Environ. Sci. Technol. 1994,28,2133-2138
Henry’s Law Constants and Infinite Dilution Activity Coefficients for Volatile Organic Compounds in Water by a Validated Batch Air Stripping Method Frands Nlelsen’ and Erik Olsen National Institute of Occupational Health, Lersoe Park All6 105, 2100 Copenhagen, Denmark
Aage Fredenslund Department of Chemical Engineering, Technical University of Denmark, 2800 Lyngby, Denmark
An improved batch air stripping technique has been developed for the determination of Henry’s law constants and infinite dilution activity coefficientsof volatile organic compounds in water. The experimental design confirms that the two fundamental assumptions in batch air stripping are fulfilled: (i) equilibrium between vapor and dissolved organic in the top of the stripping column; (ii) homogeneity of the liquid phase. Various organics in water, representing a range of Henry’s law constants from 5 X lo3to 2 X 106 kPa, were investigated. When accurate pure component vapor pressure data are available,accurate infinite dilution activity coefficientscan be calculated from the ratio of the Henry’slaw constant to the pure component vapor pressure. For certain aqueous systems, the UNIFAC model for hydrophobic compounds still fails to give accurate predictions of thermodynamic properties.
Introduction Reliable Henry’s law constants and corresponding infinite dilution activity coefficients for volatile organic compounds in water are of increasing interest due to the larger emphasis being placed on pollutants’ environmental fate and occupational risk assessment. For environmental purposes, the Henry’s law constant gives a direct measure of the partitioning between air and water and determines the volatilization or absorption tendency. In occupational hygiene, the infinite dilution activity coefficient is an important parameter in modeling evaporation rates from, for example, water-thinable products. Henry’s law constants are often estimated by an indirect method as the ratio of the pure component vapor pressure to the aqueous solubility, because solubility data are more abundant. This method assumes very small mutual solubilities and that Henry’s law is valid up to the saturation solubility limit of the compound. Hence, it should only be applied to highly hydrophobic compounds. However, reported solubility data for these compounds are often inaccurate due to analytical limitations ( I , 2). Various experimental techniques for direct measurement of Henry’s law constants have been proposed. The most widely used methods are batch air stripping (BAS), based on a dynamic principle originally developed by Mackay and co-workers (3),and equilibrium partitioning in closed systems (EPICS),based on a stationary principle ( 4 ) . In BAS, the organic compound dissolved in water is purged using an inert gas, and the Henry’s law constant is determined from a linear regression of the logarithm of concentration versus time. In EPICS, equal amounts of the organic compound are loaded into two different liquid volumes, resulting in two different concentrations, and
* Address correspondence t o t h i s author. 0013-936X/94/0928-2133$04.50/0
0 1994 American Chemical Soclety
equilibrated. The Henry’s law constant is then determined from headspace concentrations of the organic compound and the mass balances in the two systems. The primary advantage of these methods is that merely relative rather than absolute concentrations are required, provided that the detector response is linear. In BAS, this is checked automatically since any deviation from linearity will result in a nonexponential decay of the solute concentration. In EPICS, the linearity has to be checked separately for each compound. Both methods have an upper limit with respect to the magnitude of the Henry’s law constant that can be measured. In BAS, this limitation is due to two conflicting requirements: (i)equilibrium between vapor and dissolved organicmust be achieved in the top of the stripping column, which demands a tall column; (ii) homogeneity of the liquid phase, which is more easily achieved in a short column. Commonly, equilibrium is assumed but not checked, and poor axial mixing biasing the results has been reported (5). Only for polychlorinated biphenyls (61, having relative low Henry’s law constants, and for benzene (3) has equilibrium been checked. In EPICS, the limitation is due to a decrease in sensitivity with increasing Henry’s law constants ( 4 , 7 , 8 ) . As a result, EPICS cannot be used for Henry’s law constants above approximately 2 X 106 kPa. EPICS is associated with some potential systematic errors due to adsorption of the organic compound onto the relatively large vapor-vessel interfacial areas and absorption by diffusion into Teflonhubber septa. Experiments indicate that these effects are present, though small, even when the equilibration time is less than 5 h (9).Thus, when equilibration time exceeds 24 h, which is typically the case, adsorption and absorption may not be neglected. In BAS, adsorption is unlikely to take place due to the dynamic principle and the highly turbulent conditions. The main sources of error in EPICS, however, are attributed to the addition of volatile solute and the collection of headspace samples for gas analysis. Hence, for Henry’s law constants below 1 X lo4 kPa, the application of EPICS is questionable (IO). This makes BAS the more preferable of the two methods. This work presents an approach for the determination of Henry’s law constants and infinite dilution activity coefficientsfor volatile organic compounds in water, based on an improved batch air stripping technique and an experimental design, which confirms that the basic assumptions concerning equilibrium and homogeneity are fulfilled. Differentapproaches to correlate experimental data with the aim of constructing predictive models for the thermodynamic behavior of organic compounds in water have been evaluated. Quantitative structure-activity relationEnviron. Scl. Technol., Vol. 28, No. 12, 1994 2133
