724
Znd. Eng. Chem. Res. 1994,33, 724-729
Solubility of Solutes in Compressed Gases: Dilute Solution Theory Xiaorong W a n g a n d Lawrence L. Tavlarides' Department of Chemical Engineering and Materials Science, Syracuse University, Syracuse, New York 13244
A dilute solution theory is developed for describing the thermodynamic behavior of a compressed gaseous dilute solution. The considerations follow generally accepted statistical treatments for describing dilute liquid solutions. The theory is self-consistent with the ideal gas law for dilute gases and with Henry's law for dilute liquid (or solid) solutions. Further, it provides a simple linear relationship which represents well the solubility behavior of a heavy solute (solid or liquid) in a gaseous solvent over relatively wide density regions of the solvent (i.e., 0 Ip I2.0/Vc). Introduction The recently large increase in the use of supercritical extraction for separation processes requires the knowledge of theoretical interpretations and predictions of the solubility behavior of a solute in a compressed gaseous solvent. Unfortunately, there are relatively few reliable predictive methods currently available that have sufficient accuracy to be used in the design of these processes. Classical thermodynamic models, such as those using a cubic equation of state (Johnston and Peck, 19891, generally require the critical parameters of both solvent and solute, and the latter are often unavailable in the literature. Nonclassicalmodels, though they show promise to be applied in critical loci, regard the critical parameters as an input rather than output for their scaling-law equations (Rainwater, 1991). For systems where a heavy solute (i.e., solid or liquid) is in equilibrium with a compressed gaseous solvent, the solubility of the solute seldom exceeds a few mole percent (Ewald et al., 1953;Li et al., 1991;Schmitt and Reid, 1986; Tsekhanskaya et al., 1964), and mostly these systems can be simply classified as dilute solutions. In the literature, traditional models dealing with gaseous solutions are frequently based on calculations of the interaction parameters and the interaction molecular sizes (Johnston and Peck, 1989). However, the behavior of dilute gaseous solutions could be generalized by regarding them as a special class between ideal gases and dilute liquid solutions. A survey of theories (models) and experimental results on the behavior of dilute liquid solutions suggests that the thermodynamic properties of these systems submit to some simple laws (e.g., Henry's law) which are independent of the complex molecular interactions and molecular geometries. Also, the effect of interactions and geometries can be ignored for gaseous mixtures at low pressures because these mixtures obey the ideal gas law. As to compressed gaseous dilute solutions, which are of interest here, these sytems should follow a behavior somewhere between ideal gas solutions and dilute liquid solutions. In this work, a dilute solution model is developed for describing the thermodynamic behavior of compressed gaseous dilute solutions. The theory is self-consistent with the ideal gas law for dilute gases and with Henry's law for dilute liquid (or solid) solutions. Theoretically, the proposed model predicts that there are simple relationships between the solubility behavior of a heavy solute and the density of a gaseous solvent. A detailed discussion of the results is included. Theory For sufficiently dilute solutions, where the solute molecules (2) have almost zero opportunity to contact each Oags-sss5/94/2633-0724$04.50lQ
other, all of the mutual interactions between solute molecules can be ignored. If the solute molecules are placed in a free space (or volume v), the solute molecules would move freely in the volume V, and the molecular partition function of a given molecule would be directly proportional to the volume. Accordingly, N2 solute molecules in the space have a partition function of the form ti2v)"
N2! where j 2 represents the partition function for all internal degrees of freedom of the molecule itself and also includes the rotation and motion contributions of the solute molecules. The factor N2! accounts for the indistinguishability of the solute molecules. Obviously, this simple formula of the partition function yields the ideal gas law (Hill, 1956). If a dilute solution, whether liquid or solid, is of concern, the solute molecules (2) can be treated as a perfect quasi-gas moving freely in a space V which has constant potential energy r12 that depends on the nature of the solute and the nature of solvent. The partition function of the solute is then expressed as
G2v~ X P ( - ~ , ~ / ~ T ) I ~ ~ N,!
