Environ. Sci. Technol. 1992, 26, 1828-1831
tional Symposium on Chlorinated Dioxins and Related Compounds, Research Triangle Park, NC, Sept 23-27,1991; Abstract PD85. (27) Konduri, R. K. N. V.; Altwicker, E. Analysis of time scales pertinent to dioxinlfuran formation on fly ash surfaces in municipal solid waste incinerators. 11th International Symposium on Chlorinated Dioxins and Related Corn-
pounds; Research Triangle Park, NC, Sept 23-27, 1991; Abstract P95. Received for review December 12, 1991. Revised manuscript received April 28, 1992. Accepted May 27, 1992. L.C.D. acknowledges the financial support of the Alexander von Humboldt Foundation, Federal Republic of Germany.
Infinite Dilution Activity Coefficients and Solubilities of Halogenated Hydrocarbons in Water at Ambient Temperatures Davld A. Wrlght, Stanley I . Sandler," and Davld DeVoll Department of Chemical Engineering, University of Delaware, Newark, Delaware 197 16
A differential static cell equilibrium apparatus is used here to measure the infinite dilution activity coefficients of C,-C, chlorinated and brominated hydrocarbons separately in water over a range of environmentally relevant temperatures. We also show that the static cell method can be used to accurately measure low aqueous solubilities of volatile solutes without compositional analysis. The estimation of the aqueous solubility limit for these highly volatile, nonideal systems from our measured infinite dilution activity coefficients is discussed. W
Introduction Solubility of pollutants and their infinite dilution activity coefficients in water are useful in waste minimization and water remediation calculations and in fate and transport studies ( I ) . Further, when combined with infinite dilution activity coefficients in the organic phase of a 1-octanol/water mixture, octanol/water partition coefficients can be calculated. For the toxic, hydrophobic chemicals studied, octanol/water partition coefficients are of particular interest in the assessment of bioaccumulation (2).
Here we report the results of direct measurements of the infinite dilution activity coefficients of C,-C, chlorinated and brominated hydrocarbons separately in water at several temperatures around ambient. The measurements were made with a differential static cell equilibrium apparatus (Figure 1). With this equipment one measures the equilibrium vapor pressure of a gravimetrically prepared mixture at fixed temperature. Although a small correction must be made to the measured data, as will be discussed later, this method of measurement is superior to dynamic techniques, such as ebulliometry, for solvents with poor boiling properties such as water or for mixtures with high relative volatility, both of which are the case here. Often, infinite dilution activity coefficients are not directly measured, but rather extrapolated from vapor/ liquid equilibrium (VLE)data throughout the composition range (see, for example, ref 3). However, since these chemicals exhibit low mutual solubilities with water (less than 1.0 w t %), neither extrapolation nor dynamic methods are plausible. Accurate composition measurement at such high dilutions is difficult. It is demonstrated here that the static cell apparatus can be used to determine the aqueous solubility limit accurately, and in the same experiment in which the infinite dilution activity coefficient is measured. In addition, we discuss the estimation of the aqueous solubility limit from our measured infinite dilution activity coefficients. 1828
Environ. Sci. Technol., Vol. 26, No. 9, 1992
Theory of the Measurements From the equilibrium relation = where fi is the fugacity of species i, Gautreaux and Coates ( 4 ) derived the equations which relate the activity coefficient at infinite dilution to isothermal total pressure-composition measurements. Their expression for low pressures and moderate temperatures is
r,
where
/3 = 2Bi, - Bii - B ,
Here
e is the vapor pressure of the solute component i,
Pwis the water vapor pressure, uk and Bii are respectively the liquid molar volume and the second virial coefficient of pure i, and Bjw is the second virial coefficient corresponding to the i-w interaction. In our measurements, we determine the change in total pressure P on a series of successive gravimetric additions of solute to water, and in this way determine (dP/d~~)~"+'. Then, with virial coefficients computed from the Hayden and O'Connell correlation (5) and published Antoine constants (6, 7), can be computed. At the conditions of our experiments, the l and 8 factors are very close to unity; thus an error of only 1-2% would result in computing ylF from
Equipment and Procedure Our static cell apparatus was designed and constructed specifically to measure the equilibrium vapor pressure of dilute, gravimetrically prepared binary mixtures at constant temperature. We use two static cells, one a reference cell containing only the pure solvent and the other containing the solvent and solute mixture, so that pressure differences can be measured directly. Further, a differential apparatus minimizes the effect of small temperature fluctuations.
