J . Phys. Chem. 1990, 94, 6041-6048 Figures 3 and 4 illustrate the best fit to the experimental P / d 2 against m plots achieved by the two models (models 1 and 2) which assumed a single-step formation of the primary micelle. The values of the equilibrium constants and molar enthalpies of formation of aggregates are given in Table 11. Whilst neither of these models gave a satisfactory fit to all systems it is clear that a model of micellar growth which assumed a cooperative mode of association (model 2) provided a better representation of the data than an association model in which K was independent of concentration. Figure 4 shows an improvement of fit with model 2 as the salt content of the system was increased; indeed in 0.6 mol dm-’ NaCl the fit might be considered satisfactory, as was reported previously.6 However, the higher cmc of systems of lower salt content permitted a more thorough evaluation of the fit in the pre-cmc region and it is clear from Figure 4 that this model is not able to predict the correct curvature of the plots in the premicellar region. The discrepancy between experimental and predicted values of P / d 2 in this low-concentration region was in excess of the experimental uncertainty ( X i 1 kJ mol-’) and consequently this model was rejected. Figures 5 and 6 show an excellent representation of the experimental data over the whole concentration range for both models (models 3 and 4) which assumed the formation of the primary micelle by a continuous association process and its subsequent growth by cooperative association. This fit was maintained over the whole range of electrolyte concentration studied with no dependence of the value of n on the concentration of added electrolyte for either model (see Table 11). The values of the equilibrium constants and molar enthalpies of formation of aggregates which relate to these models are given in Table 11. Both models gave good fits to the data over the range of electrolyte concentration studied, and both generated the expected increase of equilibrium constants with increase of added electrolyte. The values of K calculated for the promethazine/0.6 mol dm-’ NaCl system compare with a K value of 242 mol kg-’ as derived from a previous light-scattering study4 using a similar post-cmc association scheme. The relatively large decrease of AHA for model 3 suggests that the formation of the primary aggregate is becoming less favorable with increase in the salt concentration. whereas the
604 1
opposite is indicated by the predicted increase of KA. Model 4, which indicated an increasingly exothermic formation of the primary micelle with increasing electrolyte concentration, is more consistent with the effects which would be expected and is probably a more realistic model. Our computations have indicated that the fit in the pre-cmc region for both of these models was highly sensitive to the assumed aggregation number, n, of the primary micelle. Figures 7 and 8 show the poor fits which resulted when the value of n was varied by only 1 unit from the best fit values of Figures 5 and 6. Similar effects were noted at all electrolyte concentrations. The concentration-dependent changes in the percentage of the various species present in solution, as calculated from model 4, are shown in Figure 9 for sodium chloride molarities of 0.1 and 0.6 mol dm-’. It is apparent that our studies have provided clear evidence of limited premicellar association in these systems. The deviation of the osmotic coefficient in water of several phenothiazine drugs, including promethazine hydrochloride, from ideal values at concentration below the cmc has led to similar conclusions.2 Evidence for a stacking arrangement of monomers in the micelles of the phenothiazine drugs has been presented from N M R datal3 and it has recently been suggested that the micelles formed in aqueous solution may be formed from several short stacks hydrophobically bonded together to form roughly symmetrical units.I4 The results of the present study lend support to this idea and suggest that the short stacks envisaged by these workers may be composed of some three or four monomers. Registry No.
Promethazine hydrochloride, 58-33-3.
Supplementary Material Available: Tables of values of P / d 2 as a function of molality for promethazine hydrochloride in 0.1, 0.2,0.4, and 0.6 mol dm-’ NaCl (1 1 pages). Ordering information is given on any current masthead page. (13) Florence, A. T.; Parfitt, R. T. J . Phys. Chem. 1971, 75, 3554. (14) Atherton, A. D.; Barry, B. W.J . Colloid Znferface Sci. 1985, 102, 479.
