interactions of nitric acid ( H N 0 3 ) and dinitrogen pentoxide (N205)with polar stratospheric cloud particles have been postulated as important steps in the catalytic destruction of ozone.1*2*4 An outstanding question is whether the heterogeneous reactions implicated in the polar stratosphere occur in the nonpolar stratosphere as well. Aerosols in the mid-latitude stratosphere, 1625-km altitude region, are principally composed of aqueous sulfuric acid in the range 60-80 wt 9% (0.2-0.4 mole fraction) sulfuric acid as governed by the water vapor mixing r a t i ~ . ~The . ~ size of the aerosols is in the range 0.1-1 pm, and the surface area is estimated to be in the range 10-9-10-8 cm2/cm3.’ The ambient temperature in this region is between 21 5 and 220 K where the acid aerosol ‘Current address: Air Force Geophysics Laboratory, Hanscom AFB, MA 01731-5000.
is expected to be a supercooled liquids6 There have been several attempts to assess the impact of heterogeneous processes on global ozone reductions outside the polar regions.’~* Hofmann and Solomon modeled the observed ozone depletions following the eruption of El Chichon and concluded that heterogeneous reactions may have been responsible for part of the anomalously low ozone levels observed a t midlatitudes in early 1983.’ To properly assess the importance of heterogeneous processes, reliable experimental kinetic data must be obtained for these reactions as a function of temperature and aerosol composition. Particularly important in their model is the conversion of N 2 0 5to HNO,
N205+ H20(aq)
-
2HN03(aq or g)
(R1)
(1) Solomon, S.Reu. Geophys. 1988, 26, 131-148. (2) Wofsy, S. C.; Molina, M. H.; Salawitch, R. J.; Fox, L. E.; McElroy, M. B. J. Geophys. Res. 1988, 2442-2450. (3) Salawitch, R.J.; Wofsy, S.C.; McElroy, M. B. Geophys. Res. Lett. 1988, IS, 871. (4) KO,M. K. W.; Rodriguez, J. M.; Sze, N. D.; Profitt, M. H.; Starr, W.
L.; Krueger, A.; Browell, E. V.;McCormick, M. P. J. Geophys. Res. 1989, 94, 16, 683. (5) Rosen, J. M. J . Appl. Meteorology 1971, 10, 1044-1046. (6) Steele, H. M.; Hamill, P.; McCormick, M. P.; Swissler, T. J. J . Amos. Sci. 1983, 40, 2055-2067. (7) Hofmann, D. J.; Solomon, S . J. Geophys. Res. 1989,94,5029-5041. (8) Rodriguez, J. M.; KO,K.W.; Sze, N. D. Geophys. Res. Lett. 1988, I S , 257-260.
0022-3654/91/2095- 1684$02.50/0 0 1991 American Chemical Society
Uptake of N 2 0 5and HNO, by Aqueous H2S04
The Journal of Physical Chemistry, VoZ. 95, No. 4, 1991
Temperature Conlroiled Cooling Coil ,
I
I
TABLE I: Details on the Spectral Lines Used in the Detection of Trace Molecules
i -1
Trace Gas HZO,He
J
molecule HN03
+-ToPump Diode Lass1Beam
NZ05
CH4 (ref) Gas Flow Tube
/ Ditlerential Pressure Transducer
While
Temperature
Figure 1. Schematic of experimental apparatus. These studies have modeled N 2 0 5 / H N 0 3 heterogeneous chemistry using kinetic parameters derived from available laboratory measurements. The latter include experimental study of N205/HN03interactions with liquid water? ice,’OJ’ and sulfuric acidI2-l5surfaces. Taken together, the results of these experiments clearly indicate that (RI)is fast enough to be significant in the stratosphere. However, important quantitative questions remain concerning the detailed kinetics. Heterogeneous reactions begin with the gas-phase species striking the droplet and entering into it. The fundamental kinetic parameter governing gassurface interaction is the mass accommodation coefficient defined as
-
with our earlier temperature dependence studies of uptake into pure water? provides insight into the fate of N 2 0 5and HNO, in the mid-latitude stratosphere. Experimental Techniques and Results Uptake Coefficient Measurements. The uptake measurements were performed in the flow tube apparatus shown in Figure 1 which has been described previously in detail.16 Briefly, a monodisperse train of droplets of known composition and temperature passes through a flow tube, and trace gas depletion due to droplets is measured. The observed uptake coefficient, yo, is calculated from the fractional change in trace gas concentration from its value in the absence of the droplet train to its value in the presence of the droplet train or
no. of molecules absorbed by the surface no. of molecular collisions with the surface
F~ An
Yobs
This parameter determines the maximum flux of gas into a liquid. In many circumstances, however, the actual net gas uptake is smaller. It may be limited by several processes, among which are gas-phase diffusion and Henry’s law saturation. In an actual experiment subject to these limitations, the measured flux of gas-phase molecules into a surface is expressed in terms of an uptake coefficient, Yobs, as
J = n,Ey0,/4
(1)
