8768
J. Phys. Chem. 1995,99, 8768-8776
Reactive Uptake of Cl2(g) and Br2(g) by Aqueous Surfaces as a Function of Br- and I- Ion Concentration: The Effect of Chemical Reaction at the Interface J. H. Hu, Q. Shi, and P. Davidovits" Department of Chemistry, Merkert Chemistry Center, Boston College, Chestnut Hill, Massachusetts 02167
D. R. Worsnop, M. S. Zahniser, and C. E. Kolb Center for Chemical and Environmental Physics, Aerodyne Research, Inc., Billerica, Massachusetts 01821 Received: November 30, 1994; In Final Form: March IO, 1995@
The uptake of gas-phase Cl2 and Br2 by aqueous NaBr and NaI solutions has been studied as a function of to 0.5 M), temperature (263-293 K), and gas-liquid interaction time (2-15 ms). concentration (2.5 x The uptake of O3 by aqueous NaI solutions has also been studied for the purpose of comparison. These measurements were conducted in a droplet apparatus in which a stream of well-defined droplets (120-250 p m in diameter) is passed through a low-pressure flow tube containing the halogen molecules. Since the solubility of the halogen molecules X2 (X = C1 or Br) is low, the measured uptake is primarily due to the YXY X-. The aqueous reaction of the species with the halide ion Y- (Y = Br or I) via X2 magnitude of the measured halogen uptake and its functional dependence on ion concentration are not in accord with a simple bulk-phase reaction mechanism. The data indicate that reactions at the gas-liquid interface have a significant role in the gas uptake process. On the other hand, the 0 3 uptake shows no evidence of interfacial reaction. The atmospheric implications of the halogen uptake results are discussed.
+ -. +
Introduction The importance of chlorine and bromine in the stratospheric ozone destruction process is well established.'.2 In the troposphere, chlorine radicals are believed to be an important ~ x i d a n t .The ~ importance of bromine radical reaction processes in the lower atmosphere has also been r e c o g n i ~ e d . ~In .~ particular, it has been suggested that the species Br and BrO are responsible for the very low levels of near-surface 0 3 observed during the Arctic spring.6-8 Inorganic halogens are injected into the troposphere primarily via sea salt aerosols generated by breaking waves on ocean surface^.^ While most of these species remain in the condensed phase and are returned to the ocean by dry and wet deposition, a significant fraction (3-20% for C1) is converted to inorganic halogen vapor via heterogeneous mechanisms such as acid displacement reactions and reactions involving gaseous NO2, ClN03, and N205.'0.'' However, the measured inorganic halogen level in the marine boundary layer is not consistent with these known heterogeneous mechanisms.I2 The lack of reliable data for halogen sources and sinks has made it difficult to model the global halogen cycle. A more detailed understanding of the heterogeneous chemistry of halogenated species in the marine boundary layer is required. In this context, we have carried out a series of experiments to study the uptake of Cl2 by aqueous surfaces as a function of aqueous Br- and Iconcentration and the uptake of Br2 as a function of Iconcentration. The uptake of 0 3 by aqueous surfaces as a function of I- concentration has also been studied for the purpose of comparison.
Uptake of Gas Molecule by a Liquid Surface Heterogeneous reactions begin with the gas molecule striking the surface of the liquid and entering into the liquid phase. A
* Author to whom correspondence should be addressed. @
Abstract published in Advance ACS Abstracts, May 1, 1995
0022-365419512099-8768$09.00/0
phenomenological description of the entry of gases into liquids is straightforward. First, the gas-phase molecule is transported to the liquid surface, usually by gas-phase diffusion. The initial entry of the species into the liquid is governed by the mass accommodation coefficient, a, which is the probability that an atom or molecule striking a liquid surface enters into the bulk liquid phase.
a=
no. of molecules entering the liquid phase
no. of molecular collisions with the surface
(1)
The mass accommodation coefficient determines the maximum flux, J, of gas into a liquid, which is given by J=-
ngca 4
Here ng is the density of the gas molecules, and c is the trace gas average thermal velocity. As the species enters the liquid, a fraction may evaporate back into gas phase due to the limited solubility of species in water. The equilibrium relationship between gas-phase halogen [X2(g)] and solvated halogen [X2(aq)] concentration is determined by Henry's law coefficient, H (M atm-'), as [X,(aq)l = HWX,(g)l
(3)
Here R is the gas constant in units of atm M-' K-I. At equilibrium, the liquid is saturated, and the flux of molecules into the liquid is equal to the rate of desorption of these molecules out of the liquid. Saturation can be delayed by an irreversible sink for the species in the liquid. In our experiments, this sink is provided via the reaction with the halide ion Y(Y- = Br- or I-); that is,
x, + Y-
k2
XY
+ x-
(4)
Here k2 is the second-order coefficient for the reaction. In a
0 1995 American Chemical Society
Reactive Uptake of C12 and Br:, by Aqueous Surfaces
J. Phys. Chem., Vol. 99, No. 21, 1995 8769
I -
Upon substitution from eqs 5-7, this expression becomes
Ys
1
2
Ymeas
Yrxn
ydiff Ysol
> Liquid
Gas
Figure 1. Electrical circuit analogue for the gas uptake process. Explanation is found in the text.