Uptake of SO,(g) by Aqueous Surfaces as a Function of pH: The Effect of Chemical Reaction at the Interface J. T. Jayne, P. Davidovits,* Department of Chemistry, Boston College, Chestnut Hill, Massachusetts 02167
D. R. Worsnop, M. S. Zahniser, and C. E. Kolb Aerodyne Research, Inc., Billerica, Massachusetts 01821 (Received: December 6, 1989) The uptake of SO2@)by fast-moving water droplets was measured as a function of pH and surface-gas contact time in the range 0.5-10 ms. In the high pH range (>5) a parameter governing the uptake of S02(g)by water is the rate for the reaction of SO2with H 2 0 to form HSO,-. The experimentally observed uptake is significantly greater than predicted by the rate measured for this reaction in bulk liquid water. Likewise at low pH, where uptake is limited by Henry’s law solubility, the uptake is significantly greater than predicted. These observations together with the observation of uptake as a function of time suggest that at the gas-liquid interface the S02-H20reaction is facile, forming a HS03--H+ surface complex which is in equilibrium with the gas-phase SO,. The species enters the bulk water as HS03- via this complex. The equilibrium ratio of densities of the surface complex (cm-2) and gas-phase SO,(cm-’) is 0.13 cm-I at 10 O C . Kinetic and thermodynamic parameters governing surface interactions are derived and discussed. Introduction Heterogeneous gas-liquid reactions involving water droplets in clouds and fogs are important mechanisms for the chemical 0022-3654/90/2094-6041$02.50/0
transformation of atmospheric trace gases. In such heterogeneous reactions, the rate for trace gas uptake is pivotal to understanding of the transformation process. (See, for example, refs 1-5.) An atmospherically important heterogeneous process is the trans@ 1990 American Chemical Society
6042 The Journal of Physical Chemistry, Vol. 94, No. 15, 1990
Jayne et al. Filter
formation of SO2 gas into sulfurous acid and then sulfuric acid in cloud and fog droplets. This process is represented in eqs 1 a, 1 b, and IC. In equilibrium the concentrations of the sulfur(1V) S02(g)
=SO2(aq) Hss
K
+
HS03- & S032- H+
QENERATfON Pump
(2)
number of molecules absorbed by the surface a= (3) number of molecular collisions with the surface
DROPLETlQAS INTERACTION CHAMBER
Pump Cellbraled Volume Ar
DROPLET COLLECTION CHAMBER
-k;
1
Temperature Controlled Cooling Coil
, Vlbraling Orifice
--
~
Reservoir Droplet Nz
--.
I
:
1
Transducer
’ :
I
-
Droplet Dellector
~
Diode Laser Beam
I
(4)
The measurement of mass accommodation coefficients is a difficult task. The experimental problem is due to the difficulty of separating the effects of the various processes on the rate of gas uptake. We have developed a laboratory method, using fast-moving droplets, for measuring gas uptake in a way that allows control of the factors affecting gas uptake. In previous publications we described the technique and we reported studies showing the effect of gas-phase diffusion and liquid-phase saturation on the uptake of SO2by water droplets.’~* The temperature dependences of the mass accommodation coefficient for both SO2 and H 2 0 2 were also measured.* Here we describe experiments and discuss implications of studies showing the effect of pH and gas-liquid contact time on the uptake of SO2. Graedel, T. E.;Coldberg, K. 1. J. Geophys. Res. 1983, 88, 10865. Heikes, B. G.;Thompson, A. M. J . Geophys. Res. 1983,88, 10883. Chameides, W. L. J. Geophys. Res. 1984,89,4739. Schwartz, S.E . J . Geophys. Res. 1984,89, 11589. ( 5 ) Jacob, D. J. J . Geophys. Res. 1986, 91, 9807. (6) Schwartz, S. E. In Mass-Transport Considerations Pertinent to Aqueous Phase Reactions of Gases in Liquid- Water Clouds, Chemistry and Multiphase Atmospheric Systems; NATO AS1 Series, Vol. G6; Jaeschke, W.. Ed.; Springer-Verlag. Berlin, 1986; p 415. (7) Gardner, J. A.; Watson, L. R.; Adewuyi, Y.G.; Davidovits, P.;Zahniser, M. S.;Worsnop, D. R.; Kolb, C . E . J . Geophys. Res. 1978.92, 10887. (8) Worsnop, D. R.; Zahniser, M. S.; Kolb, C. E.;Gardncr, J. A.; Watson, L. R.;Van Doren, J. M.; Jayne, J. T.; Davidovits, P.J. Phys. Chem. 1989, 93, 1159.
- H,O
Figure 1. Schematic of coaxial droplet gas flow apparatus.
I
Equation 2 yields the maximum flux of gas into a liquid. In many circumstances, however, the actual gas uptake is smaller. It may be limited by several processes, the most important of which are gas-phase diffusion and Henry’s law saturation.6 Henry’s law saturation in turn involves liquid-phase diffusion and, in some cases, surface and liquid-phase chemical reactions. In a laboratory experiment subject to these limitations, the measured flux into a surface is conveniently expressed in terms of an uptake, coefficient, -fobs$ as
(1) (2) (3) (4)
CHAMBER
(IC)
Here ng is the density of gas molecules, E is the average thermal velocity, and a is the mass accommodation coefficient. This coefficient is defined as
J = n,EyOb/4
-570
(la)
compounds are determined by Henry’s law constant and by the equilibrium constants K,and K2 The conversion of sulfurous acid to sulfuric acid involves further oxidation from state (IV) to state (VI) which requires an oxidizing agent such as O3or Hz02. In order to model the kinetics of such a process one must known the rate of uptake for SO2gas as well as for the gaseous species involved in subsequent oxidation. As will be shown, the study of gas uptake yields information about the nature of the gas-liquid interaction at the interface. Heterogeneous reactions begin with the gas molecule striking the surface of the droplet and entering into the liquid phase. Simple gas kinetic theory shows that the flux of gas molecules ( J ) into a surface is given by J = n,Ea/4
/
Temperature Controlled Baln
Figure 2. Schematic of transverse droplet gas flow apparatus.
