General Properties of Coherent Boundaries
Coherent boundaries, regardless of their origin, have various characteristic properties, of which the most striking are the following. Each coherent boundary has its “affinity cut” between two adjacent species in the affinity sequence A , B, . . . , N . The cut divides the species into a high-affinity group and a low-affinity group. Thus, if the cut is j/k-i.e., is behigh-affinity group comprises j tween species j and k-the and all species preceding it in the affinity sequence, and the low-affinity group comprises k and all species following it in the affinity sequence. T h e significance of the cut is that the concentrations of all species of one group are higher on the upstream than on the downstream side of the boundary, while those of all species of the other group behave in the opposite manner. If the concentrations of the high-affinity species are higher on the upstream than on the downstream side, the boundary is self-sharpening ; in the opposite case, the boundary is nonsharpening. Only the two species marking the affinity cut can appear or disappear at the boundary-i.e., be absent from either the upstream or downstream side. Furthermore, the n - 1 possible positions of the affinity cut are related to the n - 1 eigenvalues of the concentration velocity ux in the following manner. A given composition travels with its lowest eigenvalue of ux if it is in a boundary with A / B cut, with the next higher eigenvalue if it is in a boundary with B / C cut, etc. As a rule, boundaries travel faster the lower the affinities of the species marking their cut (in exceptional cases, such as displacement development, boundaries having different cuts
can travel a t equal rates). Applied to the special case of uniform presaturation and constant feed, the stated rules for coherent boundaries are equivalent to the rules advanced by Klein, Tondeur, and Vermeulen. Nomenclature
h hi hi‘
= argument of H function, dimensionless = ith root of H(h,X,,,,) = 0 or H(h,X) = 0, dimensionless
ith root of H(h‘,Xfsed) = 0, dimensionless H function, defined by Equation 4 t = time, sec. = velocity of bulk mobile-phase, cm./sec. u, = concentration velocity of concentration xi, cm./sec. uxi ux = concentration velocity of composition X,cm./sec. = mobile-phase composition ( x A , xB, . . . ,x N ), dimensionX less vector = composition (xd, xB, . . ., x N ) of feed, dimensionless vector X,,,. = composition ( x A , xB, . . , , xhr) of presaturant, dimensionless vector = distance from column inlet, cm. z All other symbols are the same as in preceding papers (2, 3 ) .
H
= =
Literature Cited
Y.,unpublished manuscript. (2) Klein, G., Tondeur, D., Verrneulen, T., IND. ENO. CHEM.6, 333 (1967). ( 3 ) Tondeur, D., Klein, G., Zbid., p. 351.
(1) Marcel Dekker, Inc., New York, N.
RECEIVED for review August 31, 1966 ACCEPTED February 27, 1967
PREDICTION OF QUATERNARY LIQUID EQU I LI BRIA ROBERT W.
R I E B L I N G
Jet Profulsion Laboratory, California Institute of Technology, Pasadena, Calif.
JAMES J. CONTl Department of Chemical Engineering, Polytechnic Institute of Brooklyn, Brooklyn, N . Y .
A wholly empirical method for predicting quaternary liquid-liquid equilibria in 2-phase systems comprising two Type I ternaries, wherein quaternary tie lines are determined from the ternary tie lines by geometric construction, was suggested some years ago. Historically, this method was verified experimentally for only several quaternary systems. This paper describes a research study initiated to determine under what conditions, if any, the method could be extended to other quaternary systems. Predicted solubility and equilibrium data were compared with experimentally determined values for the systems pyridine-tolueneethanol-water and chloroform-acetone-formic acid-water at 2 5 ” C. and 1 atm. Good agreement was found for the former system; some appreciable discrepancies were found for the latter. The results are interpreted in terms of the nature of the quaternary solubility surface, and the effects of variable distribution coefficients.
