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GENERAL RESEARCH Classification of Homogeneous Binary Azeotropes I. Shulgin,† K. Fischer,‡ O. Noll,§ and J. Gmehling*,‡ Technische Chemie, Carl von Ossietzky Universita¨ t Oldenburg, Postfach 2503, 26111 Oldenburg, Germany, Department of Chemical Engineering, State University of New York at Buffalo, Amherst, New York 14260, and Centre Re´ acteurs et Processus, Ecole Nationale Supe´ rieure des Mines, 35 rue Saint Honore´ , 77305 Fontainebleau, France
The boiling point curves of binary liquid mixtures provide sufficient information leading to the characterization of the real-phase equilibrium behavior. The extremes of these curves indicate azeotropy. The topological consideration of all possible forms of boiling point curves in homogeneous binary systems suggests a new classification of vapor-liquid equilibrium (VLE) behavior. Rigorous thermodynamic relations are derived, whereby component vapor pressure Psi and limiting activity coefficients γ∞i are required only to identify the azeotropic behavior of binary mixtures without the need of extensive measurements or calculations. The validity and the application of the derived conditions are proved by using experimental VLE, Psi , and γ∞i data. 1. Introduction For almost 200 years it has been known that the separation of components by simple distillation is impossible, if the mixture exhibits an azeotrope at a specified temperature and pressure. Several decades passed by before it was clear that the particularity of azeotropic points is not based on special effects such as chemical reactions but can be explained by ordinary molecular interactions quantified by activity coefficients. Eighty years ago, azeotropic data were the first type of thermodynamic data extensively collected and compiled.1 The reliable knowledge of azeotropic behavior is very important, because distillation is the most common industrial separation process. The Dortmund Data Bank (DDB)2 contains azeotropic information for more than 20 700 binary, ternary, and quaternary systems (about 43 000 azeotropic and zeotropic points). A large part of these data is available in printed form.3 According to their vapor-liquid equilibrium (VLE) behavior, the binary systems can be subdivided into zeotropic (azeotrope-free) and azeotropic systems. The latter may contain one azeotrope (an azeotropic or monoazeotropic system) or two azeotropes (a double azeotropic system). Double azeotropic systems were discovered at the end of the 1960s, and up to now less than 10 systems are known.3 Zeotropic systems can exhibit both positive and negative departure from Raoult’s law, but there are also zeotropic systems with a more complex behavior (e.g., positive and negative departure from Raoult’s law depending on the composi* Corresponding author. Tel.: ++49-441-798-3831. Fax: ++49-441-798-3330. E-mail:
[email protected]. † State University of New York at Buffalo. ‡ Carl von Ossietzky Universita ¨ t Oldenburg. § Ecole Nationale Supe ´ rieure des Mines.
tion range). The published criteria for characterizing azeotropic behavior (see section 2) have been proven to be useful in most cases, but according to our knowledge, no classification scheme covers all types of azeotropic and zeotropic behavior. Hence, the aim of this paper is to develop a scheme for homogeneous binary mixtures, which includes all types. The topologically derived classification scheme remains practically useful, because as for the existing methods experimental or estimated Psi and γ∞i data are required only and simple inequality conditions have to be checked to distinguish between the types of azeotropic and zeotropic behavior. The suggested simple scheme, graphically presented in Figure 4, may be useful to anticipate separation problems or their solutions when designing distillation processes. 2. Current Classification Scheme for Homogeneous Binary Azeotropes 2.1. Theoretical Background. The simple classification of azeotropic diagrams is based on the consideration of maximum and minimum azeotropes as presented in numerous publications.4 The condition for the existence of binary azeotropes is usually derived from the relative volatility R12, expressed as
R12 )
γ1Ps1 φs1Φ1 φv2 γ2Ps2 φv1 φs2Φ2
≈
γ1Ps1 γ2Ps2
(1)
where γi is the activity coefficient and Psi is the vapor pressure of component i. Relation (1) is obtained from the isofugacity condition, implying that the combined influence of the Poynting factor Φi, the pure-component fugacity coefficient at saturation φsi , and the vaporphase fugacity coefficient in the mixture φvi is negligible. Even if the fugacity coefficients differ significantly
10.1021/ie990897c CCC: $20.00 © 2001 American Chemical Society Published on Web 05/18/2001
Ind. Eng. Chem. Res., Vol. 40, No. 12, 2001 2743
Figure 1. Ratio of the component vapor pressures and the activity coefficients for the binary system triethylamine (1)-ethanol (2) at 338 K using the Wilson equation fitted to VLE data.9
Figure 2. Ratio of the component vapor pressures and the activity coefficients for the binary system acetone (1)-chloroform (2) at 328 K using the Wilson equation fitted to VLE data.10
from unity, their ratio may approach unity. Nonetheless, the expression (1) is invalid at higher pressures and for strongly associating compounds such as carboxylic acids. The index 1 always refers to the more volatile component (Ps1 > Ps2). For certain similar volatile compounds, a Bancroft point may be observed,5 where the vapor pressure curves intersect each other and the index has to be exchanged. The binary systems considered in this paper are far away from the critical point. Because homogeneous azeotropic points obey the condition R12 ) 1, the following expression may easily be derived from eq 1:3,6-8 Figure 3. Slopes of the Px curve at infinite dilution at constant temperature.
