Ind. Eng. Chem. Fundam. 1980, 79, 225-227
tribution function of the reactor can be determined directly from the radioisotope data by smoothing and differentiation. If patterns of mixing are determined coincidentally with chemical reaction studies, important information on micromixing mechanisms can be obtained. In addition to impulse injection studies, the gamma camera system can also be used to study mixing under quasi-steady-state conditions. In this kind of experiment multiple feed streams are used, one of which contains a constant level of radioisotope. The count rate data from one region-of-interest can be subjected to standard time series analysis techniques such as spectral or auto-correlation analysis. More important, the data from multiple regions-of-interest can be used directly to calculate cross-correlations and other statistical measures related to mixing and hydrodynamics. An alternate quasisteady-state approach would employ a single inlet stream
225
and continuous infusion of a short-lived radioisotope tracer such as krypton-8lm, a 190-keV y emitter with a half-life of 13 s. In summary, this new technique has the potential of providing detailed data on intravessel flow patterns and mixing with good spatial and excellent temporal resolution, and in a form suitable for automated processing. Literature Cited Anger. H. O., Mortimer. R. K.,Tobias, C. A., Proc. Int. Conf. PeacefulUses A t . Energy, 14, 204 (1956). Nishirnura, Y., Matsubara, M., Chern. Eng. Sci., 25, 1785 (1970). Weber, P. M., “Digital Analysis of Dynamic Time Dependent Data in Nuclear Medicine. Computers in Laboratory Medicine”, pp 102-129, D. Enlander, Ed., Academic Press, New York, N.Y., 1975. Weinstein, H.. Adler. R . J., Chern. €ng. Sci., 22, 65 (1967).
Receiued f o r revieur August 1, 1979 Accepted January 14, 1980
COMMUNICATIONS Azeotropic Composition from the Boiling Points of Components and of the Azeotropes
+
The Malesinski equation, x 2 = 0.5 ( T I - T2)/2z,,,after testing on 60 systems, gave overall slightly better results than those obtained by the Prigogine equation, x 2 = a/(l a ) . When the differences in the vaporization entropies of the components were taken into account, the modified Prigogine equation was found superior to Malesinski’s equation, which in this case requires evaluation of the upper part of the azeotropic range, z, (the quantity which is not readily available).
Introduction Lecat (1918) first observed that the composition of a binary azeotrope is related to the difference between the boiling points of the components. He also used a power series to relate the above quantities for the systems formed by a common substance with members of a homologous series. Since then several methods were developed, mostly graphical and of empirical nature (Mair et al., 1941; Horsley, 1947; Meissner and Greenfield, 1948; Skolnik, 1948; Johnson and Madonis, 1959; Seymour, 1946; Seymour et al., 1977) with a view of correlating the composition of the azeotropes within series of organic compounds. The regular solutions theory also offers the possibility of computing the azeotropic composition. The first to use the regular solutions equations for this purpose were van Laar (1925) and Herzfeld and Heitler (1925). Extensive studies were made by Kireev (19411, Prigogine (1954), and more recently by Malesinski (1965). However, the Malesinski and Prigogine equations for calculating the composition of a binary azeotrope seem to be more useful from a practical viewpoint. This is due to the fact that unlike the Kireev equation, for instance, they relate the azeotropic composition expressed in mole fraction, x2 to the readily accessible data, namely the boiling temperatures of the pure components, T1,Tz,and that of the azeotrope, TAz. According to Malesinski, the composition of an azeotrope formed by the components having equal vaporization entropies (Aslo= Aszo) is given by the relation 0 196-4313/80/1019-0225$01 .OO/O
+
where z12 is the half-value of the symmetrical azeotropic range. (The symmetrical azeotropic range means that both parts of the range (the upper and the lower part) are equal.) The values of z12can be computed from the formula (611/2 621/2)2 = zI2. When the vaporization entropies of the pure components are different, the expression for the azeotropic composition is
+
where 2, stands for the upper part of the azeotropic range. According to Swietoslawski (1963), the quantity z, is defined as the difference between the boiling temperatures of the highest boiling representative (homologue) Hkof series (H) and the azeotropic agent A forming the tangent “azeotropic” isobar. Although the correction term ~ ~ ~ / -2 A( S1 ~ ~ / A is S~~) usually not large, it sometimes improves the results, when taken into account. On the other hand, the Prigogine equation for equal vaporization entropies of the components is usually written in the form a (3) x2 = -l + a where a = (61/S2)1/2. 0 1980 American Chemical Society
228
Ind. Eng. Chem. Fundam., Vol. 19, No. 2, 1980
Table I. Calculated and Observed Azeotropic Compositions for Some Binary Systems composition, x 2 , mol % no.