(1942) developed a graphical method for predicting equilibria in a two-phase Type I quaternary liquid system, based on a tetrahedral representation of its solubility and phase-equilibrium properties. If the quaternary system is made up of two Type I ternaries and two completely miscible ternaries, Hunter’s method is claimed to predict quaternary equilibrium distributions and solubilities from the data for the Type I ternaries. UNTER
364
l&EC FUNDAMENTALS
This method was used (Brancker et al., 1941) to predict equilibrium data for the system acetic acid-acetone-chloroform-water, and the results were in excellent agreement with the experimental values reported earlier by Brancker et al. (1940). However, the method has apparently been verified for only two other Type I quaternary systems. Cruickshank et al. (1950) and Prince (1954) state that the data of Pratt and Glover (1946) for water-acetaldehyde-acetone-vinyl acetate
are in agreement with Hunter’s prediction method. More recently, Solomko et al. (1962) reported that equilibria in the system water-acetone-ethanol-1-butanol follow Hunter’s method. If the method were generally valid for quaternary data prediction, this geometric procedure might prove of great value, for many Type I ternary systems have been studied, and e q d i b r i a for a large number of quaternary systems could be generated analytically through the application of modern, high-speed computational techniques to Hunter’s geometric method. Given sufficient equilibrium data, either predicted or experimentally measured, quaternary extraction calculations could then be made using the graphical methods of Hunter (1942) or Smith (1944), or computerized versions of these. Francis’ discussion (1963) of quaternary systems provides interesting background material. This paper present:, the results of a study to determine whether the geometric prediction method could be applied to other quaternary systems. Prediction of Quaternary Equilibria
A tetrahedral representation of a quaternary liquid system ABCD is shown schematically in Figure 1. One face is the phase diagram for the Type I ternary BAD. Its binodal curve EUF and tie lines cd lie in plane BAD. An adjacent face represents the Type I ternary CAD, with binodal curve EVF and tie lies j k contained in plane CAD. T h e remaining faces BCD and ABC represent the other two constituent ternary systems, in which the #componentsare miscible in all proportions. ‘The ternary solubility curves EUF and EVF are the intersections with planes B.4D and CAD, respectively, of the quaternary solubility surface. This surface represents equilibrium in the four-component system and is analogous to the binodal curve in a three-component system. If a plane of section (not shown in Figure 1) perpendicular to both base ACD and edge A D is passed through any point U on curve EUF, it will intersect curve EVFin, and define, a corresponding point ?’. A line connecting U and V, when moved parallel to itself with U and 1’. constrained to move along EC’F and
EVF, respectively, will be a generatrix of the quaternary solubility surface. In the general case, there is no reason to suppose that this generatrix UV will be a straight line, or even one of constant curvature. A key assumption in Hunter’s geometric prediction method is that all lines UV are straight, so that the quaternary solubility surface has but one degree of curvature. Equilibrium between coexisting liquid phases is represented by quaternary tie lines X Y terminating in the solubility surface. T h e planes PCQ, containing the ternary tie line cd and its opposite vertex C, and BZL, containing ternary tie line j k and its opposite vertex B , intersect the solubility surface in the curves cYXd and j Y X k . (Only the former is shown in Figure 1 for simplicity.) Hunter claims these are quaternary solubility curves-that is, curves defining the locus of quaternary tie lines. PCQ and BZL also intersect each other in the line R T , which in turn intersects the solubility surface in the line X Y . This is asserted by Hunter to be a quaternary tie line associated uniquely with the specific ternary tie line pairs cd and jk. Thus, a second key assumption of this graphical prediction method is that quaternary tie lines may be determined by the intersection of planes passed through tie lines in each of the two Type I ternaries and their opposite vertices. Repetition of this procedure will generate a whole series of quaternary solubility curves and their corresponding tie lines. T h e mechanics of the graphical manipulations were outlined by Hunter (1942), and discussed at length by Riebling (1961), and will not be repeated here. Using- the graphical method of Hunter, data for the ternary systems pyridine-toluene-water (Vriens and Medcalf, 1953) and ethanol-toluene-water (Washburn et al., 1939) a t 25’ C. and 1 atm. were combined to predict quaternary equilibria for the system pyridine-tolueneethanol-water at the same conditions. The predicted data are presented in Table I. Similarly, data for the ternaries chloroform-formic acidwater (Ku, 1959) and chloroform-acetone-\\ ater (Brancker et al., 1940) a t 25’ C. and 1 atm. were used to predict equilibria for chloroform-acetone-formic acid-water, as shown in Table 11. Experimental Equilibria Studies
T h e experimental procedure for each quaternary system consisted of two parts: a qualitative determination of whether the “generatrix” L‘V of the solubility surface (Figure 1 ) was actually straight, as assumed by Hunter, and a quantitative chemical analysis to check the validity of the predicted equilibrium concentrations. Specially purified, analytical reagent grade liquids were used, and all kvork was carried out in a water bath maintained at 25’ i 0.1 ’ C. Determination of Solubility Surface Protlles
Figure 1. Generalized phase diagram for Type I quaternary liquid systems
From the graphical constructions prepared in predicting the equilibria for each quaternary system, the concentrations of components A , B , and D in the various points U (Figure 2), along with those of A , C, and D in each of the corresponding points V , were known. Assuming for convenience the mixture of equal masses of ternaries of compositions U and V , the masses and compositions of the resultant quaternaries Z , were calculated by material balance. (Regardless of the shape of the profile UV, Z must alivays lie o n a straight line joining C and V.) However, any quaternary of mass and composition corresponding to Z is also equivalent to a ternary mixture of mass and over-all composition Z’,to which the proper amount of pure-component C has been added. For each of several pairs UI’ in both systems, a two-phase three-component mixVOL. 6
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~~
~
Table 1.
