Environ. Sci. Techno/. 1995, 29, 1171-1178
Bubble Column Apparatus For Gas- Liquid Hetkogeneous Chemisty Studies JEFFREY A. S H O R T E R , + WARREN J. DE BRUYN, JAINHONG H U , ERICK SWARTZ, AND PAUL DAVIDOVITS* Department of Chemistry, Eugene F. Merkert Chemistry Center, Boston College, Chestnut Hill, Massachusetts 02167
DOUGLAS R. WORSNOP, MARK S. Z A H N I S E R , A N D CHARLES E. KOLB Center for Chemical and Environmental Physics, Aerodyne Research, Inc., Billerica, Massachusetts 01821
A bubble column apparatus has been designed to conduct time-resolved gas-liquid interaction studies of interest in atmospheric chemistry. In the apparatus, a l o w pressure gas flow, carrying trace gas diluted in helium carrier gas, is 'bubbled' through a flask containing 3.5 L of temperature-controlled liquid. The outlet gas flow is then sampled by a differentially pumped mass spectrometer. The position of the bubble injector, which determines the gas-liquid contact time, is computer controlled by means of a stepping motor. Modeling of the gas uptake and the validation of the apparatus performance are described. The apparatus in the present configuration can measure Henry's law coefficients (H) for nonreactive species in the range 0.01-2.0 M/atm. For reactive species (reaction rate k) the apparatus measures W 2 values in the range 0.08-100 (M/atm) s-'l2.
Introduction Heterogeneous reaction pathways involving aqueous droplets and aerosols in clouds and fogs have been recognized as major mechanisms for the chemical transformations of atmospheric trace gases. Such reactionsare important both in the troposphere and in the stratosphere. Tropospheric chemistry modeling studies have emphasized the role of heterogeneous mechanisms for several important processes, among them the oxidation of SOZ,the formation of HN03, and the production of hydrogen peroxide in cloud droplets (1- 7). Heterogeneouschemistry of nitrogenoxides and atmospheric sulfur species such as DMS, HzS, and MSA has been shown to be central in the formation of aerosols, which in turn affect solar scattering both directly and via clouds whose formation they initiate (8-10). Recently, the effect of heterogeneous cloud processes in regional to global scale tropospheric ozone photochemistry has been emphasized (11, 12). Similarly the role of heterogeneous processes in stratospheric ozone depletion is now well established (13- 16). In a laboratory experiment designed to study heterogeneous interactions, the uptake of the trace gas of interest is measured and can be expressed in terms of an uptake coefficient, ymeas,defined as
Ymeas
- no. of molecules lost to surface (molecule s-') no. of gas-surface collisions (collision s-l)
The experimentally measured uptake coefficient (ymeas) is a function of the mass accommodation coefficient,gas and liquid phase diffusion,Henry's law saturation,gas-surface interaction time, and, in some cases, liquid and surface chemistry. The challengeis to design experiments in which these effects can be separated. The atmospheric importance of heterogeneous interactions has led to the development of several laboratory techniques to study such processes. Among the most widely used techniques are the Knudsen cell reactor (17), wettedwall flow tubes ( I S ) , and the droplet train flow tube (1921). Each of these techniques has its range of applicability, a set of advantages, and draw-backs. (For a review, see ref 22). In this paper, we describe a new technique, the bubble column. This technique utilizes a well-characterized column of bubbles, containing a trace gas, rising through a liquid of interest. The technique is capable of measuring the uptake of gases with relatively small uptake coefficients; ymeasin the range 10-4-10-7. As such, this technique complements the droplet train flow tube apparatus, which is designed to measure relatively large gas uptakes (ymeas > 5 x low4).The primary difference between the bubble column and droplet experiments lies in the gas-liquid interaction times: t = 0.1- 1 s for bubbles and 1-20 ms for droplets. The longer interaction time in the bubble column increases the number of gas-liquid collisions and, thus, the sensitivity to small uptake ( y ) values. Bubblers have been employed to promote gas-liquid interactions since the inception of the field of chemistry. Present address: Mission Research C o p . , One Tara Blvd., Nashua, NH 03062. +
0013-936XJ95/0929-1171509.0010
1995 American Chemical Society
VOL. 29, NO. 5, 1995 /ENVIRONMENTAL SCIENCE &TECHNOLOGY
1171
Mechanical Pump
4
Bubble Column
Trace Carrier Motorized TransI at i on Stage
t
FIGURE 1. Schematic of gas bubble column reactor.
