Xnd. Eng. Chem. Fundam. 1981, 20, 177-180
react with water, calculated Henry's constants are too high. For example, aqueous solubility data for carbon monoxide (Wilhelm et al., 1977) are very well represented over the range 0-85 "C using up = 0.395 nm and t 2 / k = 134 K. When these parameters are used to calculate Henry's constants for carbon monoxide in the region 250-300 "C, calculated results are about twice those measured by Jung et al. (1971). However, these authors report appreciable chemical reaction between water and carbon monoxide at temperatures above 250 "C, explaining the higher observed solubility. While scaled-particle theory may provide a useful basis for correlating phase-equilibrium data, it is clear that there is a large gulf between the assumptions of the theory and the properties of real systems, especially aqueous systems. This gulf is partly absorbed in the adjustable parameters but at the cost of physical plausibility. It is strange, for example, that the best up for carbon dioxide (0.332 nm) should be smaller than the best up for carbon monoxide (0.395 nm). Scaled-particle theory is strongly sensitive to the value of up;therefore, it is important to evaluate this parameter carefully from reliable experimental data, while recognizing that its physical significance is only approximate.
177
Acknowledgment
The authors are grateful to the US. Department of Energy for financial support and to the Deutscher Akademischer Austauschdienst for a fellowship to G.S. L i t e r a t u r e Cited Benson, B. B.; Krause, D. J. Chem. Phys. 1878, 64, 691. Cramer, S. D. Ind. Eng. Chem. Process Des. Dev. 1980, 79, 300. Edwards, T. J.; Mawer, G.; Newman, J.; Prausnitz, J. M. AIChE J . 1978, 24, 1966. Jung, J.; Knacke, 0.; Neuschiitz, D. Chem. Ing. Tech. 1971, 43, 112. Hayduk, W.; Laudie, H. AIChE J. 1873, 19, 1933. Hayduk, W.; Buckley, W. D. Can. J. Chem. Eng. 1871, 49, 667. Curtiss, C. F.;Bird, R. 8. "Molecular Theory of Gases and Hlrschfeider, J. 0.; Liquids", Wlley: New York, 1954. Pierotti, R. A. Chem. Rev. 1978, 76, 717. Potter, R. W.; Clynne, M. A. J. So/ut&n Chem. 1878, 7 , 837. Pray, H. A.; Schweickert, C. E.; Minnich, B. H. Ind. Eng. Chem. 1852, 4 4 , 1150. Wiihelm. E.; Battlno, R. J . Chem. 73ermcdyn. 1971, 3 , 379. Wilhelm, E.; Battlno. R.; Wilcock, R. J. Chem. Rev. 1977, 77, 226.
Chemical Engineering Department and Lawrence Berkeley Laboratory University California, Berkeley Berkeley, California 94720
Gunther Schulze J. M. Prausnitz*
Received for review June 17,1980 Accepted February 17,1981
Azeotropic Composition from the Activity Coefficients of Components
+
An equation for calculating the composition of a binary azeotrope, x p = (1 a)-',has been tested on 45 systems exhibiting small, medium, and large deviations from regularity. When corrections for the real behavior of the vapor phase were taken into account for the case in which one component is associated in the vapor phase, e.g., acetic acid, the results obtained for the azeotropic composition improved considerably. The effect of the differences in the vaporization entropies of the components on the azeotropic composition, as exemplified by the systems containing acetic acid and n-paraffins, was found to be small compared to that of the dimerization of the acM in the vapor phase.
and observed (experimental) azeotropic compositions Ax2 = xp(calcd) - ~2(0bsd). It is expected that as a result of this study, a clearer picture will emerge regarding the suitability of Kireev's equation for computation of the azeotropic composition. To calculate the azeotropic composition, eq 1requires knowledge of the values of pFs, which in turn can be found from equations correlating the vapor pressure and temperature. However, the p"-T data are not available for a large number of organic compounds. This in itself may be considered as a disadvantage. In view of this fact, it also seemed worthwile to compare in a general way the results obtained by eq 1with those computed by using the equations developed by Prigogine (1954) and by Malesinski (1965). The results obtained by these equations for the azeotropic composition of some binary systems were reported by Kurtyka and Kurtyka (1980). But in both cases the azeotropic composition can be computed from the easily accessible data, namely the boiling temperatures of the pure components and of the azeotropes.