(2)
where k is Boltzmann's constant and T represents temperature. The factor exp(-F1dkT) accounts for the average interaction between a single solute molecule and the surrounding solvent molecules. This treatment of solute molecules in a dilute solution (whether liquid or solid) yields Henry's law and Nernst's distribution law for the solute, and Raoult's law for the solvent, as shown by Guggenheim (1952). The system we are examining here is a solution in which the solute has been dissolved into a compressed gaseous solvent. The situation is not simple since, in general, the interactions of molecules are functions of the positions and configurations of the solvent and the solute molecules. The problem of evaluating the partition function which contains not only solvent but also solute contributions is then rather complicated. However, it may be considerably simplified when the problem is restricted to a dilute solution. Consider a gaseous mixture of volume V which contains N1 solvent molecules and N2 solute molecules where N1 >> N2. A t high density and low temperature, the typical configuration in the gaseous solvent may be regarded as consisting of essentially isolated and randomly moving clusters of solvent molecules (Fisher, 1967; Hill, 1956). 0 1994 American Chemical Society
Ind. Eng. Chem. Res., Vol. 33, No. 3, 1994 725 These clusters will be in dynamic equilibrium. The relative proportions of differently sized clusters will change with temperature and pressure. However, the overall volume of all the clusters will be constant, i.e., Nit, where { represents the average volume occupied by a solvent molecule in cluster. Now if a solute molecule moves in a solvent cluster, the solute molecule is then considered to be situated in an environment of constant potential energy r12. The partition function of the solute molecules is taken to be of a similar form of the expression (21, where r1z still only depends on the nature of the solute and the nature of the solvent. If a solute molecule stays outside of these clusters, the solute molecules would behave like an ideal gas. The partition function of the solute molecule is of a form similar to the expression (1). In this respect, the solute molecules in the solution are considered to be composed of a number of ideal gas-like molecules and a number of perfect quasi-gas-likemolecules moving throughout the volume, though they are dynamically exchangeable and indistinguishable. Therefore, the following partition function is ascribed to solute molecules in the dilute solution (jzVjNrNZfljzVexp(-I',,/ kT)1Nat N2!
(3)
where Nzf represents the number of the solute molecules (or perfect quasi-gas molecules) which possess an interaction potential r12. The factor Nz!still accounts for the indistinguishability of solute molecules. When the solution is in an equilibrium state, the probability of finding a solute molecule of perfect quasigas type is expressed in terms of N1{ weighted by the Boltzmann factor. Therefore, the quantity N2f can be expressed as
Nit exp(-r12/kT) Nzf= NzV- Nl{+ N,{exp(-I',,/kT)
(4)
where N1{ accounts for the overall cluster volume (or overall interaction regions in the view of solute molecules) and V - Nlpaccounts for the overall free-moving regions. We note that these two types of regions randomly distribute and move in the space V. Thus, a solute molecule, in any position of the space V, is either a perfect quasi-gas type or an ideal gas type. It is seen, that, when the interaction region (NlD approaches zero (followed by Nzf approaching zero), expression 3 reduces to expression 1, and the solute molecules behave like ideal gases. On the other hand, when the interaction region (NlD fills the space V (followed by N z approaching ~ Nz), expression 3 reduces to expression 2, and the solute molecules will behave as those in dilute liquid (or solid) solutions. In this case the solute behavior follows Henry's law (i.e., the fugacity of the solute in the solution is proportional to its mole fraction). The above treatment is therefore a natural extension of the dilute solution theory, which is usually used to describe liquid (or solid) solutions, to dilute gaseous solutions. The canonical partition function (Q) of the solution (i.e., a mixture of solute and compressed gaseous solvent) is given by
(jzVlNrNZfLjz V exp(-I',,/ k T)]Nzf Q = Qi N,!
