J. Phys. Chem. B 1999, 103, 7319-7323
7319
Measurement and Modeling of the Water-R143A Partition Coefficients of Organic Solutes Using a Linear Solvation Energy Relationship Anthony F. Lagalante,* Adam M. Clarke, and Thomas J. Bruno National Institute of Standards and Technology, Physical and Chemical Properties DiVision 838.00, 325 Broadway, Boulder, Colorado 80303 ReceiVed: April 19, 1999; In Final Form: June 25, 1999
The water-R143a partition coefficients for a set of thirteen organic solutes have been measured using highpressure spectroscopy. Water partition coefficients of the organic solutes were measured in the gas and supercritical phases of 1,1,1-trifluoroethane (R143a). A linear solvation energy relationship (LSER) was developed to predict the measured water-R143a partition coefficients using the Abraham descriptors of the solute and an additional solvent descriptor as independent variables. Considering the entire water-R143a partition coefficient data, the LSER model has an average absolute relative deviation of 49.5%. Considering only the data above the critical density of R143a, the LSER has an average absolute relative deviation of 40.7%.
Introduction A number of papers have reported the predictive capability of a linear solvation energy relationship (LSER) as applied to partitioning between water and an immiscible, or partially miscible, organic solvent.1-6 Methods for the reliable prediction of water-solvent partition coefficients are especially important in pharmaceutical research and wastewater cleanup. With the production phase-out of chlorinated solvents, as mandated by the Montreal Protocol, interest in alternative solvent technology has grown significantly. In many industrial applications, supercritical fluids are being evaluated as replacements for chlorinated solvents and the need for a systematic approach to replacement is great. At present, LSERs have been used to predict solidfluid enhancement factors for supercritical CO2 systems7 and retention factors in supercritical fluid chromatography.8 Recently, we reported a model for a published set of watersupercritical CO2 partition coefficients for six organic solutes using an LSER.9 The data set used in the LSER model was limited to only six solutes, and therefore a follow-up study, that included a more extensive set of water-supercritical fluid partition coefficients, was conducted in our laboratory. In the follow-up study, the partitioning of eleven organic solutes from water into 1,1,1,2-tetrafluoroethane (R134a) was measured and predicted using an LSER with an average deviation of 17% for the data above the critical density of R134a.10 The success of this follow-up study has led us to measure the partitioning of thirteen organic solutes from water into 1,1,1-trifluoroethane (R143a) reported herein. The critical temperature (73.1 °C) of R143a is significantly higher than that of CO2 (31.1 °C), yet lower than that of R134a (101.1 °C). Higher temperatures, though not a serious disadvantage from an economic perspective, may be damaging in the case of biological or pharmaceutical separations. The critical pressure of R143a (3.76 MPa), however, is significantly lower than that of CO2 (7.38 MPa). Clearly, from an industrial perspective, it is the elevated pressure of supercritical CO2 that requires the design of expensive containment vessels with the appropriate safety features, which can lead to * Author to whom correspondence should be addressed. Fax: 303-4975224. E-mail:
[email protected].