However, up till now bubblers have not been used to conduct quantitative time-resolved studies. The bubbler apparatus described here is suitable for such quantitative studies. By measuring the uptake as a function of various parameters among them liquid additives, gas-liquid interaction time, and temperature, information can be obtained about the individual processes governing gasliquid interactions. For the species studied in the bubble column apparaNS, the uptake rate is relatively slow so that mass accommodationand gas phase diffusion do not limit uptake and therefore need not be taken into account. An analysis of the gas uptake measurementsyields information about Henry’s law coefficients (HI and interfacial or bulk phase reaction rates (k)for the species. One such study describing the heterogeneousinteractions of carbonyland haloacetyl halides is presented in the followingcompanion article.
Experimental Considerations Description of Gas Bubble Column Reactor. A schematic ofthe bubble column reactor apparatus is shown in Figure 1. In the configuration shown, a low pressure gas flow, containing a trace gas diluted in helium carrier gas, is ‘bubbled‘through a flask containing 3.5 L of liquid. This could be water. an aqueous solution, or sulfuric acid. The liquid is temperature controlled by a coolant flowing through a glass jacket surrounding the flask. The position of the bubble injector, which determines the bubble travel distance, is computer controlled by means of a stepping 1172 m ENVIRONMENTAL SCIENCE &TECHNOLOGY I
VOL. 29, NO. 5.1995
motor. The outlet gas flow is sampled by a differentially pumped mass spectrometer. In principle, the experimentsare straight forward. The outlet gas density is simply measured as a function of the distance the bubbles pass through the liquid and as a function ofliquid composition. In practice, several factors must be taken into account and held under control. After the bubble breaks at the surface, the subsequent interaction time of the gas with the liquid surface must be minimized. This is accomplished by means of gas inlets positioned tangential to the liquid surface. These inlets, which carry a flow of helium at least 10 times greater than the helium flow containing the trace gas, are focused on the bubble breakingregionand immediatelydilutethe trace gas as the bubbles breaks at thesurface. Thedilutionandentrainment rapidlyremove the trace gas from the “wet”environment, minimizing unwanted heterogeneous interactions above the liquid. An experimental run begins with the bubble injector above the liquid surface. At thispoint, the gas flowsthrough the injectorwithout interaction with the liquid surface. The computer-controlled translation stage then starts the 40cm descent of the injector. The first centimeter of the translation is above the liquid the next 39 cm are below the surface. Bubbles are formed as the injector crosses the liquid surface. Once formed, the bubble, which contains the trace and carrier gases, becomes saturated with water vapor. Secondary bubble injectors, carrying helium gas,
are positioned just below the surface. These secondary bubblers achieve two purposes. First, they provide a steady equilibrium-determinedsource ofwater vapor in the region above the liquid surface, thus minimizing the pressure/ flow change when the trace gas bubble injector crosses the liquid surface. Second, the flow through the secondary bubble injectors is continually churning the liquid surface, providing a constant “surface state” independent of the position of the trace gas injector. These auxiliarygas flows have been varied over a sufficientlywiderange to ascertain that they do not affect the uptake measurements. The bubble column reactor experiment is akinetic study in which the time-dependent gas uptake into liquid is measured. The gas-liquid molecular collision rate and the gas-liquid interaction times depend on bubble size, shape, and speed. To determine these quantities, several detailed measurements were required to fully characterize the apparatus. The residence time of a bubble in the reactor, the acceleration speed history of the bubble, and its travel distance had to be determined. In addition, the bubble shape distortion had to be studied since the surface to volume ratio of the bubble determines the number of gasliquid collisions per unit volume. Specifks of the Jkperiment. The computer-controlled stepping motor and translation stage are manufactured by Velmex Inc. The stage has a linear speed range from 0 to 3 cm s-l. In our experiments, the translation stage was operated at a speed of 0.2 cm s-l. At this speed, the injector orifice descends from the surface to a depth of 40 