(5)
where Q1 is the partition function of the pure gaseous solvent. In the limit of N2 approaching zero, Q approaches
81. Since a particular function Q1 can yield all of the thermodynamic properties of the solvent, the treatment used here is obviously general. It is noted that the same treatment has been used by Guggenheim (1952) for dilute liquid solutions. The relationship between the Helmholtz free energy of the mixture (A,) and the canonical partition function (Q) is A , = -kT In(&)
(6)
Substitution eq 5 into eq 6,and applying Stirling's formula for Nz!, we obtain,
A , = -kT ln(Q,) - kTNz In
- kTNz- N2- b* (7)
where the parameters b* = -[NIT exp(-I'l~/kT)II'1~and c* = Nl{[exp(-I'12/kT) - 11. The physical significance of r 1 2 and jz has already been discussed. The important property of r1z and { is the independence of each term from the number of solute and solvent molecules. The chemical potential p2p' for each solute molecule can be obtained by differentiation of eq 7 with respect to Nz, at constant temperature, volume, and N1, *:p
= -kT Intiz)
+ kT In
b*
(8)
Here the superscript (g*)indicates that the solute molecule is in an environment of gaseous solvent. Alternatively, using the dilute condition (i.e., N1 >> Nz), we can rewrite eq 8 on a mole basis in the following form:
where yz is the mole fraction of the solute and is defined as yz = Nz/(N1 Nz). The molar chemical potential of the solute pzg = Na/l.~g',where Na is Avogadro's number. Vi is the molar volume of the pure gaseous solvent. The parameters b and c are defined as
+
b=-[Na~e~~(-~lz/kT)lrl~, c = NJ[exp(-rlZ/kT) - 11
For a two-phase system at constant temperature and pressure which consists of a heavy (solid or liquid) phase and a light (gaseous) phase, the general equation of equilibrium for the solute in two phases states that the chemical potentials of the component in the light phase and in the heavy phase are equal:
Here pph is the chemical potential of the solute in a heavy phase (i-e., solid or liquid phase), and pzg is the chemical potential of solute in a light phase (i.e., gaseous solution phase). For asymmetric systems of interest in this study, generally the critical temperature of a solute is much greater than the critical temperature of the gaseous solvent, and the saturation pressure of the solid (or liquid) solute, at the critical temperature of the solvent, is usually about 10-10-10-3 bar. If the heavy phase is present as a pure solid or a pure liquid and if the saturation pressure of the heavy phase is considerably smaller than 1 bar, the chemical potential of the solute in the heavy phase is
726 Ind. Eng. Chem. Res., Vol. 33, No. 3, 1994
represented by (Prausnitz et al., 1986) pph
= p 2 ref
+ R T 1n(P2")+ V,h(P - P2")
(11)
where the quantity p2 ref is related to an arbitrary reference state, P2" is the saturation pressure of the pure solute phase (solid or liquid) at temperature T, and Vzh is the molar volume of the solute of the heavy phase. In eq 11, the term Vzh(P-Pz") arises from the Poynting correction; however, it only has a negligible contribution as compared to R T ln(P2") when pressure P is not too high. It also can be ignored when the system is in the region of the critical loci (discussed below). Thus, the equation of equilibrium of component 2 (solute) in two phases is
decompose or react at a temperature well below their critical points, sometimes even below their melting points. In this research, it is found that the solubility enhancement ( E )of a solid in a gaseous solvent can be expressed by a relative simple form (eq 14) as a function of solvent density ( p ) . This formulais free from the arguments which use empirical equations of state and mixing rules and which generally require the critical parameters of solutes. The present theory is derived from the properties of dilute solutions using statistical thermodynamics. Actually, the behavior of a dilute solution is quite general since it is independent of solute molecule geometry and interactions. The importance of the present theory is highlighted through an underlying consistency with the ideal gas law for dilute gases and with Henry's law for dilute liquid (or solid) solutions. Further, when pressure is low or volume is large (i-e., VI >> c), eq 14 reduces to
+
Using the accepted definition for the solubility enhancement factor of the solute in the gaseous solvent, E = y2p/P2", and rearranging eq 12, one obtains