where nBis the gas-phase number density at the droplet surface and F is the average molecular velocity. In order to model heterogeneous reactions, it is important to understand the processes and parameters that govern the uptake of the gas-phase species by the droplets. In this work we report uptake measurements of gas-phase N z 0 5 and HNO, by aqueous sulfuric acid droplets (73 wt 7’% or 0.33 HzS04mole fraction) at 283 K. In connection with the heterogeneous reaction of N 2 0 5with an aqueous surface two questions arise. What fraction of the N 2 0 5reacts to form H N 0 3 , and in what state is the HNO, formed? We have performed branching ratio experiments that address these questions. This work, together (9) Van Doren, J. M.;Watson, L. R.; Davidovits, P.; Worsnop, D. R.; Zahniser, M.S.; Kolb, C. E. J . Phys. Chem. 1990, 94, 3265. (IO) Tolbert, M. A.; Rossi, M. J.; Golden, D. M. Science 1988, 240, 1018-1 02 I . (11) Leu, M.-T. Geophys. Res. Letr. 1988, IS, 851-854. (12) Harker, A. B.; Strauss, D. R. Kinetics of the Heterogeneous Hydrolysis of Dinitrogen Pentroxide Over the Temperature Range 214-263 K. Rockwell International Science Center, Federal Aviation Administration Publication AAA- EE-8 I - 3, I 98 I . (13) Tolbert, M.A.; Rassi, M.J.; Golden, D. M. Geophys. Res. Len. 1988,
I S , 847-850.
wavenumber, cm-I 1332.54 1242 1241.863” 1241.949‘ 1332.547
density of line strength! species for 10% cmz molecule-’ absorption: cm-’ molecules 2.67 X 2.1 x 1013 1.62 X cmZd 1.7 X IOI4 6.51 X 1.6 x 1014 6.51 X 1.6 x 1014 1.9 x 1013 5.68 X
a Different lines were used in different experiments depending on laser operation. b Line strengths from HITRAN line compilationz1unless otherwise noted. ‘The line used is identified as an R-branch transition with J” = K,” = 14.2z,z3 The line strength reported is calculated by using the formula for a prolate topz4 and reported groundstate constants.25 The calculated value was corrected for apparent systematic error based on a comparison of observed and calculated line strengths for the nearby J” = K,” = 16-19 t r a n s i t i ~ n s . ~Estimated ~*~~ error is *13%. “Estimated error is *20%. CEstimated using the Doppler line width at 283 K and a path length of 360 cm.
dkl
Controlled Bath
ff=
1685
(14) Tolbert, M.A. Personal communication, 1989. (15) Mozurkewich, M.;Calvert, J. G. J. Geophys. Res. 1988, 93, 15889.
= -Y4EA n
where n is the trace gas concentration, Fg is the volume rate of flow in the flow tube, E is the trace gas thermal velocity, and A is the total surface area exposed to the trace gas. To attain the desired droplet temperature, the nozzle assembly producing the droplets is cooled. The temperature of the droplets is maintained by controlling the water vapor pressure to match the equilibrium density in the droplet generating region and in the flow tube. The droplet collection flask is also temperature controlled. The temperature of the droplet was measured with a thermocouple and found to be within f l deg of 283 K. Although the flow tube was not actively cooled, the gas temperature one mean free path above the surface of the droplet is expected to be a t most 1 deg warmer than the droplet Reagent grade sulfuric acid (95-98 wt ’3%) is diluted with distilled water to the desired concentration. The concentration of the solution is determined by a measurement of its density. The reported concentrations are accurate to f2%. In the course of experiments the droplet orifice was etched by the aqueous sulfuric acid passing through it. As a result, the orifice diameter increased during the 3-month period of these experiments. The orifice diameter for each experiment was evaluated from measurements of liquid flow rate through the orifice as a function of backing pressure. In the high-pressure limit the square of the orifice diameter (d:) is proportional to the slope of a linear plot of liquid flow rate versus the square root of the backing pressure. The exposed droplet surface area, A, used in evaluating yo, is also proportional to d,Z. We estimate the uncertainty in A to be about 10%. (16) Watson, L. R.; Van Doren, J. M.; Davidovits, P.; Worsnop, D. R.; Zahniser, M. S.; Kolb, C. E. J. Geophys. Res. 1990, 95, 5631. (17) 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, 1159-1 172.
1686 The Journal of Physical Chemistry, Vol. 95, No. 4, 1991
Van Doren et al.
TABLE 11: Measured Uptake Coefficients for N20, and HNO, on Aaueous Sulfuric Acid Droplets at 283 K
molecule
droplet composition (H2S04mole fraction, wt W )
YOhS'
PtOtal, Torr
orifice diameter, pm
atm cm2 s-'
Y'
0.33 (73) 0.33 (73)
0.055 f 0.006 0.093 f 0.014
11.61 10.90
95 97
0.475 0.482
0.058 i 0.006 0.1 1 i 0.01
205
HN03
D,b
'Error bars represent f l u including both random and systematic errors (see text). bBinary diffusion coefficient for trace gas in a mixture of He and H 2 0background gases estimated from eq 5 .