10.1021/jp991264e
a prohibitively expensive separation process. In contrast to CO2, perhaps the most important feature of many of the fluorinated ethanes is that they possess a permanent dipole moment. R143a has a dipole moment of 2.32 D which is advantageous for dissolving polar solutes.11 R143a has the highest dipole moment of all the fluorinated ethanes because it possesses the most highly asymmetrical arrangement of fluorine and hydrogen atoms. The physical properties of fluorocarbon-based solvents suggest that they are better supercritical fluid solvents than CO2 from strictly solubility parameter-based arguments.12 Experimentally, the addition of fluorinated surfactants to CO2 has dramatically enhanced the extraction of polar solutes,13,14 yet reports of fluorinated ethanes as stand-alone supercritical fluids are scarce. We intend to illustrate that the use of an LSER as a predictive model in supercritical solvents can be beneficial in the selection of the proper fluorinated solvent and the conditions for a particular application. We further hope that this approach may be beneficial in the comparison of fluorinated solvents with CO2 in calculating the economics of a separation process. LSER Approach. As shown by Abraham,5 water-solvent partition coefficients K are reliably modeled using five solute descriptors: the excess index of refraction R2, the dipolarity/ polarizability πH2 , the effective hydrogen bond acidity RH2 , the effective hydrogen bond basicity βH2 , and McGowen’s15 intrinsic volume VX. The general form of the LSER is
log10 K ) C1 + C2R2 + C3πH2 + C4RH2 + C5βH2 + C6VX (1) where the Cis are the coefficients of the linear regression. The partition coefficients in this study are defined as the ratio of the concentration (mol L-1) of the solute in the organic phase to the concentration (mol L-1) of the solute in the aqueous phase. These coefficients represent vector quantities, each having a magnitude and direction in relationship to the equilibrium property of the system that is being modeled. In modeling partition coefficients between water and conventional organic solvents, the solvent descriptors are not generally included in the LSER equation. Rather, a separate LSER is generated for each organic solvent considered. This approach is valid for modeling partition coefficients in these solvents because the partitioning is commonly measured at
This article not subject to U.S. Copyright. Published 1999 by the American Chemical Society Published on Web 08/07/1999
7320 J. Phys. Chem. B, Vol. 103, No. 34, 1999
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TABLE 1: Measured Partition Coefficients of the Organic Solutes p F143a T (°C) (MPa) (mol L-1)
log K143a
p F143a T (°C) (MPa) (mol L-1)
log K143a
p F143a T (°C) (MPa) (mol L-1)
log K143a
p F143a T (°C) (MPa) (mol L-1)
log K143a
79.7 79.9 79.6 79.4 79.5
3.24 3.95 4.13 4.26 4.44
1.74 2.79 3.39 4.34 5.95
Benzene -0.02 79.6 0.25 79.5 0.42 79.6 0.55 79.6 0.68 79.4
4.64 5.52 6.86 13.63 20.19
6.72 7.92 8.61 9.98 10.64
0.83 0.93 1.40 1.58 1.80
79.5 80 78.9 79.9 79.2
3.68 4.20 4.53 5.04 5.46
2.30 3.65 6.67 7.39 7.92
4-Methyl-2-pentanone 0.51 81.9 6.53 0.80 79.7 10.38 0.87 80.7 13.99 0.92 80.3 20.34 0.95
8.26 9.49 9.98 10.62
0.99 1.08 1.11 1.13
81.8 81.2 79.3 79.9 81.9 82.1 82.1 82.4
1.22 2.24 2.77 3.38 3.82 4.11 4.23 4.68
0.47 0.97 1.34 1.88 2.39 2.93 3.29 5.69
Benzoic Acid -2.58 81.9 -2.28 81.3 -2.11 81.9 -1.88 80.9 -1.62 83.4 -1.17 84.6 -1.10 83.3 -1.06 82.9
5.08 5.79 6.52 8.65 11.53 14.55 17.95 21.39
7.04 7.88 8.25 9.06 9.50 9.88 10.31 10.62
-1.01 -0.97 -0.95 -0.92 -0.86 -0.84 -0.82 -0.78
79.5 79.4 80.4 81.8 81.5 80.9
3.10 3.79 4.14 4.31 4.58 4.99
1.61 2.49 3.27 3.69 5.62 7.11
4-Nitroaniline -1.45 79.5 5.68 -1.44 79.9 6.93 -1.32 81.5 10.43 -1.14 81.7 14.56 -1.04 81.3 21.43 -0.98
8.03 8.61 9.40 10.01 10.67