γ2 Ps1 ) γ1 P s
(2)
2
The features of this relation are to be discussed in detail for homogeneous binary azeotropes, where systems with positive and negative deviations from Raoult’s law have to be distinguished. 2.1.1. Positive Deviation from Raoult’s Law. For the azeotropic system triethylamine-ethanol exhibiting a positive deviation from Raoult’s law (γi > 1), the ratios of activity coefficients and vapor pressures at 338 K are shown in Figure 1. The lines intersect at a mole fraction of x1 ≈ 0.62. A simple criteria for azeotropy may be formulated:
γ∞2
>
Ps1 Ps2
pressure maximum azeotropes
(3)
2.1.2. Negative Deviation from Raoult’s Law. For homogeneous binary systems with a negative deviation from Raoult’s law (γi < 1), a similar expression may be derived. Figure 2 shows the behavior of the binary system acetone-chloroform at 328 K, where an intersection of the two lines is observed at a mole fraction of x1 ≈ 0.40. A pressure minimum azeotrope will occur, if the following condition is fulfilled:
γ∞1
1 at x1 f 1 or R12 > 1 at x1 f 0 and R12 < 1 at x1 f 1, azeotropic behavior according R12 ) 1 must occur within the interval 0 < x1 < 1:
γ∞2 g
γ∞2
e
Ps1 Ps2 Ps1 Ps2
g
1 γ∞1
pressure maximum azeotrope
(5)
e
1 γ∞1
pressure minimum azeotropes
(6)
This approach allows one to distinguish between pressure maximum azeotropes and pressure minimum azeotropes. However, besides these cases, systems containing two azeotropic points (e.g., the system benzene-hexafluorobenzene) and zeotropic systems with a more complicated behavior than only positive or negative deviations from Raoult’s law are known.3 The classification suggested in this paper provides simple criteria to characterize all types of azeotropic and zeotropic behavior of subcritical homogeneous mixtures. 3. New Classification Scheme for Homogeneous Binary Azeotropes At a constant temperature for the pressure slope at infinite dilution (x1 f 0 and x2 f 0), three different cases for each component (1a-3a and 1b-3b) may be distinguished, as shown in Figure 3. From the graphic it may be concluded that case 1b furnishes a maximum pressure azeotrope and case 1a gives a minimum pressure azeotrope. The combination of cases 1a and 1b leads to a double azeotrope. Case 3a or 2a together with case
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Figure 4. Classification of VLE in binary homogeneous systems including bubble-point curves for different types of VLE behavior: - -, Raoult’s law; (s), Px curve; b, azeotropic point.
2b or 3b usually gives rise to zeotropic behavior, but a double azeotrope may be evoked as well. For the cases shown in Figure 3, inequality relations between the pure-component vapor pressures, the activity coefficients at infinite dilution, and the slopes of the Px curve at infinite dilution can be formulated. If validity of the truncated isofugacity relation,11 already established in the preceding section in order to simplify eq 1, is superposed, the following expressions are obtained:
∂P ∂x1 ∂P ∂x1
| |
) γ∞1 Ps1 - Ps2
for x1 ) 0
(7)
) Ps1 - γ∞2 Ps2
for x1 ) 1
(8)
T
T
Equations 7 and 8 can be related to the geometrical cases indicated in Figure 3. This simple consideration suggests a new classification for azeotropic behavior of binary mixtures and allows one to distinguish between all types of zeotropic and azeotropic behavior in terms of component vapor pressures and activity coefficients at infinite dilution.