second step, the molecule XY may further react with Y- to form Y2. As a result of the above reaction, a steady-state flux of molecules into the liquid can be sustained. The magnitude of this flux is a function of the reaction rate. Because of the limitation imposed by gas-phase diffusion and liquid-phase saturation, under typical experimental conditions, the net flux of molecules into the liquid is smaller than that given by eq 2. The four processes we have discussed, namely, gas-phase diffusion, mass accommodation, Henry's law saturation, and liquid-phase chemical reaction, are coupled to each other, and therefore, the description of the transport process involves coupled differential equations. General solutions for such equations are not available. In special cases, however, the equations can be s01ved.I~ It is possible to obtain a simple approximate expression for the gas-liquid transport by decoupling the processes. In one such approach, the gas-liquid transport is represented by an electrical circuit analogy shown in Figure l.I4,I5 The dimensionless conductances representing the gas-phase diffusion (ydiff), Henry's law saturation (ysol), and chemical reaction (yrxn) processes are given in eqs 5, 6, and 7, respectively.I6 The
- I + - + Cdf a go,
kIi2
+ 2(nt)-'I2 ) -1
(10)
ymeasrepresents the total integrated uptake during the gasliquid contact time, t (i.e., from 0 to t). Equation 9 or 10 represents the uptake under conditions when the various processes are decoupled. The coupling is stronger between the reactive and solubility processes. Therefore, eq 9 is a good representation of the uptake process only when one of the terms Yrxn or ysol is negligible with respect to the other. In the present studies, yrxn>> ysol,and eq 9 is in accord with the exact solution to the applicable differential equation. The applicability of eq 10 was demonstrated by Worsnop et al.I7 The nontrivial challenge in gasfliquid interaction studies is to design techniques that allow the deconvolution of the several processes involved in the overall uptake of the gas and, in that way, determine the basic parameters affecting the uptake.
Experimental Section The Cl2, Br2, and 0 3 uptake studies were conducted using a droplet apparatus described previously in detail." The gas uptake is measured by passing a controlled train of droplets through a low-pressure (6-20-Torr) flow reactor which contains the gas species of interest entrained in a flowing carrier gas of water vapor and helium. This fast moving stream of small monodispersed droplets (120-250 p m in diameter) is produced in a separate chamber by a vibrating orifice jet. The density (n,) of the trace gas is monitored downstream of the flow tube with a quadrupole mass spectrometer as the surface area of the droplets passing through the flow tube is changed in a stepwise fashion. The change in the trace gas signal (An,) corresponds to the uptake of gas by the droplet surface. The uptake coefficient (ymeas)is calculated from the measured change in trace gas signal via eq 11. Here Fg is the carrier gas volume
(5) Ydiff
8Dg
(7) coefficient y s shown in Figure 1 represents uptake due to reactions at the interface and will be defined later. In eq 5, df is an effective droplet diameter from the point of view of gasphase diffusion," and D, is the gas-phase diffusion coefficient of the species. The term -'/2 in eq 5 accounts for distortion of the Maxwellian-Boltzmann collision rate (n,c/4) when there is net gas uptake at the surface.'* In eqs 6 and 7, t is the gasliquid contact time, D1 is the liquid-phase diffusion coefficient for the species, and k is the pseudo-first-order rate coefficient for the aqueous reaction; Le., k = kz[Y-]. The net molecular flux into the liquid is then given in terms of a measured uptake coefficient, ymeas,as
where ymeasis connected to the transport processes by 1 -I+-+ 1 Ymeas
a
Ydiff
1 Yrxn
+ Ysol
(9)
rate of flow (cm3 s-l) through the system, AA is the change in the total droplet surface area in contact with the trace gas, and n, and n,' are the trace gas densities at the inlet and outlet of the flow tube, respectively (Le., ng = n,' Ang). An important aspect of the experimental technique is the careful control of all the conditions within the apparatus. Water vapor pressure control is especially important because the temperature of the droplets is determined by the partial pressure of H20 in both the droplet generation chamber and the flow tube.I7 The present experiments are done with the pressure of H20 in the reaction zone between 17.5 and 2.15 Torr corresponding to temperatures between 20 and - 10 "C, respectively. The lower temperatures, below 0 "C,are obtained by evaporatively cooling the droplets which are supercooled but not frozen. l7 The overall pressure balance in the flow tube is further checked by monitoring the concentration of a reference gas, in this case krypton. Because Kr is effectively insoluble in water, any change in Kr concentration with droplet switching determines the "zero" of the system and is subtracted from observed changes in trace gas concentration. The system has been tested to ascertain that the droplet surface is not perturbed by the motion of the drop. In several studies, gas uptake was measured as a function of gas-droplet interaction time and from the Henry's law coefficient data, and in some cases, reaction rates were also obtained. The extraction
+
Hu et al.
8770 J. Phys. Chem., Vol. 99, No. 21, 1995
1
t
O0.10
-
l
S
i
c.
-5 v
0.051
1
0.001 ' ' ' " " " " " " ' ' ' I " ' 0.0 2.0 4.0 6.0 8.0 10.0 12.0
Mr/4F,
Figure 2. Plot of ln(ng/ng' ) AAc/4Fg for Br2 with a 0.01 M NaI solution at a droplet temperature of 293 K. The slope of the line is ymeasand in this case equals 0.088 i 0.003. of these parameters from the uptake data is based on the assumption of an unperturbed surface and simple liquid-phase diffusion transport. Where comparison could be made, the parameters measured in our experiments were in good agreement with values obtained using more conventional techniques.I6 This indicates that convective transport or surface distortions are negligible. The transit time of the droplets through the flow reactor is on the order of 20 ms. The gas-droplet interaction time can be varied from 2 to 15 ms by selecting the gas inlet port and by varying the droplet velocity. These two methods of varying the contact time were shown to be equivalent. The density of ozone and halogen molecules in the flow tube was varied from 5 x 10l2 to 1 x lOI4 ~ m - ~The . ion concentrations in liquid droplets were varied from 1.25 x to 0.5 M (in Br2D- experiments, the lowest concentration was 5 x 10-4M; in 0 3 / I - experiments, iodide concentrations were varied from 0.5 to 3.0 M). The chemicals in NaBr and NaI were used to provide Br- and I- ions. The reagent Cl2 (99.5%) and the reference gas Kr (99.998%) were purchased from Matheson. Liquid Br2 (99.5%) was obtained from Aldrich. The species were used without further purification. Ozone was produced in a Welsbach ozonizer. The ozone was stored on silica gel in a trap, kept to -78 "C with a dry ice-isopropyl alcohol bath. The 0 3 was introduced into the flow tube by passing a flow of helium through this trap.