cm in 200 s. During the descent, the mass spectrometer signal is sampled at a rate of 20 s-l. The acquired data is averaged and saved at intervals of 1.25 s, which corresponds to 0.25 cm of downward translation movement. The pressure is also monitored at the same rate to ensure that pressure instabilities have not occurred. Such pressure instabilities could affect the density measurement at the mass spectrometer. The normalized mass spectrometer signal is plotted as a function of the bubble vertical travel distance (4 in the liquid. In order to maintain smooth flows, the vessel pressure was maintained at 10 Torr above the water vapor pressure with added carrier gas. The absolute trace gas density in the bubbles was determined by measuring with calibrated flow meters the mass flow of the trace and carrier gases into the bubbles. The entry of water vapor into the bubble was accounted for by using a dilution factor that was determined by a series of measurements using noble gases to calibrate the effect of dilution at the mass spectrometer. The bubble injector is a 0.06 cm i.d. Teflon tube supported inside a 114411. 0.d. glass capillary tube. Gas flows were measured using a mass flow meter (Matherson 8100 Series). The following gas flows were used in these experiments: Helium carrier gas flow for the formation of bubble and trace gas entrainment was 0.1 (STP) s-l. Helium flow above the liquid surface was 1-4 ~ m (STP) - ~ s-l. Helium gas flow for the formationofbubbles just below the liquid surface was 0.1 ~ m (STP) - ~ s-l. The trace gas density inside the bubble was varied from 5 x 1014to 5 x ioi5 ~ r n - ~ . Characterization of Bubbles. The size and shape of the bubbles and the distance between them were determined by analyzing video recordings of the bubbles under all appropriate conditions, using frame capturing techniques to examine the images. The bubble sizes were
determined by direct measurement with a ruler placed inside the vessel. The frequency of the bubbles was measured directly using a stroboscope. The frequency of the strobe light was adjusted until the bubbles appeared stationary at the fundamental frequency. The bubble speed can be determined from the distance between bubbles and the bubble frequency. Three stages of the bubble evolution are clearly evident and must be taken into account: (i)the growth of the bubble as it is formed prior to detachment from the injector, (ii) the acceleration of the bubble to its terminal speed, and (iii) the steady-staterise of the bubble at its terminalvelocity. (i) The formation of bubbles at submerged orifices is well documented in the literature (23-27). The size of the bubbles is a complex function of the orifice diameter, the volume beneath the orifice, gas flow rate, surface tension, and liquid inertia. Depending on the combination of conditions, several stable bubble-forming regimes can be identified. The volume beneath the orifice is an important parameter in the bubble formationprocess. Below a critical size of this volume and at relativelylow gas flows, the volume of the bubble formed remains constant and as the gas flow is increased, the frequency of the bubbles increases proportionally to the gas flow. If the gas flow is increased past a certain point, a new regime is reached in which the bubble frequencyremains constant and the bubble volume grows proportionally to the gas flow. In our experiments, bubble formation is in the constant frequency regime for the first 30 cm of injector descent. At greater depths, bubble formation is in the constant volume regime. In most experiments only data from the constant frequency regime is used. The growth of the bubble, as it is formed prior to detachment from the injector,can be expressed analytically in terms of the measured gas flow rate and bubble frequency. Bubble volume at the point of detachment from the orifice is calculated from the relationship V = volume gas flowlbubble frequency. For these experiments, bubble volume calculated in this way was in good agreement with the expressionderived by Kupferberget al. (24)for volumes in the constant frequency regime [Le., V = 1.378 x (gas flow ratel,z/gravitationalac~eleration~.~)]. Deviationsfrom this expression as one moves into the constant volume regime also agreed well with their data for an orifice of similar size. Under our experimental conditions, the diameter of the bubbles was in the range 2-4 mm, depending on the specific flow conditions, temperature, and position of the bubble. (ii)The accelerationof the bubble to its terminal velocity was traced by video techniques. The acceleration is a function of buoyant and drag forces (28). This interaction oE forces is formulated analytically,and the formulation is used in the numerical model. The equation of motion is acceleration = ~ ( -1d/v,,*)