In all of the experimental runs the gas flow contained helium, water, the trace gas of interest, and a trace of methane. Methane is an insoluble species which is not taken up by the droplets. The density of CH4 is monitored to correct trace gas density changes for flow and pressure fluctuations. Concentrations of the trace gases H N 0 3 , N2O5, and CH4 are measured by absorption of infrared radiation from a tunable diode laser (Laser Analytics) in a multipass white cell downstream of the droplet train. The spectroscopic details of the absorption lines used in the detection are presented in Table I. To improve the signal-to-noiseratio, the output of the diode is frequency modulated and the second harmonic signal is detected. This technique is used for HNO, and CH4. The absorption of N20Sis a continuum even at Doppler-limited resolution. Therefore, for this species the density is obtained from direct absorption measurements of mechanically chopped radiation. The assignment of the observed absorption to the presence of N205was verified by tuning the laser over the 1250-cm-' band and observing the structure in the abThe absorption at line center of all trace gases is kept to less than 10%. N2O5 was synthesized by using the procedure of Viggiano.26 Briefly, the synthesis involves the formation of NO2 and NO3 from the sequential oxidation of NO (99.0%) by 03.N z 0 5 is formed by the three-body association of NOz and NO3. The ozone was formed from O2(99.8%) by use of a standard ozonizer (Welsbach Model T-408). Care was taken to eliminate all moisture from the apparatus and the experimental gas inlet in order to prevent the heterogeneous reaction of NzOSwith water. By use of infrared absorption, the H N 0 3 impurity arising from the N20S sample and reactions in the inlet is estimated to be less than 1% of the N 2 0 Sconcentration. The prepared sample was kept cold at all times (196 K between experiments and 228 K during experiments) to prevent thermal decomposition. Some heterogeneous conversion of NzO5 to H N 0 3 on the flow tube walls was unavoidable. This was minimized by keeping the walls as dry as possible. For experiments measuring gaseous H N 0 3 evolution from N20S uptake, extreme care was taken in this regard so that the HN03(g) background near the droplets was negligible compared with the HN03(g) density produced from N205(g) reaction with the droplets. For the N20S uptake experiments, HN03(g) background levels were not routinely monitored. However, at low trace gas densities (SlOI4 ~ m - giving ~, aqueous [HNOJ IOP3 M), we do not expect secondary interactions of N 2 0 5and background H N 0 3 to have any measurable effect on N205uptake. The uptake coefficients of HNO, and N 2 0 5by aqueous sulfuric acid droplets were measured at 283 K with a droplet concentration of 73 wt % H2S04. The observed uptake coefficients, yob,are
-
(18) Murcray, D. G.; Murcray, F. J.; Bonomo, F. S.; Goldman, A.; Blatherwick, R. D. High Resolution Infrared Laboratory Spectra. Department of Physics, University of Denver, 1984. (19) Lovejoy, R. W.; Chackerian, C., Jr.; Boese, R. W. Appl. Opt. 1980, 19, 744. (20) Camy-Peryet, C.; Flaud, J.-M.; Lechuga-Fossat, L.; Laverdet, G.; Le Bras, G.Chem. Phys. Lett. 1987, 139, 345. (21) Rothman, L. S.; Gamache, R. R.; Goldman, A.; Brown, L. R.; Toth, R. A.; Pickett, H. M.; Poynter, R. L.; Flaud, J.-M.; Carny-Peyret, C.; Barbe, A.; Husson, H.: Rinsland. C. P.; Smith, M. A. H. Appl. Opt. 1987, 26, 4058-4097. (22) May, R. D.; Webster, C. R. J . Quant. Spectrosc. Radiat. Transfer 1987, 38, 5. (23) May, R. D.; Webster, C. R. J . Mol. Spectrosc. 1989, 138, 383-397. (24) Perrin, A.; Lab-Bordowsky, 0.;Valentin, A. Mol. Phys. 1989, 67, 249-270. (25) Maki, A. G.;Olson, W. M. B. J. Mol.Spectrosc. 1989, 133, 171-181. (26) Viggiano, A. A. Ph.D. Dissertation, University of Colorado, 1980.
Weight Percent of H2S0,
0 HNO,
0.20
Aerosol
.-5
I
0.15
Q
8
3
0.10
n
3
0.05
1
$
.. . .. .. . .. . .. . .. .. . .. . .. ............... .. ... ... .... ... ... ... ... ....... ... ..... ... ...
I
0.00 0.00
0.10
0.20 0.30 Mole Fraction of H2S04
0.40
Figure 2. Uptake coefficient for N205 and HNOl versus H2S04concentration in the droplet at 283 K.
shown in Table 11. These values are an average of at least nine experiments in which the volume rate of flow and droplet surface area have been varied. The experimental trace gas-droplet interaction time was 1.5 ms. Each experiment typically consisted of 10 on/off cycles. The reported error includes both the experimental precision, estimated to be the standard deviation of the mean of the measurements (flu), and uncertainties in gas flow rate (2%), pressure (OS%), and total droplet surface area (10%).