Results and Model Analysis In these experiments, uptake measurements were performed as a function of liquid-phase ion concentration, droplet area, gas flow rate, gas-droplet contact time, and droplet temperature. Uptake Measurements. As an example of the measurements, we show in Figure 2 a plot of ln(n,ln,') as a function of cAA/4FEfor Br2 with a 0.01 M NaI solution at 293 K. Here, cAA/4FEwas varied by changing the gas flow rate and the effective droplet surface area (AA). Each point is the average of at least 10 area change cycles, and the error bars represent 1 standard deviation from the mean in the experimental Anln value. As is evident in eq 11, the slope of the plot in Figure 2 yields a value of Ymeas. Such plots are obtained for the full range of uptake studies. In these studies, the uptake signal Anln
Gas-Droplet Contact Time (ms) Figure 3. Gas uptake coefficient as a function of gas-droplet contact time for Br2 and C12 with 0.01 M NaI solutions at a droplet temperature of 293 K. Dashed lines are the least-square fit to the data.
varied typically from 2% to 30%. The linearity of the plots over an order of magnitude in the uptake signal validates the measurement procedure. In Figure 3, we show Ymeas as a function of gas-droplet contact time for both Cl2 and Br2 obtained with 0.01 M NaI solutions at 293 K. The lines are least-squares fit to the data. Within the accuracy of our data, on our experimental time scale, the uptake coefficients are independent of gas-liquid contact time. Such time independence was observed for all the ion concentration in this study. This time-independent behavior over the 10-ms gas-liquid contact time is in accord with expectations, as is evident from the following considerations. At 0 "C, the Henry's law coefficients (H) for Cl2 and Br2 are 0.16 and 2.70 M atm-I, respe~tively.'~-*'Wtih a liquid-phase diffusion coefficient of cm2 s-'?* the parameter ysol for Br2 in eq 6 is 8 x calculated to be about 4 x at 10 ms. This is negligible compared to the range of Ymeas in these studies. This implies that the uptake due to the ysOl-l channel in Figure 1 can be neglected. Effect of Gas-Phase Diffusion. The diffusion coefficient (Dg,cm2 s-') for the species studied (X2) in the background gas is"
Here P is the partial pressure of the subscripted gas species, and &,-H,o and DX2-He are the binary gas-diffusioncoefficients for species X2 in H2O and He, respectively. Gas-phase diffusion coefficients for C12 and Br2 are not available in the literature. However, they can be calculated by using the CHEMIUN computer program.24 The program uses Lennard-Jones potential well depths (elk& Lennard-Jones collision diameters (o), polarizabilities (a'),dipole moments @), and rotational relaxation collision numbers (Zot) at 298 K as input parameters. This method of estimating the diffusion coefficient has been validated e~perimentally.~~ The input parameters as well as the calculated diffusion coefficients are listed in Table 1. The required input parameters are not available for 03; therefore, such calculations could not be performed for 03.The
J. Phys. Chem., Vol. 99, No. 21, 1995 8771
Reactive Uptake of Cl2 and Br:! by Aqueous Surfaces
TABLE 1: Calculated Binary Gas-Phase Diffusion Coefficient (0)at 273 K and the Required Input Parameters for the Calculation dke,”
o , ~
molecule
K
lo-* cm
Br2 Clz
507.9 316.0
4.296 4.217
0 3
C1,
a’,b Dx?-H>o, Dx>-H~, cm3 ZrOtcatm cm2 S K I atm cm2 s-I 7.02 4.61
4.90d 4.90
0.087 0.103 0.093
+ Br’
Td = 293K
0.06
0.422 0.458 0.423
Reference 23. Reference 26. Reference 27. The rotational relaxation collision number for Br2 is not available; the number is assumed to be the same as that for C12. a
diffusion coefficients for 0 3 were scaled relative to ethanol by the inverse ratio of the square root of the mass. Ethanol instead of Cl2 was chosen because both ethanol and 0 3 have dipole moments while Cl2 has not. This scaling was in accord with the variation of the coefficients for the molecules calculated via CHEMKIN.25 The calculated diffusion coefficients for 0 3 are also listed in Table 1. In our experiments, the temperature used to calculate D, was the average temperature between the droplet surface and the ambient gas. This way of treating the temperature gradient in the ambient gas is discussed in Worsnop et al.” It is also shown there that the effect of this gradient on the droplet temperature is negligible. The obtained diffusion coefficients were used in eqs 10 and 12 to take into account the diffusive transport of species to the droplet surface. Effect of Liquid-Phase Chemical Reaction. The uptake for both C12 and Br2, by pure water, has been examined. Because of the small values of the Henry’s law coefficients, the uptake by pure water is very small and cannot be detected in the droplet apparatus. As stated earlier, the uptake of gas-phase halogen molecules Cl2 and Br2 by the liquid is enhanced due to reaction with Br- or I- ions in the solution. Since the primary and secondary products are relatively insoluble halogen or interhalogen molecules, they partially evaporate back into the gas phase and can be observed mass spectrometrically. The observed primary and secondary reaction products were IC1 and 12 in the C12L- reaction, BrCl and Br2 in the C12Br- reaction, and IBr and 1 2 in the Br2L- reaction. In Figure 4a, we plot ymeasfor Cl:! at 293 K as a function of Br- activity.28 The broken line in Figure 4a is the calculated uptake coefficient obtained via eq 10 using a recently obtained value for the Cl2 Br- bulk aqueous-phase reaction rate coefficient of k2 = 7.7 x lo9 M-I s-I at 298 K.31 This rate coefficient is very close to the diffusion-limited rate calculated in terms of the water viscosity coefficient 7 (k2 = 8RT/37), which is 1 x 1Olo M-I s-l at 298 K. Since the broken line plot was calculated with a = 1, it represents the maximum uptake attributable to bulk liquid phase reaction. An unlikely large reaction rate coefficient of about 10” M-’ S K I would be needed to match the experimental results via eq 10. Another aspect of the discrepancy becomes apparent when the experimental results are plotted in the form l/ymeasvs l/a[~,-]’/~ as shown in Figure 4b for the Cl2 Br- reaction. According to eq 10, such a plot should be linear, with the slope proportional to k2-lI2 and a positive intercept equal to l / a l/ydff. The broken line in Figure 4b is such a plot, corresponding to the broken line in Figure 4a. The relationship between the experimental l/ymea,and l/a[B,-]”* is, in fact, linear at low Br- concentrations, with the slope corresponding to k2 in the expected magnitude range. However, at higher Br- concentrations, the measured data clearly depart from linearity. Thus, we conclude that the results of the X2N- uptake studies are not consistent with a model based on a solely bulk-phase reactive uptake described by eq 10.