(2)
where B is the buoyant acceleration = 380 cm*/s; vo is the terminal bubble velocity = 42 cm s-l. The bubble reaches terminal velocity after about 4 cm of ascent. (iii)The steady-state motion of bubbles through liquids is well described in the literature (28). The terminal velocity of the bubbles is given by the product of the distance between the bubbles and the bubble frequency. These parameters were determined using frame capture and VOL. 29. NO. 5,1995
I ENVIRONMENTAL SCIENCE & TECHNOLOGY 1 1173
stroboscopic techniques. The velocity was found to be about 40 cm s-l, which is consistent with the predicted terminal velocity of 2-4 mm diameter bubbles (28). Due to the liquid drag, bubbles with diameters of 2-15 mm assume an ellipsoidal shape and spiral through the liquid as they travel to the surface. The distortion from the spherical shape was determined from the frame-grabbed images. At terminal velocity, the increase in surface area due to distortion is 1.3, which corresponds to a height to width ratio of 2:7 for an oblate spheroid. During acceleration, prior to reaching a stable spheroid shape, the bubble undergoes a mushroom-shaped inversion. The effect of this distortion is observable in the gas uptake profile and was included in the model as a transient area increase. As the bubble rises, the pressure on the bubble decreases, and as a result the bubble volume increases. Under our experimental conditions, the maximum volume increase from the injector to the liquid surface is about a factor of 2. In terms of surface to volume ratio (or radius), which is the relevant parameter in the uptake process, this corresponds to a factor of 1.26. This effect is also included in the modeling discussed below.
Modeling the Gas Uptake Gas uptake in the bubble column experiment is governed by the same physical processes that govern the gas uptake by droplets (20).As stated in the Introduction,the measured uptake is a function of the mass accommodation coefficient, gas and liquid phase diffusion,Henry’slaw saturation, gassurface interaction time, and in the case of reactive species, also liquid and surface chemistry (22). Danckwerts (29) solved the uptake equations analyticallyfor the case where the species in the gas phase is not substantially depleted. In certain limits, simplified expressions for the uptake coefficient can be obtained. We present here these limiting values of y in order to show their functional dependence. When the uptake is limited by the solubility of the species, the uptake coefficient ysOlis Ysol =
--&8HRT(D1 7) , I 2
When the uptake is limited by the reactivity of the species the uptake coefficient ym is
Here 0 is the liquid phase diffusion coefficient of the species, c is the average molecular velocity, k is the liquid phase pseudo-first-order reaction rate to an irreversibly solvated species, and H is the Henry’s law constant (in M/atm) (22). Extensive analysis of the bubble column uptake data has shown that even in the stated limits eqs 3a and 3b are not rigorously valid. This is not surprising. Equations 3a and 3b are intended to characterize the uptake into a stationary liquid. Bubbles of course rise within the liquid, and therefore there is appreciable convective mixingwithin the liquid-water layer surroundingthe bubbles. As a result, liquid transport cannot be simplydescribed by liquid phase diffusion alone (i.e., Q). A key task in the development of the bubble column technique into a quantitative tool has been the proper modeling of the gas uptake and the validation of the apparatus performance. 1174 1 ENVIRONMENTAL SCIENCE & TECHNOLOGY I VOL. 29. NO. 5 , 1 9 9 5
GAS
/
INTERFACE
I
CONDENSED PHASE
--diffusion
diffusion
____t
accommodation
solubility
evaporation
-c-
reaction
\
FIGURE 2. Schematic representation of the flux at the interface.
We were unable to formulate an analytical model for the gas uptake in the bubble column reactor. Therefore, a finite element numerical method was adopted to solve the complex coupled equations for gas absorptioddesorption, diffusive mass transport, mixing, and liquid phase reactions. In this approach,the physical gas-liquid system is broken up into grid cells. A system of equations is used to move species from one cell to the others. By choosing the length of the time steps and the size of the cells in the numeric model, complex equationswith varying boundary conditions can be solved. The details of the implementation of the finite element model are given in ref 30. Here, we present the fundamentalequationsof the process with their boundary conditions.