-0.90 -0.82 -0.68 -0.60 -0.51
80.7 81.9 82.8 79 81.1 81.2
2.03 2.78 3.76 4.08 4.37 4.56
0.86 1.32 2.25 3.34 4.29 5.66
2-Nitrophenol -0.98 80.6 5.08 -0.93 81.3 5.74 -0.58 81 8.13 0.26 80.4 13.09 0.54 80.7 20.12 0.59
7.32 7.85 8.91 9.88 10.59
0.65 0.67 0.73 0.80 0.90
80.3 80 82.4 79.4 81.2 81
4.11 4.44 4.60 5.01 5.33 5.86
3.19 5.62 5.26 7.45 7.51 7.97
4-Nitrophenol -1.01 80.7 6.14 -1.00 81.4 6.68 -0.99 81.5 8.36 -0.98 81.9 14.54 -0.97 81.2 17.27 -0.96 81.9 21.08
8.17 8.37 8.94 10.00 10.32 10.63
-0.94 -0.93 -0.90 -0.83 -0.80 -0.78
81 80.2 81.6 81 81.2 80.8 81.9
3.49 3.80 4.19 4.21 4.66 5.11 5.69
1.98 2.45 3.26 3.42 6.16 7.31 7.73
Phenol -1.50 80.7 -1.46 81.6 -1.08 81.5 -1.00 83.8 -0.95 82.4 -0.90 81.6 -0.87
6.73 8.29 10.48 14.40 16.77 20.35
8.46 8.92 9.41 9.90 10.22 10.58
-0.83 -0.80 -0.75 -0.71 -0.68 -0.68
79.7 81.4 81.7 81.7 82.1 80.4
1.60 2.52 3.50 4.18 4.46 4.60
0.64 1.14 1.97 3.19 4.43 6.28
4-tert-Butylphenol -1.28 80.6 5.11 -1.27 80.4 5.95 -0.99 80.6 7.93 0.27 81 14.54 0.33 80.3 21.40 0.37
7.35 8.10 8.88 10.03 10.70
0.44 0.49 0.58 0.69 0.79
84.7 79.7 79.9 79.9 79.9 79.9 79.9 79.9
0.35 1.26 3.17 3.77 4.13 4.60 5.24 6.01
0.12 0.49 1.67 2.42 3.32 6.48 7.63 8.19
Benzyl Alcohol -2.30 80 -2.18 79.9 -2.12 80 -1.75 79.7 -1.21 80 -1.00 81.5 -0.86 80 -0.77
83.6 82.7 81.2 81.8 83.7 80.8
4.05 4.19 4.27 4.43 4.69 5.13
2.67 3.07 3.65 4.39 5.14 7.33
Caffeine -1.49 82.2 -1.48 82.7 -1.45 82.6 -1.43 83 -1.40 83.8 -1.39 83.7
82.7 81.1 80.1 78.1 81.5
4.06 4.28 4.63 5.06 5.71
2.76 3.72 6.52 7.73 7.80
6.70 7.50 8.20 11.40 14.48 18.13 21.10
8.51 8.80 9.00 9.66 10.07 10.39 10.69
-0.75 -0.72 -0.69 -0.64 -0.61 -0.58 -0.55
5.53 6.06 6.73 9.68 14.76 20.62
7.54 7.90 8.28 9.17 9.94 10.53
-1.38 -1.38 -1.38 -1.36 -1.34 -1.32
4-Chloroaniline -0.12 78 6.24 0.02 80.2 7.88 0.10 80.2 11.44 0.12 80 15.72 0.18 81.1 21.62
8.49 8.90 9.65 10.21 10.69
0.19 0.27 0.33 0.37 0.42
83.9 83.1 82.9 82.7 82.9
3.99 4.20 4.55 4.84 5.42
2.55 3.06 4.65 6.23 7.31
Cyclohexanone -0.05 82.8 6.54 0.02 83.1 10.14 0.07 83.1 15.34 0.10 83.3 20.42 0.14
78.5 82.5 83.4 85.4 85.1 85.2
1.37 2.21 3.31 3.73 4.15 4.44
0.54 0.95 1.73 2.12 2.76 3.44
2-Hexanone -1.17 84.9 -0.88 85.2 -0.46 85.3 -0.13 85.3 0.41 85.3 0.52
4.80 5.63 6.91 13.03 20.64
8.17 9.26 10.04 10.53
0.18 0.23 0.29 0.34
5.16 7.17 8.12 9.65 10.48
0.58 0.64 0.70 0.75 0.80
ambient temperature and pressure. At ambient temperature and pressure the solvent descriptors are constant and therefore will be accounted for in the LSER constant term. Supercritical fluids, however, have a tunable solvent strength as evidenced by the density-dependent dipolarity/polarizability of the solvent π1.16-20 Therefore, any derived LSER approach for supercritical fluids will probably require additional density-dependent solvent terms. In a recent paper, we reported measurements of π1 for six fluorinated ethanes including R143a.20 The π1 values for R143a can be fitted to a cubic polynomial in R143a density given by
π1 ) -1.054 + 0.3905FR143a - 0.05178F2R143a + 0.002395F3R143a (2) where FR143a, expressed in mol L-1, is the density of the pure solvent calculated using an extended corresponding states
method with R134a as a reference fluid.21 Equation 2 was determined at temperatures of 50, 75, and 90 °C, and π1 was found to be insensitive to temperature over the density range investigated (0 to 12 mol L-1). The π1 values sharply inflect at the critical density of R143a (5.16 mol L-1) and extrapolate to the gas-phase value of the solvatochromic probe. Experimental Section Chemicals. R143a (99.9% purity), benzene (99% purity), benzoic acid (99% purity), benzyl alcohol (99% purity), caffeine (99% purity), 4-chloroaniline (98% purity), cyclohexanone (99.9% purity), 2-hexanone (98% purity), 4-methyl-2-pentanone (99.5% purity), 4-nitroaniline (99% purity), 2-nitrophenol (98% purity), 4-nitrophenol (98% purity), phenol (98% purity), and 4-tert-butyl phenol (99% purity) were obtained from commercial