ship techniques,QSARs (I),confined to single compounds in water have been shown to estimate Henry's law constant? with reasonable accuracy. For general applications, however, predictive activity coefficient models, which are capable of calculating interactions in dilute mixtures, are more interesting. The group-contrihutionmcdelUNIFAC (11) has been used to calculate different environmental properties, e.g., Henry's law constants, solubilities, and octanol/water partition coefficients (9,12-16). UNIFAC has been revised and extended on several occasions (1719), and an extensive parameter table (UNIFAC water) for hydrophobic compounds has lately been published by Fredenslund (16). The group interaction parameters in UNIFAC water have been revised using infinite dilution activity coefficients, which has improved the model considerably. A comparison with experimental infinite dilution activity coefficients from this work, however, shows that thermodynamic properties of certain aqueous systems cannot yet he accurately predicted. Theoretical Section A mathematical description of batch air stripping is possible when the solution is infinitely dilute with respect to the organic compound and the exit vapor is in equilibrium with the solute. The derivation by MacKay (3) is briefly repeated for convenience. Having an isothermalhomogeneous liquid at constant volume, a mass balance for the solute gives the transfer rate as
where Vis the volume of the liquid (m3),G is the gas flow rate (m3s-l), Cj is the aqueous-phase solute concentration (molm-3), Pi is the partial pressure of the solute (kPa), Hi' is the Henry's law constant (kPa m3 mol-'), R is the gas constant (kPa m3mol-' K-9, Tis the system temperature (K), and t is time (8). When the partial pressure of the organic compound is small compared to the total pressure, eq 1can be integrated from initial conditions when t = 0 and Ci = Ci0 to give log(
2) -(g)
t = at
=
(2)
Hence, the Henry's law constant is readily calculated from a straight line fit with slope a by regression of log concentration versus time. The corresponding infinite dilution activity coefficient 7:- can then be obtained from the following relation assuming ideal gas behavior: ~
Yi
Hi Htp Pi" MP:
=-=-
(3)
where Hi is the Henry's law constant on a molar basis (kPa), Pis is the pure component vapor pressure (kPa), p isthedensityofthesolution (gmq),andMisthemolecular weight of the solution (g mol-').
DP
0
N2 Flgure 1.
Diagram of apparatus.
tube connected to a glass frit with pore diameter of 4 r m laid inside the column in ita entire length. The vertical position of the glass frit could be chosen freely. A schematic overview of the apparatus is given in Figure 1. Pure nitrogen from a high-pressure cylinder (N2) was passed through a low-pressure regulator (V) at a constant flow rate and presaturated with water in a small vessel (Cl) in order to keep the liquid volume in the stripping column constant. It was not necessary to thermostat the small vessel to the temperature prevailing in the stripping column, since a difference in temperature of 5 "C was found to correspond to less than a 0.1 % decrease in liquid volume in 10 h;the typical duration of an experiment was 0 . 5 1 h. Via the glass frit, gas was then bubbled through the stripping column (C2) stripping the water for the organic compound. Homogeneity of the liquid phase was maintained by recirculating the content of the column usinga Caster MPA 114magneticallydrivenseallesspump (P) with a capacity corresponding to a liquid exchange rate of approximately 1m i d . Liquid was sucked from the top of the column to minimize the influence of heat released hy the pump. The liquid temperature, kept at 23*0.loCbyawaterjacket(WJ)connectedtoaconstant temperature bath with heating and cooling facilities,was measured just below the liquid surface with a stem thermometer (Tl)calibrated against a certified thermometer. Exit vapors were passed through a photoionization detector AID Model 580 (PID) where possible condensation of vapors was avoided by heating with an infrared lamp (IR). The temperature TFMof the gas leaving the PID and the pressure drop (-W during the passage of the PID were measured by a stem thermometer (T2) calibrated against a certified thermometer and a MANOFIX X05D digital manometer (DP), respectively. The flow rate G in the top of the stripping column was then calculated according to the ideal gas law from the flow rate Gm measured by a digital SKC soap bubble flowmeter (FM) with calibration certificate:
Experimental Section Apparatus. Batch air stripping was performed in a glass column containing water and the volatile organic compound at very low concentration. The stripping column was 90 cm high with a diameter of 5 cm. A glass 2154 Environ. Scl. Technal.. Vol. 28. No. 12, 1994
where P is the ambient pressure (kPa) measured by a mercury barometer. The mathematical description of the
stripping process then becomes
of the organic compound at infinite dilution given by
fk = yrxiP; = Hixi
(8)
and fiG = cpiyiP