0013-936X/92/0926-1828$03.00/0
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The essential features of our measurements are as follows. T w o 50-mL Pyrex cells, each containing a magnetic stirring bar, and equipped with double septa over an injection port, are cleaned, dried, and weighed. They are then filled with about 45 g of water, which has been distilled, fitered, and deionized to a resistivity of 16 Mfbcm. A third cell contains the solute. Each cell has a port fitted with a valve and a vacuum connection. The water-containing cells are each degassed by alternatively applying vacuum while both are submerged in an ultrasonic bath. A s i m i i procedure is used for moderately volatile solutes. Solutes of high volatility are degassed using freeze-evacuate-thaw cycles in liquid nitrogen. The degassed water cells are then reweighed on a Sartorius 310A balance, connected to the pressure transducer manifold, and submerged in a thermostated water bath. The system is then allowed to equilibrate, and the MKS Baratron 221 AD differentialpressure transducer is zeroed. The transducer is housed in an insulated and thermostated box,and the external valves and plumbing are also heated to prevent condensation above the cells. A Hamilton gas-tight syringe, Model 1702N or 1725N, is then used to withdraw about 10 p L of previously degassed solute from the third cell and inject it into the cell designated as the mixture cell. Each injection is made by closing the mixture cell valve and lowering the bath until the water surface is just above the cell septum. The surface tension of the water film serves as a barrier to prevent air infiltration during a solute injection. Since the syringe is weighed on a Mettler H80 balance before and after an injection, the amount of solute injected is hown. The water bath is then raised, the magnetic stirrer is turned on, and the cells are allowed to equilibrate. The stirrer is then turned off, and the differential pressure is recorded until a stable value is obtained. This injection procedure is repeated at least three times at each temperature. For solutes whose volatility is similar to that of water, the composition of the liquid phase can he determined directly from the gravimetric measurements. However, when a very volatile solute is used, a significant portion of it may vaporize into the vapor space, which is largely
in the transducer. Since direct measurement of the vapor-phase composition is not possible, a vaporization correction must be made to each of the known feed compositions. This is done as follows. At each data point k, the total number of moles vaporized, NZ, is calculated from the ideal gas law:
where APk is the differential pressure at data point k, V is the total volume (cell + tubing + transducer), and Nk is the number of moles of liquid in the cell. To compute the equilibrium vapor (y) and liquid (x) compositions, we use a balance on the solute (4) Nik = WYik + Nbik Now usingthe phase equilibrium condition in t e r n of the solute volatility, Kik
we obtain the following equation for the corrected liquidphase mole fraction of the solute )I.
zk
Nik
NIKik + Nk
Initially, 7; (and hence K J is computed from a linear fit of the differential pressure versus feed composition data. With this, corrected xik are computed, leading to a new value of 7:. This iterative procedure is repeated until the infinite dilution activity coefficient converges to within 0.01%.
Results Figure 2, for 1,2-trans-dichloroethylenein water, is typical of the data we obtain for APk versus corrected liquid-phase composition. Also shown is a linear fit of the data, i.e.