Experimental Section Apparatus and Procedures. Two apparatuses were used in the present studies. They are shown in Figures 1 and 2. The apparatuses and procedures have been discussed previously in and will be described here briefly. The basic features of the two devices are the same. Each apparatus consists of three regions: a droplet generating region, the reaction zone (which is the flow tube), and the droplet collection region. The droplets are generated by forcing water at the desired pH through a vibrating orifice. The diameter of the orifice was 60 pm. Nitrogen from 2 to 18 bar is used to provide the backing pressure. Droplets of uniform size and spacing are produced by vibrating a piezoelectric ceramic at a subharmonic of the natural droplet break-up frequency. Frequencies from 8 to 200 kHz produce droplets between 110 and 230 pm in diameter. The velocity of the droplets is between 1700 and 5300 cm s-’ depending on the backing pressure. The droplets enter and leave the flow tube reaction region through small holes approximately 1 mm in diameter. In the first apparatus (Figure 1) the droplet train is passed coaxially down a 20.5-cm flow tube 1.5 cm in diameter. In the second apparatus (Figure 2) the droplet train passes transversely
~
Uptake of S02(g) by Aqueous Surfaces across a 2.7-cm-diameter flow tube. In the reaction chamber the droplets interact with the S02(g) which flows through the tube. The main functional difference between the two apparatuses is the gas-droplet interaction time. In the first apparatus reactive gas can be introduced through one of three inlets along the flow tube. Through the choice of inlet and droplet velocity, the interaction time can be varied in the range of 12 to 2 ms. In the second apparatus the interaction time is determined by the droplet velocity and can be varied in the range of 2-0.5 ms. The droplet train is monitored by a cylindrically focused HeNe laser beam in the path of the droplets. The droplets pass out of the reaction chamber through a hole into the third chamber where they are collected. The concentration of S02.gas downstream of the droplets is measured by infrared absorption spectroscopy by using a tunable infrared diode laser (Laser Analytics) and a multiple-pass "White" cell. The absorption is monitored as the droplets are switched on and off in 5-1 5-s cycles by a solenoid-activated deflector. An important aspect of the experimental technique is the careful control of all the conditions within the apparatus. The pressure in the apparatus is kept as low as possible to reduce gas diffusion limitations. The minimum operating pressure is determined by the water vapor partial pressure, which is carefully kept at saturation with respect to the equilibrium vapor pressure of water at the droplet temperature so that the droplets neither grow nor evaporate. The present experiments were done between 12 and 2 OC. The pressure of H 2 0 in the reaction zone corresponding to these temperatures is 10 and 5 Torr, respectively. The equilibrium between ambient water vapor and the droplet train temperature is carefully maintained by controlling the partial pressure of H 2 0 vapor in both the flow tube and the droplet generating chamber. This equilibrium is monitored by measuring changes in pressure in the flow tube as the droplets are switched on and off. In addition, in the fast flow apparatus a differential pressure transducer continuously monitors the pressure difference between the flow tube and the other chambers. Overall balance in the flow tube is checked further by monitoring the concentration of a reference gas, in this case methane, which is added to the flow. Because methane is effectively insoluble in water, any change in methane concentration with droplet switching determines the *zero" of the system and is subtracted from observed changes in trace gas concentration.' Loss of SO2 to humidified walls is prevented by heating the walls of the flow tube. Most of the experiments have been performed with the flow tube walls heated to 27 OC. Results were shown to be independent of this temperature up to 50 OC. A laboratory AT style computer is programmed to alternate the diode frequency between the SO, and CHI absorption lines for cycles of droplets on/droplets off and to monitor the output of the lock-in amplifier for these cycles. The data is collected and averaged over 10-40 cycles. A more complete description of the experimental technique, computer-controlled data acquisition, and system monitoring is found in ref 8. The result of these measurements is the value of the fractional change in SO, density (Anln) due to contact with the droplets. The gas uptake coefficient yobsis calculated by using eq 4 which in terms of the measured parameters becomes Yobs
=
F~ An 1 ; -?A 4