Vapor pressure depression due to the curvature of the bubbles (the Kelvin effect) can be neglected, because the radius of the bubbles was approximately 1 mm, which corresponds to a vapor pressure depression of only 0.1% . Data Acquisition. The detector response, which was proportional to the gas-phase concentration of the compound measured was recorded continuously on a personal computer (PC) connected to the PID using a 12-bit A/D converter. This gave a resolution better than 0.2 % of full detector response, Least-squares regression was performed using statistical software from Minitab Inc. To control that there were no interferences like adsorption, leaks, change of PID zero point, etc., measurements were also performed using liquid sampling and gas chromatography in addition to the real-time detection. Aliquots were sampled before and after each experiment and analyzed by gas chromatographyon a Hewlett Packard 5840A gas chromatograph equipped with a flame ionization detector. Both peak area and peak height were measured, and the linearity of the detector response was checked using a series of dilutions covering the whole concentration range. Chemicals. Chemicals used for the experiments were of high purity [for analysis, purity larger than 99.5% (w/ w)]. The purity of the nitrogen used was larger than 99.998% (v/v) with a hydrocarbon content below 5 ppm; the vapor-phase concentration of the solute was typically between 500 and 1000 ppm. The possible presence of volatile hydrocarbons was accounted for by a zero setting of the PID against nitrogen with the column empty. The water was ion exchanged, and the absence of volatile organic compounds was confirmed by a constant zero response of the PID before the addition of solute. Solute concentrations always corresponded to mole assuring the validity of Henry's fractions less than law for most nonassociating compounds. Deviation from Henry's law or nonlinearity of the PID would be reflected in the residuals of the regression line. Experimental Design. If axial mixing was not sufficient, depletion of the solute would take place in the bottom of the column, where the driving force is largest, and concentration gradients might occur. Homogeneity of the liquid phase was checked by varying the gas flow rate. The recirculation rate of the liquid was constant; hence, the lower the gas flow rate, the slower the stripping and the more efficient the axial mixing. The mass transfer area and the gas flow rate influenced the approach to equilibrium as it is seen from a mass balance over a differential height of column followed by integration over the total mass transfer area A:
where Ki is the overall mass transfer coefficient (m s-l) andfiLandfiG(kPa) are the liquid- and gas-phase fugacity
Pi
(9)
where cpi is the fugacity coefficientandyi is the mole fraction of the organic compound in the gas phase. The larger the mass transfer area and the lower the gas flow rate, the more likely equilibrium was to be achieved. When the gas flow rate was varied, the AIG ratio remained virtually constant however; the only change being due to the coalescence of bubbles. Hence, equilibrium should not be checked by varying the gas flow rate as it has been practiced (20). The mass transfer area must be changed at a constant gas flow rate. This was accomplished by varying the vertical position of the glass frit, thereby changing the residence time of the bubbles in the column. By applying the two-film theory (21) for the mass transfer coefficient in eq 7, it has been shown that the approach to equilibrium is also favored by a low Henry's law constant (3). Since the exact mass transfer mechanism was not known, it is not possible, however, only from the magnitude of the Henry's law constant to tell whether equilibrium would be obtained or not. Thus, a full factorial experiment was performed for each compound to confirm that the fundamental assumptions about equilibrium and homogeneity were fulfilled. The factors were the vertical position of the glass frit and the gas flow rate. The glass frit was placed at either a low position or a high position, reducing the residence time approximately 30 72, The gas flow rate was maintained at either a low level or a high level, decreasing the stripping rate by 50%. Each experiment was carried out in duplicate on different days to account for possible day-to-day variation. The eight experiments were conducted in random order. The approach to equilibrium, i.e., the measured value divided by the true Henry's law constant, is given by the bracketed term in eq 7: Hi(measured) = 1- exp( Hi(true)
7)
(10)
Assuming that the mass transfer area is directly proportional to the vertical position of the glass frit, eq 10 can be solved by iteration for Hi(true) and KiA at a given gas flow rate. The average values of the Henry's law constants from each pair of measurements are used for the calculations, which are performed when the effect of the position of the glass frit is significant at a 2.5 % level. To perform the corrections, the liquid-phase concentration, calculated from eq 5, must be constant during the bubble residence time according to eqs 6 and 7. All measurements were performed at the standard laboratory temperature of 23 "C (22). Uncertainties of Measurement. The variables in eq 5, used for calculation of the Henry's law constant, are unrelated, i.e., there is no covariance. Hence, the uncertainty can be evaluated from a propagation of errors. The error in the slope (Y of the regression line is taken to be 2 72 , approximately equivalent to a monotonous increase or decrease in liquid temperature of 0.2 OC. The error in liquid volume V is 10 mL, as estimated from five measurings of column with water; total hold up is 1800 Environ. Sci. Technol.. Vol. 28, No. 12, 1994 2135
Batch Air Stripping benzene 5.4,
4.54
0
I
j
1W
XK)
300
4w
€00
500
700
800
I
900
W(SBC)
Flgure 2. Typical plot of log concentration vs time for benzene.
