4273
J. Phys. Chem. 1995, 99, 4273-4277
High-pressure Phase Equilibria and Critical Curve of the Water 200 MPa and 723 Kt
+ Helium System to
N. G. Sretenskaja Institute of Experimental Mineralogy, Russian Academy of Sciences, Chemogolovka 14 24 32, Russia
Richard J. Sadus Computer Simulation and Physical Applications Group, Department of Computer Science, Swinbume University of Technology, P.O. Box 218, Hawthom, Victoria 3122, Australia
E. Ulrich Franck” Institut f i r Physikalische Chemie und Elektrochemie der Universitat Karlsruhe, Kaiserstrasse 12, Karlsruhe, 0-76128 Germany Received: July 13, 1994; In Final Form: December I , I994@
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The phase equilibria of the binary water helium system are examined at high temperatures and pressures. The equilibrium surface in T, p , x space (where T denotes temperature p pressure, and x mole fraction) has been determined experimentally. The coordinates of the critical curve are also identified to 180 MPa. The critical curve commences from the critical point of water and proceeds directly to higher temperatures and pressures without passing through a temperature minimum. This behavior is characteristic of “gas-gas immiscibility” of the first kind. Supercritical molar volumes are also reported at temperatures of 683, 703, and 723 K and pressures from 60 to 200 MPa. The critical curve was calculated using different equations of state and compared with experimental data. Equations of state based on an accurate representation of the repulsive interaction of hard spheres (e.g., the Camahan-Starling model) failed to adequately predict the critical locus whereas calculations using the simple van der Waals equation were quantitatively accurate. Using the van der Waals equation yields very good results for both the pressure-temperature and pressurecomposition behavior of this system. It is concluded that theoretically accurate hard-sphere models overestimate the contribution of repulsive interactions between helium and water.
I. Introduction Binary ,mixtures of water and a noble gas are of considerable interest because they enable the study of the interactions of a small, highly polar component (water) and a spherical, nonpolar atom (the noble gases). Therefore, changes in the phase behavior of these mixtures can be unambiguously attributed to the change in interaction between water and a progressively larger spherical component. Extensive high-pressure phase equilibria data are a~ailablel-~ for all of the water noble gases with the exception of the system containing helium. Some preliminary results for the water helium mixtures have been reported,“ but a comprehensive description of the high-pressure phase equilibria is not available in the literature. However, some solubility data are available5for helium in water at high pressure. The water helium mixture is of particular interest because, according to the theory proposed by Temkin: it should exhibit so-called “gas-gas immiscibility” of the first kind. Many mixtures of water another component exhibit type 111critical behavior in accordance with the classification scheme of van Konynenburg and Scott.’ The critical curve, starting from the critical point of water, passes through a temperature minimum before rising steeply to high pressure. In rare cases, a temperature minimum is not observed and the critical curve extends directly to temperatures and pressures above the critical
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* Author for correspondence. @
Experimental work performed at the Universittit Karlsruhe. Abstract published in Advance ACS Abstracts, March 1, 1995.
point of either component. Temkin6 predicted that this phenomenon would be observed in all mixtures obeying the van der Waals equation if v 1 12
0.42v22
(1)
+ +
where P22 =- P11. For mixtures of water noble gases, Temkin’s theory predicts that this phenomenon should be restricted to the water helium and water neon systems. Recent experimental measurements3 for water neon have c o n f i e d this prediction whereas the critical curves of other water noble gas mixtures pass through a temperature minimum. The high-pressure phase behavior of systems containing helium is also of potential interest to the study of the atmospheric behavior of the outer planets.8 This work reports the experimental pressure-temperature isopleths at several compositions and the coordinates of the critical curve at pressures up to 180 MPa. Experimental data are also presented for the supercritical molar volumes of the binary mixture. The critical curve exhibits gas-gas immiscibility of the first kind as predicted by Temkin’s theory.6 The critical curve is calculated using the simple van der Waals, Guggenheim,g and Heilig-Francklosll equations of state. The van der Waals equation can be used to quantitatively represent the critical transitions to an accuracy which is within experimental uncertainty.
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0022-3654/95/2099-4273$09.00/0 0 1995 American Chemical Society
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Sretenskaja et al.