bIRT ln(2) ln(E) = Vl
where ln(2) is negligible for 2 = 1 when P is low. It, therefore, follows that the theory agrees with the description of solubility when one uses the second virial coefficient equation of state (Ewald et al., 1953) at low densities. Since the parameter b -[exp(-rl2/kT)1rl2 and the parameter c [exp(-I'12/kT) - 11, the temperature dependence of parameters b and c is obvious. The variations of parameters b and c with the change of temperature are always proportional to the quantity r121 (kP). For van der Waals interactions I'121kT is of a magnitude of unity or less. Accordingly, quantity r12/ (kP) would be much smaller than 1 (for instance, at T = 300 K) and dominates the values of dbldT and dc/dT. It is therefore possible to regard both b and c as constants when the change of temperature is small. Considering this situation, eq 14 can be rewritten as
-
with
+
X = &f ln[RTG2)1 RT
- -
The quantity X can be determined through the use of the ideal gas law. When the pressure P Pz" > bIRT and c, PVIIRT 1, and also ln(E) 0, then X = 0. This conclusion exists particularly in two-phase equilibria. With this result, the rearrangement of eq 13 yields
-
b RT[ln(E) - ln(Z)] = v1+ c
(14)
where 2 = PVlIRT is the compressibility factor of the gaseous solvent. The density of the gas p = llV1. Theoretically, this simple form directly relates the solubility enhancement of a solute to the molar volume or density of the mixture (or as a good approximation, to the molar volume of the gaseous solvent at dilute conditions). This form suggests that the molar volume or density is an appropriate parameter for monitoring the solubility behavior for these systems. For the case where parameters b and c can be determined independently, eq 14 can be used for the prediction of the solubility behavior of a solute (liquid or solid) in a gaseous solvent.
Discussion Traditional methods of modeling the solubility behavior of a heavy solute in a compressed gas are based on the calculation of the fugacities by means of a suitable equation of state. Results of the fugacities are then used in the general phase equilibrium equation (i.e., equality of chemical potentials in the two phases) to calculate the solubility for comparison with experimental data. These traditional methods, however, require the critical parameters of both the solvent and solute, and the latter are often unavailable in the literature. Although these parameters can sometimes be estimated empirically by Lydersen's technique (Lydersen, 1982), large errors and uncertainties can occur for some solutes. Difficulties also exist in making experimental measurements since, for many heavy solutes of interest, they may chemically
(15)
-
1 T[ln(E) - ln(2)I
(16)
Equation 16 indicates that experimental solubility data of a system are expected to have a linear behavior in a lI{T[ln(E) - ln(Z)lj versus V1 plot. Examples of this linear behavior can be shown for various solvent and solute systems with data from the literature. For example, Li et al. (1991) measured the solubility of caffeine in gaseous carbon dioxide at a temperature range from 40 to 95 "C, and over a pressure range from 90 to 300 bar. Figure 1 is a plot from their data of lI{T[ln(E) - ln(2)I) versus the mole volume of pure carbon dioxide. The experimental data follow the theoretical prediction well. Figure 2 shows a similar plot for benzoic acid in supercritical ethane, as measured by Schmitt and Reid (1986). Figures 3 and 4 show the plots for naphthalene in ethylene, as measured by Tsekhanskaya et al. (1964), and fluorene in carbon dioxide,as measured by Johnston et al. (19821, respectively. These plots illustrate the application of eq 16. Each system shows a linear behavior when plotted in this fashion. All of the data collapse onto a single linear curve. The slope and interception of the plot represent the values of parameters Rib and Rclb. The collapse phenomenon covers a range from the nearly ideal gas state to the highly nonideal state (i.e., the supercritical state), rather than being limited to the critical region of the pure solvent as proposed in the literature (Harvey, 1990). The source of this phenomenon is that the sensitivity of parameters b and c on temperature is not significant as long as the temperature range is small, as discussed previously.