Table 1. Full Factorial Experiment with Benzene poaitionof glass frit
gas flow rate
low high low high low high low high
high high low low high high low low
Hi (PID). (kPa)
HI(GC)* (kPa)
2.75 X 10' 2.68 X lo" 2.74 x 104 2.69 X 10' 2.65 X 10' 2.68 X 10' 2.70 X lo"
2.76 X lo" 2.74 X 10' 2.83 X lo" 2.76 X lo" 2.68 X lo" 2.56 X lo" 3.01 X 10' 2.46 X 10'
2.67
x 104
*
PID,real-timedetectionofexitvapors. GC,gaschromatography on liquid samples before and after run.
mL. According to the calibration certificate of the soap bubble flowmeter, the exit gas flow rate GFM can he measured within 2%. The error contributions from measuring pressure drop (-hp) and ambient pressure (P) are negligible. Also the error in measuring the exit gas temperature (TFM) due to temperature fluctuations in the air surrounding the apparatus may he neglected. The uncertainty of the Henry's law constants is then less than 2.7 % . For most hydrophobic compounds having relatively high vapor pressures, the error in estimating pure component vapor pressure from the five constants correlation in the Design Institute for Physical Property data collection (DIPPR) is less than 1%(23). Hence, the combined uncertainty of the infinite dilution activity coefficients obtained from Henry's law constants and vapor pressure data is expected to he less than 2.9%. Results and Discussion The technique was tested with benzene, for which experimental Henry's law constants and solubility data exist from a series of investigators. A typical plot of log concentration versus time and r2 value for benzene at 23 "C is shown in Figure 2. According to Tahle 1,showing the full factorial experiment for benzene, the results are accurate with a high precisionusingthe real-time detection of exit vapors; they are highly repeatable and do not depend significantly on the position of the glass frit nor on the gas flow rate. The standard deviation is 1.1% ,which is less than the estimated uncertainty calculated from the propagation of errors. Applying a paired-sample t test, the mean values using the PID and GC method cannot he distinguished ( t = 2196 Envlron. Scl. Technal.,
Val. 28. NO. 12, 1994
-0.57). Hence, the trueness of the twomeasuring methods can he considered to he equal. The precision, however, is much better using real-time detection. The larger scattering using the GC method is primarily due to uncertainties in the sampling and gas chromatographic procedure. To get an indication of the limitations of the technique, Le., to find a compound with a value of the Henry's law constant for which equilibrium is not fully achieved, a number of volatile compounds were tested. Using the gas flow rates of 250 and 500 cm3/min trichloroethylene was found to exhibit these characteristics. The values of the Henry's law constant obtained from experiments with the glass frit at a high position and using a high gas flow rate are lower than the rest. This indicates deviation from equilibrium. An analysis of variance (F-test) shows that the effect of the position of the glass frit is significant at a 2.5% level. The bubble residence time was observed to he close to 3 s; hence for trichloroethylene,the concentration remained virtually constant (CP/CiD= 0.996, when the gas flow rate is 500 cm3/min). The measurements are corrected for bias, resulting in a standard deviation of 0.7%, which is less than the estimated uncertainty. Similarly, using the gas flow rates of 100 and 200 cm3/ min, the upper limit was reached for cyclohexene. The standard deviation is 2.7%, just equal to the estimated uncertainty. Also here the concentration remained virtually constant (C&Cio = 0.991, when the gas flow rate is 200 crn3/min). The factorial experiments with trichloroethylene and cyclohexene indicate that an even more hydrophobic compound such as hexane may he expected to show a more pronounced deviation from equilibrium. An analysis of variance for hexane shows that the effect of the position of the glass frit is significant at a 1% level. Also the effect of the gas flow rate is significant, at a 5% level, indicating that the measurements are biased not only due to the lack of equilibrium hut also due to insufficient axial mixing and the occurrence of concentration gradients. A lower limit for the technique with respect to the magnitude of the Henry's