Partition Coefficients of Organic Solutes suppliers and were used as received. Water was distilled and deionized prior to use. Partition Coefficient Measurement. The water-R143a partition coefficients of the solutes were measured using a highpressure spectroscopic cell. Details of the spectroscopic cell design and the experimental partition coefficient measurements were previously reported,10 and therefore only modifications to the experimental procedure for this work will be described. Solutions of known concentration (ranging from 10-3 to 10-5 mol L-1) of the organic solute in distilled water were volumetrically pipetted into the bottom of the spectroscopic cell. Solute concentrations were chosen to give absorbance values at peak maxima of approximately 0.7 and were therefore dependent on the molar extinction coefficient of the solute. An initial absorbance spectrum was measured using a UV-vis photodiode array spectrophotometer that had a resolution of 2 nm. The cell was quickly flushed with gaseous R143a (to displace air above the solution) and heated to 80 °C. The fluid was mixed with an integral poly(tetrafluoroethylene)-coated stirring bar. When the temperature had stabilized, the cell was pressurized with R143a using a syringe pump. The temperature was measured both by a platinum resistance thermometer (PRT) in the stainless steel cell wall (nominally 80 ( 0.2 °C during all experiments) and an internal J-type thermocouple in direct contact with the fluid. The thermocouple showed considerable deviations (approximately (2 °C) from the 80 °C setpoint measured by the PRT. The temperature reading from the internal thermocouple, rather than the PRT temperature, was regarded as a more reliable indicator of the system temperature because the thermocouple was in direct thermal contact with the internal contents of the cell. Pressure within the cell was measured by a resonating quartz crystal transducer that had a range of 0-68 MPa and an uncertainty of (0.1%. Radiation from the spectrophotometer was passed only through the aqueous phase to ascertain when an equilibrium partitioning had been achieved. When a constant absorbance was obtained, the absorbance was recorded (at the UV-peak maximum), as well as the pressure and temperature of the system. The pressure in the cell was then increased to obtain representative intervals of the R143a density over an isotherm. Results Partition Coefficient Data. Equilibrium within the cell was typically reached within 20 min, although for some of the solutions it was necessary to wait up to 1.5 h between data points. The molar absorbtivity of the organic solute was calculated from the Beer-Lambert law using the measured absorbance value at the UV peak maximum and the known molarity of the aqueous solution. For every solute studied, the wavelength maximum of the UV-peak remained constant from the initial absorbance reading at the lowest pressure to the highest pressure studied. The number of moles of solute that were transferred into the R143a phase was calculated from the decrease in absorption of the UV-peak, and by using the internal cell volume, the concentration in mol L-1 of the organic solute in R143a phase was calculated. The partition coefficient was determined by calculating the ratio of the molar concentration of organic solute in the R143a phase to the molar concentration of the organic solute in the aqueous phase. Table 1 lists the experimentally determined log10 KR143a values for the 13 solutes studied and the temperature, pressure, and density of pure R143a at each measurement. The average relative standard uncertainty in each water-R143a partition coefficient measurement was 2% based on 3 replicate measurements of of a single partition coefficient isotherm.