AP=a+bx (7) where b is the derivative of interest, ( ~ P / C ~ The X ~ ) ~ ~ ~ calculated infink dilution activity coefficients and limiting slopes from our measurements are given in Table I. A sample error analysis was done to determine the accuracy of our measurements. The likely error, 6, in the Environ. Scl. Technol.. VoI. 26. No. 9, 1992 182s
Table I. Measured Infinite Dilution Activity Coefficients and Limiting Slopes compound (1)
temp, "C
(dPldr1) TX4, 7;
kPa
7090 f 110 dichloromethane 10.0 235 f 5 11600 f 600 20.0 251 f 14 17100 f 500 30.0 250 f 8 17000 f 50 chloroform 20.0 818 f 20 32900 f 500 35.0 847 f 30 58100 f 750 50.0 862 f 27 carbon tetrachloride 20.0 12200 f 250 147000 f 2000 30.0 13100 f 100 244000 f 1000 40.0 13100 f 300 368000 f 6500 26500 f 200 1,l-dichloroethane 20.0 1100 f 15 55300 f 600 35.0 1240 f 20 681002t 1500 45.0 1050 f 25 5090 f 30 1,2-dichloroethane 20.0 585 f 6 10300 f 150 35.0 597 f 12 17700 f 150 50.0 559 f 6 l,l,l-trichloroethane 76600 f 900 20.0 5880 f 75 111000 f 1000 30.0 5480 f 60 164000 f 2500 40.0 5410 f 80 3730 f 10 1,1,2-trichloroethane 20.0 1520 f 10 35.0 1410 f 125 7550 f 630 13000 f 150 50.0 1220 f 20 1,1,1,2-tetrachloroethane 20.0 9280 f 730 10900 f 200 30.0 8530 f 635 17800 f 350 40.0 8830 f 645 31 100 f 700 1,1,2,2,-tetrachloroethane 20.0 3850 f 660 2240 f 235 30.0 2970 f 625 3 170 f 480 40.0 3570 f 245 6660 f 90 18400 f 100 1,2-cis-dichloroethylene 20.0 856 f 44 28800 f 200 30.0 884 f 43 41700 f 1550 40.0 866 f 65 42700 f 300 1,2-trans-dichloroethylene 20.0 1200 f 60 68800 f 600 30.0 1310 f 65 103000 f 2000 40.0 1370 f 75 trichloroethylene 20.0 5410 f 160 42000 f 200 30.0 5180 f 195 64000 f 1000 40.0 5580 f 290 106000 f 3000 12000 f 100 1,2-dichloropropane 20.0 2340 f 30 19300 f 150 30.0 2310 f 30 27600 f 300 40.0 2090 f 30 6760 f 120 1,3-dichloropropylene 20.0 1360 f 30 11000 f 200 30.0 1430 f 25 16800 900 40.0 1460 f 85 4040 f 100 20.0 869 f 45 dibromomethane 7840 f 155 35.0 801 f 35 14000 f 300 50.0 740 f 32 bromoform 20.0 3530 f 260 1890 f 125 35.0 3080 f 425 3980 f 530 50.0 4050 f 220 11500 f 550
*
vapor pressure of water using the Antoine coefficients reported by Ohe (6) is 0.00267 kPa, while the average absolute deviations for the halogenated hydrocarbons taken from Stephenson and Malanowski (7) are reported as 0.02-1.0 K, depending on the compound. These temperature deviations were converted into pressure deviations at the experimental temperature through the Antoine equation. The error in the limiting slope was taken to be the standard deviation in the least-squares regression. Combining these we obtained y; f sy;
=
,
. .
and an average error of 4.2%, though this varied from compound to compound, depending on the accuracy of the vapor pressure data. The error bounds to each of our measured values are given in Table I. Though our measurements were used to determine the infinite dilution activity coefficient of a substance in water, 1830 Environ. Sci. Technol., Vol. 26, No. 9, 1992
2
B
a-
U
1
0
O.Oo0
0.020
0.040
0.060
0.080
0.100
solubility, mol%
Flgure 3. Direct experimental determination of the aqueous solubility ilmit of 1,1,2,2-tetrachloroethane at 40 O C .