All types of binary azeotropes are shown in Figure 4. In this diagram the activity coefficients at infinite dilution for the higher boiling component 2 are plotted versus those of the more volatile component 1. Any binary system at a specified temperature is represented by a single point given by γ∞1 and γ∞2 in this diagram, which may be related to the pure-component vapor pressures (dashed lines in Figure 3) and the ideal behavior (γi ) 1, continuous line in Figure 3). The vertical lines with γ∞1 ) 1 and γ∞1 ) Ps2/Ps1 and the horizontal lines with γ∞2 ) 1 and γ∞1 ) Ps1/Ps2 produce nine sectors, which classify all possible types of binary VLE behavior. The corresponding bubble-point curves are schematically drawn in Figure 4 along with the criteria in terms of activity coefficients at infinite dilution and component vapor pressures. In three cases (VI, VIII, and IX), two topologically different shapes of the bubble-point curves may exist, which are marked by a, indicating a zeotropic system, or by b, identifying a double azeotropic system. These subtypes cannot be identified by knowing the γ∞i values only. The approach allows the classification of 12 different types of azeotropic behavior of binary mix-
Ind. Eng. Chem. Res., Vol. 40, No. 12, 2001 2745 Table 1. Examples for the Different Types of VLE Behavior system benzene-hexafluorobenzene ethanol-triethylamine
ref
14, 16 17 9, 17 n-octane-2-methylpyridine 18, 19 chlorine-sulfur dioxide 20 triethylamine-acetic acid 21 benzene-N-methyl-6-caprolactam 22, 23 methyl acetate-1,2-epoxybutane 24, 25a acetone-chloroform 10 chloroform-tetrahydrofuran 26, 27, 28 n-butane-methyl tert-butyl ether 20 29 20 diethylamine-methanol 30 30 pentafluoroethane-ammonia 15 15 propylene-ethanethiol 31 31 pentafluoroethane-1,1,1-trifluoroethane 32
T [K]
type
303-343 283 293-338 313-348 243-323 333-353 313-373 298-348 288-328 303-337 273 363 373 298-348 399 254-276 308-323 253 323 280-300
I II III III III IV V VIa VII VII VIa IXa VIIIa VII IXb IXa VIb VIa IXa IXb
a The double azeotrope at 298 K24 has not been confirmed by reinvestigating measurements.25
tures: four zeotropic types (V, VIa, VIIIa, and IXa), two types with one pressure maximum azeotrope (II and III), two types with one pressure minimum azeotrope (IV and VII), and four types of double azeotropic systems (I, VIb, VIIIb, and IXb). The criteria proposed in this work mean an extension of those published in the literature.3,6,12,13 The criteria for monoazeotropic systems are already given by eqs 3-6. Equation 4 include types I, IV, and VII of azeotropic behavior and the inequality (3) types I-III. If both conditions are fulfilled, a double azeotropic behavior of type I is observed. Condition (6) includes types IV and VII, and expression (5) represents types II and III. Neither the classical criteria nor those proposed in this work are sufficient to decide definitely in every case if a binary azeotrope exists or not, although Wisniak et al.13 emphasized the sufficiency of their criteria for double azeotropes. The double azeotropic systems of types VIb, VIIIb, and IXb cannot be distinguished from the zeotropic ones of types VIa, VIIIa, and IXa acquiring the activity coefficients at infinite dilution and the component vapor pressures only. If the composition dependence of the activity coefficients is known, an appropriate numerical algorithm may reveal the desired distinction. The criteria for type V identify zeotropy unambiguously. 4. Experimental Examples Experimental isothermal VLE data from the DDB2 were retrieved to validate the significance of the proposed classification. Except for case VIIIb, examples are listed in Table 1. Certain systems were selected to demonstrate that the VLE type may change with respect to temperature. If the component vapor pressure ratio changes, the sectors alter as well, and for the distinct condition that both pure-component pressures are equal, zones 2a and 3b in Figure 3 vanish and classes II, IV-VI, and VIII disappear; thus, Figure 4 reduces to Figure 5. Two interesting examples are shown in Figures 6 and 7. Both systems exhibit two azeotropic points as indicated by the two extremes in the Px curve and the double intersection of the activity coefficients ratio curve with the line of the vapor pressure ratio. The systems belong to different types. In Figure 6 the pressure
Figure 5. Classification of VLE in homogeneous binary systems at the Bancroft point (Ps1 ) Ps2).