J. Phys. Chem. B, Vol. 103, No. 34, 1999 7321 TABLE 2: Solute Descriptors Used in the LSER Model solute
R2
πH2
RH2
βH2
VX
benzene benzoic acid benzyl alcohol caffeine 4-chloroaniline cyclohexanone 2-hexanone 4-methyl-2-pentanone 4-nitroaniline 2-nitrophenol 4-nitrophenol phenol 4-tert-butyl phenol
0.610 0.730 0.803 1.500 1.060 0.403 0.136 0.111 1.220 1.015 1.070 0.805 0.810
0.52 0.90 0.87 1.60 1.13 0.86 0.68 0.65 1.91 1.05 1.72 0.89 0.89
0.00 0.59 0.33 0.00 0.30 0.00 0.00 0.00 0.42 0.05 0.82 0.60 0.56
0.14 0.40 0.56 1.35 0.31 0.56 0.51 0.51 0.38 0.37 0.26 0.30 0.41
0.716 0.932 0.916 1.363 0.939 0.861 0.970 0.970 0.991 0.949 0.949 0.775 1.339
LSER Modeling. Table 2 lists the solute descriptors that were used as the independent variables in the water-R143a partition coefficient LSER.5,7 Although the reported solute descriptors were measured at 25 °C, we have assumed that the values, relative to each other, remain constant up to 80 °C. Additionally, the dipolarity/polarizability descriptor of R143a, calculated using eq 2, was used in the LSER. Using these five solute descriptors and one solvent descriptor, the resultant LSER is
log10 KR143a ) -0.4741R2 - 0.1734πH2 - 2.481RH2 2.855βH2 + 2.597VX + 2.037π1 (3) n ) 150, r ) 0.966, ksd ) 0.477, %ARRD ) 49.5%. The percentage average absolute relative deviation (%AARD) in predicting the measured KR143a values, the correlation coefficient of the regression r, and the standard deviation sd of the LSER equation multiplied by a coverage factor,22 k ) 2, are also reported. Figure 1 illustrates the correlation between the predicted and measured values of the water-R143a partition coefficient. Equilibrium data below the critical point of a solvent are not of great practical interest since the solubility enhancement in supercritical fluid solvents occurs near or at the critical point of the solvent. Considering only the portion of the partition coefficient data above the critical density of R143a (5.16 mol L-1), the LSER in eq 3 can be reevaluated to give
log10 KR143a ) -0.4459R2 - 0.2074πH2 - 2.575RH2 3.145βH2 + 2.763VX + 1.885π1 (4) n ) 96, r ) 0.974, ksd ) 0.380, %ARRD ) 40.7%. Discussion Figure 2 depicts a comparison of the measured water-R143a, water-134a, and water-supercritical CO2 partition coefficients of phenol. The water-supercritical CO2 partition coefficients23 were reported in mole fractions and have been converted to mol L-1 for this comparison plot. Figure 2 shows that, at the temperatures studied, partitioning into R134a is favored (at a given density) over R143a, despite the higher dipole moment of R143a. In comparing our data from the two fluorinated ethane studies, we found that the solutes studied all had higher partition coefficients in the water-134a system than in the water-143a system. Partitioning into both R134a and R143a is favored over CO2 indicating that the fluorinated ethanes-based solvents possess better solvating ability than CO2 at a given solvent density.
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Figure 1. Comparison of the measured water-R143a partition coefficients and those predicted by the LSER of eq 3.
Figure 2. Comparison of the measured water-R143a, water-134a, and water-supercritical CO2 partition coefficients of phenol.