Tie Line 1-1 1-2 1-3 1-4 1-5 1-6 1-7 1-8 1-9 2-1 2-2 2-3 2-4 2-5 2-6 2-7 2-8 2-9 3-1 3-2 3-3 3-4 3-5 3-6 3-7 3-8 3-9 4-1 4-2 4-3 4-4 4-5 4-6 4-7 4-8 5-1 5-2 5-3 5-4 5-5 5-6
Predicted Quaternary liquid Equilibria in the System Pyridine-Toluene-Ethanol-Water at 25’ C. Composition of Toluene-Rich Layers, W t . yo Composition of Water-Rich Layers, W t . Water Pyridine Toluene Water Ethanol Pyridine Toluene
14.25 14.13 14.10 13.95 13.65 13.53 13.35 13.05 12.75 22.23 22.05 21.90 22.26 21.81 21.54 21.36 20.85 20.13 26.97 26.79 26.55 26.31 26.07 25.71 25.53 24.99 23.76 28.86 29.19 29.55 29.85 28.80 28.29 27.45 26.97 37.80 37.80 37.50 37.35 37.80 36.60
84.05 83.39 83.10 82.35 80.55 79.89 78.85 76.95 75.25 74.49 73.85 73.40 72.58 71.03 70.22 69.08 67.45 65.19 69.31 68.87 68.25 67.63 66.01 65.03 63.99 62.67 58.08 67.28 66.47 65.65 64.55 62.40 60.77 59.15 54.51 54.30 53.10 53.00 50.55 47.90 42.80
0.55 0.69 0.80 0.85 0.95 1.09 1.25 1.65 1.75 1.39 1.65 1.90 1.78 2.13 2.32 2.38 ~. 2.75 3.29 1.71 1.77 2.05 2.13 2.51 2.83 2.99 3.01 4.98 1.78 2.07 2.05 2.05 3.10 3.67 4.55 6.01 4.40 4.70 4.90 5.75 6.70 9.30
1.15 1.79 2.00 2.85 4.85 5.49 6.55 6.95 10.25 1.89 2.45 2.80 3.38 5.03 5.92 7.18 .
8.95 11.39 2.01 2.57 3.15 3.93 5.41 6.43 7.49 8.67 13.18 2.08 2.27 2.75 3.55 5.70 7.27 8.85 12.51 3.50 4.40 4.60 6.35 7.60 11.30
ture of over-all composition 2’ was prepared, and the exact mass of pure C required to produce a solution with the mass and composition of the corresponding point Z was calculated. Pure C was then titrated into each mixture 2’. If turbidity
6
C
A
D Figure 2. surfaces 366
Determination of profiles of solub iIity
I&EC FUNDAMENTALS
5.49 4.77 4.40 4.17 4.08 3.90 3.84 3.95 4.08 14.20 13.16 12.15 10.84 10.40 9.72 9.73 9.26 9.56 28.20 25.94 24.98 22.76 21.42 24.68 18.97 17.86 17.56 39.70 38.08 36.46 32.84 31.53 29.51 27.70 25.78 49.04 47.21 46.45 42.94 40.69 38.38
0.97 0.91 1.03 1.51 2.24 3.90 5.52 8.78 13.74 1.07 1.31 1.35 1.99 2.93 4.86 6.76 10.02 15.62 1.80 2.26 2.77 4.01 5.36 6.17 9.78 14.05 22.35 3.97 4.71 5.45 7.45 8.89 11.76 15.57 23.81 8.65 10.36 11.62 15.89 20.04 27.81
82.77 75.81 70.03 60.81 55.14 47.80 42.82 36.18 28.94 74.67 68.51 63.85 55.99 51.03 44.26 39.56 33.62 26,52 60.90 56.86 52.98 46.81 42.85 35.67 33.58 28.24 21.16 48.06 44.70 41.95 37.76 34.49 30.06 26.46 20.51 33.15 30.86 28.62 24.88 21.84 16.60
70
Ethanol
10.77 18.51 24.54 33.51 38.54 44.40 42.82 51.09 53.24 10.06 17.02 22.65 31.18 35.64 41.16 43.95 47.10 48.30 9.10 14.94 19.27 26.42 30.36 33.48 37.67 39,85 38.93 8.27 12.51 16.14 21.95 25.09 28.67 30.27 29.90 9.16 11.57 13.31 16.29 17.43 17.21
disappeared after less than the calculated quantity of C had been added, say at some point Z’, curvature of UV toward the face ABD was indicated (line UZ’V in Figure 2 ) . If the mixture became homogeneous upon the addition of exactly the calculated amount of C, as a t point Z in Figure 2 , a straight line UZV was indicated. Finally, if more than the computed mass of C had to be added to Z o to cause the disappearance of the two heterogeneous phases, say a t point Z”, UV would be bowed toward apex C (line UZ“V of Figure 2 ) . T h e results for the system pyridine-toluene-ethanol-water are presented in Table 111. For each of four lines UV checked the