system
eq 1*
eq 3**
obsd
AX,*
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
benzene-cyclohexane ( 2 ) -cyclohexene -n-hexane -n-heptane -2,2-dimethylpentane pyridine-n-heptane -n-octane -n-nonane phenol-2,4,6-collidine -aniline -n-tridecane 2,4,6-collidine-o-cresol -m-cresol -gl y c 01 acetone-chloroform -n-hexane -carbon disulfide cyclohexane-thiophene -ethanol -1-butanol ethanol-n-hexane -chloroform 1-butanol-0-xylene -m-xylene -p-xylene o-cresol-gly col aniline-pseudocumene -p-cymene -n-nonane -n-decane -n-undecane -n-dodecane -n-tridecane -n-tetradecane quinoline- 2-methylnaphthalene mesitylene- 2,7-dimethyloctane o-toluidine-n-decane -n-undecane -n-dodecane -n-tridecane m-xylidine-n-undecane -n-dodecane -n-tridecane -n-tetradecane acetic acid-pyridine -n-hexane -n-heptane -n-octane -n-nonane -n-decane -n-undecane propionic acid-n-heptane -n-octane -n-nonane -n-decane 3,4-xylenol-naphthalene -quinoline carbon disulfide-n-pentane -cyclopentane -methyl formate
47.2 33.0 89.0 0.14 53.0 72.6 37.5 8.2 42.6 60.2 10.9 67.2 76.3 11.0 60.6 36.5 60.9 40.7 52.0 13.6 58.5 20.6 15.7 19.0 21.8 30.2 83.5 63.2 82.8 60.7 38.9 27.6 11.3
47.4 38.5 82.8 5.0 53.5 72.7 37.6 8.4 42.3 57.9 14.7 67.1 76.2 14.7 61.5 36.5 60.9 39.3 52.1 13.7 58.0 23.8 15.8 19.1 21.9 30.2 82.3 65.8 82.8 60.1 39.0 23.9 11.5 2.4 10.2 66.7 84.9 56.2 31.6 13.1 74.1 51.6 24.9 2.3 48.5 90.5 66.8 44.4 27.1 13.2 4.5 90.9 68.6 39.1 16.2 82.7 64.3 82.9 39.2 63.7
46.0 34.2 95.0 0.1 52.0 71.7 35.2 6.4 41.5 58.2 9.4 65.6 75.0 17.3 65.8 37.6 60.8 3 9.4 45.5 11.0 66.8 16.0 18.9 21.8 23.5 37.6 83.3 61.8 82.3 53.4 29.3 17.8 7.0 2.3 6.4 68.5 82.3 50.7 23.5 9.3 85.1 54.8 21.2 1.6 42.2 90.8 54.9 31.8 17.4 7.4 2.4 97.3 70.3 33.0 11.2 83.3 63.7 89.5 34.8 72.0
1.2 -1.2 -6.0 0.04 1.0 0.9 2.3 1.8 1.1 2.0 1.5 1.6 1.3 -6.3 -5.2 -1.1 0.1 1.3 6.5 2.6 -8.3 4.6 -3.2 -2.8 -1.7 -7.4 0.2 1.4 0.5 7.3 9.6 9.8 4.3
...