Introduction
The composition of an azeotrope in a binary regular solution is given by the equation xp = (1 + a)-1
(1)
In eq 1, x 2 is the mole fraction of component 2 in the azeotrope and a is the square of the ratio of logarithms of the activity coefficients y 2 and yl,Le., (In y2/ln y1)1/2. At the azeotropic point the composition of the liquid and the vapor phase are equal, x 2 = y2, and in the case where the vapor phase is ideal, the expressions for y1 and y2take a simple form, namely 71 = P/P1°
(2)
= P/PZ0
(3)
72
where p l 0 and p p oare the vapor pressures of component 1 and 2, respectively at the boiling temperature of the azeotrope, and p is the total pressure of the mixture. Equation 1, although in somewhat different form, due to Kireev (1941), has not been tested for computing the azeotropic composition of the systems exhibiting small, medium, and large deviations from regularity. Moreover, it also became interesting and useful to modify eq 1in a way that would take into account vapor phase nonideality and thus show to what extent that correction affects the deviations between the calculated 0196-4313/81/1020-0177$01.25/0
Results and Discussion
The azeotropic data, except those for the systems containing water (Andon et al., 1957), were taken from Horsley's book (1973). When doubts arose, original papers were consulted. 0
1981 American Chemical Society
178
Ind. Eng. Chem. Fundam., Vol. 20, No. 2, 1981
Table I. Azeotropic Compositions, x2,Computed with Eq 1 for Some Binary Systems at Atmospheric Pressure mol % no.
system
1 2 3 4 5 6 7 8 9 10
benzene-n-hexane ( 2 ) -n-heptane -cyclohexane -cyclohexene acetone-n-hexane -n-heptane -chloroform ethanol-cyclohexane -n-hexane 1-butanolcyclohexane -m -xylene -p-xylene phenol-aniline -n-tridecane aniline-n-nonane -n-decane -n-undecane -n-dodecane -n-tridecane -n-tetradecane acetic acid-pyridine -2-picoline -3-picoline -4-picoline -2,6-lutidine
11
12 13 14 15 16 17 18 19 20 21 22 23 24 25
mol %
87.9 4.6 40.8 35.9 37.2 8.2 65.9 51.2 61.4 88.1
95.0 0.1 46.0 34.2 37.6 6.9 65.8 54.5 66.8 89.0
Ax, -7.1 4.5 --5.2 1.7 -0.4 1.3 0.1 -3.3 -5.4 -0.9
19.3 22.7 61.4 13.0 84.5 61.9 34.0 24.5 12.2 4.8 49.0 57.6 67.4 67.2 73.4
20.8 23.5 58.2 9.4 82.3 53.4 29.3 17.8 7.0 2.3 42.2 51.2 59.6 59.7 65.4
-1.5 -0.8 3.2 3.6 2.2 8.5 4.7 6.7 5.2 2.5 6.8 6.4 7.6 7.5 8.0
X 2 ( ~ ~ d "z(obsd) )
no. 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41a 41 b 41c 4 2a 42b 43a 43b 44 45
a
At 69.86 "C.
system xz(calcd) "z(obsd) Axz acetic acid-n-hexane 90.0 90.8 -0.8 -n-heptane 67.2 54.9 12.3 -n-octane 44.6 31.8 12.8 -n-nonane 27.2 17.4 9.8 -n-decane 12.5 7.4 5.1 -n-undecane 3.9 1.5 2.4 propionic acid33.8 31.4 2.4 pyridine -2-picoline 43.8 39.4 4.4 -n -heptane 90.2 97.3 -7.1 -n-octane 68.9 -1.4 10.3 -n-nonane 40.6 33.0 7.6 -n-decane 16.5 5.3 11.2 71.7 pyridine-n72.9 1.2 heptane -n -octane 37.4 35.2 2.2 -n-nonane 5.7 -0.7 6.4 -water 75.5 -14.2" 61.3 -water 63.2 74.5 -11.3b -water 63.1 75.0 -11.9 3-picoline-water 78.8 89.3 -10.5" -water 78.6 88.8 -10.2b 4-picoline-water 80.3 -10.3" 90.6 -water 80.1 89.9 -9.8b 2-picoline-n57.7 53.0 4.7 octane -n-nonane 8.9 12.1 -3.2
At 89.83 "C.