In contrast to our previously reported water-supercritical CO2 and water-R134a LSERs, the water-R143a LSER developed in this study provides a somewhat poorer predictive capability. However, the LSER approach is predicting phase equilibria for 13 different systems and potentially could be applied to many other systems whose solute descriptors are known. This is in contrast to a typical equation-of-state (EOS) approach using empirical interaction terms. EOS modeling for supercritical fluids relies on physical constants of the solute that are often difficult to obtain experimentally, such as vapor pressure, critical constants, and acentric factors. If data are available or can be estimated, adjustable interaction terms are included to fit the experimental data to the EOS. These interaction terms are empirical and to date cannot be estimated from any thermophysical constant of the solute. Using both attractive (k12) and repulsive (l12) interaction terms in the EOS model, %AARD values on the order of 10-20% are obtainable.24 However, separate k12 and l12 values must be calculated for each solute
for each isotherm. In the LSER models of our previous studies, we calculated a set of six empirical coefficients that describe the phase equilibria of many different systems. Though we have measured the phase equilibria for the R134a and R143a systems only at one temperature, the LSER of the water-supercritical CO2 partitioning data set was able to model data at three temperatures above the critical point of CO2.9 This is due to the inclusion of a temperature-independent, density-dependent π1 term that takes into account the changing dipolarity/ polarizability of the solvent over a wide range of pressures and temperatures. Next, we compared the LSER developed in this study and the LSER developed in the water-R134a study.10 The solutes were largely the same in the two studies (in the water-143a study we have also included benzene and 4-nitrophenol because of their lower βH2 values), and R134a differs only by the replacement of an H atom with an F atom on the CH3 group of R143a. In both studies, the best fits to the experimental data gave LSERs of the same functional form. Comparison of the coefficients of both eqs 3 and 4 are provided in Table 3, and it is readily apparent that the coefficients are not only of the same sign but also one of the same order of magnitude. This suggests that the solutes behave similarly in their partitioning between water and each of the fluorinated ethanes at a given density. In fact, the density dependent π1 curves of the two solvents are almost coincidental, which suggests that the two solvents would behave similarly in a strongly π1 dependent process. However, the data for CO2, R134a, and R143a cannot be combined into one data set and successfully modeled using an LSER. Again, in the LSER of eq 3 we find the use of a separate term to account for the tunable dipolarity/polarizability of the solvent yields a better predictive ability than using a solvent-solute cross term, such as πH2 π1. The coefficients of eqs 3 and 4 indicate that the three largest factors governing water-R143a partitioning are RH2 and βH2 , which favor water, and VX, which favors R143a. The negative coefficient on the βH2 term reflects the differences between the hydrogen-bond acidity of water and R143a. R143a is believed to have no hydrogen-bond basicity, and therefore, the RH2 and βH2 coefficients should be similar to those in other systems where the organic solvent phase has no hydrogen-bond acceptor or donor ability. The RH2 coefficients of water-alkane and water-cyclohexane systems are approximately -3.6,5 while the RH2 coefficient of water-R143a is -2.6. Similarly, the βH2 coefficient of water-alkane and water-cyclohexane systems is approximately -4.9, while the βH2 coefficient of waterR143a is -3.1. One rationalization for the coefficients in the water-R143a system being more positive than the water-alkane and water-cyclohexane systems may be due to temperature. It is known that the RH2 and βH2 coefficients in gas-solvent partitioning diminish with increasing temperature, which may explain the decreased coefficient values in the water-R143a system at 80 °C.25
TABLE 3: Comparison of the LSER Coefficients for Water-R134a and Water-R143a Partioning with Standard Erros of the LSER Coefficients variable
water-R134a eq 3
water-R143a eq 3
water-R134a eq 4
water-R143a eq 4
R2 πH2 RH2 βH2 V2 π1
-0.4778 ( 0.0962 -0.3164 0.0949 -2.512 ( 0.1203 -2.587 ( 0.1273 2.778 ( 0.1005 1.841 ( 0.0962
-0.4741 ( 0.0902 -0.1734 ( 0.0804 -2.481 ( 0.0944 -2.855 ( 0.1087 2.597 ( 0.0837 2.037 ( 0.0813
-0.4078 ( 0.0865 -0.3742 ( 0.0817 -2.593 ( 0.0993 -2.777 ( 0.1065 2.884 ( 0.0827 1.955 ( 0.1407
-0.4459 ( 0.0929 -0.2074 ( 0.0797 -2.575 ( 0.0960 -3.145 ( 0.1120 2.763 ( 0.0845 1.855 ( 0.3396
Partition Coefficients of Organic Solutes The magnitude of the πH2 coefficient in the LSER for R134a is nearly double the value of the term in the LSER for R143a. Presumably, this is a reflection of the higher dipole moment of R143a, which permits πH2 to favor the R143a phase to a greater extent. The magnitude of the πH2 coefficient is considerably less than the value in the water-alkane partition LSER developed by Abraham.5 This is complicated because the π1 term of R143a has values far below and above the dipolarity/ polarizability of alkane solvents depending on its density. It is not surprising that the coefficient of π1 in the water-R143a LSER is large and positive, because the increase in density (directly related to polarizability), usually results in increased solvent strength. The VX coefficient is less than the corresponding value of the VX coefficient for water-alkane partitioning, implying that the cohesive energy density of R143a is higher than that of alkane solvents. This is again a complex term because the cohesive energy density of R143a is a function of the density of the fluid. The same solute descriptors that have been used to measure water partition coefficients at ambient conditions can thus be used to model the water partition coefficients at conditions above the critical temperature and pressure of the solvent. The success of this model suggests that other types of equilibrium processes in supercritical fluids may be reliably modeled using an LSER and that the nonidealities of the supercritical fluid state may be better described using empirical solvent descriptors instead of EOS modeling. Acknowledgment. A.F.L. acknowledges the Professional Research Experience Program at the National Institute of Standards and Technology. References and Notes (1) Meyer, P.; Maurer, G. Ind. Eng. Chem. Res. 1993, 32, 2105. (2) Meyer, P.; Maurer, G. Ind. Eng. Chem. Res. 1995, 34, 373.