law constant cannot he specified, hut for slightly volatile compounds, the sensitivity of the detector is the limitingfactor. Hence, the larger the vapor pressure and the lower the ionization potential of the specific compound, the more likely it is that the technique will he adequate. Time may also he considered a limiting factor since the duration of an experiment is inversely proportionaltothemagnitudeoftheHenry'slawconstmt. Mean values and 95% confidence intervals (t-test) for some experimental Henry's law constants from this work are given in Tahle 2 along with references in the literature and ratios of vapor pressure to aqueous solubility (PIS ratio). Thereportedvalues are mainlyohtainedfrom BAS and EPICS. The components are chosen in order to illustrate the application range of the method in terms of the magnitude of the Henry's law constant. A fair agreement is seen between Henry's law constants from this work and reported values. There is a tendency, however, that the reported values, especially those ohtained by EPICS, are higher. It is believed, on the basis of the experimental design used in this work ensuring unbiasedresults, that thesediscrepanciescan he attributed toalowaccuracy associated withEPICS. This issustained by a relative large variance in the results reported using EPICS.
Table 2. Experimental Henry's Law Constants and Infinite Dilution Activity Coefficients at 23 "C compound i
Hi (exp) (X103kPa)
diethyl ether diisopropyl ether benzene
4.82 f 0.11 11.6 f 0.3 27.1 f 0.2
toluene
35.6 f 0.8
trichloroethylene
44.1 f 0.3
cyclohexene
Hi (ref) (X103 kPa) 11.4 (20)b 27.7 (3)b 29.5 (5)d 48.2 28.4 (25)f 28.6 (20)b 33.5 (3)b 35.0 (5)d 39.0 33.3 (24)" 31.3 (20)b 44.3 (4)j 53.5 (5)d 47.7 (10)k 51.0 (4)' 67.8 51.9 (25)"' 49.9 (24)" 44.1 (26)o
220 f 4
PIS ratio (ref) (X103 kPa) 4.16 (27)a 11.4 (27)c 28.2 (2)s
32.8 (2)i
yi" (exp)
72.9 639 2350
10400
yi-
(UNIFAC water) 163 3980 2220
7000
4880
240 (2)p
20400
4960
a Single solubility measurement at 25 "C. By extrapolation of data from BAS at 25 "C using the multiplication factor (Pi'(23 ac)/Pis(26DC)), assumingthe infinite dilution activity coefficientbeing constant in the narrow temperature interval corrected for. Singlesolubility measurement at 20 OC. d By interpolation of data obtained from EPICS at 10, 15, 20, 25, and 30 "C, assuming a van't Hoff-type relation between Hi and temperature. e By extrapolation of data from EPICS at 20 "C using the multiplication factor (Pist23oc)/Pi720OC)), assuming the infinite dilution activity coefficient being constant in the narrow temperature interval corrected for. f By interpolation of data obtained from BAS at seven different temperatures between 1 and 27 "C, assuming a van't Hoff-type relation between Hi and temperature. 8 Average of 19 independent solubility measurements at 25 "C. A standard deviation without statistical significance of 2.3% is reported. By interpolation of data obtained from BAS at eight different temperatures between 1and 23 "C, assuming a van't Hoff-type relation between Hi and temperature. i Average of 14 independent solubility measurements at 25 "C. A standard deviation without statistical significanceof 3.8 % is reported. j By interpolation of data obtained from BAS at five different temperatures between 10 and 30 "C, assuming a van't Hoff-type relation between Hi and temperature. k By interpolation of data obtained from BAS at four different temperatures between 10 and 35 "C, assuming a van't Hoff-type relation between Hi and temperature. By interpolation of data obtained from BAS at five different temperatures between 10 and 30 "C, assuming a van't Hoff-type relation between Hi and temperature. By interpolation of data obtained from a multiple equilibrium method at six different temperatures between 10 and 30 "C, assuming a van't Hoff-type relation between Hi and temperature. n By interpolation of data obtained from BAS at 22 different temperatures between 1and 26 "C, assuming a van't Hoff-type relation between Hi and temperature. 0 From infinite dilution activity coefficient measured by inverse gas chromatography at 20 "C, assuming a constant value in the narrow temperature interval corrected for. p Average of six independent solubility measurements at 25 "C. The standard deviation without statistical significance is 33%.