4274 J. Phys. Chem., Vol. 99, No. 12, 1995
TABLE 2: Experimental Isotherms: Composition-Pressure Phase Equilibrium Relations for Helium Water Obtained Using the Analytic Method (x(He) = Mole Fraction of Helium)
TABLE 1: Experimental Isopleths: Pressure-Temperature Phase Equilibrium Relations.at Constant Compositiorw for Helium Water Obtained with the Synthetic Method (x = Mole Fraction He)
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+
523 K
X
0.2
0.3
0.6
0.4
0.8
T/K plMpa T/K plMPa TK plMPa T/K plMPa T/K pMPa 680 677 674 665 662 657
181 145 123 88 74 60
694 688 685 673 667 645
210 171 151 111 93 50
694 684 681 677 672 655 631 620
193 154 144 124 112 76 48 40
687 680 661 652 637 616
207 176 119 104 83 59
647 639 630 611 594 586 568
0.036 0.031 0.028 0.026 0.024 0.019 0.017 0.016 0.013 0.011 0.006
178 158 142 108 84 75 59
11. Apparatus and Procedure The experimental techniques used here to determine the phase equilibria and pTx-data (where p is pressure, T temperature, and x mole fraction) of the helium water mixture have been described in considerable detail e l s e ~ h e r e . ~Consequently, ~~~-~~ only a brief summary is presented. The experimental procedures can be described as “synthetic” and “analytic”. The synthetic approach involved heating known amounts of water and helium in an autoclave of known volume and recording the pressure increase with temperature. The variation of pressure with respect to temperature was curved in the twophase region of the pT projection. A discontinuity, Le., a “break point”, indicated the transition to homogeneous one-phase behavior and to an almost linear @,T) isochore. Each break point represents a point on the three-dimensional binodal pTx surface. It could also be determined by visual observation through an axial sapphire window. A set of break points produced an “isopleth” along the three-dimensional two-phase boundary surface. Continued heating beyond the break points permitted the determination of pVT data of the system in the supercritical one-phase region to 723 K. This procedure has been previously used for the water methane,17 water k r y p t ~ n and , ~ water neon3 binary mixtures. The analytic m e t h ~ d ~is~ an , ’ ~altemative to the synthetic method. It is applied for low helium mole fractions. The overall composition of the mixture is not known beforehand. Instead, samples from the liquid phase must be extracted and analysed. Typically, samples of between 0.5 and 1.5 g were extracted into a glass vessel and cooled to 77.3 K to volumetrically determine the amount of gas. A correction (not exceeding 2%) for nonideality was applied and the amount of water was determined from the weight of the sample to an accuracy of 1%. Additional experiments were conducted to determine the influence of the variation of the total pressure during sampling. This involved changing the ratio of the volumes of the liquid and gas phases and preparing and analyzing special homogeneous test samples.
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593 K
623 K
643 K
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111. Results
The experimental data for the phase coexistence boundary are presented in Tables 1 and 2. The data were obtained using the synthetic and analytic methods, respectively. The estimated experimental uncertainties were AT = f1.5 K, Ap = f 0 . 2 m a , and either Ax = fO.01 (Table 1) or Ax = fO.OO1 (Table 2). Tables 3 and 4 represent smoothed p-T-x data obtained from the analysis of the primary experimental data. The experimental critical curve can be deduced as a high-temperature envelope of isopleths and the coordinates of this curve are presented in Table 5. Experimental supercritical molar volumes are recorded in Table 6.