0.00
0.20
0.10
0.30
0.40
4
200 150 100
50
20
10
30
40
a[Br-l-1/2 (M-’~~) Figure 4. (a) Uptake coefficient y,,,
for Cl2 as a function of Bractivity at 293 K. (b) Plot of l/ymeasvs a [ ~ , - ] - ~for ’ * Cl2 at 293 K. The ion concentrations at the left and right extreme points of the plot are 0.5 and 1.25 x M. The broken lines are the maximum calculated uptake coefficients resulting from the bulk-phase reaction of Cl2 with Br-. 250
+
+
+
200
150
.1 r
3
100
50
0 0.0
0.5
1.0
1.5
2.0
a [1-]”/2 (M’”)
Figure 5. Plot of 1/ymeaSvs a[I-]-112 for 0 3 at 277 K. The solid line is the least-square fit to the data. The ion concentrations at the left and right extreme points of the plot are 3.0 and 0.5 M.
For comparison, we show in Figure 5 the analogous plot for the 0 3 f I- reaction at 277 K. In these studies, the I-
Hu et al.
8772 J. Phys. Chem., Vol. 99, No. 21, 1995 concentration ranged up to 3.OM. The slope of the line in Figure 5 yields a value for the second-order rate coefficient for the O3 I- reaction of k2 = 4 x lo9 M-‘ s-I at 277 K. Within experimental accuracy, this is in agreement with the value of 2 x lo9 M-’ s-l at 298 K given by Hoigne et While the range of X- concentrations in the ozone studies is, because of experimental limitations, only a factor of 3, the halogen species exhibit a clear nonlinearity and departure from bulk-phase behavior in this range of X- concentrations. On the other hand, the relationship between l/ymea,and l / u [ ~ - ] for ” ~ O3 remains linear over this range of I- concentrations. The intercept of the line in Figure 5 yields a value of 0.1 for the mass accommodation coefficient ( a )for 0 3 . Because of the uncertainties in the intercept, this value of a is to be considered only as an estimate. Utter et reported that a for 0 3 is in the range 2 x to 1. Our results certainly fall within this range. Modeling the Ch and Brz Uptake. The Cl2 and Br2 uptake results can be explained by assuming that an additional channel participates in the uptake process. This channel involves a direct reaction of the halogen molecule (X2) with the halide ion (Y-) at the interface. That is, for C12/Br-, as an example,
+
C12(g)
+ Br- - (Cl,Br)-(interface)
-
Cl-(aq)
TABLE 2: Physical Size of Species Xz and Y- and the Geometric Cross Section for the Reaction X f l reaction
X-X distance
cm)‘ radius of Ycm). X2-Y- distance ( cm) cross section a ~ - ( l O -cm2) ~~ a
Br2
+ I-
2.28 2.06 3.20 3.22
Cl2
+ 1-
1.99 2.06 3.06 2.94
C12 t Br-
1.99 1.82 2.82 2.50
Reference 44.