9.9 66.7 81.4 55.7 30.0 7.8 86.5 51.6 24.8 2.3 48.8 90.5 66.8 44.3 27.0 12.9 4.3 92.0 68.7 39.1 16.1 82.5 64.4 82.8 39.2 63.8
When Asla # As2', it is assumed that the ratio of Asla/AsZa = c 2 and then x2
a' = 1+a'
(4)
In this case a' = ca. The quantities b1 and b2, known otherwise as azeotropic deviations, for positive azeotropes are defined by 6, = T1- Th and b2 = T2- Th. In the case of negative azeotropes we have b1 = Th - T , and 82 = Th - T2. The purpose of this work was to compare and analyze the results obtained by the Malesinski and Prigogine
...
3.5 -1.8 -1.1 5.0 6.5 -1.5 1.4 -3.2 3.6 0.7 6.6 -0.3 11.9 12.5 9.6 5.5 1.9 -5.3 -1.6 6.1 4.9 -0.8 0.7 -6.7 -4.4 -8.2
Ax***
1.4 4.3 -12.2 4.9 1.5 1.0 2.4 2.0 0.8 -0.3 5.3 1.5 1.2 -2.6 -4.3 -1.1 0.1 -0.1 6.6 2.7 -8.8 7.8 -3.1 -2.7 -1.6 -7.4 -1.0 4.0 0.5 6.7 9.7 6.1 4.5 0.1 3.8 -1.8 2.6 5.5 8.1 3.8 -11.0 -3.2 3.7 0.7 6.3 -0.3 11.9 12.6 9.7 5.8 2.1 -6.4 -1.7 6.1 5.0 -0.6 0.6 -6.6 -4.4 -8.3
equations for the systems showing small, medium, and large deviations from regularity. Results and Discussion Equations 1 and 3 were tested on 60 systems. Only relatively recent azeotropic data, with a few exceptions, were selected. They were taken from Horsley's monograph (1973). In doubtful cases, original papers were consulted. The systems selected in this work covered positive and negative azeotropes. Moreover, the azeotropes in these systems were formed by unpolar, slightly polar, and polar components. No attempts were made to evaluate the reliability of the azeotropic data. In fact, there is no rigid
Ind. Eng. Chem. Fundam., Vol. 19, No. 2, 1980
Table 11. Azeotropic Compositions, x 2 , Computed from Eq 4,and Ax2 for Binary Systems Formed by Acetic and Propionic Acids with n-Paraffins and Pyridine no. 1
2 3 4 5 6 7 8 9
10 11 12
L*2r
AX,,
system
mol %
mol %
acetic acid-n-hexane ( 2 ) -n-heptane -n-octane -n-nonane -n-decane -n-undecane -pyridine propionic acid-n-heptane -n-octane -n-nonane -n-decane -pyridine
89.1 63.0
40.1 24.4
--1.7 8.1 8.3 7.0
11.8
4.4
4.0
1.6
43.7 90.3 66.7 38.0 15.7 30.0
1.5 -7.0 --3.6 5.0 ~
4.5 1.4
criterion for the azeotropic point in the absence of vapor-liquid equilibrium data. However, it seems reasonable to accept on the basis of the information available that in most cases the azeotropic composition is accurate to h0.5 mol 70. The results obtained are listed in Table I. It is seen from Table I that the Malesinski equation generally gives better results than those obtained by the Prigogine equation, particularly for the systems formed by two unpolar substances (systems 1-51, This is clearly shown in the case of the systems in which the azeotropic points lie close to those representing the composition of one of its components as typified by systems 3 and 4. For the systems containing one slightly polar or polar component, the Malesinski equation also offers slightly better results. On the other hand, both equations with two exceptions gave similar results for the systems containing two polar components. These systems, except those of no. 17, 26, and 60, form negative azeotropes. As expected, the large differences between the calculated and observed azeotropic composition, Axq = XZ(&d) x ~ ( , , ~were ), obtained for the systems containing polar and associated components such as alcohols and low-molecular fatty acids. The high values of Ax2 are to be attributed, among other things, to large deviations from regularity occurring in such systems and to the differences in the vaporization entropies of the components. The first factor cannot be assessed quantitatively. What is possible is to evaluate the effect of the differences in the vaporization entropies of the components on the azeotropic composition. It becomes apparent that eq 4 has advantage over eq 2 because it does not involve evaluation of any quantity which would not be easily available, such as z,,. It should be pointed out that only a few data are available for evaluating the 2 , values (Kurtyka and Trabczynski, 1958; Kurtyka, 1961). The systems suitable for this purpose are those of acetic acid with normal paraffins (Kurtyka and