No attempts were made to evaluate the accuracy of the azeotropic data. However, it seems reasonable to accept on the basis of the information available that in most cases the observed azeotropic composition is accurate to f0.5 mol %. In cases where appreciable differences occur in the azeotropic data from a single investigator, only the most recent data were used. The situation is more complicated when a few data are reported on a particular system by different investigators. Such a case requires a special study of the original papers. Generally, the more recent data are favored, but there are exceptions from that pattern. For instance, the azeotropic composition, x 2 , for the system pyridine-water (2) at atmospheric pressure, according to Andon et al. (19571, is 0.750. This value is in exact agreement with the value found by Ibl et al. (1954), in close agreement with that found by Zawidzki (1900),viz. 0.753, but in poor agreement with that found by Fowler (1952), viz. 0.766. Similar observations were made in relation to the boiling temperatures of some azeotropes. The piovalues were computed from the Antoine equation (1888). The values of the constants A, B, and C of that equation were taken from the tables compiled by Hala et al. (1968) and by Hirata et al. (1975). For the systems containing water, the Antoine constants were taken from a paper by Herington and Martin (1953). The results obtained by Eq 1 for 45 binary systems are listed in Table I. It is seen that eq 1 gives satisfactory results for the systems containing a hydrocarbon and a polar but nonassociated and not a high-boiling component. This behavior is exemplified by the systems of acetone with n-hexane and n-heptane. As expected, poor results were obtained for the systems formed by polar and associated components such as acetic and propionic acids with n-paraffins, and by those of water with pyridine and its derivatives. It appears that in the systems water and isomeric methylpyridines (2-picoline, 3-pico1ine7and 4-picoline) the position of the substituent methyl group in the pyridine
ring does not greatly affect the azeotropic composition, x2, and in turn Ax2 values. The situation remains essentially unchanged for the systems containing a component with an additional methyl group, e.g., 2,6-lutidine. A tendency is observed for the Axz values to decrease with increasing temperature for isothermal azeotropic data in the systems containing pyridine or its methyl derivatives and water. It has also been found that, for the systems containing two nonpolar components, eq 1 gives worse results than those obtained from the Malesinski equation. In case of the systems where the composition of one component in the azeotrope is low, as typified by the systems of benzene with n-hexane and n-heptane, the comparison for eq 1is unfavorable only in relation to the Malesinski equation. For the systems containing a polar or a polar and associated component and a hydrocarbon, eq 1was found to be as indequate for the calculation of the azeotropic composition as is also true for the above-mentioned equations. On the contrary, for the systems in which negative azeotropes are formed, eq 1is inferior to the Prigogine and Malesinski equations. An exception was found only for the system acetone-chloroform. I t should be pointed out that although the three equations were derived on the general assumption that the components for a regular solution, eq 1 has a built-in unfavorable factor since it requires knowledge of the vapor pressures of the pure components, pi0 at the boiling temperature of the azeotrope. The piovalues are almost exclusively computed by the equations correlating the PO, T data. It becomes clear that in our case the accuracy of pio values is related to the values of the constants of the Antoine equation. Therefore, as a rule, an additional error is introduced while computing the pio values. However, the effect of differences in pio values on the azeotropic composition is usually small, except in cases where the boiling temperature of the azeotrope is close to the boiling temperature of one component
Ind. Eng. Chem. Fundam., Vol. 20, No. 2, 1981
of the system. Azeotropic Composition and Vapor Phase Nonidealit y In broad terms two cases may be distinguished in relation to the departure of vapor phase from the ideal gas law. The first case involves a slightly nonideal vapor phase, while the second takes account of association in the vapor phase. In view of the fact that eq 1is limited to ideal behavior of the vapor phase, it became interesting to investigate the effect of vapor phase nonideality on the composition of a binary azeotrope. For a binary solution with a slightly nonideal vapor phase, the expressions for In y1and In yzat the azeotropic point take the form
178