quantities of pyridine, toluene, and water corresponding to the points Z o , and the calculated amounts of pure ethanol to be added to cause the disappearance of turbidity are shown, along with the actual quantities added. The amount of ethanol added to the disappearance of turbidity is in excellent agreement with that calculated in each case, indicating that the solubility profile UV for this system is essentially straight. This assumption of Hunter’s method therefore holds for this system. For chloroform-acetone-formic acid-water, however, the quantity of formic acid added to the disappearance of turbidity was always less than that calculated (Table IV), indicating that the solubility surface is warped toward the chloroform-water binary. The degree of warp is relatively slight near the water vertex, but increases very strongly in the vicinity of the chloroform vertex. Thus, the assumption of a straight solubility surface “generatrix” UV is not valid for this system.
_______~
Table 11.
T i e Line
Predicted Quaternary liquid Equilibria in the System Chloroform-Acetone-Formic Acid-Water at 25' C.
Combosition of Chloroform-Rich Lavers. w t . % Formic acid Water Acetone Chloroform
Acetone
Composition of Water-Rich Layers, Wt. 7 0 Chloroform Water Formic acid
1-1 1-2 1-3 1-4 1-5 1-6 1-7 1-8
13.40 13.40 13.40 13.40 13.38 13.38 13.38 13.05
85.0 85.0 85 .O 85 .O 84.7 84.7 84.7 82.5
0.73 0.73 0.73 0.73 0.74 0.74 0.74 0.45
0.87 0.87 0.87 0.87 1.18 1.18 1.18 4.00
2.16 2.18 1.94 2.00 2.02 2.02 2.21 3.65
2.63 3.88 4.45 5.13 5.97 7.04 8.05 22.20
79.53 65.87 55.75 49.93 41.08 35.13 30.76 8.68
15.68 28.07 37.86 42.94 50.93 55.81 58.98 65,47
2-1 2-2 2-3 2-4 2-5 2-6 2-7 2-8
23.10 23.10 23,OO 22.95 22.92 22.90 22.85 22.61
74.4 74.4 74.0 73.9 73.8 73.7 73.5 72.8
1.40 1.40 1.44 1.45 1.35 1.34 1.37 1.46
1.10 1.10 1.56 1.70 1.93 2.06 2.28 3.18
7.03 6.16 5.68 5.60 5.16 5.08 4.97 8.82
2.65 3.84 4.70 5.35 6.57 7.72 8.64 26.70
75.56 63,05 53.41 47.83 39.48 33.31 29.54 7.56
14.76 26.95 36.21 41.22 48.79 53.89 56.85 56.92
3-1 3-2 3-3 3-4 3-5 3-6 3-7 3-8
31 .OO 30.95 30.85 30.80 30.79 30.78 30.75 29.45
65.7 65.7 65.5 65.4 65.4 65.3 65.2 62.5
1.88 1.89 1.93 1.94 1.94 1.77 2.07
1.42 1.46 1.75 1.87 1.87 1.98 2.28 5.98
11.84 10.54 9.40 9.16 8,79 8.45 8.54 14.41
3.05 4.18 4.85 5.45 6.76 7.97 9.36 28.60
70.75 59.49 51.07 45.85 37.87 32.38 28.25 7.20
14.36 25.79 34.68 39.54 46.58 51.20 53.85 59.79
4-1 4-2 4-3 4-4 4-5 4-6 4-7 4-8
36.30 36.30 36.25 36.20 36.20 36.10 35.80 33.80
59.0 59.0 58.9 58.8 58.8 58.7 58.2 54.2
2.60 2.60 2.61 2.63 2.63 2.67 2.66 3.03
2.10 2.10 2.24 2.37 2.37 2.53 3 34 8.97
15.46 13.92 12.70 12.22 11.88 11.57 11.71 23.15
3.14 4.26 5.06 5.83 7.36 8.75 10.19 35.90
67.65 57.05 48.87 44.03 36.24 30.95 26,99 5.69
13.75 24.77 33.37 37.92 44.52 48.73 51.11 35,26
5-1 5-2 5-3 5-4 5-5 5-6 5-7 5-8
41.4 41.4 41.2 41 .0 40.9 40.8 40.7 34.3
53.5 53.5 53.2 53.0 52.9 52.8 52.6 44.2
3.10 3.10 3.17 3.22 3.21 3.19 3.24 4.28
2.00 2.00 2.43 2.78 2.99 3.26 3.51 17.22
19.39 17.85 16.10 14.82 15.35 15.01 14.85 34.30
3.34 4.46 5.23 5.77 7.90 9.31 10.75 44.20
63.94 54.14 46.92 43.11 34.48 29.49 25.85 4.29
13.33 23.55 31.75 36.30 42.27 46.19 49.55 17.21
6-1 6.2 6-3 6-4 6-5 6-6
47.45 47.40 47.40 47.20 47.30 46.95
42.7 42.6 42.3 42.1 42.0 41.5