185 141 117 104 94 76 68 61 48 38 23
0.046) 189 158 0.042 150 0.037 119 0.035 102 0.031 97 0.028 87 0.022 61 0.016 44 0.006 16 0.044
0.067 0.062 0.061 0.054 0.050 0.046 0.041 0.035 0.034 0.031 0.027 0.020
216 165 151 123 110 96 87 70 66 58 51 40
0.093 0.087 0.083 0.077 0.072 0.071 0.061 0.056 0.043 0.036 0.028 0.020
219 174 152 132 119 115 115 77 58 48 40 30
0.116 223 0.113 195 0.107 162 0.095 121 0.079 83 0.065 63 0.061 58 0.047 47 0.031 32
TABLE 3: Smoothed Isopleths: Pressure-Temperature Phase Equilibrium Relations for Helium Water Obtained from the Data in Table 1 (x(He) = 0.2-0.8) and Table 2 @(He) < 0.2) (Temperatures in K) x(He) pMPa 0.03 0.05 0.07 0.09 0.2 0.3 0.4 0.6 0.8
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+
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553 K
x(He) p/MPa x(He) p/MPa x(He) plMPa x/(He) p/MPa x(He) p/MPa
~
’
50 75 100 125 150 175 200
628 588 565 523
640 620 607 597 588 582 578
661 641 628 620 613 609 606
656 646 642 631 627 623
652 661 669 674 677 680 681
646 659 669 678 684 689 693
631 654 666 676 683 690 695
607 630 649 664 673 680 686
586 605 621 634 646 656
TABLE 4: Smoothed Isotherms: Pressure- Composition Phase Equilibrium Relations for Water -t Helium (Compositions in Mole Fractions of Helium) p/MF’a
523K
553K
593K
623K
643K
25 50 75 100 125 150 175 200
0.006 0.014 0.020 0.025 0.030 0.033 0.035 0.037
0.009 0.017 0.025 0.032 0.038 0.042 0.045 0.047
0.013 0.026 0.037 0.047 0.054 0.060 0.064 0.066
0.016 0.037 0.054 0.066 0.075 0.082 0.087 0.091
0.022 0.05 1 0.073 0.087 0.097 0.104 0.110 0.114
TABLE 5: Critical Properties of Water iHelium x(He) TK plMPa 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
647 652 654 658 664 67 1 680 696
22.1 31 40 55 77 98 130 180
IV. Discussion The experimental isopleths and the critical curve deduced from these measurements are illustrated in Figure 1. Fluidfluid coexistence was observed at temperatures and pressures well above the critical point of water. Consequently, critical points can be deduced commencing from the critical point of water and extending directly to greater temperatures and pressures. This phenomenon is characteristic of gas-gas immiscibility of the first kind and it is correctly predicted by Temkin’s theory.6 It is of interest of calculate the critical curve of this system to test the reliability of theoretical models. Good results have been previously for the comparison between theory and experiment for other water noble gas mixtures. These calculations utilized the Heilig-Franck’O.”
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Phase Equilibria of the Water
+ Helium System
J. Phys. Chem., Vol. 99, No. 12, 1995 4275
TABLE 6: Pressure and Composition Dependence of the Molar Volumes (cm3 mol-') of the Water Helium Mixture at Three Supercritical Temperatures
+
200 -
We) pMPa
0
60 70 80 90 100 120 140 150
30.6 29.1 28.1 27.3 26.6 25.6 24.7 24.4
60 70 80 90 100 120 140 150 160 180
33.5 31.4 29.9 28.8 27.9 26.6 25.6 25.1 24.8 24.2
70 80 90 100 120 140 150 160 180 200
34.1 32 30.5 29.4 27.7 26.5 26 25.6 24.9 24.3
0.2
0.3
50.8 44.6 40.7 40 34.8 32.4 31.2
T = 683 K 73 63.5 71.0 55.5 61.5 49.1 54.6 44.3 49.5 39.9 42.7 38.6 36.7
48.6 43.5 40.1 36.4 33.7 32.6 31.5 29.2
T = 703 K 78 68.6 77.2 59.7 68 52.7 60 47.3 56.2 40.3 45.5 36.7 40.5 35.2 38.6 33.6 36.8 31.3 34.1
52.4 46.4 42.4 38 35.1 33.8 32.5
0.4
T = 723 K 72.3 79.6 63.6 70.2 55.8 62 50.4 56.3 42.8 48 38.2 42.2 36.7 40.1 37.2 38.3 32.5 35.3 32.9
0.6
0.8
180
1
-
160 -
65.3 60 51.4 46 45
79.2 71.3 65.4 59 53.9
92.2 81 72.4 67.3 57 49.5 47
110 -
.g 120 -r
100 -
80-
67.7 62.4 53.1 48.9 46.7
82.2 73.5 67.2 60.2 55
95.3 83.5 75.5 69 59 51 48
60
-
LO
-
69.5
64 54.6 49.3 47.5
99 86.5 78 71.3 61 52.5 49
equation which is based on an extension of the CamahanStarling hard-sphere square-well attractive term equation proposed by Christoforakos and Franck.16 Only a brief outline of the computation procedure is presented here. Extensive descriptions of the use of these equations of state3J0J1J7and the calculation procedurela are available. The critical locus was determined for the temperature (T), volume (v), and composition (x) which satisfied the following conditions:18
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The Helmholtz (A) function was determinedla from conformal solution theory,lg the one-fluid model, and a suitable equation of state. Three different hard sphere attractive term equations of state were used in this work. The simplest equation of state capable of at least qualitatively predicting the phase behavior of fluids is the van der Waals model:
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p = RT/(V - b) - a/V2
(6)
where b accounts for the covolume occupied by hard-sphere molecules and a is a parameter which reflects the contribution of attractive interactions. The Guggenheimg equation employs the same type of attractive term but the first term is replaced
5 8 0 620-
660 700 T/ K Figure 1. Experimental pressure-temperature isopleths for water helium at constant helium mole fractions, x(He) = 0.03 (0),0.05 (O),
500
510
~
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0.07 (A), 0.09 (o),0.2 (o),0.3 (+), 0.4 (x), 0.6 (#, and 0.80 (0). The solid line represents in inferred critical curve.