Table 11. Azeotropic Compositions, xz,for Binary Systems Acetic Acid-n-Paraffins, Computed with the Corrections Taking Account of Association (Dimerization) of the Acid in the Vapor Phase (a), and Those of Vapor Phase Nonideality (b), Computed by Using Formula 6 (a), mol % no. system x, Ax2 1 acetic acid-n-hexane (2) 86.6 -4.2 2 -n-heptane 56.5 1.8 3 -n-octane 35.6 3.8 4 -n-nonane 21.7 4.3 5 -n-decane 9.7 2.5
(b), mol % x,
Ax,
93.0 2.2 68.3 13.6 39.9 8.1 23.3 5.9 9.1 1.9
Table 111. Azeotropic Compositions, x2, Computed from Eq 8, and A x 2 for Binary Systems Formed by Acetic Acid with n-Paraffins and Pyridine ~
P In y1 = In ylid + bl = In 7 + bl P1 P In yz = In y i d + bz = In - + bz
(4)
PZ0 where bl and bz are the corrections accounting for the departure of vapor phase from the ideal gas law. To compute the correction, bi, for component i, it is necessary to know, besides the values of pio and p , also those of the second virial coefficient, Bi,the second virial cross-coefficient, Bij, and the liquid molar volume, Vio. For practical purposes, however, due to the lack of Bij values for a large number of organic substances (Mason and Spurling, 1969; Dymond and Smith, 1980) it is assumed that this quantity is the arithmetic mean of Bc and Bjp Then the correction, bi,Van Ness (1964), is given by
(Vio - Bii)(p - Pi") (6) RT However, it seems fair to say that in most cases the residual value of the correction involving Bij, i.e., (1 yi)2(2Bii- Bii - B..) RT, after taking into account the approximation B:="/l/z(Bij + Bjj),is small indeed. In cases where large deviations from ideality are caused to a large extent by the association of one component in the vapor phase, it is necessary to introduce into the expression for yi at the azeotropic point a correction termed the association factor (Marek and Standart, 1954). Accordingly, the activity coefficient, yi, after neglecting other molecular interactions, is related to the so-called association factor, Zi,by the expression
bi =
yi =
yi'dZi
(7)
The systems that are well suited for such an investigation are those of acetic acid with n-paraffins, where one component, namely acetic acid, is largely dimerized in the liquid and the vapor phases (Tsonopoulos and Prausnitz, 1970). The effect of the association in the vapor phase by one component of the system on the azeotropic composition was studied by two methods on the systems containing acetic acid and n-paraffins. The first method was based on the second virial coefficient correction, but this time the second virial coefficients of acetic acid were estimated from its vapor density data (Ritter and Simons, 1945). The second method involved the use of the relations developed by Marek and Standart (1954). The values of the dimerization equilibrium constant of acetic acid at the boiling temperatures of respective azeotropes with n-paraffins were computed from the equation used by Wisniak and Tamir (1975). The vapor pressures of pure acetic acid at the boiling temperatures of the azeotropes were computed with the equation by
mol % no. 1 2 3 4 5 6
7
system acetic acid-n-hexane (2) -n-heptane -n-octane -n-nonane -n-decane -n-undecane -pyridine
XZ
88.6 64.0 41.0 24.4 10.9 3.4 44.2
AX2
-2.2 9.3 9.2 7.0 3.5 1.0 2.0
Brown and Ewald (1950). The second virial coefficients of the hydrocarbons were estimated from the correlation of Pitzer and Curl (1957). In Table I1 are summarized the results obtained for the azeotropic composition for the series acetic acid-nparaffins, computed with the corrections for the dimerization of the acid in the vapor phase and those of the vapor phase nonideality. In the latter case formula 6 was used. It is easy to note from Table I1 that the Axz values for the series acetic acid-n-paraffins, except that for the system containing n-hexane, are reduced to a reasonable magnitude when the corrections for the dimerization of the acid were taken into account. This shows, beyond any doubt, that the dimerization of acetic acid in the vapor phase is the dominant factor contributing to the large differences between the calculated and observed azeotropic composition. On the other hand, the Axz values still remain high for the cases in which the corrections for vapor phase nonideality were evaluated classically by using the values of the second virial coefficients of acetic acid estimated from ita vapor density data. For the systems in which there is no apparent association in the vapor phase by one component, the results obtained for the azeotropic composition computed with the corrections given by formula 6 were found to be similar to those obtained by eq 1. It should be added that although the differences in the values of In y1 and In y2 were found, they were insufficient to cause any substantial change in the values of (In yz/ln y1)1/2.The x i s were hardly affected. Azeotropic Composition and Differences i n the Vaporization Entropies of Components It is known that the differences in the vaporization entropies of components, as exemplified by the systems containing acetic acid and n-paraffins, contribute to the possible errors in the compositions of binary azeotropes. For components with unequal vaporization entropies, Aslo # Asz', eq 1 takes the form x2