Here n is the trace gas concentration (molecules cmw3),FBis the carrier gas volume rate of flow (cm3 s-I) through the system, ? is the trace gas average thermal velocity (cm SI), and A is the total droplet surface area in contact with the trace gas. This total is given by the product AdN, where N is the number of droplets to which the trace gas is exposed and Ad is the surface area of each droplet (cm,). The measurement of the volume flow rate F is described in ref 8. In these experiments it was in the range 68-80 cm3 SI. In the coaxial apparatus (Figure 1) the gas-droplet interaction region is relatively long which can result in a significant con-
The Journal of Physical Chemistry, Vol. 94, No. 15, 1990 6043 centration gradient of S02(g) down the flow tube (e.g., &I > 0.1). This is properly taken into account by integrating the density (n) along the interaction path, resulting in yobshaving a logarithmic dependence on An. The resulting formulation (analogous to eq 5) is shown in ref 8. Several studies were performed to elucidate the nature of SO, uptake. First, the gas uptake coefficient for SO, was measured as a function of pH in the range from 0 to 12 bulk droplet pH. Measurements were performed at 2 ms and at 10 ms gas-droplet interaction times. These experiments were done a t 10 OC using the apparatus in Figure 1. The time dependence of the uptake was studied in greater detail in the range 0.5 to 2 ms by using the apparatus in Figure 2. Here the experiments were done at 2 OC and bulk droplet pH at 11, 5, and 1. The uptake was also measured as a function of SO, density. Droplets were produced from filtered deionized Milli-Q water. The pH of the droplets was raised by adding NaOH and was lowered by adding H2SO4. The pH was measured by using a standard KCl/AgCl pH electrode. Solutions at pH = 0 were titrated against standardized NaOH to determine the total hydrogen ion content. The procedure was used because the pH meter is inaccurate in this region. In order to test the effect of the counterion (SO4,-) on SO, uptake, some experiments were also conducted with HCl to acidify the droplets. The SO, uptake was unchanged. The SO2gas density in the flow was monitored by measuring the absorbance at 1343.585 cm-' with a tunable diode laser (Laser Analytics). The absorption cross section of this line is 3.9 X cm2 molecule-I cm-' with the experimentally determined broadening coefficient of 0.010 cm-I/Torr of H 2 0 vapor. A multiple-pass White cell with an effective path length of 240 cm was used as the absorption cell for the low SO2density experiments. Higher SO, density experiments were performed with a 10 cm path length cell.
Results and Discussion ( a ) Uptake as a Function of pH. Gas uptake coefficients (yobs) are plotted as a function of bulk droplet pH for 2 ms and for 10 ms contact times in Figure 3 and Figure 4, respectively. The coefficient was obtained from the measurements via eq 5. Open and closed symbols refer to experiments with S02(g) densities of 1 X 1013and 1 X lOI5 ~ m - respectively. ~, Each point in the figures is an average of at least 13 individual measurements. The limiting effect of Henry's law saturation on the gas uptake is evidenced by the decrease in yobswith decreasing pH as well as with increased gas-droplet contact time. However, in order to properly interpret the data in Figures 3 and 4, one first has to take into account two effects; gas-phase diffusion and the additional acidification of droplets produced by dissolved SO,. Dissolved S(IV) species within the droplet diffuse to a depth ( D I t ) ' l 2where DI is the liquid diffusion coefficient and r the droplet-gas contact time. In our experiments the longest r was about s. For DI = 8 X lod cm2 s-' at 10 OC, this corresponds to a depth of -3 pm. The diameter of the droplets in our work is on the order of 100 pm. Therefore, the experiments probe a shell of this depth just below the droplet surface. Acidification due to S02(g) uptake into this shell in the droplet is calculated by using mass balance. Under equilibrium conditions the [H+] ion density is given by8 [H+] = H'+ ( H a + K,
+ K,[S02])1/2
H' = ([H+Io - Kw/[H+l,)/2
(6)
where [H+l0 is the initial H+ concentration and K, is the equilibrium constant for water (3 X M2 at 10 "C). The first and second acid dissociation constants as defined by eq 1 are K, M at 10 0C.9 In the above = 1.93 X M and Kz = 6.7 X expression it is assumed that the second dissociation to S032-is negligible. This is true for pH < 7. The plateau in the data between pH 5 and 9 is due to the dissolved SO2 which a t gas density of 1013cm-3 dominates the pH in this region and holds it constant at about 4. The effect of dissolved S(IV) on pH is
6044
The Journal of Physical Chemistry, Vol. 94, No. 15, 1990 0 0 8 ,
I
,
~
s
,
,
I
,
1
,
,,
,
Jayne et al. I
I
I
I
1
b 0o08o s
I
-
.... O O O t ' L ' 00 20
.........
Bulk Kinetics Prediction
*..........