minimum is followed by the maximum azeotrope, while in Figure 7 the order is inverse, which is caused by the opposite curves of the activity coefficients ratio. Consequently, the system benzene-hexafluorobenzene at 323 K belongs to class I and the system pentafluoroethaneammonia at 323 K to type VI. The different VLE types are irregularly distributed. Usually azeotropes require a similar volatility of the components or activity coefficients largely different from unity. Because most frequently a positive deviation from Raoult’s law is observed, types III and VIa occur more often than types VII and VIIIa and the latter ones appear more often than the remaining classes. 5. Discussion and Conclusions The proposed simple method for classifying the VLE behavior of binary systems topologically requires component vapor pressures and activity coefficients at infinite dilution only. The described method allows one to identify the type of azeotropic behavior, avoiding tedious VLE measurements or iterative calculations. For many substances, component vapor pressure data are available and activity coefficients at infinite dilution can be taken from experimental data collections (e.g., DDB2 and DECHEMA Chemistry Data Series33,34) or predicted using group contribution methods such as UNIFAC,35 modified UNIFAC,36,37 or revised ASOG.38 Except for one type, experimental examples have been found for all classes. Although a few examples are given here, the entire VLE database of the DDB has been analyzed. The criteria for azeotropy are derived for homogeneous mixtures at isothermal conditions. Principally, equivalent rules may be established for the topologically analogous isobaric systems; however, the inequalities would be more complex, because temperature effects need to be considered. For the isothermal case, Raoult’s law, which has been chosen as the reference state, furnishes a straight Px curve, while the corresponding Tx curve, assuming unity for all activity coefficients, is nonlinear at isobaric conditions. Furthermore, activity coefficients depend on the composition and significantly
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Figure 6. Bubble-point curve and ratio of vapor pressures and activity coefficients for the system benzene (1)-hexafluorobenzene (2) at 323 K using the Wilson equation fitted to VLE data.14
Figure 7. Bubble-point curve and ratio of vapor pressures and activity coefficients for the system pentafluoroethane (1)-ammonia (2) at 323 K using the NRTL equation fitted to VLE data.15
on the temperature, perplexing the derivation and application of classification criteria. Heterogeneous binary systems are not investigated separately because their topological characteristics are equivalent with respect to the principle of the classification. According to eqs 7 and 8 and Figure 3, the classification is based on the characteristics in the vicinity of the pure compound, which may be considered to be homogeneous generally. If for any Px curve in Figure 4 at any concentration a horizontal line is introduced, which resembles a miscibility gap, the topology with respect to the azeotropic behavior and thus the validity of the derived criteria remain unaltered. The consideration of immiscibilities may lead to a further refinement of the suggested types, but the criteria are identical or homogeneous and heterogeneous systems. The distinction between zeotropic and double azeotropic systems of type VI, VIII, or IX requires the concentration dependence of the activity coefficients, which may be described by a correlative model. The classification of type VI, VIII, or IX demands 1/γ∞1 < Ps1/