5.30 5.31 5.21 5.27 5.23 5.36
4.55 4.69 5.14 5.48 5.47 6.19
28.10 26.00 24,45 24.19 23.41 23.75
4.12 5.52 6.85 7.85 9.80 11.90
55,64 47.33 40,28 36.34 30.08 25.09
12.14 21.15 28,42 31.62 36.71 39.26
7-1 7-2 7-3 7-4 7-5 7-6
51.65 51.20 50.60 49.87 48,30 44.50
31 . O 30.45 29,85 29.35 27.92 23.93
9.89 10.12 10.42 10.80 11.44 13.66
7.46 8.23 9.13 10.00 12.34 17.91
40.0 39.05 37,75 37.20 38.00 44.50
6.66 8.68 10.81 12.20 15.79 23.93
41.86 35.19 29.71 26.59 21.23 13.68
11.48 17.08 21.73 24.01 24.98 17.89
1.90
Table 111. Determination of Curvature of Profile of Solubility Surface for System Pyridine-Toluene-Ethanol-Water at 25' C.
Pyridine, MI.
Toluene, 'MI.
Water, MI.
9.573 15.273 20.67 17.753
0.96 2.00 8.15 31.107
47.243 35.04 20.53 7.053
Ethanol, MI. Predicted Actual
12,247 19.003 23.86 19.30
13.55 19.00
24.00 19.28
Table IV. Determination of Curvature of Profile of Solubility Surface for System Chloroform-Acetone-Formic Acid-Water at 25' C. Acetone, Chloroform, Water, Formic Acid, MI. MI. MI. MI. Predicted Actual
16.80 28.00 36.50 36.65
1.57 2.07 6.55 23.50
71 .OO 51 .OO 25.00 1.405
11.47 20.05 30.50 29.55
11,55 19,OO 8.50 1 .oo
Determination of Phase Equilibrium
For each quaternary system, the equilibrium concentrations represented by five predicted tie lines were checked by chemical analysis. For each of the selected tie lines XY (Figure 1) the corresponding over-all mass fractions of the four components a t the point J bisecting XY were calculated by material balance from the graphically predicted compositions of X and Y. T h e several mixtures J were then prepared by adding together and agitating the exact masses of each of the four pure components required to produce the calculated over-all compositions of J. These mixtures were held a t a constant temperature of 25' 3= 0.1' C. Since all mixtures J were located in the two-phase region, upon standing under isothermal conditions they separated into two homogeneous liquid layers in equilibrium. T h e two layers were then withdrawn, weighed, and subjected to chemical analysis, the VOL. 6
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367
experimentally determined compositions of each layer being compared to the compositions of the predicted equilibrium layers X and Y . Chemical Analysis
I n the system pyridine-toluene-ethanol-water, pyridine was determined to h0.770 in the water-rich layers by titration with standard sulfuric acid, using methyl orange indicator as well as a p H meter. Water was determined to A270 in the water-rich layers by back-titration with carefully standardized Karl Fischer reagent in a n apparatus designed to exclude atmospheric moisture positively. Toluene was determined to f1% by comparing the refractive indices of the water-rich layers with those of test solutions made u p with the experimentally measured mass ratios of pyridine and water, and known toluene concentrations. Toluene concentrations were also checked by gas chromatography, with results from the two methods being in excellent agreement. Since all the analytical procedures for ethanol reported in the literature involve many sequential steps, each with its own error, it was decided to determine ethanol by difference, as the method of greatest Ethanol