= (1 + a y
(8)
where a' = ca and c = ( A S ~ ~ / A S ~ ' ) ~ ~ ~ . In Table I11 are listed the results obtained by eq 8 for the azeotropic composition, x2, in the systems of acetic acid
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Ind. Eng. Chem. Fundam., Vol. 20, No. 2, 1981
with n-paraffins and pyridine. The vaporization entropies of acetic acid, pyridine and the hydrocarbons used in calculations were 14.85, 21.9, and 20.0 cal./g-mol, respectively. Table I11 shows that the effect of the differences in the vaporization entropies of the components on the azeotropic composition is small, compared to the deviations from regularity caused, among other things, by the dimerization of acetic acid in the vapor phase. Conclusions The Malesinski and Prigogine equations and also eq 1 gave only marginal differences in general applicability. For example, comparing 30 systems which were studied in the previous and the current papers, the average deviations between the computed and experimental azeotropic compositions as absolute values were 4.5 mol % for Malesinski’s equation and eq 1, and 4.9 mol % for Prigogine’s equation. A further distincton to the specific systems, Le., polar-nonpolar, polar-polar, and nonpolar-nonpolar did not give an answer that would show which of the three equations is preferable. This was expected in view that these equations were derived on general assumption that the components form a regular solution. A binary regular solution is defined as one in which the excess free energy of mixing, gE, is given by the equation gE = A l Z X l X Z where A12is a characteristic constant for the system under given conditions of temperature and pressure, and x1 and x 2 are the mole fractions of the components. Only a choice between the equations can be made on the availability of the data appearing in these equations. From this point of view, the Malesinski and Prigogine equations are preferable to eq 1. The modified Prigogine equation and eq 8 gave essentially similar results for the azeotropic compositions in the systems where the differences in the molar vaporization entropies are substantial, i.e., acetic acid with n-paraffins and pyridine. On the other hand, the modified Malesinski equation, taking account of the differences in the vaporization entropies of components, is considered inferior to
the modified Prigogine equation and eq 8, mainly due to the difficulties involved in evaluating z, (the upper part of the azeotropic range). The effect of the differences in the vaporization entropies of the components on the azeotropic composition is small, compared to the deviations from regularity caused, among other things, by the association of one component, i.e., acetic acid in the vapor phase. Literature Cited Andon, R. J. L.; Cox, J. D.; Herington. E. F. G. Trans. Faraday Soc. 1957, 53,410 Antoine, C. Compt. Rend. 1888, 107, 681, 636, 1143. Brown, I.; Ewaid, A. H. Aust. J . Sci. Res. 1950, 3A, 306. Dymond, J. H.; Smith, E. B. “The Second Virlal Coefficients of Pure Cases and Mixtures. A Critical Compllatlon”, 2nd ed.; Oxford University Press: New York, 1980. Fowler, R. T. J . Appl. Chem. 1952. 2 , 246. Hala, E.; Wichterle, I:Polak, J.; Boublik, T. ”Vapor-Liquid Equilibrium Data at Normal Pressures”, Pergamon Press: Oxford, 1968. Herington, E. F. G.; Martin, J. F. Trans. Faraday Soc. 1953. 49, 154. Hirata, M.; Ohe, S.; Nagahama, K. “Computer-Alded Data Book of VaporLiquid Equilibria”, Kodansha-Eisevier: Tokyo, Amsterdam, 1975. Horsiey, L. H. “Azeotroplc Data-III”, American Chemical Society: Washington, D.C. 1973. Ibl, N.; Dandilker, G.; Trumpier, G. Hehr. Chlm. Acta 1954, 37, 1661. Kireev, V. A. Acta Physicochim. URSS. 1941, 14, 371. Kurtyka, Z. M.; Kurtyka, A. Ind. Eng. Chem. fundem. IS80, 70. 225. Malesinski, W. ”Azeotropy and Other Theoretical Problems of Vapor-Liquid Equilibrium”, Interscience: New York, 1965. Marek, J.; Standart, G. Gollect. Czech. Chem. Commun. 1954. 19, 1074. Mason, E. A.; Spurling, T. H. “The Vklal Equation of State”, Pergamon Press: Oxford, 1969. Van Ness, H. C. “Classical Thermodynamics of Non-Electrolyte Solutions”, Pergamon Press: Oxford, 1964. Pitzer, K. S.;Curl, R. F., Jr. J . Am. Ctwm. Soc. 1957, 79, 2369. Prigogine, I.; Defay, R. “Chemical Thermodynamics”, translated by D. H. Everett; Longmans, Green: London, 1954. Ritter, H. L.; Simons, J. H. J. Am. Chem. Soc. 1945, 87, 757. Tsonopouios, C.; Prausntlz, J. M. Chem. Eng. J. 1970, 1 , 273. Wisnlak, J.; Tamir, A. J. Chem. Eng. Data, 1975, 20, 168. Zawidzki, J. Z . Phys. Chem. 1900, 35, 129.
Department of Chemical Technology University of Warsaw 02-093 Warsaw, Poland
Zdzislaw M. Kurtyka* Adam Kurtyka
Received for review June 26, 1980 Accepted January 5, 1981 Address correspondence to this author at 59 Blaxland Drive, Dandenong, Vic. 3175, Australia.