"
"
"
"
40
80
80
I00
"
120
'
.... ,
1
0 00
140
0.0
10
20
30
Figure 3. Uptake coefficient as a function of initial droplet pH. Gasdroplet interaction time is 2 ms. Error bars are l o deviation of averages of experimental data. Lines are model calculations of yh by correcting yta from eq 20 for gas diffusion by inverting eq 7. Solid and dotted lines are for nSo2(*)= 1 X 10" and 1 X 1OIs respectively. ,
, ~,
,
,
I
,
d0 0 0 4
i
nso2(g):
0
10i3cm-3
N
1015
5.0
6.0
70
,
,
,
,
>
,
Figure 5. Gas uptake data recalculated to correct for gas-phase diffusion and droplet acidification due to SO2 uptake. Gas-droplet interaction time is 2 ms. Symbols and data are the same as in Figure 3. Solid and dotted lines are model calculations from eq 20 for %(e) = 1 X loi3and 1 X 10" cm-), respectively. Broken line at bottom shows maximum uptake predicted from bulk kinetic parameters (eq 13). 1
t = 10 msec oo8
4.0
PH
Initial pH
008,
_ _ - - -4
/.'
0 10
-
008
-
008
-
I
t = 1 0 msec nso,(p)
lO"cm-' 10"
t
+
i Bulk Kinetics Prediction
0.02
0.0
2.0
4.0
8.0
8.0
100
120
14.0
Initial pH Figure 4. Gas uptake coefficient as a function of initial droplet pH. Gas-droplet interaction time is 10 ms. Lines as in Figure 3.
0 00
- -'.--..... 00
10
I
20
30
40
50
80
70
PH Figure 6. Gas uptake data recalculated to correct for gas-phase diffusion and acidification due to SO2uptake. Gas-droplet interaction time is 10 ms. Symbols and data are the same as in Figure 4. Lines as in Figure
greatest for droplets of high initial pH. With SO2gas at IOI3 ~ m - ~ , 5 . an initial pH of 12 is reduced to about 6. The acidity of droplets is evident from eq 7, the effect of gas diffusion decreases with yobs. with pH less than 2 is unaffected by SO2 uptake. Droplet pH values have been adjusted to include acidification due The effect of gas-phase diffusion on the gas uptake has been to uptake of SOz. The closed symbols are data measured with studied by Worsnop et aL8 It has been shown that for a train of SO2 gas density of 1 X I O l 5 c ~ n - ~The . fact that these data points moving droplets the relationship between the observed uptake are now largely congruent with the lower density data confirms coefficient yobsand the zero pressure limit, y, is that acidification is properly taken into account. (See below for 1 more discussion about dependence on SO2 gas density.) Y = (7) 1 rdc The lower broken line in Figures 5 and 6 shows the maximum values of the uptake coefficient calculated from properties of the Yobs 8 4 bulk liquid. The calculation is outlined in the next subsection (b). Here, df is an effective orifice diameter, df = 1.9d0, where do is As can be seen, the measured uptake is significantly higher than the actual diameter. The diffusion coefficient (DJ for SO2 in predicted from the bulk water parameters. The upper lines in the background gas (cm2 s-I) is given by the figures are calculations based on a modified model discussed in subsection c. ( 6 ) Modeling ofthe SOz(g) Uptake. Because of the limited solubility of SOz in water, reevaporation of SOzdue to Henry's law saturation must be considered in calculating the SO2 uptake Here P is the partial pressure of carrier gas species and Dso coefficient. The equilibrium relationship between molecules in = 0.40 atm cmz s-I and DSO2-H20 = 0.1 15 atm cm2 s-I at 283 k8 the gas phase at a pressure P and the molecules dissolved in the A small correction for the non-Maxwellian velocity distribution liquid is given by Henry's law. of the trace gas near the droplet surface is also made as discussed nSO,(aq) = HP = nso1(g)RTH (9) in Worsnop et aI.* This correction is 5% or less. In Figures 5 and 6 we show the uptake coefficients for 2- and Here nSpl(aq)and nsql(g) are the liquid- and gas-phase concenIO-ms contact times, respectively, recalculated to take into account trations in moles per liter, and H i s Henry's law coefficient which gas-phase diffusion and the altered velocity distribution. Note for SO2 in water at 10 "C is 2.2 M a t ~ n - ' . ~ that the gas diffusion correction brought about an increase in the highest measured coefficient from Yobs = 0.06 to y = 0.1 1. As (9)Goldberg, R. N.; Parker, V.B. J . Res. Narl. Bur. Stand. 1985,90, 341.