Flux acrossthe Interface. In order to model the uptake of a gas at the gas-liquid interface, three processes must be taken into account. These are (i) absorption from the gas phase into the liquid phase, (ii) desorption from the liquid to the gas phase, and (iii)mass transport in the liquid awayfrom the interface. By accountingfor these processes and coupling them to the bulk phase transport discussed below, the net uptake rate from the gas to the liquid can be calculated as a function of time. These processes are shown schematically in Figure 2 and are discussed below. The rate of absorption of molecules from the gas phase to the liquid phase is given by the product of the number of collisions with the surface and the mass accommodation coefficient (a), which is the probability that a molecule that collides with the surface enters the bulk liquid. Due to the slow uptake rates of the species studied in this experiment,the effect of gas phase diffusion is negligible. Thus, the absorption rate of molecules at the interface at a given time is absorption rate = ang(c/4)A
(4)
Here ngis the gas phase density, andA is the exposed surface area, Le., the area of the bubble (which is experimentally determined as a function of depth). The desorption rate of a molecule from the liquid interface to the gas phase is defined so that at equilibrium, when the net transport rate across the surface is equal to zero, Henry’s law is satisfied. That is n1= n p R T
(5)
Here n1 is the liquid phase density, H is the Henry’s law coefficient, R is the gas constant, and Tis the temperature. Combining eqs 4 and 5, we obtain an expression for the
aesorption rate:
C = c1
desorption rate = an,(c/4lA/(HR7J (6) The net absorption is simply the absorption rate minus the desorption rate: net absorption rate = a(c/4)A[ng- nl/(HR7Jl (7) A molecule which enters the liquid and does not desorb
back into the gas phase will diffuseaway from the interface into the “bulk” liquid. This diffusion into the bulk liquid is modeled using Ficks second law. The population differenceterm ng - n1/(HRZ‘lis always very small since a near-equilibrium condition exists at the interface. Yet, the net transport rate of molecules into the liquid is determined by this difference. Therefore, care must be taken that the net flux of molecules into the liquid during a time step of the model is properly matched to the liquid diffusion of molecules away from the surface. The matching equations are provided in ref 30. The time-dependent change of the trace gas density in the bubble is given by the product of the net absorption rate and the chosen time step. The new density is then determined by dividingthe number of molecules remaining in the bubble by the bubble volume. Liquid Phase Transport. Liquid phase transport has a pivotal role in the gas uptake process. The transport of molecules away from the interface shifts the equilibrium shown schematically in Figure 2, causing a change in the amount of gas uptake. An increase in the species transport awayfrom the surface will result in a corresponding increase in the gas uptake to maintain the interfacial region at a near equilibrium steady-state. Liquid phase transport is the least tractable aspect of the phenomena associated with the rising bubbles. We assume here that the liquid medium surrounding the moving bubble can be characterized by two regions. The first region of width Xd begins at the gas-liquid interface and is stationarywith respect to the bubble. In this region, transport of the trace species occurs via liquid phase diffusion. Convective mixing begins graduallyin the second region adjacent to the stationary zone. The transition to convective mixing is characterized by a half-Gaussian function with its peak at Xd. The width (C)of the Gaussian mixing function is held constant throughout the motion of the bubble. However, the width of the unmixed boundary is parameterized so as to allow a variation as a function of bubble distance from the injector. Both Xd and the width of the Gaussian are functions of temperature. In addition, x d is also a function of the distance (4 of the bubble from the injector. Nonlinear least-squaresoptimization provides the parameters defining the transport regions as a function of time and temperature by fitting the uptake of species with known Hand k. The parameter xd is assumed to be of the form: xd
=A
U,/d2
+ U2d’”
f
U3d
(8a)
Here & is in units of micrometers and d is in units of centimeters. A = b,
and
+ b,T2,,+ b3T2t
+ c2TZ0+ c3T22
The constants as determined by the optimization procedure are as follows: bi = -2.59 b2 = 0.76 b3 = -1.76