The measured yOb in Table I1 must be corrected for gas-phase diffusion and for distortion of the molecular velocity distribution. Worsnop et aI.I7 showed that for a train of moving droplets the relationship between the observed uptake coefficient, yob,and the zero-pressure limit, yo, is (3)
--Tot6
8D
Here, df is an effective diameter, d f = 1.8d0. This equation, based on work of S~hwartz,~' represents the reduced trace gas density at the droplet surface due to diffusion limitations. As also discussed by S ~ h w a r t zthis , ~ ~steady state is reached on a 10% time scale. Therefore, the steady-state treatment is appropriate for the lW3-s experimental gas/liquid contact times in our experiment. The diffusion coefficient ( D ) for the trace gas in the mixed background gas is given by (4)
Here P is the partial pressure of carrier gas species in atmospheres and DX-H20and DX+ are the binary diffusion coefficients for the trace gas (X) with water vapor and helium, respectively. The (27) Schwartz, S. E. Mass-Transport ConsiderationsPertinent to Aqueous Phase Reactions of Gases in Liquid-Water Clouds. In Chemistry of Mulriphase Atmospheric Systems; Jaeschke, W., Ed.; NATO AS1 Series; Springer-Verlag: Berlin, 1986; Vol. G6, pp 415-471.
The Journal of Physical Chemistry, Vol. 95, No. 4, 1991
Uptake of N2O5 and H N 0 3 by Aqueous H2SO4 partial pressure of water vapor for a solution of 73 wt 5% H2S04 at 283 K is 0.21 Torr.28 The diffusion coefficient and velocity values are evaluated at the average temperature of the droplet train and flow tube walls, 290.5 K. The binary diffusion coefficients for H N 0 3 with water and helium were chosen to equal the values for SO, with these species while the coefficients for N 2 0 5 were taken to equal these same values multiplied by a correction for the reduced mass difference. The value of DS02-H20 is 0.124 atm cm2 s-I at 298 K29with a calculated temperature dependence of T2.22 The value of Dso2-Hewas calculated to be 0.514 atm cm2 s-I at 290.5 Ka30 Finally, a small correction for the non-Maxwellian velocity distribution of the trace gas near the droplet surface must be applied to the data. This correction decreases with decreasing yobs and was 10% or less for these data. Both the diffusion and the velocity distribution corrections were applied to yobto calculate y. The results are listed in Table IT. The error bars for y include experimental precision (fl a), uncertainties in the gas flow rate, pressure, and total droplet surface area as well as an uncertainty of f20% in the value of the diffusion coefficient. The results are plotted in Figure 2 together with our value of y on water.g Branching Ratio Measurements in the Uptake of N205.The heterogeneous reaction of N20, with water may form nitric acid in the gaseous or aqueous phase as well as other products. Further, aqueous-phase nitric acid may dissociate or it may reevaporate to form HN03(g):
absorption coefficients for H N 0 3 and N205 (uHNo~/Q~o~). This ratio is calculated from the data shown in Table I. Further, we note that A[N20,] in eq 5 was not measured simultaneously. Rather, the total density of N 2 0 5at the droplets was measured, and A[N20,] was calculated by using the previously determined value of the uptake coefficient via eq 2. The value of the branching ratio obtained from our measurements ranges from 0.23 to 0.37 and appears to increase with increasing gas-liquid contact time. Our results are presented in Table 111. The reported values are averages of 4-16 on/off cycles.
-
Nz05 (B) HzO/H@4(1)
-E
2HN03 (Q) 2HN03 (q)
(R2)
In our uptake studies of N20S we measure the disappearance of N205(g) as well as the appearance of gas-phase H N 0 3 . We will define a branching ratio (BR) obtainable from our experiments as BR =
~
~
~
~
~
3
~
~
~
1
/
~ ( 5 )~
This branching ratio is measured in a manner similar to that used for evaluating uptake coefficients. A trace flow of N 2 0 5is exposed to droplets, and the gas-phase H N 0 3 concentration produced as a result of the exposure is monitored. The concentration of gas-phase H N 0 3 formed as a result of N205-droplet interaction is obtained via absorption measurements in the multipass White cell. A complication in this experiment is the presence of background gas-phase H N 0 3 which may be produced by the heterogeneous reactions of NzOSwith the walls of the flow tube. If there is a significant amount of background HN03(g) at the droplet train, then the concentration of HN03(g) measured in the White cell will reflect both the uptake of this background HN03(g) and the production of HN03(g) from the reaction of N20S(g)with the droplets. To minimize the background HN03(g) at the droplets, the N,OS(g) was added through a moveable injector -2 cm upstream of the droplets and the injector-droplet distance was varied to ascertain that HN03(g) production upstream of the droplets was below the limits of detection. Unfortunately, it is not possible to completely eliminate the production of H N 0 3 ( g ) on the walls of the flow tube downstream of the droplet train. Therefore, the HN03(g) evolved from the droplets is distinguished from other sources such as wall production downstream of the droplets by modulating the droplet surface area in the reaction zone. This is done by changing the droplet frequency while keeping the liquid flow rate constant.” This method of droplet modulation rather than turning the droplets on and off allows a more constant water vapor density in the reaction zone. In order to obtain the branching ratio from the optical absorption measurements, one needs to know the ratio of the optical (28) Gmitro, J. I.; Vermeulen, T. AIChE J . 1964, 10, 740. (29) Kimpton, D. D.; Wall, F. T. J . Phys. Chem. 1952, 56, 715. (30) Kee, R. J.; Dixon-Lewis, G.; Warnatz, J.; Coultrin, M. E.; Miller, J. A. A Fortran Computer Package for the Evaluation of Gas-Phase Multi-
component Transport Properties. Sandia National Laboratory Report, SAN086-8246, 1986.