with a different representation of repulsive interaction between hard spheres, Le.,
p = RTlV(1 - b/4w4 - d V 2 (7) The Guggenheim equation has been widely used to study critical equilibria in a diverse range of binary20-22 and temary18*23 mixtures. The Heilig-FrancklOJ1 equation uses the CamahanStarling2 representation of repulsive forces between hard-sphere and a square-well representation for attractive forces. p = RT(V3
+ pV2 + p2V 4- V3)/{ V(V - p)} + RTB/{V2 + V(C/B)}
(8)
where p = bC(P/7JZ, bCis the critical molecular volume and, in this implementation, z = 0. At low to medium densities, either the Guggeheim model or the Camahan-Starling formula describes repulsive hard-sphere interactions with a similar degree of accuracy. The difference between eqs 7 and 8 is primarily due to the different attractive terms. The B and C terms in eq 8 represent the contributions from the second and third vinal coefficients, respectively, of a hard-sphere fluid interacting via a square well potential. This potential is characterized by three parameters reflecting intermolecular separation (a),intermolecular attraction (EIRT), and the relative width of the well (A). The following universal values3 are obtained by solving the critical conditions of a one-component fluid: ii = 1.266 84, N A U ~ I= F 0.249 12, and c/RF = 1.511 47, where NA denotes Avogadro's constant. The extension of either equation of state parameters or, equivalently, conformal parameters (fand h) obtained for a onecomponent fluid to mixtures typically requires the use of mixing rules. The van der Waals one-fluid mixing rules18 were used in this work and the contribution of unlike interactions was obtained from the following combining rules: (9)
4276 J. Phys. Chem., VoE. 99, No. 12, 1995
Sretenskaja et al.
,
240
1
220
1601 *0° 180
160 140
1
I
1 loo] 80
6o
1
60
'":
4
20
0 640
"
650
660
670
680
690
700
I
640
710
T/K Figure 2. Comparison of experiment (0)with theory for the critical curve of water helium in the pT projection using the Guggenheim ( 0 , t= 1, 5 = 0.68) and Heilig-Franck (A, 6 = 1,c = 0.65) equations of state.
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where ( and 5 are adjustable parameters. There is considerable that the value of 6 reflects the strength of intermolecular interaction. However, the use of adjustable parameters can also be interpreted as indicating a deficiency in the theoretical model. Initially, the critical properties of water helium were calculated using the Heilig-Franck equation and no adjustable parameters (i.e., ( = 1, 5 = 1). The qualitative features of gas-gas immiscibility of the first kind were reproduced but the calculated critical curve occurred at substantially greater temperatures than the experimental data. The calculations were repeated using the Guggenheim equation which yielded nearly identical results. The agreement between theory and experiment can only be improved by utilizing an unrealistically small value of the 5 interaction parameter. These calculations are illustrated in Figure 2. There is very little difference between calculations using these two equations of state. The agreement between theory and experiment is unsatisfactory and, at relatively high pressures, the calculated trajectory of the critical curve does not coincide with experimental data. The calculated critical curve passes through a temperature maximum whereas no temperature maximum is evident from the experimental data. The hard-sphere repulsive term of the Heilig-Franck and Guggenheim equations is expected to be of similar accuracy at the densities encountered along the critical curve of water helium. The difference between these equations of state is primarily confined to different assumptions regarding atttractive interactions. The calculations of the critical locus of helium f water were repeated with the van der Waals equation which has a very different repulsive term than either of the other two equations of state but the same attractive term as the Guggenheim equation. The equation of state parameters for water (a = 338 960.28 J cm3 mol-2, b = 18.67 cm3 mol-') and helium ( a = 2766.97 J cm3 mol-2, b = 19 cm3 mol-') were evaluated from the pure component critical properties, F and VC. There is exact agreement for the critical point of water because the
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650
660
6$0
680
690
700
710
T/K Figure 3. Comparison of experiment (0)with theory (-), for the critical curve of water helium in the pT projection using the van der Waals equation of state (5 = 0.95, 5 = 1).