In this model, we assume that the interfacial reactions occur within a thin surface layer (d,). In order to estimate the thickness of this layer, we note the results of a molecular dynamics calculation which shows that there is no significant change in free energy in transporting F- and C1- from the bulk liquid to within two water molecular layers of the interface.40 This is also likely to be the case for the ions in this experiment: Brand I-. Therefore, a reasonable estimate for the thickness of the interfacial layer is 2 times the diameter of water plus the diameter of the ion, which is about lo-’ cm. The experimental results lead us to assume y, of the form
+ products
For several reasons, the rates of such interfacial reactions may Here C, is a t e h proportional to the surface reaction rate. The be expected to be more rapid than the rates of bulk-phase denominator in the expression for y s takes into account possible reactions. First, facile reactions that are diffusion controlled saturation of the surface at high ion concentrations. This in the bulk may be more rapid at the interface where transport formulation is similar to one obtained from the Eley-Ridealof the gas-phase molecule (X2) to the aqueous reagent (Y-) at type surface me~hanism.~’ the interface is not limited by liquid-phase diffusion. Second, The introduction of the probability parameter,p s with potential the activity of the solvated molecules at the interface may be values between 0 and 1, into eq 14 is mandated by experimental higher than in the bulk. Specifically, the concentration of the observations. Without p s , eq 14 implies that y , approaches unity halogen species [Xz(aq)] at the interface may be larger than at high ion concentrations. If that were the case, ymeaswould given by Henry’s law equilibrium. Such enhanced concentration approach Ydiff. However, at high ion concentration, the asympof the polar solute in water has been predicted and totic value for ymeasis less than Ydiff. p s takes this into account. For butanol, the concentration in the interface is at least 10 The introduction of p , seems reasonable. The chemical higher than the equilibrium concentration in the bulk. While reaction at the interface is not likely to occur unless the halogen surface concentration studies for the less soluble nonpolar molecule is hydrated. We identify p , as the probability of such species are not available, one might suggest from entropic a hydration. p , is likely to be different from the mass arguments that in these cases as well surface enhancement is accommodation coefficient, a. a is the probability of hydration likely. Finally, a new reaction mechanism may be activated at by pure water, while p s is the hydration probability for the gas the interface since in this region, reaction hindrance due to a molecule which strikes the surface within a certain distance of steric effect is likely to be reduced,35and solvent reorientation the ion. Hydration in the latter case may be aided by the necessary to achieve reaction may proceed more r e a d i l ~ . ~ ~ , reacting ~~ halide ion at the interface, probably via a chargeIn our previous study of the SO2 uptake by aqueous surfaces,38 induced dipole moment. we likewise observed an enhanced uptake which could be An expression for C, can be obtained by following a attributed to increased rate at the interface for the reaction SO2 procedure similar to that used in obtaining an expression for H20 HS03- Hf.In that study, we also noticed evidence The uptake flux at low ion concentrations is equated for enhanced SO2 concentration at the interface. Our acetalto the interfacial reaction rate per unit area. That is, dehyde uptake studies on aqueous droplets also presented evidence for surface reaction enhanced uptake.I5 More recently, some features in the uptake measurements of CION02 by HC1J = - CngYs = psnscOsdsa[Y-l 4 doped sulfuric acid solutions obtained by Hanson and Ravishankara have been interpreted as possibly a result of a surface reaction.39 Here ng and n, are the species concentration in the gas phase and at the interface, respectively, and parameter usis the ionThere are several possible ways of representing the effect of interfacial reactions on the gas uptake. A feature of the surface halogen surface reaction cross section. For simplicity, we will uptake is its linear dependence on the ion activity rather than assume that at the interface, as an bulk equilibrium,n, = ngHRT. the square root dependence exhibited by the bulk reactionFor convenience of discussion, we will express os in terms of dependent uptake. Here we will represent the surface-enhanced the geometric ion-halogen cross section OY- as us= SOY-.The uptake by the uptake coefficient y , which is simply connected dimensionless constant S is introduced in order to relate the as the resistor ys-’ across the terminals 1 and 2 in Figure 1. surface reaction cross section to the geometric cross section. The geometric cross section OY- can be calculated from the The current halogen uptake studies present sufficient information to allow a semiquantitative modeling of the surface-enhanced physical radii of the molecule (X2) and the ion (Y-) listed in uptake process via this representation. Table 2.
+
-
+
yrxn.42343
Reactive Uptake of C12 and Br2 by Aqueous Surfaces
J. Phys. Chem., Vol. 99, No. 21, 1995 8773
Rearrangement of eq 15 yields
TABLE 3: Input Parameters for the Global Fit of the Data
Since qy-1 is in units of mol L-I, the factor N~l1000(NAis the Avogadro number) is included so that UY- and d, may be expressed in units of cm2 and cm, respectively. Both C,and p , will be determined experimentally. Bulk liquid-phase reactions are characterized by a diffusion depth (Dllk)’/*.At relatively low reactant ion concentrations, (Dllk)”2 is significantly greater than the interfacial depth (d,), and interactions at the interface are not significant. However, as (Dllk)’” approachesd,, the bulk and interfacial reactions begin to compete. When (D~/k)l/~ equals or is smaller than d,, reaction occurs entirely in the interfacial region. To take this into account in terms of Figure 1, bulk-phase reaction must be reduced as (Dllk)”* approaches d,. In the present model, we will do this (somewhat arbitrary) by multiplying yrxn by the factor 1 - y,. The factor 1 - y , is simply the probability that a gas molecule passes through the interface region without reacting and is subject to bulk-phase reaction. With the surface channel included and ysol negligible, eq 9 becomes
1 Ymeas
l +
1 ( l - Y&b
Ydiff
+ YS
--Yb
a
+-
1-a
x x
x x
0.2578 0.1655 0.1097 0.0747
4.816 2.697 1.569 0.953
18.45 11.79 9.73 3.56
22.79 14.90 8.14 4.57
Reference 22. References 19 and 20. Reference 21.
40
30
20
10
0
20
40
60
80
aII.]-1’* (M’”)
Figure 6. Plot of lly,,,, vs a [ ~ - ] - ’for / * Brz at 263 and 293 K. The lines are the model fits to the data. The ion concentrations at the left and right extreme points of the plot are 0.5 and 2.5 x M.