it is also possible to use our equipment to determine its aqueous solubility limit. This is done by noting that if the solubility limit of a component in water is exceeded, two liquid phases form, and as long as there is some vapor space, the total pressure in the cell remains constant on further solute additions. This is shown in Figure 3, where the first three solute injections remain below the solubility limit, so that the differential pressure increases with each injection while the solubility limit has been exceeded on subsequent injections, and a limiting pressure difference is achieved. From the intersection of the corrected (dP/ dxi)TZz-O line with the limiting pressure line, we compute that the saturation solubility of 1,1,2,2-tetrachloroethane in water a t 40 O C is 0.0308 mol %, which compares favorably with the value of 0.0321 mol % reported by Horvath (8)based on a regression of all available data. The advantages of the static cell method of determining solubilities are that no chemical analysis is involved and that the method is quick. Further, the infinite dilution activity coefficient and the aqueous solubility can be measured in the same experiment. It should also be noted that reasonable estimates of aqueous solubilities can be obtained directly from our measured infinite dilution activity coefficienta. Assuming that the solubility of water in the organic solute is negligible, which is reasonable for the systems under consideration, we have at saturation x ? yi(xf) = 1
(9)
where x i is the saturation mole fraction of the organic in water. Further, assuming that at high dilutions the composition dependence of the activity coefficient follows a two-suffix Margules relation, we have yi(xf) = exp[Ai(l - X P ) ~ ] = exp[ln r;(l
- x ? ) ~ ](10)
since 7; = exp[Ai]. Combining eqs 9 and 10 gives
which can be solved by iteration. It should be noted that if y l > 1000, eq 10 reduces to (9) yi"
N
l/x?
(12)
Values of x f computed from eqs 10 and 11 are presented in Table I1 for all components, together with recommended solubility values which have been reported (10) for some
Table 11. Aqueous Solubilities (mol %) of Halogenated Hydrocarbons Calculated Using eqs 9 and 12, Together with Recommended Values by Sarenson and Arlt ( l 0 ) O compound (1) dichloromethane chloroform carbon tetrachloride 1,l-dichloroethane 1,2-dichloroethane l,l,l-trichloroethane 1,1,2-trichloroethane
1,1,1,2-tetrachloroethane
1,1,2,2,-tetrachloroethane 1,2-cis-dichloroethylene 1,2-trans-dichloroethylene trichloroethylene 1,2-dichloropropane 1,3-dichloropropylene dibromomethane bromoform
add, %
temp,
O C
10.0 20.0 30.0 20.0 35.0 50.0 20.0 30.0 40.0 20.0 35.0 45.0 20.0 35.0 50.0 20.0 30.0 40.0 20.0 35.0 50.0 20.0 30.0 40.0 20.0 30.0 40.0 20.0 30.0 40.0 20.0 30.0 40.0 20.0 30.0 40.0 20.0 30.0 40.0 20.0 30.0 40.0 20.0 35.0 50.0 20.0 35.0 50.0
lit.
eq 12
eq 11
0.423 0.417 0.416 0.123
0.426 0.398 0.400 0.122 0.118 0.116 0.00820 0.00763 0.00763 0.0909 0.0806 0.0952 0.171 0.168 0.179 0.0170 0.0182 0.0185 0.0658 0.0709 0.0820 0.0108 0.0117 0.0113 0.0260 0.0337 0.0280 0.117 0.113 0.115 0.0833 0.0763 0.0730 0.0185 0.0193 0.0179 0.0427 0.0433 0.0478 0.0735 0.0699 0.0685 0.115 0.125 0.135 0.0283 0.0325 0.0247
0.447 0.417 0.419 0.124 0.120 0.118 0.00821 0.00764 0.00764 0.0909 0.0816 0.0965 0.175 0.171 0.183 0.0171 0.0183 0.0185 0.0664 0.0716 0.0829 0.0108 0.0117 0.0113 0.0261 0.0339 0.0281 0.119 0.115 0.117 0.0843 0.0772 0.0738 0.0185 0.0194 0.0178 0.0430 0.0436 0.0482 0.0743 0.0706 0.0692 0.117 0.127 0.138 0.0285 0.0326 0.0248
6.8
7.2
0.113 0.0091 0.0096 0.0944 0.157 0.191 0.0178 0.0171 0.0589 0.0117 0.0121 0.0309 0.0323
aAverage absolute deviations (AAD) on eqs 11 and 12 are also reported.