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calculations used conformal solution theory with water as the reference substance. In contrast to the other calculations, very good agreement between theory and experiment for the pressure-temperature behavior of helium water was obtained using the van der Waals equation (Figure 3). The agreement between theory and experiment illustrated in Figure 3 is impressive. The calculated critical locus quantitatively reproduces the observed phenomena, and the calculations are certainly well within experimental error. These good results were obtained without adjusting the 5 term (Le., 5 = 1) and using a reasonable 6 value (Le., 6 = 0.95). These equations of state must fail if the volume at very high pressure falls below the covolume limit. At 180 MPa, however, the predicted critical volume is approximately 31 cm3 mol-', which compares with a covolume parameter b = 18.67 cm3 mol-' for pure water. Consequently, at 180 MPa the volume is well above the covolume limit. The calculations also predict the variation of composition with respect to pressure reasonably well (Figure 4). In some respects, the agreement obtained with the van der Waals equation and the poor results obtained from either the Guggenheim or Heilig-Franck equations are contrary to intuition. The latter equations undoubtedly incorporate a more accurate description of hard-sphere repulsion and, in most cases, outperform the simple van der Waals model. The HeiligFranck equation has been used p r e v i o u ~ l yto ~ *calculate ~ the critical properties of other water noble gases with a satisfactory degree of accuracy. It would be incorrect to infer that these equations are generally not suitable for predicting gas-gas immiscibility of the first kind. For example, similar phenomena in the water neon mixture can be adequately de~cribed.~ The fact that the Guggenheim and van der Waals equations have the same simple attractive term also excludes the adequacy of the representation of attractive forces are the primary source of the discrepancy. The influence of "quantum effects" is also an unlikely explanation. In common with the other equations, the van der Waals equation does not take account of quantum influences and it is, nonetheless, more accurate. Also, quantum
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Phase Equilibria of the Water
J. Phys. Chem., Vol. 99, No. 12, 1995 4271
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water argon2 and water xenon1 systems at progressively lower temperatures. Therefore, a continual progression in the phase behavior can be observed as the atomic weight and size of the noble gas is increased. This is in contrast to homologous water n-alkane mixtures which all exhibit a minimum in their critical curve.18
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V. Conclusions
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The water helium mixture exhibits gas-gas immiscibility of the first kind. The critical curve does not pass through a temperature minimum but instead proceeds directly to higher temperatures from the critical point of water. The simple van der Waals equation of state can be used to predict this phenomenon with a high degree of accuracy. The discrepancy between theory and experiment is certainly within experimental error. More sophisticated equations, incorporating an accurate representations of repulsion of hard-spheres, failed to adequately predict the critical properties of this system. It appears likely that they overestimate the role of repulsion between water and helium. 0 1 0.5
I
0.6
,
I
0.7 0.8 x(water)
0.9
1
Figure 4. Comparison of experiment (0)with theory (-), for the critical curve of water helium in the px(water) projection using the van der Waals equation of state (6 = 0.95, 5 = 1).