J. Phys. Chem. B, Vol. 103, No. 34, 1999 7323 (3) Kamlet, M. J.; Doherty, R. M.; Abraham, M. H.; Marcus, Y.; Taft, R. W. J. Phys. Chem. 1988, 92, 5244. (4) Kamlet, M. J.; Doherty, R. M.; Carr, P. W.; Mackay, D.; Abraham, M. H.; Taft, R. W. EnViron. Sci. Technol. 1988, 22, 503. (5) Abraham, M. H.; Chadha, H. S.; Whiting, G. S.; Mitchell, R. C. J. Pharm. Sci. 1994, 83, 1085. (6) Kamlet, M. J.; Doherty, R. M.; Abboud, J. M.; Abraham, M. H.; Taft, R. W. Chemtech 1986, 16, 566. (7) Bush, D.; Eckert, C. A. In Supercritical Fluid Extraction; Abraham, M., Sunol, A. Eds.; ACS Symposium Series 670; American Chemical Society: Washington, DC, 1997; p 37. (8) Weckwerth, J. D.; Carr, P. W. Anal. Chem. 1998, 70, 1404. (9) Lagalante, A. F.; Bruno, T. J. J. Phys. Chem., B 1998, 102, 907. (10) Lagalante, A. F.; Clarke, A. M.; Bruno, T. J. J. Phys. Chem. B 1998, 102, 8889. (11) Bruno, T. J. Handbook for the Analysis and Identification of AlternatiVe Refrigerants; CRC Press: Boca Raton, FL, 1995. (12) Roth, M. Anal. Chem. 1996, 68, 4474. (13) Dardin, A.; DeSimone, J. M.; Samulski, E. T. J. Phys. Chem., B 1998, 102, 1775. (14) Zhibin, G.; DeSimone, J. M. Macromolecules 1994, 27, 5527. (15) Abraham, M. H.; McGowan, J. C. Chromatographia 1987, 23, 243. (16) Sigman, M. E.; Lindley, S. M.; Leffler, J. E. J. Am. Chem. Soc. 1985, 107, 1471. (17) Smith, R. D.; Frye, S. L.; Yonker, C. R.; Gale, R. W. J. Phys. Chem. 1987, 91, 3059. (18) Yonker, C. R.; Smith, R. D. J. Phys. Chem. 1988, 92, 235. (19) Engel, T. M.; Olesik, S. V. Anal. Chem. 1991, 63, 1830. (20) Lagalante, A. F.; Hall, R. L.; Bruno, T. J. J. Phys. Chem., B 1998, 102, 6601. (21) Huber, M. L.; Ely, J. F. Int. J. Refrig. 1994, 17, 18. (22) Taylor, B. N.; Kuyatt, C. E. Guidelines for eValuating and expressing the uncertainty of NIST measurement results. Technical. Note 1297; National Institute of Standards and Technology, U.S. Department of Commerce: Washington, DC, 1994. (23) Brudi, K.; Dahmen, N.; Schmieder, H. J. Supercrit. Fluids 1996, 9, 146. (24) Caballero, A. C.; Herna´ndez, L. N.; Este´vez, L. A. J. Supercrit. Fluids 1992, 5, 283. (25) Abraham, M. H.; Andonian-Haftvan, J.; Du, C. M.; Diart, V.; Whiting, G. S.; Grate, J. W.; McGill, R. A. J. Chem. Soc., Perkin Trans. 2 1995, 369.