Discussion The uptake coefficients for H N 0 3 and N 2 0 5into 0.33 H2S04 mole fraction (73 wt %) solutions, listed in Table I1 and plotted in Figure 2, are consistent with published measurements from other laboratories. Tolbert et al.I3J4 measured H N 0 3 uptake onto cold H2S04surfaces. They reported lower limits for H N 0 3 uptake coefficients of y > 0.014 and y > 0.01 for 0.183 H2S04mole fraction ( 5 5 wt %) at 198 K and 0.355 H2S04mole fraction (75 wt %) at 228 K, respectively. These limits are consistent with our value of y = 0.11 f 0.01 for 0.33 H204mole fraction at 283 K. The significance of the temperature difference is discussed below. Mozurkewich and Calvert15measured y 0.1 at 274 and 293 K for N 2 0 5uptake into small (4-80 nm) H2S04droplets with composition in the range -0.25-0.41 H2S04mole fraction (64-77 wt %), The value of y did not depend on H2S04 concentration over this small range (within experimental error), consistent with the similarity we observed for N 2 0 5uptake into pure water and 0.33 H2S04mole fraction plotted in Figure 2. Their y values, however, are approximately twice as large as our y = 0.058 f 0.006. We have no explanation for this difference except to note that the experimental conditions for the measurements were significantly different. In particular, for the small droplets and long gas/droplet contact times (tens of seconds) in the Mozurkewich dissolved N 2 0 5 and its ~ ~ ~ 2and~ Calvert15 5 ( S experiment, ~ l products accumulate in the droplets and build up significant solution-phase concentrations. Interpretation of experimentally measured uptake rates requires understanding the nature of the uptake mechanism. Overall, the above results indicate that there is no dramatic change in either H N 0 3 or N 2 0 S uptake with increasing H2S04 concentration. However, the uptake coefficients in Figure 2 do show a -40% increase for N 2 0 5and a 40%decrease for H N 0 3 , in going from pure water to 0.33 mole fraction H2S04.These observed uptake coefficients (y) place lower limits on the mass accommodation coefficient (a).Whether a measured y is a direct measure of a depends on the solubility of the gaseous species in the liquid, measured by its Henry’s law constant (If). If H is too small, y measures net uptake, reflecting the competition between accommodation and reevaporation of dissolved gaseous molecules. N205Uptake. In the case of N20S,the situation is complicated by the reactive nature of the N 2 0 S / H 2 0interaction (R2) where it is believed that N 2 0 5 forms H N 0 3 in aqueous solution. The mechanism for (R2) is not known. One possibility involves initial solvation followed by liquid-phase reaction:
-
2H+(q) + 2N037aq)
other produds
1687
/
N,O,(g)
* N,Os(aq)
N205(aq) + H 2 0
22HN03(aq)
(R3) (R4)
In steady state, the rate of N,OS(g) uptake for this mechanism can be expressed in terms of the c o e f f i ~ i e n t l ~ ~ ~ ~ a
y= I +
Ea 4HR T(D l k4)
(6)
where H and DI are the Henry’s law solubility (for the (R3) equilibrium) and liquid diffusion coefficient of N,O,(aq),. respectively, and k4 (s-I) is the pseudo-first-order rate coefficient for (R4). This expression convolutes the rates of mass accommodation, liquid diffusion, reevaporation, and reaction to give the
1688 The Journal of Physical Chemistry, Vol. 95, No. 4, 1991 net steady-state uptake. The derivation assumes that ( R 4 ) is irreversible. Without independent knowledge of N 2 0 5 solubility and reactivity, it is not possible to determine whether the mass accommodation coefficient or the solubility and reactivity are rate limiting. However, a measurement of y does place a lower bound on the product H(k4)II2in eq 6 ; in the limit a = 1 yT