1
Yrxn
The measured quantity in eq 17 is ymeas,which is obtained as a function of ion concentration and temperature. As expressed here, the unknown quantities are the mass accommodation coefficient a , the surface parameters S and p , used to define y,, and the bulk liquid-phase reaction rate coefficient k2. These parameters are extracted from the measured results using a nonlinear least-square-fit method. All input parameters for the fitting procedure are listed in Table 3. It was shown previously that a can be expressed as20
a --
a
5.37 7.89 1.12 1.52
(17)
Here Yb represents the overall uptake coefficient for mass accommodation and bulk-phase reaction processes and is given by 1-1
263 273 283 293
1
t r
- exp(-A&,,,/RT)
where the parameter may be regarded as the Gibbs freeenergy barrier (with respect to the gas phase) of the transition state toward solvation (A@,b, = - TAS0bS).l7The mass accommodation coefficient was obtained by a global fit of the temperature-dependent uptake data. In the current surface uptake model, we assume that p , has a temperature dependence of the form
0
10
20
30
40
Figure 7. Plot of llymeasvs all-l-iizfor C12 at 263 and 293 K. The
(20)
lines are the model fits to the data. The ion concentrations at the left M. and right extreme points of the plot are 0.5 and 1.25 x
As in the case of a,here also we associate AG*, (AG*, = AH, - TAS,) with the Gibbs free energy of the transition state toward surface hydration. p , was obtained by a global fit of the temperature-dependent uptake data. The experimental results for the reactions Br2/I-, C12/I-, and C12/Br- are plotted in the form lly,,,, vs the inverse square root of activity in Figures 6 , 7 , and 8, respectively. For clarity
of presentation, data are shown only at two temperatures (the lowest and highest). We should point out that for a given concentration of the halide ion, the measured uptake for the Br2& reaction is significantly greater than for the other two reactions. Therefore, the scale for the Br2/I- plot is different from the scales in the other two plots. Further, as can be seen in Figure 6, even at
p s = exp(-AG’,/RT)
Hu et al.
8774 J. Phys. Chem., Vol. 99, No. 21, 1995 TABLE 4: Surface Reaction Parameter@ system 263 K 273K 283K Br2AS = 7.65 C,, M-' Ps
Ys C12A-
62 1 0.43 0.37
362 0.26 0.20
219 0.17 0.12
137 0.1 1 0.06
13.1 0.27 0.031
8.17 0.21 0.017
6.02 0.16 0.009
4.25 0.13 0.005
1.12
0.75 0.31 0.002
S = 3.32
C,, M-I Ps
Ys C12Br-
293 K
S = 0.33 C,, M-'
0.41
Ps Ys
0.005
0.36 0.19
0.001
Values for yEare calculated from eq 14 at an activity of 0.01 M.
TABLE 5: Values of UDtake Coefficient9 system 263 K 273 K 283 K 0
10
20
30
40
Br2A-
Ydiff Ymeas
YS (1 - Y s ) Y b
Figure 8. Plot of l/y,,,, vs a [ ~ ~ - l -for l ' ~Cl2 at 263 and 293 K. The lines are the model fits to the data. The ion concentrations at the left M. and right extreme points of the plot are 0.5 and 1.25 x the lowest iodide concentration of 2.5 x M, the relationship between l/ymeaS and l/q-]'/* is still not linear. This indicates that the interfacial component of the reaction is much larger for the Br2K reaction than for the other two reactions and is effective even at these low ion concentrations. In order to reach a linear zone, we would have had to study the uptake at concentrations lower than 2.5 x M. At such low concentrations, the kinetics deviates from the pseudo-first-order condition, which requires that the ion concentration [Y-] be significantly higher than the concentration of the solvated halogen. The mass spectrometer detection sensitivity in our apparatus is such that the gas density in the flow tube must be greater than 5 x 10l2 ~ m - ~Using . the relationship in eq 3, it can be shown that the corresponding ion concentration in the liquid must be greater than about M in order to maintain pseudo-first-order reaction conditions. The experimental results are not sensitive to the value of a since at high values of the uptake (when a may be the ratelimiting parameter), the bulk-phase uptake path is bypassed and the uptake is dominated by the surface reaction channel. On the other hand, at low values of uptake, the bulk-phase chemical reaction is the rate-limiting process and the effect of a is again diminished. By examining the results, we estimate for both Cl2 and Br2 that m o b s and hSobs are -13(f0.6) kcal mol-' and -50(f2) cal mol-' K-I, respectively. The results for p s are expressed with reference to eq 20 in the form of AH, and AS,. In units of kcal mol-' and cal mol-' K-', these values are for the reaction Br2/I- AHs = -7.1 and AS, = -28.5, for the reaction C12A- AHs = -3.8 and AS, = -17, and for the reaction C12Br- AHs = -4.0 and AS, = -17. We note that the values of AHs and AS, for the reactions C12/ I- and C12/Br- are nearly identical. The accuracy of these values is estimated to be about 20%. The parameters C,, S, and p , representing the interfacial uptake coefficients ( y s )are shown in Table 4. In this table, the values of y s at ion activity of 0.01 M are also shown. In order to illustrate the role of each uptake process, we show in Table 5 values for ydlff, ymeas,y s , and (1 - ys)yb. The latter three are values at 0.5 M ion concentration (Le., activity of 0.35 M). The values for the bulk-phase second-order reaction rate coefficients are listed in Table 6.
C12A-
Ydiff Ymeas
Ys (1 - Y s ) Y b
ClzBr-
Ydlff
Ymeas
Ys (1 - y s ) ~ b
1.521 0.328 0.428 0.096 0.959 0.202 0.220 0.067 0.959 0.159 0.114 0.066
0.764 0.220 0.258 0.094 0.543 0.155 0.155 0.065 0.543 0.119 0.064 0.060
0.349 0.128 0.168 0.097 0.260 0.101 0.109
0.061
293 K 0.177 0.083 0.108 0.083 0.133 0.073 0.078 0.059 0.133 0.054 0.021 0.055
The values for ymeas,y s and (1 - Ys)Yb refer to uptake coefficients at 0.5 M ion concentration = 0.35 M ion activity.