Uptake of S02(g) by Aqueous Surfaces
The Journal of Physical Chemistry, Vol. 94, No. 15, I990 6045
It can be shown that if S(IV) in the water were solely in the form of S02(aq) then the water surface would saturate in a characteristic time T~ given by6-10v11 T~
= (~RTH/&Y)~DI
(10)
Here R is the gas constant, T is the temperature (K), and D, is the diffusion coefficient of SO2 in water. We know that a must be at least as large as our experimental value of y = 0.1 1 shown in Figures 5 and 6 . With this value of a, calculations yield T~ = 3 X l p s which is considerably shorter than the transit time of the droplet through the reaction zone. We note that the characteristic time T~ represents the time for saturation of the surface if there were no chemical removal of the species within the liquid. In fact, as is indicated in eq 1, S(IV) is dissolved in the liquid also in the form of HSO) and SOj2-. The capacity of the liquid to hold S(IV) is therefore increased, and the degree of saturation is reduced and delayed. The equilibrium concentration of the total amount of S(IV) dissolved in the liquid can be expressed according to Schwartz6Jo in terms of an effective Henry’s law coefficient H* as ns(Iv)(l)/nso2(g)= H*RT
(11)
In equilibrium, H*, which refers to all S(1V) species in solution, is given by
By use of the values of H, K1,and K 2 at 10 OC, H* is 44 at pH 3 and 4400 at pH 5 . A simplified analysis of the uptake yields a time-dependent uptake coefficient y ( t ) , where t is the gas-droplet interaction I
y(t) =
1 1
\ I , -
(13)
It should be noted that y ( t ) in eq 13 and our experimental uptake parameter yobsin eq 5 both represent the total integrated uptake during exposure time t (Le., from 0 to t ) . The uptake rate is maximum (y(0)) at t = 0. As gas-liquid equilibrium is approached with time, the net uptake of gas, as measured by the coefficient y,decreases. The time dependence in eq 13 corresponds to the net uptake limited by saturation of the time-dependent diffusion limited depth (D,t)II2discussed above. Because this depth is much shallower than the radius of the droplets used in these experiments, it is appropriate to ignore the sphericity of the droplets as in eq 13. In our region of operation eq 13 is in good agreement with the more complex expression derived by Dankwerts for spherical dr0p1ets.I~ The applicability of eq 13 was demonstrated by Worsnop et al. where the first time-dependent SO2 uptake results were presented.8 The value of y(0) to be used in the model depends on how SO2(@enters the liquid phase. In the simplest hypothesis one assumes that SO2enters the liquid as S02(aq) and then reacts with water to form HSO). In such a case the full capacity of the water to hold S(IV) is not compute available to the uptake process because the conversion of S02(aq) to HS03- occurs at a finite rate k l . If the corresponding T,,” = (k1)-’is longer than T~ then a significant fraction of S02(aq) will evaporate before reacting to form HS03-. The finite reaction rate can be taken into account by expressing y(0) in eq 13 as6qi0J1
(10) Schwartz, S. E.; Freiberg, J. E. Amos. Enuiron. 1981, 15, 1129. ( I 1 ) 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 Enuironmenr, Saltzman, E. S., Cooper, W. J., Eds.;ACS Symposium Series No. 393; American Chemical Society: Washington, DC, 1989; p 504. (12) Danckwerts, P. V. Trans Faraday SOC.1951, 47, 1014.
Inserting the expressions for
T~~~ and T~
this becomes
a
Y(0) =
I +
aE
(15)
4HRT(Dlk1)1/2
Equation 15 compares the rates of S02(aq) diffusion and reaction in a depth ( D , / / c , ) I / ~The . pseudo-first-order rate constant k l for the conversion of S02(aq) to HSO) was measured by Eigen et al.I3 to be 3.4 X IO6 s-,, giving ( D l / k 1 ) 1 /-150 2 A. Using this value of k , and assuming the mass accommodation coefficient a = I , we compute an upper limit of y = 0.03.7,8As can be seen in Figures 5 and 6 , in the limit of pH > 5 (where H* > IOOO), the measured y is significantly greater than this calculated upper limit. For eq 15 to yield the measured maximum value of y = 0.1 1 (with a = l), kl has to be about 12 times higher than obtained from the published values for the relevant parameters. Previously obtained results for H20?Il and recent datal4 for HCl, H N 0 3 , and N205,suggest that in general a is in the range 0.05-0.5, indicating that k , must be yet larger. Furthermore, eq 13 is inconsistent with the observed uptake behavior at low pH, where SO2uptake should be independent of y(0). The broken line in Figures 5 and 6 plots the pH dependence of y ( t ) according to eq 13 with y(0) calculated from k , (eq 15). Equation 13 underestimates the observed uptake across the pH scale. At low pH < 2, observed uptake is about 20 times larger than calculated. In order to explore the significance of this discrepancy between the measured y and