concentrations were probable accuracy (+2.5%). checked by gas chromatography; good agreement with the values determined by difference was found. T h e compositions of the toluene-rich layers were found by material balance. T h e experimentally determined equilibria are compared with the predicted values in Table V. T h e experimental data are in reasonably good agreement with the predicted values, with the exception of the ethanol concentrations. There is less ethanol in the water-rich layers than predicted, and more in the toluene-rich layers.
Table V.
For the second quaternary system, formic acid was determined to *0.6% in the water-rich layers by titration with standard sodium hydroxide. Water was determined to +2% in the water-rich layers using Karl Fischer reagent, as before. Acetone was determined to i 0 . 6 7 0 by titrating with standardized sodium thiosulfate solution for excess iodine remaining after reacting the acetone with iodine in a n alkaline medium to form iodoform. Chloroform concentrations in the water-rich layers were found by difference to within about h 4 % . There is serious doubt whether direct analysis would have yielded a higher estimated accuracy, because of the complexity of standard wet methods for chloroform. The compositions of the chloroform-rich layers were again found by material balance calculations. Riebling (1 961) discussed errors in the chemical analysis and material balance calculations at great length. T h e values reported above are estimates of the maximum errors expected. T h e experimentally determined equilibria are compared with corresponding predicted values in Table VI. The predicted values do not agree well with those determined by experiment. I n particular, the water-rich layers actually contain more chloroform and less formic acid than predicted, while the chloroform-rich layers contain more formic acid and less chloroform than predicted. Concentrations of acetone and water in both layers are very nearly those predicted. Discussion of Results
The following explanation of the experimental results is proposed. There are two major assumptions made in the graphical prediction method: that profile UV (Figure 1) of the solubility surface is a straight line and that the quaternary tie
Comparison of Experimental and Predicted Equilibria in the System Pyridine-Toluene-Ethanol-Water at 25’ C. and 1 Atm.
(Concentrations in weight per cent; figures in parentheses are predicted concentrations) Tie Line
1-6 2-7 3-4 4-5 5-4
Pyridine
Water Layers Toluene Ethanol
3.90 (3.90) 9.03 (9.73) 26.56 (22.76) 33.28 (31.53) 43,44 (42.94)
8.85 (3.90) 8.50 (6.76) 4.26 (4.01) 7.55 (8.89) 17.01 (15.89)
39.42 (44.40) 39,39 (43.95) 22.48 (26.42) 22.48 (25.09) 14.70 (16.29)
Water
Pyridine
Toluene Layers Toluene Ethanol
47.83 (47.80) 42.08 (39.56) 46.70 (46.81) 36.53 (34.49) 24.82 (24.88)
13.49 (13.53) 21.86 (21.36) 22.59 (26,31) 27.49 (28,80) 38.07 (37.35)
74.64 (79.89) 66.45 (69.08) 66.05 (67.63) 59.83 (62.40) 47.08 (50.55)
10.60 (5.49) 11.17 (7.18) 8.18 (3.93) 9.13 (5.70) 8.10
(6.35)
Water
1.27 (1.09)
0.52 (2.38) 3.18 (2.13) 3.56 (3,lO) 6.75 (5.75)
Table VI. Comparison of Experimental and Predicted Equilibria in the System Chloroform-Acetone-Formic Acid-Water at 25’ C. and 1 Atm.