a1 = 0.039 -2.46 a3 = 0.19 a2 =
ci = 410 ~2=115 ~3 = 0.8
Diffusive Transport. The region of diffusive molecular transport extends from the gas-liquid interface to a distance Xd into the bulk. Ficks second law is used to model the diffusive transport. To obtain an analytical expression for the diffusion, specific boundary conditions must be set. Here, the assumed conditionsare as follows: (1)the number of molecules remains constant (Le., mass balance); (2) chemical reactions are treated in a separate step; (3) at each time step, molecules in each cell are initially located at a point; and (4) diffusion is one dimensional. As is discussed in ref 30, these boundary conditions are valid as long as the definition of the cells and time steps are chosen appropriately. Convective Transport. In the region beyond Xd, convective mixing is simulated by removing from the system a portion of the liquid containing the solvated trace molecules and replacing that liquid with liquid free of the trace species. The magnitude of the mixing depends on the location of the cell with respect to Xd and is calculated using a half-Gaussian function. The convective mixing function is x 5
fraction removed = 0 = (1- exp - ( x - xd)’/G
X
Xd
’x d (9)
Initially, Xd is far from the gas-liquid interface, and diffusive transport controls the uptake. As the bubble detaches from the injector and accelerates, the vertical distance d increases and the diffusive region narrows. (See eq 8.) When the bubble attains its terminal velocity and spiralstoward the surface,thevalue OfXd becomes negative, indicating that transport is now fully convective. Convective mixing increases the rate of species removal from the interfacial region. This in turn increases the concentration gradientsand results in fastermass transport. Gas uptake at the interface is accelerated to maintain the gas-liquid interface at near equilibrium. Liquid Phase Chemical Reactions. Liquid reactions are modeled with pseudo-first-orderkinetics. The rate expression is n,(t+ At) = n,(t)exp(-kAt) (10) Here k is the pseudo-first-order reaction rate, At is the duration of the time step, and nl(t)and nl(t+ At) are liquid phase concentrations at t and t At, Chemical reaction steepens the concentration gradient by additional removal of species from the mass transport profile and results in a further enhancement in the net uptake rate. The higher the reaction rate, the steeper is the gradient and hence the higher the uptake rate. The implementation of the chemical reaction in the model is discussed in ref 30. Analytical Testing of the Model. To test the numerical model, several sets of boundary value problems for which analytical solutions are available were solved with the model. The problems were from the fields of gas-liquid transport (29)and heat transfer (31). The problems solved
+
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1175
Time (s) 0.2
0.0
1.0
Time (s) 0.6
0.4
0.8
r
0.4
0.2
0.0
I
0.6
0.8
0.8
2OD 0.6
0.60
0.4
0.40
-
0.2
0.20
-
0.0
0
1
2
3
Distance
”*
4
6
5
I
+
I
p’ o CH,Br x CH,CI
a”‘
-
,,d
CHF,Ci
Jd sp”’
Experimental (M atm’l)
FIGURE 4. Henry’s law coefficients as determined by the computer fit tothe experimentaldata versus literaturevalues of H.The literature values were obtained as described in the text.
included conditions equivalent to constant gas density, varying gas density, and reactive uptake. In all cases, the model was in accord with the analytical solutions.
Experimental Results Both apparatus and model were calibrated and validated by measuring the uptake of eight nonreactive gas phase species with known Henry’s law coefficients. These were 0 3 , CH3Br, HzS, CH3C1, CFzClH, COS, DMS, and SOZ,the latter at low pH to suppress hydrolysis. In Figure 3, we show as an example the uptake ofDMSat two temperatures as a function of the square root of the bubble travel distance (4.The uptake is plotted versus d1I2to emphasizethe shorttime data, which are most sensitive to the gas uptake rate. The gas-liquid interaction time is of course proportional (although not linearly) to the travel distance and is shown on the top axis of the figure. The solid line is the nonlinear least-squares fit of the model to the data. The discontinuities in the model curves reflect the bubble formation and acceleration processes discussed above. Similar data are obtained for the other species. 1176
1
3
2
4
5
6
Distance”* (cm”*)
FIGURE 3. Uptake of DMS as a function of dn at two different temperatures. Here d is the travel distance of the bubble rising through the liquid. The corresponding gas-liquid interaction time is also shown. The solid line is the computer fit to the data.