the upper limits set by the calculation we first ask whether the bulk liquid phase values for H , DI,and kl used to calculate y are applicable in the uptake process which occurs near the surface. As stated earlier, the diffusion-limited reaction depth (Dl/k1)1/2 is about 150 A or approximately 50 molecular diameters. Modeling calculations suggest that the thickness of the surface to bulk water transition region is about 4 molecular diameters.1s,’6 Therefore, the diffusion/reaction depth is predominantly within the bulk liquid. Overall our experiment probes the time-dependent depth (Dit)'/* (eq 15) which for t 10.5 ms is on the order of several micrometers, clearly within the bulk liquid. Therefore, the values for these liquid-phase parameters in this region are not likely to differ significantly from the literature values for bulk liquid. This suggests the need to reexamine the nature of the gas uptake process. The reexamination is further motivated by the measured time dependence of yobsin the low pH region (5, and mid-pH, 3-4, y t is approximately proportional to t and +I2, respectively, in agreement with the functional behavior predicted by eq 13. However, at low pH < 2, y t is virtually independent o f t . This low pH behavior corresponds to a fixed number of SO2 gas molecules “sticking” per unit surface area. The time dependence of y t versus t is plotted directly in Figure 8 for pH = 4.7 and pH = 1 (open circles and squares, respectively). The functional difference in the uptake is evident. Also included in Figure 8 are data (solid squares) at low pH and high nso2(g). The lower broken line plots eq 13 for pH = 1 where y t depends only on H* = H a n d DI,not on k l or nso2(g).The discrepancies (13) Eigen, M.; Kustin, K.; Maass, G . 2.Phys. Chem. (Munich) 1%1,30, 130. (14) Van Doren, J . M.; Watson, L. R.; Davidovits, P.; Worsnop, D. R.; Zahniser, M. S.; Kolb, C. E. J . Phys. Chem. 1990, 94, 3265. (15) Matsumoto, M.; Kataoka, Y. J. Chem. Phys. 1988,88, 3233. (16) Goh, M. C.; Hicks, J. M.; Kemitz, K.; Pinto, G . R.; Bhattacharyya, K.; Eisenthal, K. B.; Heinz, T. F. J . Phys. Chem. 1988, 92, 5074.
Jayne et al.
6046 The Journal of Physical Chemistry, Vol. 94, No. 15, 1990 h
liquid h
H
H
0
Figure 9. A schematic diagram of a possible configuration for the reaction of SOzwith HzOat the interface. Broken lines represent bonds which are broken. Dotted line represents the newly formed bond.
the vapor-liquid interface which in reality is a transition region of varying density with molecules both entering and departing. However, such a picture of a well-defined surface interaction is consistent with recent experiments on and theoretical simulations of water surfaces.'s-" The bulk rate constant for the reaction SOz(aq) + HzO HSOy H+ measured by Eigen indicates a severe hindrance of the reaction. This pseudo-first-order rate constant is smaller by about a factor of IO6 then obtains for a facile diffusion-limited reaction. In an Arrhenius model such a factor corresponds to an activation energy of about 8 kcal mol-'. This hindrance to the reaction may in part be due to additional hydrogen bonds that need to be broken in going from SOz(aq) to HS03- and/or to a steric barrier in the bulk liquid. At the interface where the water molecules are exposed as shown in Figure 9 the reaction of SOz with H20may be entirely facile resulting in the formation of a complex for each favorably oriented collision. In that case the maximum measured value of y = 0.1 1 may simply indicate the probability of a favorable collision configuration. The equilibrium density of the chemisorbed surface complex can be evaluated from the gas uptake at low pH. In this pH region the capacity of the bulk liquid to hold S(IV) is so small that the associated uptake is not measurable in our experiment. The measured time-independent uptake is due entirely to the surface complex which is formed and reaches equilibrium on a time scale much shorter than the experimental gas-droplet interaction times. We will express the density of the surface complex SO2* as the ratio ( A * ) of its density (in units cmm2)to the gas-phase density nsoz(s). At low pH, its equilibrium value (A*,) can be obtained from
+
.
3
nwHs,: 0 0 - 1 O"cm-'
____
10'5
DH = 4.7
I
----___-----Bulk Solubility
Prediction
(PH = 1 )
oooolOb
' 2b
'
40 ' 6 b
' 6b
' li0
Time (msec)
' 1210
'
Figure 8. Product of yt at high and low pH as a function of time. Solid line at top shows behavior at pH = 4.7 (If* = 2300 M atm-I) where uptake is nearly linear with time (note logarithmic scale). Middle lines (pH = 1) show fixed uptake which is limited to SO2* on surface. Dotted line at left shows reduced A*q due to surface saturation at high S02(g) density (eq 21). Broken line at bottom shows maximum uptake at pH = I from bulk solubility prediction (If* = H = 2.3 M atm-I in eq 13).