227
Trabczynski, 1958). This is due to large differences in the vaporization entropies of the components. With the value of z, = 77 " C (obtained from the difference in the boiling temperatures of n-undecane and acetic acid) the improvement in the value of Axz was observed only for the systems of acetic acid with n-heptane and n octane, respectively. The x 2 and Axz values were found to be 56.6 and 1.7 for the system acetic acid-nheptane, and 41.8 mol % of hydrocarbon and 10.0 mol % for the system acetic acid-n-octane, respectively. On the contrary, eq 4 showed improvement in the values of Ax2 for the series of binary systems acetic acid-nparaffins and propionic acid-n-paraffins. The exceptions were found for the systems acetic acid-n-hexane, propionic acid-n-heptane, and propionic acid-n-octane. The results obtained for binary systems of acetic and propionic acid with n-paraffins and pyridine are summarized in Table 11. This table shows that the extent of improvement in the azeotropic composition, as measured by the Ax2 values, for the series propionic acid-n-paraffins is smaller than that of acetic acid with n-paraffins. The explanation of this fact is that in the case of propionic acid with n-paraffins, the differences in the vaporization entropies of the components are smaller. The vaporization entropies of acetic and propionic acids are 14.9 and 17.7 cal/g-mol, respectively. Literature Cited Herzfeld, K. F., Heitler, W., Z . Elektrochem., 31, 536 (1925). Horsley, L. H., Anal. Chem., 19, 508 (1947). Horsley, L. H.. "Azeotropic Data-111", American Chemical Society, Washington, D.C., 1973. Johnson, A. I., Madonis, J. A,, Can. J . Chem. Eng., 37, 71 (1959). Kireev, V. A,, Acta Physicochim. URSS, 14,371 (1941). Kurtyka, Z.,Trabczynski, W., Rocr. Chem., 32, 623 (1958). Kurtyka, Z.,Bull. Acad. folon. Sci. Ser. Sci. Chim., 9, 745 (1961). van Laar, J. J., Lorentz, R., Z . Anorg. A/@. Chem., 148, 42 (1925); Z.f h y s . Chem., A137, 421 (1928). Lecat, M., "L'Azeotropisme", Lamartin, Bruxelles, 1918. Mair, B. J., Giasgow, A. R . , Rossini, F. D., J . Res. NaN. Bur. Stand., 27, 39 (1941). Malesinski. W., "Azeotropy and Other Theoretical Problems of Vapour-Liquid Equilibrium", Interscience, New York, N.Y., 1965. Meissner, H. P., Greenfield, S. H., Ind. Eng. Chem., 40,436 (1948). Prigogine, I., Defay, R., "Chemical Thermodynamics", translated by D. H. Everett, Longmans, Green, London, 1954. Seymour, K. M., Abstracts, 50-1, 110th National Meeting of the American Chemical Society, Chicago, Ill.. Sept 1946. Seymour, K. M.. Carmichael, R. H., Carter, J., Ely. J., Isaacs, E., King, J., Naylor, R., Northerr;, T., Ind. Eng. Chem. Fundam.. 16, 200 (1977). Skoinik. H., Ind. Eng. Chem., 40,442 (1948). Swietoslawski, W., "Azeotropy and Polyazeotropy", Pergamon Press, Oxford, London, 1963.
Department of Chemistry University of Zambia Lusaka, Zambia
Zdzislaw M. Kurtyka* Adam Kurtyka
Received for reuieu: July 18, 1979 Accepted February 15, 1980 Address correspondence to this author at 59 Blaxiand Drive, Dandenong, Vic. 3175, Australia.