TABLE 6: Bulk-Phase Second-Order Rate Coefficients k2 (M-l s-l) T, K
Br:,
+ I-
c12 ~~
263 273 283 293
a a -5.1 109 -1.5 x 1Olo
+ 1~~
1.4 x 2.0 x 2.6 x 3.9 x
C12
+ Br-
~~
1O1O 1010 loi0 10'0
9.1 109 1.2 x 10'0 2.6 x 1O1O
Values obtained for the Br2A- reaction at 263 and 273 K are not considered meaningful; see text.
Discussion As can be seen in Table 6, the magnitudes of the C12/Band C4A- bulk-phase reaction rate coefficients (k2) are on the order expected from diffusion-limited reactions. Further, these coefficients exhibit positive temperature dependence expected from a diffusion-limited process. The value of the rate coefficient for the C12/Br- reaction at room temperature is within a factor of 3 of the value measured by Wang et aL3' We note that the uptake measurements lack sensitivity to the bulk-phase reaction as is evident in eq 10, where ymeasis shown to be proportional to the square root of the rate coefficient k2. Furthermore, in the region where k2 dominates the uptake process, the magnitude of uptake signal is low and so is the accuracy of the data. An examination of the fitting trends indicates that our measured values for the bulk-phase C12Nreaction rate coefficients are accurate to about a factor of 2. However, as was pointed out previously, the interfacial component for the Br2K reaction is significantly larger than for the C 4 N - reactions. As a result, y s affects the Br2 uptake throughout the measured region, and the k2 values obtained cannot be considered meaningful. In our previous studies, mass accommodation coefficients have been measured for more than 30 species. Observed pattems in the results led to the formulation of a model for the uptake of gas-phase species.45 The model uses the concept that
Reactive Uptake of Cl2 and Br2 by Aqueous Surfaces
. I . Phys. Chem., Vol. 99, No. 21, 1995 8775
TABLE 7: Parameters for Bromine, Chlorine, and Ozone molecule
EA,"eV cm3 H , M atm-' k2,'M-I s-' a',O
Bn
c1,
2.55 7.02 2.70 ' 5 x 109
2.38 4.61 0.17 -2 x 10'0
0
2
2.10 3.21 0.02b
-3 x 109
Reference 26. Reference 46. The second-order rate coefficient for the reaction of the species with I- at 273 K. The value of k2 for the 0 3 / I - reaction is an average of a literature value32 (2 x lo9 at 298 K) and our value (4 x lo9 at 277 K) determined from the slope of the plot in Figure 5. a
the water surface is a narrow region of a dense gaslike state within which nucleation is continually occurring. In this region, clusters which are larger than a critical size grow by condensation and merge with the nearby bulk liquid. The incoming gas molecules participate in this nucleation process. If a given molecule becomes part of a critical-sized cluster, then it will be incorporated into the bulk liquid via condensation growth. The model leads to a well-defined relationship between m o b s and As,b,, which are now simply the enthalpy and entropy of the relevant critical cluster. When examining the results for p s , we note that the relationship between AHs and ASs obtained for both Cl2 and Br2 is also in accord with the cluster model of uptake. As mentioned earlier, p s is considered to be the probability of a halogen gas molecule to be hydrated at the interface due to the reacting halide ion. The hydration in this case is essentially a cluster formation process about a ion-polarized halogen molecule. This view is consistent with the fact that the magnitudes of the measured AH, and ASs are characteristic of hydrophilic polar species rather than nonpolar species such as the unperturbed halogens. We noted that the fit provided by the model is not equally good for all three systems. While the fit to the C12/I- uptake data is nearly perfect, the flattening of the uptake at high Iconcentrations for the Br2/I- system at 293 K is not well represented by the model. It is likely that we have not captured the full details of the surface uptake model. For example, the assumption that the halogen species concentration at the interface is given by n, = n,HRT, although convenient, is certainly arbitrary. While the model is not firmly determined, its overall agreement with the measurements leads us to believe that the essential aspects of the surface uptake process have been appropriately represented. As noted earlier, results for the O3/I- reaction show no evidence for a surface-enhanced reaction even though the ionic concentration in those experiments exceeds the concentration in the X2N- studies. The 0 3 0 - reaction was studied up to a I- concentration of 3.0 M. The studies with the higher concentrations were necessary because even these higher concentrations, the uptake is relatively small due to the low value of the Henry's law coefficient for 0 3 (see Table 7). We have examined several parameters that may provide a clue to the difference in the qualitative behavior of the 03Kand X2N- reactions. In Table 7 are listed the electron affinity (EA), polarizability (a'), Henry's law coefficient (Hat 273 K), and second-order rate coefficient (k2 at 273 K). As is evident, the magnitudes of these parameters decrease in the order of the magnitude of the surface effect (S). Although the second-order rate coefficient for the O3/I- reaction is smaller than that for the C12N- reaction, because of the higher concentration solutions used in OJI- studies, the highest pseudo-first-order rate coefficient for the O3fi- studies is about the same as in the X2N- studies. Perhaps more important than the magnitudes of the tabulated coefficients is the difference in the reaction mechanisms. While the X2N- reaction entails an electron
-
transfer, the principal step in the OS,!- reaction is an oxygen atom transfer ( 0 3 f I01- f 02).32 It is likely the electrontransfer process at the interface that accounts for the enhanced reactivity. Implicationsfor Atmospheric Chemistry. We can calculate whether C12, which might be generated within a sea salt aerosol photolytically or by other means, will escape or be converted to Br2 or BrCl. The characteristic diffusion time to the surface for a Cl2 molecule with diffusion coefficient DIin an aerosol of diameter d is
The characteristic liquid-phase reaction time for C12 with Brin an aerosol is
with D1 = 1 x cm2 s-I, kZ = 9 x lo9 M-' SKI, and [Br-] =8 x M typical of seawater; we conclude that 50% of C12 will escape from aerosols with diameters of about 0.07 p m and more than 50% of Cl2 will be converted to Br2 or BrCl in aqueous aerosol particles with diameters larger than 0.07 pm. Since Br-radical-catalyzed destruction of atmospheric O3 is significantly more efficient than C1 radical processes, the identity of the photolyzable halogen species escaping from sea salt aerosols is of significant interest. Our experiments show that the C12/Br- and C12/I- surface reactions become significant for bulk ion concentrations greater than about 0.05 M. It is unlikely that the Br- (or I-) concentration in marine aerosols ever reaches such levels. However, the concentrations of other ions are certainly found at such levels and higher. Therefore, other possible surface effects relevant to atmospheric processes need to be examined.