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influences would be expected to be negligible at the temperatures involved (650-700 K). It appears likely that the Guggenheim and Camahan-Starling descriptions of repulsive forces overestimate the contribution of repulsion between the water molecule and helium atom. This conclusion is supported by the unrealistically small value of 5 required to “improve” the agreement between theory and experiment for calculations involving either the Guggenheim ( 5 = 0.68) or Heilig-Franck ( 5 = 0.65) equations. Lowering the 5 value lowers the magnitude of the covolume term (b)and therefore the relative magnitude of the repulsive contribution declines. There is some evidence that this may be a general failure for other small molecules. For example, Sadus26 has reported that the van der Waals equation is superior to the Guggenheim equation for predicting critical properties of binary mixtures containing hydrogen as one component. It is possible that the good results with the van der Waals equation are partly due to a fortuitous cancellation of errors. The molar volumes of the helium water mixture obtained at supercritical conditions are consistently greater than a simple composition average of the molar volumes of the pure components under similar conditions (Table 6 ) . One potential application of the phase behavior of the water helium system is the atmospheric behavior of the outer planets. It has been suggested* that the atmosphere of Uranus contains mostly compressed water, helium, and hydrogen. The expected variation of pressure with respect to temperature in the planetary atmosphere partly coincides with the range of pressures and temperatures in this study. It is of interest to consider the phase behavior of water helium in relation to the behavior of other members of the water noble gas series. All members of the series exhibit type III phase behavior. Both water helium and water neon exhibit gas-gas immiscibility of the first kind whereas this type of behavior is not observed for other noble gases. The critical curve of water krypton passes through a temperature minim~m.A ~ similar temperature minimum is found in the
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Acknowledgment. R.J.S. thanks the Alexander von Humboldt Foundation for financial support of part of this work. N.G.S. acknowledges support in the form of a fellowship from the Deutsche Forschungsgemeinschaft. References and Notes (1) Franck, E. U.; Lentz, H.; Welsch, H. Z. Phys. Chem. Neue Forge ( F r a n e r t ) 1974,93,95. (2) Wu, G.; Heilig, M.; Lentz, H.; Franck, E. U. Ber. Bunsen-Ges. Phys. Chem. 1990,94,24. (3) Mather, A. E.; Sadus, R. J.; Franck, E. U. J . Chem. Thermodyn. 1993,25, 771. (4) Franck, E. U. J . Chem. Thermodyn. 1987,19,225. (5) Gerth, W. A. J . Solution Chem. 1983,12, 655. (6) Temkin, M. Russ. J . Phys. Chem. 1959, 33, 275. See also: Schneider, G. M. Adv. Chem. Phys. 1970,17, 1. (7) von Konynenburg, P. H.; Scott, P. L. Philos. Trans. R . SOC.London 1980,298A, 495. (8) Stevenson, D. J. Annu. Rev. Earth Planet Sci. 1982,10, 257. (9) Guggenheim, E. A. Mol. Phys. 1965,9,43. (10) Heilig, M.; Franck, E. U. Ber. Bunsen-Ges. Phys. Chem. 1989,93, 898. (11) Heilig, M.; Franck, E. U. Ber. Bunsen-Ges. Phys. Chem. 1990,94, 27. (12) Japas, M. L.; Franck, E. U. Ber. Bunsen-Ges. Phys. Chem. 1985, 89,793. (13) Tian, Yiling; Michelberger,Th.;Franck, E. U. J . Chem. Thermodyn. 1991,23, 105. (14) Michelberger, Th.; Franck, E. U. Ber. Bunsen-Ges. Phys. Chem. 1990,94, 1134. (15) Japas, M. L.; Franck, E. U. Ber. Bunsen-Ges. Phys. Chem. 1985, 89,1268. (16) Christoforakos,M.; Franck, E. U. Ber. Bunsen-Ges. Phys. Chem. 1986,90,780. (17) Shmonov, V. M.; Sadus, R. J.; Franck, E. U. J. Phys. Chem. 1993, 97,9054. (18) Sadus, R. J. High Pressure Phase Behaviour of Multicomponent Fluid Mixtures; Elsevier: Amsterdam, 1992. (19) Brown, W. B. Philos. Trans. 1957,250A, 175. (20) Christou, G.; Morrow, T.; Sadus, R. J.; Young, C. L. Fluid Phase Equilib. 1985,25, 263. (21) Mainwaring, D. E.; Sadus, R. J.; Young, C. L. Chem. Eng. Sci. 1988,42, 85. (22) Sadus, R. J.; Young, C. L.; Svejda, P. Fluid Phase Equilib. 1988, 39,89. (23) Sadus, R.J. J. Phys. Chem. 1992,96,5197. (24) Camahan, N. F.; Starling, K. E. AlChE J . 1972,17, 11. (25) Sadus, R. J. J . Phys. Chem. 1989,93,3787. (26) Sadus, R. J. J . Phys. Chem. 1992,96,3856. JP9417788