Ps2 and γ∞2 < Ps1/Ps2. An appropriate iterative algorithm may be applied to search for a maximum of the function γ2/γ1, and if the condition (γ2/γ1)max < Ps1/Ps2 is fulfilled, zeotropy is confirmed. Special interest is often paid to polyazeotropy,13,39 which has been observed for the following systems: benzene-hexafluorobenzene, diethylamine-methanol, butyric acid-butyl butyrate, propionic acid-butyl propionate, ammonia-pentafluoroethane, isobutyl acetateacetic acid, and water-dinitrogen pentoxide. A further double azeotrope in the binary system pentafluoroethane-1,1,1-trifluoroethane has been identified in this work, which has not been recognized by the authors who performed the measurements,32 because the experimental data are provided neither at isothermal nor isobaric conditions. The double azeotrope methyl acetate-1,2epoxybutane24 has not been confirmed by reinvestigating measurements.25 The procedure of analyzing the topology of the boiling point surfaces may principally be applied to ternary or higher systems analogously. The existing approaches classifying the azeotropic behavior of these systems by
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Tamir and Wisniak40 and Kudryavtseva and Toome41 have not led to general criteria yet. Acknowledgment I.S. thanks DDBST GmbH for financial support during his stays in Oldenburg in 1996 and 1998. Literature Cited (1) Lecat, M. L’Azeotropisme; Monograph: Brussels, Belgium, 1918. (2) Gmehling, J. Dortmund Data BanksBasis for the Development of Prediction Methods; CODATA Bulletin: 1985. (3) Gmehling, J.; Menke, J.; Krafczyk, J.; Fischer, K. Azeotropic Data; VCH Verlagsgesellschaft: Weinheim, Germany, 1994. (4) Malesinski, W. Azeotropy and Other Theoretical Problems of Vapour-Liquid Equilibrium; PWN-Polish Scientific Publishers: Warszawa, Poland, 1965. (5) Gmehling, J.; Brehm, A. Lehrbuch der Technischen Chemies Grundoperationen; Thieme Verlag: Stuttgart, Germany, 1996. (6) Brandani, V. Use of Infinite-Dilution Activity Coefficients for Predicting Azeotrope Formation at Constant Temperature and Partial Miscibility in Binary Liquid Mixtures. Ind. Eng. Chem. Fundam. 1974, 13, 154. (7) Stephan, K.; Wagner, W. Application of the Wilson Equation to Azeotropic Mixtures. Fluid Phase Equilib. 1985, 19, 201. (8) Gmehling, J.; Kolbe, B. Thermodynamik; VCH Verlagsgesellschaft: Weinheim, Germany, 1992. (9) Copp, J. L.; Everett, D. H. Thermodynamics of Binary Mixtures Containing Amines. Discuss. Faraday Soc. 1953, 15, 174. (10) Ro¨ck, H.; Schro¨der, W. Dampf-Flu¨ssigkeits-Gleichgewichtsmessungen im System Azeton-Chloroform. Z. Phys. Chem. Neue Folge 1957, 11, 41. (11) van Ness, H. C.; Abbott, M. M. Classical Thermodynamics of Nonelectrolyte Solutions with Application to Phase Equilibria; McGraw-Hill Book Co.: New York, 1982. (12) Konowalow, D. U ¨ ber die Dampfspannungen der Flu¨ssigkeitsgemische. 1. Abhandlung. Ann. Phys. Chem. Neue Folge 1881, 14, 34. (13) Wisniak, J.; Segura, H.; Reich, R. Polyazeotropy in Binary Systems. Ind. Eng. Chem. Res. 1996, 35, 3742. (14) Kogan, I. V.; Morachevsky, A. G. Liquid-Vapor Equilibrium in the System Hexafluorobenzene-Benzene (Formation of Two Azeotropes). Zh. Prikl. Khim. 1972, 45, 1888. (15) Chai Kao, C.-P.; Paulaitis, M. E.; Yokozeki, A. Double Azeotropy in Binary Mixtures of NH3 and CHF2CF3. Fluid Phase Equilib. 1997, 127, 191. (16) Gaw, W. J.; Swinton, F. L. Thermodynamic Properties of Binary Systems Containing Hexafluorobenzene. Trans. Faraday Soc. 1968, 64, 2023. (17) Chun, K. W.; Davison, R. R. Thermodynamic Properties of Binary Mixtures of Triethylamine with Methyl and Ethyl Alcohol. J. Chem. Eng. Data 1972, 17, 307. (18) Warycha, S. Vapor-Liquid Equilibria and Excess Gibbs Energies for Binary Systems of Pyridine Base with Hydrocarbons at 313.15 K. J. Chem. Eng. Data 1993, 38, 274. (19) Kasprzycka-Guttman, T.; Chojnacka, I. (Vapour + Liquid) Equilibria of (Pyridine or a-Picoline + a C6 to C10 n-Alkane) at 348.15 K. J. Chem. Thermodyn. 1989, 21, 721. (20) Wilson, H. L.; Wilding, W. V. Vapor-Liquid and LiquidLiquid Equilibrium Measurements on Twenty-two Binary Mixtures. DIPPR Data Series 1994, 2, 63. (21) Malanowski, S. Measurements of Vapor-Liquid Equilibrium in the Systems Formed by Acetic Acid with Ethyl Acetate, Triethylamine and Acetamide; Nitrobenzene with 1-Nonene and Phenol; Propionic Acid with Phenol. AIChE Symp. Ser. 1990, 279, 86, 38.