P
0
(cm”’)
ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 29, NO. 5, 1995
FIGURE 5. Uptake of ozone by pure water and by a 0.06 M solution of Fez+.
The uptake of the eight species was measured at three temperatures (278,288,and 293 KJyielding 24 sets of data. These sets were used to determine nine parameters (sixfor the position of Xd and three for the Gaussian width), which describe the temperature-dependent mass transport in the model (eq 8). The parameters were obtained by fixing the Henry’s law coefficient at the literature values and using a nonlinear least-squares fitting routine to determine the values for a subset of the parameters that gives the best fit of the model to all 24 data sets simultaneously. The subset of parameters was changed, and the data were refit until the global minimum best fit was found. The values of the parameters in eq 8 were obtained in this way. Using these parameters, the 24 data sets were refit by the model and yielded the final values for the Henry’s law coefficients. These were in good agreement (within 20%) with the published values. In Figure 4, we show Henry’s law coefficients as determined by fitting the model to the experimental data plotted versus the literature values. The literature values for the Henry’s law coefficients were obtained from Wilhelm et al. (32)for SOZ, CHsBr, CH3C1, COS, HzS,and CHF2Cl;from Kosak-Channingand Helz (33) for 03;and from Aneja and Overton (34) for DMS. To validate the uptake model for gas phase species that undergo chemical reactions in the surrounding liquid, a second series of uptake studies was done with reactive molecules of known H and k. These included SOz with HzOZ,0 3 with Br- and Fez+,and Clz with H20. In Figure 5, we show the uptake of ozone by pure water and a 0.06 M solution of Fez+. The effect of the reactive uptake via O3 Fez+reaction is clearly evident. In this set of experiments, the model was given the nine parameters determined above and the known Henry’s law constants for the species. The best pseudo-first-order rate constants, k, were then found by a nonlinear fit of the model to the data. In Figure 6, we show a plot of k as determined by the model fit to the experimental data versus literature values of k. As is seen, the measurements are in reasonable agreement (within about 50%) with the literature values. The literature values for k were obtained from Hoigne et al. (35) for the O3 reactions, from Robbin Martin and Damschen (36) for the SO2 H202 reaction, and from Spalding (37) for the Clz + H20 reaction.
+
+
CI,+H,O O,+O"
los i
I
Reaction of 0,with 0.06 M Fez'
'
O
b
&'
I
10'
, 1 1 1 1 1 1 4 1
1o2
1 1 1 1 1 1 1 1 l
I 1 1 6 1 1 1 1 1
10'
1o4
I 1 * 1 1 1 1 1 1
10'
Experimental ('.I)
FIGURE 6. Values of k as determined by the computer fit to the experimental data versus literature values. The literature values were obtained as described in the text.
These studies indicate that for nonreactive species the bubble column reactor in the present configuration can yield Henry's law coefficients in the range 0.01-2.0 M atm-l with an accuracy of about 20%. (Modifications to the apparatus could extend the range of measurable H to smaller values.) Further, for reactive species,ifthe Henry's law coefficient is known, then measurements of species uptake with the bubble column reactor will provide values for the first-order reaction rate constants in the range 50100 000 s-l with an accuracy of about 50%. It should also be noted that the range of measurable reaction rates depends on the solubility (Hvalue) of the molecule. This is due to the fact that the uptake is a function of Hkl", and with each specific physical configuration of the apparatus there is a limit both to the minimum and the maximum uptakes that can be measured. In the present apparatus configuration, the range of measurable Hk112 values is approximately 0.08-100 (Mlatm) s - ~ ' ~ . Interpretation of uptake data is more complicated for species with both Hand k unknown. In stationary liquids, the time-dependent gas uptake such as plotted in Figures 5 can be in principle deconvoluted to yield values of H and k. However, in our studies the liquid is not stationary with respect to the bubbles. Because of convective mixing, the dependence of the gas uptake on t and k cannot be distinguished under our experimental conditions. Still, even in this case, useful information can be obtained from the uptake data. First, an upper limit of the Henry's law coefficient (&,ax) can be obtained by a model fit of the uptake data with k set to zero. This gives the solubilitylimited uptake. Further, an upper limit of the product Hk112, an experimental uptake observable, can also be obtained by fitting the model to the uptake data with k set to a value sufficientlylarge so that the uptake is limited by the assumed reaction and nor solubility governed mass transport. In this regime, the uptake is insensitiveto kalone and depends only on the product Hk1'2as is indicated in eq 3b. This is illustrated in Figure 7 for the reactive uptake of 0 3 by a 0.06 M Fez+solution. This figure shows the model-determined best-fit value of Hk1I2as a function of k. The k values in the plot are not related to the true reaction rate of the molecule but are varied as a parameter to illustrate the
k
FIGURE 7. Model-determined best-fit value of HklR as a function of k obtained for the reactive uptake of 03 by a 0.06 M Fez+ solution. Also shown is Hlr'R determined from the literature values of H = 0.0114 M atm-l (33)and k = 10200 s-l (39.