Acknowledgment. We thank Drs. W. J. De Bruyn, J. T. Jayne, and D. V. Robinson for their help in this work. Funding for this work was provided by the NSF Grant No. ATM-9310407, the U S . EPA Grants No. R-821256-01-0 and No. CR819733-01-0. and the US. DOE Grant DE-FGQ2-91ER61208. References and Notes (1) WMO, Global Ozone Research and Monitoring Project-Report No. 25, 1991. (2) Abbatt, J. P. D.; Molina, M. J. Annu. Rev. Energy Environ. 1993, 18, 1. ( 3 ) Finlayson-Pitts, B. J. Res. Chem. Zntermed. 1993, 19 (3), 235. (4) Fan, S.-M.; Jacob, D. J. Nature 1992, 359, 522. ( 5 ) Solomon, S. Book of Abstracts, 208th ACS National Meetings, 1994, ENVR 194. (6) Sturges, W. T.; Barrie, L. A. Atmospheric Environmenr, 1988, 22 (6), 1179. (7) Barrie, L. A.; Bottenheim, J. W.; Schnell, R. C.; Crutzen, P. J.; Rasmussen, R. A. Nature 1988, 334, 138. (8) McConnell, J. C.; Henderson, G. S.; Barrie, L.; Bottenheim, J.; Niki, H.; Langford, C. H.; Templeton, E. M. J. Nature 1992, 355, 150. (9) Cicerone, R. J. Rev. Geo. Space Phys. 1981, 19 (l), 123. (10) Finlayson-Pitts, B. J. Nature 1983, 306, 676. (11) Finlayson-Pitts, B. J.; Ezell, M. J.; Pitts, J. N., Jr. Nature 1989, 337, 24 1. (12) Keene, W. C.; Pszenny, A. A. P.; Jacob, D. J.; Duce, R. A,; Galloway, J. N.; Schultz-Tokos, J. J.; Sievering, H.; Boatman, J. F. Global Biogeochem. Cycles 1990, 4 , 407. (13) Danckwerts, P. V. Trans. Faraday SOC.1950, 46, 300. (14) Schwartz, S. E. Chemistry of Multiphase Atmospheric Systems; NATO AS1 Series; Jaeschke, W., Ed.; Springer-Verlag: Berlin, 1986; p 415. (15) Jayne, J. T.; Dum, S. X.; Davidovits, P.; Worsnop, D. R.; Zahniser, M. S.; Kolb, C. E. J . Phys. Chem. 1992, 96, 5452. (16) Kolb, C. E.; Worsnop, D. R.; Zahniser, M. S.; Davidovits, P.; Hanson, D. R.; Ravishankara, L. R.; Leu, M.-T.; Williams, L. R.; Molina,
Hu et al.
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(30) Chou, K.-C.; Li, W.-C.; Reddy, R. G. Ber. Bunsenges. Phys. Chem. 1992, 96 (l), 68. (31) Wang, T. X.; Kelley, M. D.; Cooper, J. N.; Margerum, D. W. Inorg. Chem. 1994, 33, 5872. (32) Hoigne, J.; Bader, H.; Haag, W. R.; Staehelin, J. Water Res. 1985, 19 (8), 993. (33) Utter, R. G.; Burkholder, J. B.; Howard, C. J.; Ravishankara, A. R. J . Phys. Chem. 1992, 96, 4973. (34) MacRitchie, F. Chemistry at Interjaces; Academic: New York, 1990; p 34. (35) Cannon, R. D. Electron Transfer Reactions; Butterworth: New York, 1980: p 169. (36) Smith, D. L. Eng. Sci. Fa11/1992, 37. (37) Marcus, R. A. Annu. Rev. Phys. Chem. 1964, 15, 155. (38) Jayne, J. T.; Davidovits, P.; Worsnop, D. R.; Zahniser, M. S.; Kolb, C. E. J. Phys. Chem. 1990, 94, 6041. (39) Hanson, D. R.; Ravishankara, A. R. J. Phys. Chem. 1994,98,5728. (40) Wilson, M. A.; Pohorille, A. J . Chem. Phys. 1991, 95 (8), 6005. (41) Atkins, P. W. Physical Chemistry, 3rd ed.; W. H. Freeman: New York, 1986; p 782. (42) Schwartz, S. E.; Freiberg, J. E. Atmos. Environ. 1981, IS, 1129. (43) Gardner, J. A,; Watson, L. R.; Adewuyi, Y. G.; Davidovits, P.; Zahniser, M. S.; Worsnop, D. R.; Kolb, C. E. J . Geophys. Res. 1987, 92, 10887. (44) Cotton, F. A.; Wilkinson, G. Advanced Inorganic Chemistry, 5th ed.; John Wiley & Sons: New York, 1988; p 545. (45) Davidovits, P.; Jayne, J. T.; Duan, S. X.; Worsnop, D. R.; Zahniser, M. S.; Kolb, C. E. J . Phys. Chem. 1991, 95, 6337. (46) Kosak-Channing, L. F.; Helz, G. R. Environ. Sci. Technol. 1983, 17 (3), 145.
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