(22) Hradetzky, G.; Hammerl, I.; Kisan, W.; Wehner, K.; Bittrich, H.-J. Data of Selective Solvents; VEB: Berlin, 1989. (23) Bittrich, H.-J.; Hradetzky, G. Vapor-Liquid Equilibria of Binary Systems Consisting of N-Methyl--caprolactam and Hydrocarbons. Z. Phys. Chem. (Leipzig) 1989, 270, 451. (24) Leu, A. D.; Robinson, D. B. Vapor-Liquid Equilibrium in Selected Binary Systems of Interest to the Chemical Industry. AIChE Data Ser. 1991, 1, 1. (25) Monto´n, J. B.; Cruz Burguet, M.; Mun˜oz, R.; Wisniak, J.; Segura, H. Nonazeotropy in the System Methyl Ethanoate + 1,2Epoxybutane. J. Chem. Eng. Data 1997, 42, 1195. (26) Paul, H.-I. Experimentelle Untersuchung der Flu¨ ssigkeitsDampf-Phasengleichgewichte und volumetrischen Eigenschaften bina¨ rer und terna¨ rer Mischungen; VDI Fortschrittsberichte: Du¨sseldorf, Germany, 1987; series 3, p 135. (27) Thomas, E. R.; Newman, B. A.; Nicolaides, G. L.; Eckert, C. A. Limiting Activity Coefficients from Differential Ebulliometry. J. Chem. Eng. Data 1982, 27, 233. (28) Coutinho, J. P.; Macedo, E. A. Infinite-Dilution Activity Coefficients by Comparative Ebulliometry. Binary Systems Containing Chloroform and Diethylamine. Fluid Phase Equilib. 1994, 95, 149. (29) Fischer, K.; Park, S.-J.; Gmehling, J. Vapor-Liquid Equilibrium for Binary Systems Containing Methanol or Ethanol, tertbutyl Methyl Ether or tert-amyl Methyl Ether, and Butane or 2-Methylpropene at 363 K. Int. Electron. J. Phys.sChem. Data 1996, 2, 135. (30) Srivastava, R.; Smith, B. D. Total-Pressure Vapor-Liquid Equilibrium Data for Binary Systems of Diethylamine with Acetone, Acetonitrile, and Methanol. J. Chem. Eng. Data 1985, 30, 308. (31) Giles, N. F.; Wilson, H. L.; Wilding, W. V. Phase Equilibrium Measurements on Twelve Binary Mixtures. J. Chem. Eng. Data 1996, 41, 1223. (32) Widiatmo, J. V.; Sato, H.; Watanabe, K. Bubble-Point Pressures and Liquid Densities of Binary R-125 + R-143a System. Int. J. Thermophys. 1995, 16, 801. (33) Tiegs, D.; Gmehling, J.; Medina, A.; Soares, M.; Bastos, J.; Alessi, P.; Kikic, I. Activity Coefficients at Infinite Dilution; DECHEMA: Frankfurt, Germany, 1986; Vol. IX, two parts. (34) Gmehling, J.; Menke, J.; Schiller, M. Activity Coefficients at Infinite Dilution; DECHEMA: Frankfurt, Germany, 1994; Vol. IX, Supplements 3 + 4. (35) Fredenslund, Å.; Gmehling, J.; Rasmussen, P. VaporLiquid Equilibria Using UNIFAC; Elsevier: Amsterdam, The Netherlands, 1977. (36) Weidlich, U.; Gmehling, J. A Modified UNIFAC Models 1. Prediction of VLE, hE and γ∞. Ind. Eng. Chem. Res. 1987, 26, 1372. (37) Larsen, B. L.; Rasmussen, P.; Fredenslund, Å. A Modified UNIFAC Group-Contribution Model for Prediction of Phase Equilibria and Heats of Mixing. Ind. Eng. Chem. Res. 1987, 26, 2274. (38) Kojima, K.; Tochigi, K. Prediction of Vapor-Liquid Equilibria by the ASOG Method; Kodansha-Elsevier: Tokyo, 1979. (39) Cruz Burguet, M.; Monto´n, J. B.; Mun˜oz, R.; Wisniak, J.; Segura, H. Polyazeotropy in Associating Systems: The 2-Methylpropyl Ethanoate + Ethanoic Acid System. J. Chem. Eng. Data 1996, 41, 1191. (40) Tamir, A.; Wisniak, J. Correlation and Prediction of Boiling Temperatures and Azeotropic Conditions in Multicomponent Systems. Chem. Eng. Sci. 1978, 33, 657. (41) Kudryavtseva, L.; Toome, M. Method for Predicting Ternary Azeotropes. Chem. Eng. Commun. 1984, 26, 373.
Received for review December 13, 1999 Revised manuscript received March 23, 2001 Accepted March 28, 2001 IE990897C