Ind. Eng. Chem. Res., Vol. 33, No. 3, 1994 727
Naphthalene in Ethylene
I
0.00
0. IO
0.05
0.15
0.20
J
0.0s
Volume ( L h o l )
0.10
0.15
0.20
.
I
0.25
.~
a
IO
Volume (Lhol)
Figure 1. Linear plot of l/{T[ln(E) - In (Z)]) versus VI for the solubilityof caffeine in carbon dioxide. Experimentaldata are from Li et al. (1991).
Figure 3. Linear plot of lI(T[ln(E) - ln(Z)]) versus V I for the solubility of naphthalene in ethylene. Experimental data are from Tsekhanskaya et al. (1964).
Benzoic Acid in Ethane
0 45'C 0 55T
0.00
0.05
0.10
0.15
0.20
0.25
0.30
Volume ( L h o l ) Figure 2. Linear plot of l/(T[ln(E) - ln(Z)]) versus Vl for the
'
0.05
0.10
0.15
0.20
0.25
0.30
Volume (L/mol)
solubility of benzoic acid in ethane. Experimental data are from Schmitt and Reid (1986).
Figure 4. Linear plot of lI(T[ln(E)- ln(Z)]) vemw VI for the solubility of fluorene in carbon dioxide. Experimentaldata are from Johnston et al. (1982).
Recently, several semiempirical correlations have been proposed (Schmitt and Reid, 1985; Kumar and Johnston, 1988; Harvey, 1990), Le., the linear correlation of the logarithmic solubility ln(y2) versus the logarithm of the density of the pure solvent ( p ) , and the linear correlation of ln(E) versus the density of the pure solvent ( p ) . However, these correlations are not thermodynamically consistent with the ideal gas law at low densities. As indicated by several research groups (Japas and Levelt Sengers, 1989;Kumar and Johnston, 1988;Harvey, 1990), these correlations are only asymptotic results which arise from the critical diverging properties. So far, there is no clear knowledgeof the criteria over which these correlations apply. In this regard, Li et al. (1991) suggest that the applicability of these correlations is limited to a narrow temperature and density range in the critical neighborhood of the solvents. The present simple linear equation is therefore recommended to quantitatively correlate and predict the solubility behavior of a heavy solute in a gaseous solvent over a range from ideal gas state to supercritical state. In our approach, the Poynting correction is considered to contribute only a negligible effect. This originates from
the following considerations. At low pressures (say P I 50 bar), thePoynting correction is usually small (Prausnitz, 1986). When the solution is at the critical region, the Poynting factor can also be considered to be unimportant since the partial molar volume of the solute in the solution is much larger than the molar volume of the solute in the heavy phase (Kumar and Johnston, 1988). In common practice, since the critical pressures of the gaseous solvenb of interest range from 45 to85 bar (e.g., the critical pressure is 74 bar for carbon dioxide, 50 bar for ethylene, and 82 bar for water), for purposes of simplicity, when considering such solvents, it is therefore reasonable to drop the Poynting factor over a pressure range from near ideal gas state to the supercritical state. It is also noted that one may be able to evaluate parameter b from eq 15 because parameter bIRT relates to the second virial coefficient B12 in a simple fashion (Ewald et al., 1953). As noted by several researchers, the value of Bl2 may be calculated from the molecular interaction theory (Robin and Voder, 1953) or from corresponding-state correlations (McGlashan and Wormald, 1964). It is then possible to calculate band c through the use of molecular parameters. However, it is unfor-
728 Ind. Eng. Chem. Res., Vol. 33, No. 3, 1994
1400
800
Nomenclature
1 -
600-
A
31.04OC
400200
13 75QC
0
5
10
15
20
25
Density (mol/L) Figure 5. Plot of T[ln(E) - ln(Z)] versus p for the solubility of water in carbon dioxide. Experimental data are from Wiebe and Gaddy (1941). Correlation curve is evaluated on the basis of eq 14.