1%
Reaction of 0,with 0.MM Fez+
k ('.I)
FIGURE 8. Model-determined best-fit value of log H versus log k obtained for the reactive uptake of 03 by a 0.06 M Fez+solution. Also shown is a point determined from the literature values of H = 0.0114 M arm-' (33) and k = 10200 s-' (35).
functional dependence of Hk112.As is evident, the product Hk1/2reaches a constant maximum value for k greater than 100 s-l. The value of Hk"* based on the literature values of H = 0.0114 M atm-l (33) and k = 10200 s-l (35) for the 03;0.06 M Fez* system is also shown in the figure. The parameter Hk1l2displays a similar behavior for all species studied, both reactive and soluble. Additional information can be gained from the uptake measurements of species with unknown Hand k if there is available some supplementary knowledge about one of these parameters. If reasonable estimates of either H or k are available,then the other parameter can be determined from the experimental results. Techniques for estimating H (38-41) and k (42, 43) have in fact been developed for certain classes of molecules. The model-determined relationship between H and k is clearly shown in Figure 8, which is simply a reformulation of the 03-0.06 M Fez+ uptake data in Figure 7. Such a plot yields immediately the upper limit of the Henry's law coefficient (HmUat k equal VOL. 29, NO. 5, 1995 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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to zero). Further, we note that for large k the plot approaches a straight line limit with a slope of 1/2. This implies the constant Hk112value in the region of k. The literature values of H and k are again shown in the figure. In using estimated values for H or k to calculate the other parameter, care must be taken to assess properly the uncertainties in the calculationsince, as is evident in Figure 8, the relationship between H and k is in some regions highly nonlinear.
Conclusions The bubble column reactor in the present configuration can yield Henry's law coefficients in the range 0.01-2.0 M/atm with an accuracy of about 20%. (Modifications to the apparatus could extend the range of measurable H to smaller values.) For reactive species, the range of measurable H P 2 values is approximately0.08- 100 (Mlatm) s - l i Z . If the Henry's law coefficient is known, then measurements of species uptake with the bubble column reactor will provide values for the first-order reaction rate constants with an accuracy of about 50%. First-order reaction rates in the range 50-100 000 s-l have been measured. This technique has an applicability wider than the determination of solubilitiesand simple reaction rates. The device, for example, has a unique utility in studying interactions at the gas-liquid interface. It can be used to study effects of light on heterogeneous processes as well as effects of additives such as ions and various catalysts. A particularly interesting application of the device may be to the study of reactions between two different species at a liquid surface (Le., liquid surface activation).
Acknowledgments Funding for this work was provided by the U.S. Department of Energy Grant DE-FG02-91ER61208, National Science Foundation Grant ATM-93-10407, U.S. Environmental Protection Agency Grants R-815469-01-0and CR 81973301, the AlternateFluorocarbon EnvironmentalAcceptability Study, the European Chlorinated Solvent Association, and the Halogenated Solvents Industry Alliance.
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Received f o r review June 7,1994. Revised manuscript received December 21, 1994. Accepted January 13, 1995.@
E89403524 @Abstractpublished in Advance ACS Abstracts, March 1, 1995.
