I
JANOS HOLLO and T A M k LENGYEL Institute of Agricultural Chemical Technology, Technical University, Budapest, Hungary
To simplify studies of multicomponent mixtures, here is a reliable method for calculating azeotrope composition in a ternary system, developed from investigations of . . .
Vapor-Liquid Equilibrium of the System Toluene-Pyridine-1-Butanol
Rm
A T I v m Y few publications concerning the vapor-liquid equilibrium of nonideal ternary systems can be found in the literature. This can be attributed to the difficult experimental work and analyses involved, as well as to the length of the corresponding calculations. Available publications deal primarily with ternary azeotropic systems studied in solving industrial problems. While investigating nonideal multicomponent systems in this institute a special kind of ternary azeotropismsaddle point azeotropism-was thoroughly studied. In a ternary system, azeotropic point is characterized by the following equations:
xi
= yi
xi =
yj
Simultaneous conformity of phase composition at a certain temperature means that activity coefficient of the modified Raoult law for isobar equilibrium can be calculated by the following: y< =
Y,P/XiP, = P/P$
In these cases activity coefficient is usually determined by empirical and semiempirical relations. In practice, determination of composition and temperature of azeotrope formation is usually necessary. This problem cannot be solved with absolute certainty even for binary systems and for ternary and more complicated systems the problem has been unsolved until now despite numerous attempts in the literature (2, 7, 8, IO, 72).
Ternary Homoazeotropes Three principal types of the ternary homoazeotropes can be distinguished : azeotropes of minimal boiling point, those of maximal boiling point, and saddle point azeotropes. The first two types are discussed rather thoroughly in the literature; ' their common characteristic is that in spatial representation boiling point and dew point surfaces of isobar equilibrium compositions are contiguous with each other at a minimum or maximum boiling point value. When represented on the planar Gibbs diagram, boiling point and dew point isotherms form distorted ellipses in the immediate vicinity of the azeotropic point. With saddle point azeotropes there is no extreme value considered in the absolute sense, and boiling point and dew point surfaces are contiguous only at local extreme values. O n an equilibrium diagram represented by plane coordinates, isotherms in the vicinity of the saddle point are similar to hyperbolas. A distinction may be made between the saddle point azeotrope and the socalled positive-negative azeotrope. Boiling point of a saddle point azeotrope lies between the boiling points of the corresponding pure components. For the positive-negative azeotrope, this occurs only in connection with bdiling points of corresponding binary homoazeotropes. Positive-negative azeotropes have been discussed chiefly by Swietoslawski and others. Most of these studies infer a complex chemical and physical equilibrium because in the systems investigated (acetic acid and pyridine homologs) formation of complexes and compounds can be presumed ( 13, 16- 18).
No distinction is made here between these two types of azeotropism, and the term saddle point azeotropism is used. I n every azeotropic system distillation lines converge at the azeotropic point. Formation. According to earlier views, a ternary azeotrope forms when composed of compounds which form binary azeotropes ( 8 ) . However, it is more likely that formation of a saddle point azeotrope depends on the existence of azeotropes of both minimum and maximum boiling point (2). This was considered in selecting a system for investigation. , In principle, formation of several homoazeotropic compositions within a ternary system might be presumed, in which case only saddle point azeotropes can be considered. I n practice, however, no system of this kind has been found until now. Experimental Determination. Several possibilities are available for experimental determination of azeotropic composition. With the usual technique for measuring equilibria, however, even measurements close to the azeotropic point give no precise information aboui azeotrope composition. The differential ebulliometric investigations elaborated by Swietoslawki (14) thus deserve special interest. The principle involves measurement of the temperature difference between boiling point and dew point after establishing equilibrium, while changing the composition systematically. When plotting these differences At against composition a sharp minimum is observed for pure components and azeotropes. With these measurements, boiling point of the azeotrope can be determined within 0.005' C. and composition with any accuracy as components can be charged in almost infinitesimally small VOL. 51, NO. 8
AUGUST 1959
957
During operation charging is accomplished through the condenser. To prevent formation of unutilized space in stud Z during operation, it is filled with mercury maintained at constant level by proper adjustment of a leveling vessel, To avoid superheating, inner surface of the boiling space was activated by etching with hydrogen fluoride. Temperature and A6 values were measured with a Beckmann thermometer with 0.01' C. graduations. With a magnifying lens 0.005 ' C. could be read easily. Jackets surrounding the thermometers were filled with paraffin oil which served as heat medium. To prevent heat loss by radiation and considerable partial rectification an electrically heated aluminum jacket with asbestos lining was placed around the apparatus. Heating was adjusted by a toroidally wound transformator. T o compensate for heating fluctuations, the space between apparatus and jacket should be filled with asbestos insulation. Computation of Azeotrope Composition. Equilibrium measurement was used to determine probable composition of the saddle point azeotrope so that approximate conclusions could be drawn from the trend of boiling point-dew point isotherms concerning position of the azeotrope. To shorten differential ebulliometric measurements, the sole method suitable for determining azeotrope composition, a new calculation method was developed. With Margules constants of the corresponding binary subsystems toluenepyridine, toluene-butanol, and pyridinebutanol (5), as well as with a ternary equilibrium measurement, ternary constants of the ternary system in the three suffix Margules equations were determined. Within a system ternary constants of equations pertaining to logarithms of individual activity coefficients are different. Constants used in further calculations are shown in Table I . Knowing the ternary constants, and choosing from the three Margules equations relating to activity coefficients any two equations independent of each other, and substituting the expression
Figure 1. Isorefraction curves a t 20" C. of t h e system toluene-pyridine-1 -butanol Refractive index was selected as an analytical method because it can be measured quickly and precisely; values are per cent by weight
PYRIDINE
1$8
136
f#
portions. Disadvantage of the method is that nearly a day is needed to reach equilibrium. With the correlation between composition and Ai, reliable information can be obtained about the typical values and the type of azeotrope appearing in the liquid mixture. Prediction. In the literature several methods for predicting azeotropic composition of ternary systems can be found (2, 7). These methods, however, are generally based upon relations existing between individual members of homologous series; in general cases they cannot be employed. A method usable even in general cases has been described in detail by Haase ( 2 ) and Kortum ( 8 ) . The disadvantage of the method, which results from detailed mathematical deduction based on the so-called Porter equation (77) analogous to Wohl's general equations, is that the equations presuming symmetry of the system are employed under circumstances going far beyond their range of validity. Thus, it is not possible to obtain correct results with these equations, as deviations between calculated and experimental values make usefulness of the method rather doubtful.