tunately true that the calculation of virial coefficients is, at the present state, restricted to relative simple substances. This limitation is a result of the present inability to describe adequately the intermolecular potential between molecules of complex structures. In the literature, data for second virial coefficients are available only for simple molecules (Dymond and Smith, 1980). As to the highly asymmetric systems of interest, since the solute molecules are rather complicated and the molecular parameters of the solutes are often unavailable, calculation or prediction of the parameters b and c becomes impractical. If the solubility is measured at low pressures, then b can be calculated from the limiting slope of eq 15. For the cases where experimental data are only available for high pressures, b and c may be treated as fitting parameters for correlation or prediction of experimental results. It should be acknowledged that the present theory somewhat simplifies a real system since the interaction between solute and solvent molecules is assumed to follow an interaction behavior similar to the potential-well model. Also, the mean field concept is employed throughout all the theoretical derivations. Despite these simplifications, the theory possesses all the essential features of the thermodynamic problem. The importance is that the theory does not involve the use of empirical equations of state. The present theory presents a simple relationship between the solubility of a solute and the density of the solvent. The theory agrees inherently with the ideal gas law for dilute gases and with Henry’s law for dilute liquid (or solid) solutions. Further, it also provides a good correlation of experimental data over a rather wide density range. As shown in Figure 5 for the water/carbon dioxide system, the correlation follows the data over a range of 0 Ip I2.0/VC. Acknowledgment
The financial support from the National Institute of Environmental Health Sciences Superfund Basic Research Program, Grant No. NIEHS 2P4E50491303, and the New York State Legislative Grant, Contract No. C-9308979, is gratefully acknowledged. Also, X.W. gratefully acknowledges the support of the Graduate Fellowship from Syracuse University and the Assistantship from the Chemical Engineering and Materials Science Department.
A , = Helmholtz free energy of mixture BIZ= second virial cross-coefficient for binary mixture b* = parameter in eq 7 b = parameter in eq 9 c* = parameter in eq 7 c = parameter in eq 9 E = solubility enhancement ( E = y2P/Pzo) jz = partition function for all internal degrees of freedom of a solute molecule k = Boltzmann’s constant N , = Avogadro’s number N1 = number of solvent molecules Nz = number of solute molecules Nzc = number of solute molecules in solvent clusters P = pressure P 2 O = saturation pressure of solute Q1 = partition function of solvent Q = partition function of all solution R = universal gas constant V = volume V1 = mole volume of pure solvent V, = critical volume of solvent V2h = mole volume of solute of heavy phase y2 = mole fraction of solute in gaseous phase or solubility T = temperature (K) Z = compressibility factor (PVl/RT)
Greek Symbols = average interaction potential energy between solute and solvent molecules .t = average volume of a solvent molecule in a cluster p2g* = chemical potential of solute in gaseous phase per solute molecule I.L$ = chemical potential of solute in gaseous phase per mole solute molecule pzh = chemical potential of solute in heavy phase per mole solute molecule ktref= chemical potential of solute related to a reference state p = density (1/ VI), r 1 2
Subscripts 1 = component 1 or a solvent 2 = component 2 or a solute
Literature Cited Dymond, J. H.; Smith, E. B. The Virial Coefficient of Pure Gases and Mix tures; Clarendon Press: Oxford, 1980. Ewald, A. H.; Jepson, W. B.; Bowlinson,J. S. The Solubility of Solids in Gases. Discuss Faraday SOC. 1953,15,23&243. Fisher, M. E. The Theory of Equilibrium Critical Phenomena. Rep. B o g . P h p . 1967,15,615-730. Guggenheim,E. A. Mixture; Oxford University Press: Amen House, London, 1952;Chapter 5. Harvey, A. H. Supercritical Solubility of Solids from Near-critical Dilute-Mixture Theory. J. Phys. Chem. 1990,94, 8403-8406. Hill, T. L.Statistical Mechanics: Principles and Selected Applications; McGraw-HillBook Company: New York, 1956;Chapter 5.