Except for diethyl ether, agreement with values estimated as the PIS ratio is good. The discrepancy shows that Henry's law is not valid up to the saturation limit of diethyl ether. For trichloroethylene, no reliable solubility data were found. The quality of solubility data for chlorohydrocarbons is often poor, as seen from wide discrepancies between reported values (28). Also given in Table 2 are infinite dilution activity coefficients calculated from the experimental Henry's law constants together with predictions using UNIFAC water. For the aromatic compounds benzene and toluene, agreement is reasonably good, but further improvement may be possible. However, UNIFAC treats functional groups the same no matter which functional groups are adjacent. Hence, a revision of the interaction parameters between water and the groups constituting the benzene ring should be based on experimental infinite dilution activity coefficients for a number of different aromatic compounds. Parameters for the interaction between water and the group consisting of chlorine adjacent to a double bond are not available in the existing UNIFAC parameter tables, and thus no infinite dilution activity coefficients can be estimated for trichloroethylene. Interaction parameters should be determined based on infinite dilution activity coefficients for different unsaturated chlorinated aliphatics. Between the experimental values for the ethers and those predicted by UNIFAC water, large discrepancies are observed. Interaction parameters for the ether group have not been revised in UNIFAC water.
For the aliphatic compound cyclohexene, agreement is also poor. The method proposed here will only be of limited use in improving UNIFAC for aliphatic compounds, since equilibrium cannot be achieved for compounds having Henry's law constants larger than approximately 2 X lo5 kPa.
Conclusions An improved batch air stripping technique has been developed for the determination of Henry's law constants of volatile organic compounds in water. The experimental design confirms that the two fundamental assumptions in batch air stripping are fulfilled: (i) equilibrium between vapor and dissolved organic in the top of the stripping column; (ii) homogeneity of the liquid phase. Accurate Henry's law constants can be obtained for organiccompounds that are not extremely volatile in water. When accurate pure component vapor pressure data are available, equally accurate infinite dilution activity coefficients can be calculated as the ratio of the Henry's law constant to the pure component vapor pressure. For compounds having a Henry's law constant exceeding aproximately 2 X lo5kPa, equilibrium cannot be achieved. In order to achieve equilibrium for compounds of higher volatility in water, a taller column is required. Consequently, a lower gas flow rate or a higher recirculation rate of the content of the column is then demanded to avoid the occurrence of concentration gradients. Hence, BAS and EPICS are limited to the same upper limit. BAS, Environ. Sci. Technol., Vol. 28, No. 12, lg94
2137
however, appears t o be more accurate especially for lower Henry's law constants. Additional work is in progress t o measure Henry law constants for various organic compounds with t h e aim of using t h e corresponding infinite dilution activity coefficients as a basis for an extension and revision of t h e existing UNIFAC group-interaction parameter tables, thus making t h e model more generally applicable for t h e prediction of thermodynamic properties of aqueous systems for environmental, occupational hygiene and other purposes.
Nomenclature
A Ci fiG
fiL G
GFM Hi HiC
Ki M P
AP Pi Pi" R t
T TFM V Xi
Yi a P
Ti" 'Pi
total mass transfer area (m2) aqueous-phase solute concentration (mol m-3) gas-phase fugacity of solute (kPa) liquid-phase fugacity of solute (kPa) gas flow rate in top of column exit gas flow rate (m3 8-1) Henry's law constant on molar basis (kPa) Henry's law constant (kPa m3 mol-l) overall mass transfer coefficient (m 8-1) molecular weight of solution (g mol-1) ambient pressure (kPa) pressure drop (kPa) partial pressure of solute (kPa) pure component vapor pressure (kPa) gas constant (kPa m3 mol-' K-1) time (s) system temperature (K) gas temperature (K) liquid volume (ma) mole fraction in the liquid phase mole fraction in the vapor phase slope of regression line (8-1) density of solution (g m-3) infinite dilution activity coefficient fugacity coefficient
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