Experimental Analyses. Determination of at least two characteristics is required for analysis of a ternary system. Index of refraction was chosen as one characteristic, because it could be measured quickly and precisely. Isorefraction curves plotted from mode1 mixtures prepared with great care were represented on diagrams of Gibbs type (Figure 1). Absolute quantity of pyridine present was determined as the second characteristic. In an aqueous medium pyridine can be titrated with hydrochloric acid, and with a mixed indicator consisting of methylene blue-dimethyl yellow
958
the transition is very sharp. T o eliminate the disturbing effect of hydrocarbons insoluble in water, the pyridine was first quantitatively extracted into the aqueous phase in three stages. One milligram o f pyridine is equivalent to 0.126 ml. of 0.1N hydrochloric acid. After pyridine and ternary refraction have been determined, the system could be analyzed with an accuracy of 1 relative yo based on pyridine content. Details of the analytical method have been described (6). Procedures. Investigations of the system toluene-pyridine-1-butanol were begun with determination of vaporliquid equilibria. Measurements were carried out with a modified Othmertype apparatus ( 4 ) : functioning on the principle of recirculation. Reliability of the apparatus was adequate for this study. The most important procedure was ebulliometric measurement. A modified version of the original Swietoslawski apparatus (74) was used (Figure 2). On boiling, liquid splashes through stem B, functioning as a Cottrell lift, to the jacket of thermometer C which measures boiling point. Saturated vapors pass upward, condensing on the jacket of dew point-measuring thermometer, D, and returning through drop counter E and buffer F to the boiling space. A spiral form condenser is attached at G. The equipment is filled and cleaned through stud H and emptied at stud I .
Table l.
1 - xs -
(1)
XI
as well as taking into consideration that at the azeotropic point activity coefficient value is given by P/Pd, two mixed equa-
Binary and Ternary Margules Constants W e r e Used in Calculating Azeotrope Composition System
Toluene-pyridine Toluene-butanol Pyridine-butanol Toluene-pyridine-butanol
INDUSTRIAL AND ENGINEERING CHEMISTRY
.zk =
Aii 0.071 0.338 -0.158
...
A ji
Ci jrs
Cjki
Ckji
0.123
...
... ...
... ... ...
-2.161
-2,023
0.571 -0.003
...
... ...
...
S0.890
TOLUENE-PY R I D I N E - I - B U T A N O L tions of the third degree with regard to x , and x i were obtained. Because of the mixed members these equations could not be directly solved by determinants; therefore another way had to be found for determining unknown variables. Taking successively different x i values, equations with one unknown and of the third degree with regard to unknown xi are obtained for both equations, in the following general form: xf
t e x f + bx,
+
c =
0
(2)
T o eliminate the quadratic member the following substitution has to be performed : x, =
fx - a/3)
0,TO Figure 3. Composition of the ternary azeotrope is predicted by a graphical method after certain calculations a re made
cF5 i .X 0,SO
(3)
Then the following third degree reduced equation is obtained : 2 +fix
+q
=
0
(4)
With the introduced new variable, x, this equation satisfies relations formulated in the general form. The reduced equation of the third degree, as well as Equation 2, may have three roots, About the nature of these roots information is given by the discriminant 8 which is determined by definition as follows :
e
=
-4p
-
27g2
0+5L
(5)
If 8 < 0, one real root and two conjugate complex roots are obtained; the latter may not be taken into consideration in these computations. The most suitable method for determining the real root consists in employing a hyperbolic function. The expression r
appropriate solution after the substitution
can be designated by sinh $, and the area value of this expression can be found. With this value the sole real root can be expressed as follows:
is fulfilled. Always only one such solution is possible. Using this method at different x i values for both initial Margules equations and plotting the results in a coordinate system x$ us. x,, two curves can be drawn. Their sharp intersection corresponds to the required azeotropehere the saddle point because for both equations it satisfies the condition concerning the azeotrope. I n employing this method for toluenepyridine-butanol, the azeotrope appeared (Figure 3 ) at the composition corresponding to 63.7 mole yo toluene and 22.9 mole 70 pyridine. One step of the calculation method is detailed in the following. After substituting binary and ternary constants, at pyridine concentration x i = 0.1 50 (assuming the boiling point = 108.5" C.) the following equation is obtained :
=
2 m s i n h $/3
(7)
If (P/3)3 - (Y/2)2