Japas, M. L.; Levelt Sengers, J. M. H. Gas Solubility and Henry’s Law Near the Solvent’s Critical Point. AZChE J. 1989,35 (5), 705-713. Johnston, K. P.; Peck, D. G. Modeling Supercritical Mixtures: How Predictive Is It? Ind. Eng. Chem. Res. 1989,28,1115-1125. Johnston, K.P.;Ziger,D. H.; Eckert, C. A. Solubilitiesof Hydrocarbon Solids in Supercritical Fluids. The Augmented van der Waals Treatment. Ind. Eng. Chem. Fundam. 1982,21,191-197. Kumar, S. K.; Johnston, K. P. Modeling the Solubility of Solids in Supercritical Fluids with Density as the Independent Variable. J. Supercrit. Fluid 1988,1, 15-22.
Ind. Eng. Chem. Res., Vol. 33, No. 3, 1994 729 Li, S.; Varadarajan, G. S.; Hartland, S. Solubilities of Theobromine and Caffeine in Supercritical Carbon Dioxide: Correlation with Density-Based Models. Fluid Phase Equilib. 1991,68, 263280. Lyderson, A. L. In Handbook of Chemical Property Estimation Methods; Lyman, W. J., Reehl, W. F., Rosenblatt, D. H., Eds.; McGraw-Hill Book Company: New York, 1982;Chapter 12. McGlashan, M. L.; Wormald, C. J. Second Virial Coefficient of Some Alk-1-enes, and of a Mixture of Proene + Hept-1-ene. Trans. Faraday SOC.1964,60,646-652. Prausnitz, J. M.; Lichlenthater, R. N.; de Azevedo, E. G. Molecular Thermodynamics of Fluid-Phase Equilibria, 2nd ed.; PrenticeHall Inc.: Englewood Cliffs, NJ, 1986;Chapter 5. Rainwater, J. C. Vapour-LiquidEquilibriumand the Modified LeungGriffiths Model. In Supercritical Fluid Technology: Reviews in Modern Theory and Applications; Bruno, T. J., Fly, J. F., Ede.; CRC Press Inc.: Boca Raton, Ann Arbor, Boston, London, 1991; Chapter 2. Robin, S.;Voder, B. Solubilityin Compressed Gases. Discuss Faraday SOC.1953,15,233-238.
Schmitt, W. J.; Reid, R. C. The Influence of the Solvent Gas on Solubility and Selectivity in Supercritical Extraction. In Supercritical Fluid Technology; Penninger, J. M., et al., Eds.; Elsevier: New York, 1985;p 123. Schmitt, W. J.; Reid, R. C. Solubilities of Monofunctional Organic Solids in Chemically Diverse Supercritical Fluids. J. Chem.Eng. Data 1986,31,204-212. Tsekhanskaya, Yu. T.; Iomtev, M. B.; Mushkina, E. V. Solubility of Naphthalene in Ethylene and Carbon Dioxide Under Pressure. Russ. J. Phys. Chem. 1964,38 (9),1173-1176. Wiebe, R.; Gaddy, V. L. Vapor Phase Compositionof Carbon DioxideWater Mixtures at Various Temperatures and at Pressure to 700 Atmospheres. J. Am. Chem. SOC.1941,63,475-477.
Received for review August 2, 1993 Revised manuscript received November 22, 1993 Accepted December 9, 1993O
* Abstract published in Advance ACS Abstracts, February 1, 1994.