H(k4)lJ2I 4RT(Dl)1/2
(7)
for y = 0.058, and H ( k 4 ) 1 /I2 2 X IO4 M atm-’ s-Il2 (for DI = 10” cm2 s-I; see below). Our results do not preclude the possibility that N 2 0 5reacts directly at the surface, i.e. N205(g) + H20(aq) 2HNO3(aq) (R5) Harker and StraussI2 have proposed such a surface reaction, while the mechanism represented by (R3)-(R4) is consistent with discussion in Mozurkewich and C a 1 ~ e r t . l N ~ 2 0 5 uptake measurements cannot distinguish between CY, H, k4, or k5 as the rate-limiting parameter. The similarity (within a factor of 2) of our results and those of Mozurkewich and Calvert15 is strongly indicative of reactive N205uptake, since the two experiments were done with gas/liquid contact times differing by a factor of IO5. If N205(aq) were not reactive, uptake would be limited by N205(aq)solubility, and the measured y would be expected to decrease at long exposure times (see below). Presumably, the variation in y for N205uptake into water and 0.33 mole fraction H2SO4 reflects changes in some combination of CY,H, k4, or k5. Measurement of HN03(g) evolution from N 2 0 5uptake places a lower limit on other potential products from N205 reaction in aqueous solution. (The above discussion (e.& eq 6 ) is not sensitive to N 2 0 5reaction products; reaction need only be irreversible.) For a branching ratio of 0.37 for HN03(g) evolution, the heterogeneous reaction efficiency of HNO, production from aqueous N205 reaction is 0.058 X 0.37 = 0.021. However, as is discussed below, the observed time-dependent branching ratio for HNO,(g) evolution can be explained by limited solubility for HNO,(aq) and therefore could be consistent with an overall branching ratio of unity for HNO, production from heterogeneous N205reaction. H N 0 3 Uptake. For HNO, uptake into H$04 solution, the question is whether the decrease in uptake (relative to pure water) reflects kinetics (Le,, a) or solubility (i.e., H). For unreactive trace gases the general expression for the uptake coefficient is’’-” y(t) = -
(8)
,
I+-
4RTH D1
where y ( t ) explicitly depends on the gas/liquid contact time ( t ) . This expression assumes dissolved trace gas diffuses to a depth ; the liquid. For DI = IOd cm2 s-I and t = 2 X of ( D l f ) l y in s, (Dit) = 0.5 pm; this is much smaller than the droplet ( d = 200 p m ) , indicating that this steady-state solution is appropriate. The right-hand term in the denominator accounts for the reevaporation of dissolved gas, which depends inversely on H . Thus, y ( t ) measures the net uptake after accommodation and evaporation. We have previously verified the applicability of eq 8 in extensive measurements of SO2 uptake into water1’ and HC1 uptake into H2S04solutions.I6 In water at 283 K, HNO, has an H value of 2 X lo5 M atm-1.32 For t = 2 X lo-, s in our experiment, eq 8 indicates there is no measurable evaporation of dissolved HNO,. Thus, in that limit of no saturation in the liquid, a = y = 0.17 for HNO, uptake into water.9 However, the magnitude of H for HNO, in 0.33 mole fraction H2S04 aqueous solution is not known. Actually, HNO, is much more soluble in water than indicated by H, which represents only physical solubility as HNO,(aq). The (31) Schwartz, S.E.; Freiberg, J. E. Atmos. Enuiron. 1981, 15, 1129-1144.
Van Doren et al. TABLE 111: Measured HN03 Product Branching Ratio for the Heterogeneous Reaction of Nz05with 73 wt % Aqwous Sulfuric Acid harlots at 283 K as a Function of Time
BR” 0.25 f 0.03 0.23 f 0.01 0.27 f 0.01
t , ms 1.1 1.2 1.3
BR” 0.32
* 0.01
0.37 f 0.01
t,
ms
I .4 1.6
OError reported is standard deviation of the mean. Systematic error is estimated to be *25%.