(Concentrations in weight per cent; figures in parentheses are predicted concentrations) Tie tine
1-7 2-6 3-5 4-4 5-3
368
Chloroform
16.98 (8.05) 21 .77 (7,72) 22.74 (6.76) 20. ’76 (5.83) 9.02 (5.23)
Water Layers Acetone Formic acid
2.22 (2.21) 5.30 (5.08) 9.39 (8.79) 13.68 (12.22) 17.05 (16.10)
I&EC FUNDAMENTALS
51.60 (58.98) 42.95 (53.89) 34,57 (46.58) 25.58 (37.92) 26.33 (31 .75)
Water
Chloroform
29.20 (30.76) 30.08 (33.31) 33.30 (37.87) 39.98 (44.03) 45.60 (46.92)
79.26 (84.70) 64.45 (73.70) 54.06 (65.40) 46,88 (58.80) 50.67 (53.20)
Chloroform Layers Forrnic%d Acetone
14.03 (13.38) 24.86 (22.90) 33.81 (30.79) 37.47 (36.20) 41 . O O (41.20)
6.01 (1.18) 9.34 (2.06) 10.28 (1.87) 13.29 (2,37) 5.18 (2,47)
Water 0.70
(0.70) 1.34 (1.34) 1.86 (1.94) 2.36 (2.63) 3.14 (3.17)
lines may be determined by the intersection of planes passed through tie lines in each of the two Type I ternaries and their opposite vertices. If the predicted equilibrium data do not describe the actual system, then either or both of these assumptions are not valid. I n the system chloroform-acetone-formic acid-water, the solubility surface was found to be somewhat warped, invalidating the first assumptio'n, and the graphically determined quaternary curves are in error. Similar results were reported by Francis (1 954), who fmound a concave solubility surface in the system water-methanol-aniline-benzene. However, this warping is not sufficient to account for the large discrepancies between the predicted and experimental equilibrium compositions. Moreover, in the system pyridine-toluene-ethanolwater, where the solubility surface profile UV was found to be straight, and the quaternary solubility curves accordingly correct, the predicted data still do not describe the system too accurately. Therefore, the controlling factor may be the actual location of the quaternary tie lines within the solubility surface. For example, if the addition of pure component B to some point on the tie line j k in the ternary system ACD (Figure 1) alters the distribution of C between A and D , then the relative distances of points X anti Y from the Cvertex will vary with the B content, causing the quaternary tie lines, while themselves remaining straight, to t\vist out of the plane BZL. T h e surface betxveen IL and B woulid then be curved, rather than planar. A similar argument applies to the surface PCQ if the addition of pure C to A B D alters the distribution of B between A and D . These surfaces would therefore be expected to be true planes only if the presence of one solute does not affect the distribution of the other between the tbvo solvents-that is, in purely ideal systems. T h e departure of any real system from ideality (in terms of the constancy of its distribution coefficients) may well cause deviations between predicted and experimental equilibria. The interpretation advanced above is strongly substantiated by available data. I n the system chloroform-acetone-acetic acid-water, the profile L'V of the solubility surface is straight, the distribution of acetone between chloroform and water is not materially affected by the presence of acetic acid, and the distribution of acetic acid between the two solvents is altered by only a few per cent as the acetone concentration is varied over wide ranges. Accordingly, the tie line surfaces are essentially planar, with the result that there is good agreement between predicted and experimental data. I n the system chloroform-acetone-formic acid-water studied by the authors, agreement between predicted and experimental acetone concentrations is excellent, indicating that the distribution of acetone is only slightly affected by the presence of formic acid, at least in the concentration ranges investigated. HoFvever, even small amounts of acetone drastically alter the distribution of formic acid between chloroform and water, as illustrated in Figure 3. This, along with the warped solubility surface, may explain the observed discrepancies. Similar effects are illustrated in Figures 4 and 5 for the system pyridine-toluene-ethanol-water. The presence of pyridine strongly affects the distribution of ethanol between toluene and lvater, and that of ethanol disturbs the distribution of pyridine between the two solvents. Hence, neither tie line surface is lvholly planar, and even though the solubility surface has a straight profile, agreement between predicted and experimental equilibria, whik perhaps sufficient for initial design calculations, is not exact.