of the compounds at the temperatures of our experiments There we see that the calculated and recommended values agree nearly within typical experimental errors (11). However, it should be pointed out that a limitation of the
static cell method of solubility measurement is that it can only be used with volatile solutes.
Conclusion We have described here a differential static cell equilibrium apparatus designed for the accurate measurement of infinite dilution activity coefficients. This equipment was used to measure yf of several C1-CBchlorinated and brominated hydrocarbons separately in water over a range of environmentally relevant temperatures. Further, we have demonstrated that this equipment is also useful in the accurate measurement of the low aqueous solubility limits of these chemicals without a compositional analysis. Finally, we have discussed how reasonable estimates of the aqueous solubilities can be obtained from our measured infinite dilution activity coefficients. Registry No. ClzCH2,75-09-2;C13CH,67-66-3; Cl&, 56-23-5; C12CHCH3, 75-34-3; ClCH2CHZC1, 107-06-2; ClSCCH3, 71-55-6; ClZCHCH&1,79-00-5; C13CCHgCl,630-20-6; C12CHCHClZ,79-34-5; (Z)-ClCH=CHCl, 156-59-2; (E)-ClCH=CHCl, 156-60-5; C1&= CHC1, 79-01-6; ClCHZCHClCHs, 78-87-5; ClCH=CHCH,Cl, 542-75-6; Br2CHz,74-95-3; Br3CH, 75-25-2.
Literature Cited (1) Arbuckle, W. B. Environ. Sci. Technol. 1983,17,537-542. (2) Mackay, D. Environ. Sci. Technol. 1982, 16, 274-278. (3) Gmehling, J.; Onken, U. Vapol-Liquid Equilibrium Data Collection; Dechema Chemistry Data Series; Dechema: Frankfurt, 1977; Vol. I, Parts 1-8. [See all data correlations in these volumes, for example.] (4) Gautreaux, M. F.; Coates, J. AZChE J. 1955, 1, 496-500. (5) Hayden, J. G.; O’Connell, J. P. Znd. Eng. Chem. Process Des. Dev. 1975, 14, 209-216. (6) Ohe, S. Computer Aided Data4Book of Vapor Pressure, 1st ed.; Data Book Tokyo, 1976; pp 83,97,104,106,177,193, 194, 197, 198, 208, 209, 226, 227, 331. (7) Stephenson, R. M.; Malanowski, S. Handbook of Thermodynamics of Organic Compounds; Elsevier: New York, 1987; pp 10, 70. (8) Horvath, A. L. Halogenated Hydrocarbons: SolubilityMiscibility with Water; Marcel-Dekker: New York, 1982. (9) Lyman, W. J.; Reehl, W. F.; Rosenblatt, D. H. Handbook of Chemical Property Estimation Methods; McGraw-Hill: New York, 1982; Chapter 3. (10) Smensen, J. M.; Arlt, W. Liquid-Liquid Equilibrium Data Collection: Binary Systems; Dechema Chemistry Data Series; Dechema: Frankfurt, 1979; Vol. V, Part 1. (11) McNally, M. E.; Grob, R. L. J. Chromatogr. 1984, 284, 105-116.
Received for review January 22, 1992. Revised manuscript received May 14,1992. Accepted May 28,1992. This research was supported by the National Science Foundation Grant CBT8612285 to the University of Delaware.
Environ. Sci. Technol., Vol. 26,
No. 9, 1992 1891