in magnitude and in both time and nsq( ) dependences are clear. As we have previously reported7**and as discussed above, the time-dependent results for pH > 3 could be rationalized in terms of a large value of y(O), indicative of a discrepenacy in k,, H*, or 4 for SOZ(aq)(eq 20). However, as is clear in Figure 8, uptake measurements at low pH, where dissociation of dissolved S02(aq) to HS03- is negligible, are inconsistent with the mechanism represented by eq 1. Below we show that all the experimental results can be explained by assuming that SOz(g) enters the liquid not as SOZ(aq)but via a surface complex which equilibrates with gas and dissolved S(IV). The nature of this chemical interaction at the interface is explored in the following subsection. ( c ) Interactions at the Interface. A possible first step in a surface-mediated gas uptake is a chemisorption process in which the SOz(g) collides with a water molecule at the interface and forms a complex such as the one shown schematically in Figure 9. Recent experiments indicate that the orientation of the oxygen away from the bulk as shown in the figure is somewhat preferred on a water surface.I6 In such an arrangement the electron is envisioned to migrate from the H atom to one of the 0 atoms in SO2 leading to the formation of a S-O bond to the surface. Such a complex may then enter the bulk liauid as HSO,-. Of course it muit be noied that Figure 9 is a sc'hematic reprkentation of
-
where the left-hand side of the equation is the rate of gas uptake s. With at low pH. The product y t is measured to be 1.7 X ? = 3 X 1 O4 cm s-l, this gives A*q = 0.1 3 cm. Thus, for a typical nso (8) of 10" ~ m - nsoz* ~ , is I .3 x 1OI2 cm-z in our experiment. 'fhe relevant kinetic processes at the interface are shown schematically in Figure 10. The subscripts designating the rates in the gas, interface, and liquid regions are g, i, and I, respectively. We have neglected direct interconversion between SO2* and S02(aq). Such an interconversion could be included but, as discussed above, kl for SOz(aq) reaction to form H+ and HS03is not fast enough to account for the observed uptake. In what follows, by detailed balance arguments we show that the direct conversion of SO2* to H+ and HSOy dominates the uptake rate. If we assume that S02(g)enters the liquid phase only via the surface complex, then we can write
or
(17) Bhattacharyya, K.; Castro, A.; Sitzmann, E.V.;Eisenthal, K.B. J . Chem. Phys. 1988.89. 3376. (18) Laidler. K. J . Chemical Kinerics. 3rd ed.: Harwr and Row: N e w Y&k, '1987; p 235.
The Journal of Physical Chemistry, Vol. 94, No. 15, 1990 6047
Uptake of SOz(g) by Aqueous Surfaces
so2(9)
this surface saturation is given by the high nso2(g)data (solid squares) in Figure 8. The lower uptake for nso2(g)= I O l 5 can be explained by competition for surface coverage for n, surface sites. This can be expressed in terms of a Langmuir model as
I +
Ki
Figure 10. Kinetic processes at the interface.
where we have explicitly noted that the density of SOz*,expressed as A * ( t ) , is time dependent. The rate k , can be obtained from the value of A*, = 0.13 cm obtained at low pH where y ( t ) is at its lower limit, which is below our experimental sensitivity and is negligible compared to a.
-
ki, = -E a
4 A*,
With the surface uptake included in the process, the measured total uptake coefficient which we will designate as ytotis given by the following 4A*,(1 - 0 )
-
where B is the fractional coverage and A*, is the equilibrium constant in the limit B 0. In limit of high nso,(e), 0 = 1. For the dotted line in Figure 8 , B = 0.5 fits the observed data points, giving n, IOI4 cm-2, which indicates that the maximum [SOz*] corresponds to about 0.1 monolayer coverage. Likewise the dotted lines in Figures 3-6 plot eq 20 with B = 0.5 at ns @) = 10ls~ m - ~ . As can be seen in Figures 5 and 6, the effect of h i 3 nsq ) is small for pH > 3, so high w)data (solid points) were p l o t d together with lower nw) in Figure 7. Further studies are planned to more thoroughly measure the dependence of uptake on S02(g) density. ( d ) Chemisorption Kinetics and Thermodynamics. The observed uptake rate can be interpreted in terms of the kinetic scheme presented in Figure 10. Specifically, for the case of surfacemediated uptake, the parameter y(0) in eq 13 represents the uptake coefficient under conditions when the conversion of HSO, to SO2* via [H+] [HS03-]kl-i is negligible and steady state has been reached. In other words, $0) is our experimentally measured uptake coefficient a t high pH. In terms of the kinetic scheme in Figure IO, y(0) is given by
-
H S O ~+ H +
SO, (aq)
A*,nSO2(g)
(20) The left term [ y ( t )from eq 131 represents S(IV) dissolved in the diffusion-limited shell in the droplet while the second term gives the S(1V) bound as SOz* at the surface (obtained by rearranging (eq 16)). The 1 - 0 term corrects for surface saturating at high nso2 as explained below. At low pH, where y ( t ) is small, yto,is dominated by the surface density of SO2* which is proportional to A*,. At higher pH, uptake increases as solution equilibrium (la) shifts toward dissociation to HSO