P a
!! L
e
z W
+ Y W
z
E LL
+ W
a
a
E X P E R I M E N T A L WEIGHT PERCENT ACETONE IN WATER LAYERS
Figure 3. Effect of acetone on formic acid concentrations
EXPERIMENTAL WEIGHT PERCENT ETHANOL IN WATER LAYERS
Figure 4. tions
Effect of ethanol on pyridine concentra-
VOL. 6
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A U G U S T 1967
369
fluence the distribution of the other between the two solvents. Since all real systems will be nonideal to one degree or another, a decision (based on the relative magnitudes of the two effects) must be made as to whether the graphical method will yield results of the desired degree of accuracy. The relative magnitude of each effect may be rapidly estimated by experimentally checking the solubility profile of a candidate quaternary as described herein, and by checking distribution coefficients in the concentration range of interest for the proposed extraction operations. Literature Cited
Brancker, A. V., Hunter, T. G., Nash, A. W., Znd. Eng. Chem. 33, 880 119411.
Brkke;, A.‘.V., Hunter, T. G., Nash, A. W., J . Phys. Chem. 44, 683 (1940). Cruickshank. A. J. B., Haertsch.. N... Hunter. T. G.. Znd. Ene. Chem. 42, 2154-8 (1950). Francis, A. W., Znd. Eng. Chem. 46, 205 (1954). Francis, A . \V., “Liquid-Liquid Equilibriums,” Interscience, New York, 1963. Hunter, T. G., Znd. Eng. Chem. 34, 963 (1942). Ku, P. L., master’s thesis in chemical engineering, Polytechnic Institute of Brooklyn, 1959. Prince, R. G. H., Chem. Eng. Sci. 3, 175-86 (1954). Pratt, H. R. C., Glover, S. T., Trans. Znst. Chem. Engrs. (London) 54, 54 (1946). Riebling, R. W., “Equilibrium Studies in Quaternary Liquid Systems,” master’s thesis in chemical engineering, Polytechnic Institute of Brooklyn, 1961. Smith, J. D., Znd. Eng. Chem. 36, 68 (1944). Solomko. V. P.. Panasvuk. V. D.. Zelenskava. A. M.. J . Abbl. Chem. USSR (English ;rand.) 35, 602 (1962): ’ Vriens, G. N., Medcalf, E. C., Ind. Eng. Chem. 45, 1098 (1953). Washburn. R., Beguin, A. E., Beckord, 0. C., J . A m . Chem. Sod. 61, 1964 (1939)-
-
EXPERIMENTAL WEIGHT PERCENT PYRIDINE IN WATER LAYERS
Figure 5. Effect of pyridine on ethanol concentrations Conclusions
T h e use of intersecting planes is a n approximation to the actual situation of intersecting curved surfaces. T h e graphical method of Hunter would be expected to predict actual quaternary solubility and equilibrium data accurately only when the profile of the three-dimensional solubility surface is straight, and when the presence of one solute does not materially in-
RECEIVED for review August 30, 1966 ACCEPTEDMarch 2, 1967
A GENERAL SOLUTION T O THE PROBLEM OF
HYDROGEN SULFIDE ABSORPTION IN ALKALINE SOLUTIONS FRANCESCO G l O l A A N D G l A N N l A S T A R I T A Istituto di Chimica Industriale, University of Naples, N a p l a , h l y
A theoretical solution for the case of absorption followed by an instantaneous reversible ionic reaction is presented. The theory is particularly useful for the absorption of HzS in solutions of a salt of a strong base and a weak acid, inasmuch as the main reaction is a proton-transfer reaction and, therefore, it may be assumed instantaneous. The following cases of chemical absorption of HzS are reviewed: in hydroxide solutions, in alkaline buffer solutions, in monoethanolamine solutions, in aqueous solutions of a salt of a strong base and a weak acid-e.g., NaAc and NaaP04, and in inert solutions-e.g., NaCl (inert as far as HzS absorption is concerned). The simultaneous absorption of H2S and COZin hydroxide solutions is also reviewed. Absorption data already published as well as original data are presented and discussed, showing good agreement with theory. HE chemical absorption of H2S in aqueous alkaline soluTtions occurs according to a mechanism that is in some aspects different from that occurring for other similar acid gases. The difference is mainly due to the fact that the hydrogen sulfide is able to transform into the HS- ion by a simple proton-transfer reaction. This allows one to assume that the
370
l&EC FUNDAMENTALS
chemical reaction occurring in the liquid phase can be considered instantaneous with respect to the diffusional processes even for slightly basic solutions. The same assumption is not possible for the chemical absorption of other seemingly similar acid gases, For example, carbon dioxide (Astarita and Gioia, 1964), in order to transform into the HCOa-ion, has to undergo