effective s o l ~ b i l i t y is ~ ~much - ~ ~ larger, since in aqueous solution most HN03(aq) dissociates HN03(aq) s H+(aq) + N03-(aq)
(R6) which is described by the acid equilibrium constant K,. One expects the degree of HNO,(aq) dissociation to decrease as acidity increases with increasing H2S04concentration, and in fact this has been measured spectr~scopically.~~ Above 0.25 H2S04mole fraction (65 wt %), there is no significant dissociation of HNO, via ( R 6 ) . For 0.33 H2S04mole fraction (73 wt %), uptake of HNO, is not sensitive to ( R 6 ) , because of the large physical solubility of undissociated HNO,. This contrasts with measurements of HC1 uptake, which showed a sharp decrease in uptake into solutions H2S04mole fraction >0.12 (40 wt %).I6 In that case, solubility is limited by the sharp decrease in the degree of HCI dissociation via its reaction analogous to ( R 6 ) . Thus, the solubility of HNO, in 0.33 mole fraction H2S04 solution is measured by H. If we assume that LY is independent of H2S04 concentration, as is consistent with HCI uptake into H2S04solution,I6 then the decrease in y measured for HNO, uptake into 0.33 mole fraction H2S04relative to its value into water can be explained by a decrease in H , whose value can be calculated from eq 8. H N 0 3 ( g ) Evolution. These same solubility constraints can explain the observed HN03(g) evolution from N 2 0 5uptake. If we assume that HNO,(aq) is the only roduct [as in (R3)-(R4)] and that the HNO,(aq) in the (D,t)’ deep liquid region below the surface of the droplet equilibrates with HNO,(g), then one can derive a time-dependent expression for the branching ratio analogous to eq 8. The net flux of H N 0 3 into the droplet is determined by the relative rates of production from N205uptake and evaporation of HN03(aq):
P
JHNO,
= ~ J N -~naq(T/4)6 o ~
(9)
The evaporation coefficient, 6, is related to the accommodation coefficient, a,via Henry’s law 6 = a/HRT (10) where naq, E, 6, a,and H in eqs 9 and 10 refer to HNO,. The branching ratio for HNO,(g) evaporation (see eq 4) can be expressed as BR = naq(~/4)6/2J~,0, (1 1) As in the derivation of eq 8,17 we assume that the aqueous HNO, concentration can be approximated by the net HNO, flux divided by the (Dlt)’12liquid diffusion depth
Solving eqs 9 and 12 to express naq and J H N o ~in terms of J N ~ o ~ and replacing 6 with a via eq 10, we obtain (32) Schwartz, S. E.; White, W. H. Solubility Equilibria of the Nitrogen Oxides and Oxyacids in Dilute Aqueous Solution. In Advances in Environmental Science and Engineering; Pfafflin, J. R., Ziegler, E. N., Eds.; Gordon and Breach Science Publishers: New York, 1981; Vol. 4, pp 1-45. (33) Schwartz, S. E. Atmos. Enuiron. 1988, 22, 2331-2333. (34) Brimblecomb, P.; Clegg, S. L. J . Geophys. Res. 1988, 7, 1-18. (35) Deno, N. C.; Peterson, H. J.; Sacher, E. J. Phys. Chem. 1%1,65, 199. (36) In eq 9 a was replaced with the diffusion-limited value yob.= 0.13 (calculated from eq 4) for HNO, uptake into water.9 This was necessary because the HN03(g) evolution was measured under gas-diffusion-limited conditions.
"=r:"o"
The Journal of Physical Chemistry, Vol. 95, NO. 4, 1991 1689
Uptake of N 2 0 5and HNO, by Aqueous H2S04
(13)
It-
As listed in Table 111, the measurements of the time dependence of BR are consistent with that predicted from eq 13, though the range 1 .I-1.6 ms is too short for a definitive interpretation. It should be noted that eqs 9-1 3 assume that the N 2 0 5uptake rate is time independent, as indicated by eq 7. Conversely, eq 8 implies that HNO, uptake should decrease with longer gas/ liquid contact time. However, the uptake of these two species was measured at only one value of r. As discussed below, it is the mutual consistency of the three experiments reported here that supports the use of eqs 6,8, and 13 to describe the uptake of N 2 0 5 and the uptake and evolution of HNO,. HNO, Solubility. Given a value of BR, eq 13 can be used to calculate a value of H(D,)1/2as with y ( t ) and eq 8. Estimation of H requires knowledge of D,,which can be estimated by assuming DI and p (liquid viscosity) are inversely proportional. Estimating DI 1 X IO-, cm2 s-I at 283 K in water37 and extrapolating from viscosity data for up to 60 wt % H2S04sol u t i o ~ ~ a, ~value * * ~of~ p = 14 CPfor 0.33 H2S04mole fraction (73 cm2 s-l. From the data in wt %) at 283 K gives D, = 9 X Tables I1 and 111, eqs 8 and 1 336 give H values for HNO, of 4: X I O3 and 4 (& 1) X 1O3 M atm-I, respectively. These values are about 40 times smaller than H of HNO, in water at 283 K. This H N 0 3 solubility is in excellent agreement with previous measurements of Vandoni,40which have recently been reanalyzed by Jaecker-Voirol et a1.4' Extrapolation of HNO, vapor pressures, reported by Vandoni for 5, 10, and 22 wt % HNO, in H$04 solutions at 273 K,40gives H = 2.6 X IO3 M atm-' in the limit of 0 wt % HNO, in 73 wt % H2S04solution. This agreement and the self-consistency of our two calculations based on very different experimental observations gives credence to the interpretation that HN03(g) uptake and evolution are solubility controlled. It should also be noted that both the values of H extracted from our uptake data depend on the accuracy of the estimate of D,. The analysis of our data was based on three key assumptions: (1) CY (=O. 17) for H N 0 3 is independent of H2S04concentration; (2) HNO, is the sole product of N 2 0 5reaction with H 2 0 ; (3) all the H N 0 3 product from N2O5 reaction is formed as dissolved HNO,(aq) which equilibrates with HN03(g). The first is consistent with more extensive results for HC1 uptake on H$04 solutions. There has been no definitive demonstration of the second, but to our knowledge no other products have been observed from (R2). Most recently, Quinlan et al.42 report quantitative conversion of N 2 0 5to HNO, on ice at 188 K, as measured by mass spectrometric measurement of HNO, evaporation after heating the ice.
-
(37) Longsworth, L. G. Diffusion in Liquids. In American Insriture of Physics Handbook; Gray, D. E., Ed.; McGraw-Hill: New York, 1972; pp 2-226. (38) Drew, T. B.; Dunkle, H.H.; Genereaux, R. P. Flow of Fluids. In Chemical Engineer's Handbook; Perry, J. H., Ed.;McGraw-Hill: New York, 1950; p 372. (39) Wolf, A. V.; Brown, M. G.;Prentiss, P. G.Concentration Properties of Aqueous Solutions: Conversion Tables. In Handbook of Chemistry and Physics, 67th ed.; Weast, R. C., Astle, M. J., Beyer, W. H., Eds.; CRC Press: Boca Raton, FL, 1986; p D-263. (40) Vandoni, M. R. Mem. Seru. Chim. E m . (Paris) 1944, 31, 87. (41) Jaecker-Voirol, A,; Ponche, J. L.; Mirabel, P. J . Geophys. Res. 1990, 95. 1 1 . 857. --.
(42) Quinlan, M. A.; Reihs, C. M.; Golden, D. M.; Tolbert, M. A. J . Phys. Chem. 1990, 94, 3255.
The self-consistencyof the results supports the third assumption of HNO,(aq) equilibration. Such equilibration is consistent with HN03(aq) formation from solvated N20,(aq) (R4), but surface reaction R5 still cannot necessarily be ruled out. However, it d m constrain the mechanism of the latter. In one limit of a direct surface reaction, HNO, molecules formed at the surface would enter the liquid with an efficiency given by a for HNO,. The HN03(g) evolution BR would then be 1 - a = 0.83, much higher than observed. Thus, it would appear that a surface N,O,(g) reaction must involve a gas/surface interaction different from that of HN03(g) on aqueous surfaces. Stratospheric Implications. Application of these results to stratospheric chemistry requires extrapolation to lower temperatures. Jaecker-Voirol et a1.4' have parametrized the HNO, vapor pressure data of Vandoni@in terms of activity coefficients. Their analysis indicates that the vapor pressure of HNO, over 73 wt % H2S04solution will have a temperature dependence virtually identical with that of pure HNO,, which is given by43 log P (Torr) = 7.61628 - 1486.238/(T- 43)
-
Extrapolation of our results at 283 K with this temperature dependence gives H 6 X lo5 M atm-' for HNO, solubility in 0.33 H2S04mole fraction (73 wt %) at 220 K. This low-temperature value of H is consistent with the lower limit (y > 0.01) for HNO3 uptake on 0.355 mole fraction H2S04solution at 228 K reported by Tolbert et aI.I3,l4 (If one uses eq 8, the increase in H overwhelms the effect of smaller D, and longer t in their experiments.) Our analysis indicates that HNO, and N205uptake efficiencies are largely independent of H2S04 concentration. On the basis of temperature-dependent measurements of HNO, and N205 uptake into water? we expect uptake coefficients to increase with decreasing temperature. A negative temperature dependence for N205uptake by aqueous sulfuric acid surfaces has been suggested by the work of Mozurkewich and Calvertl5 and Harker and Strauss.I2 Taken together, these results imply that at stratospheric temperatures uptake efficiencies will be greater than 0.1, even approaching unity at least for HNO,. The WMO Atmospheric Ozone 1985 Report indicated that an efficiency for N205 conversion to H N 0 3 greater than 5 X lo4 will have a significant impact on the ozone budget in the midlatitude stratosphere.4 This impact can be estimated from the product of the NzOSreactive rate and the ambient aerosol surface area density (Ad)in the stratosphere. The effective loss rate of N z 0 5is given by k' = y?/4Ad At an altitude of 20 km, for typical background H2S04aerosol, Ad = 6 X cm2 cm-,.' For y = 0.06 and P = 2 X IO4 cm s-', k' = 2 X IOd s-'. This corresponds to an N205lifetime of about 5 days. When compared to the H N 0 3 photolysis lifetime of about 30 this indicates that at the peak of the background sulfuric acid aerosol in the lower stratosphere, heterogeneous conversion will shift partitioning of NO, from N 0 2 / N 2 0 5toward HNO,.
Acknowledgment. This work has been supported in part by the Chemical Manufacturers Association, by a grant from the National Science Foundation (ATM-87-13210), and by the donors of the Petroleum Research Fund, administered by the American Chemical Society. (43) Duisman, J. A.; Stern, S. A. J . Chem. Eng. Dura 1969, 14, 457. (44) World Meteorological Organization Global Ozone Research and Monitoring Project Report No. 16. Armospheric Ozone 1985; World Meteorological Organization: Geneva, 1985. (45) Brasseur, G.; Solomon, S. Aeronomy of rhe Middle Atmosphere; D. Reidel: Dordrecht, 1984; p 260.
