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Liquid-liquid equilibria of (methanol + cyclohexane + chlorobenzene) and of (methanol + methylcyclohexane) + benzene, + ethanol, and + toluene at 298.15 K
M-1683 I. C‘hcm. Thermo~vnamic.s 1984, 16. 737-741
Liquid-liquid equilibria of (methanol + cyclohexane + chlorobenzene) and of (methanol + methylcyclohexane) + benzene, + ethanol, and + toluene at 298.15 ISAMU
K
NAGATA
Department of Chemical Engineering. Kunazawa. Ishikawa 920, Japan
Kanaxwu
University.
i Received 2 February 1984) Liquid-liquid equilibria for (methanol + methylcyclohexane) + benzene, + ethanol, vaporrliquid and liquid-liquid equilibria correlated by the extended UNIQUAC well with those predicted by the equation
cyclohexane + chlorobenzene) and for (methanol + and + toluene at 298.15 K are reported. Binary for 10 mixtures constituting the ternary mixtures are equation. The ternary experimental values compare having only binary parameters.
1. Introduction A program is in progress in this laboratory to measure the liquid-liquid equilibria of ternary methanol-containing mixtures. This paper reports liquid-liquid equilibria for (methanol + cyclohexane + chlorobenzene) and for (methanol + methylcyclohexane) + benzene, + ethanol. and + toluene at 298.15 K and compares observed values with those obtained from the extended UNIQUAC equation.“’ Vapor-liquid equilibria for binary mixtures constituting the ternary mixtures studied here have been reported in the literature: (methanol + chlorobenzene)“’ at 293.15 K; (methanol + benzener3’ at 298.15 K; (methanol + ethanol)‘4’ at 298.15 K: (methanol + toluene)‘5’ at 336.73 to 343.40 K; (ethanol + methylcyclohexane)‘6’ at 298.15 K; (benzene + methylcyclohexane)“’ at 313.15 K; (toluene + methylcyclohexane)“’ at 3 13.15 K; (cyclohexane + chlorobenzene)“’ at 348.15 K.
2. Experimental Points on binodal curves were determined by turbidity titration. Tie lines were obtained by analyzing compositions of the two conjugate phases in equilibrium with a gas chromatograph (Shimadzu model GC4C) connected to an integrator (Shimadzu model ITG-2A). Sample mixtures in an equilibrium cell were maintained at (298.15f0.01) K by use of a water thermostat. Details of the experimental measurements have been reported previously.‘“’ 0021-0614/84/080737+05
%02.00/O
(‘# 1984 Academic
Press Inc. (London)
Limited
I. NAGAT’A
738
S.R. chlorobenzene, cyclohexane, methylcyclohexane, and Spectra-grade methanoi and toluene were used without further purification. C.P. benzene was purified by recrystallization. C.P. ethanol was fractionated after storage over calcium oxide. Densities of the compounds used for the experimental work were measured with an Anton Paar digital densimeter (DMA40) and compared well with literature values.” “) Tables I and 2 list the ternary experimental solubility and tie-line values at 298.15 K, respectively. The mutual binary solubilities for (methanol + cyclohexane) agree well with previous results.‘9’
3. Analysis of results Correlation of the experimental liquid-liquid equilibrium results was carried out using the extended UNIQUAC equation.“’ The activity coefficient fi of any component i in a multicomponent mixture is given by lnf;
=
M4i/xi)+
l -(~ilXi)-:Z4i{1n(~ilei) -4:
where +i = xiri/Cjxjrj and Tij = exp(-aij/T) are pure-component
ln(xjeiTij)
+
1 -(4Jei)} (1)
+ qiCj(qj*/qj)ej-qiCj{(qi*/qi)ejTijlCker’kj),
is the segment fraction, Bi = Xiq,lCjxjqj is the area fraction, is related to the binary adjustable parameter aij; r, q, and q* molecular parameters. Values of q* have been empirically
TABLE 1. Mutual solubilities at 298.15 K
0.8288 0.8069 0.7760 0.7526
0.1712 0.1845 0.2061 0.2220
0.7192 0.6841 0.6478 0.5998
0.2482 0.2764 0.3073 0.3489
0.5595 0.3856 0.4155 0.5219 0.4197 0.3630 0.4987 0.4408 0.3098 0.4796 0.4587 0.2346
0.5212 0.5712 0.6208 0.7058
0.2230 0.1775 0.1684 0.1544
0.7209 0.1430 0.8508 0.7867 0.1251 0.8749 0.8034 0.8329
x,CH30H+x&H,,CH,+(l-x,-.x2)ChH6 0.1739 0.8261 0.2498 0.6808 0.3700 0.5443 0.5940 0.3389 0.6750 0.2698 0.8027 0.1784 0.1806 0.8006 0.2764 0.6431 0.4519 0.4664 0.6256 0.3115 0.7151 0.2379 0.8386 0.1554 0.2095 0.7479 0.3169 0.6000 0.5147 0.4087 0.6484 0.2919 0.7622 0.2036 0.8547 0.1453 x,CH,OH+.U,C,H,,CH,+(I-x,-YJC,H,OH 0.1739 0.8261 0.3735 0.5493 0.5071 0.4013 0.5789 0.3243 0.7183 0.2131 0.8299 0.1533 0.2695 0.6891 0.3965 0.5187 0.5239 0.3812 0.6602 0.2530 0.7620 0.1865 0.8547 0.1453 0.3368 0.5956 0.4203 0.4885 0.5586 0.3445 0.6929 0.2297 0.7807 0.1772 0.1739 0.1860 0.2054 0.2268
0.8261 0.7901 0.7537 0.7176
0.2420 0.2979 0.3443 0.4009
x,CHJOH+x,C,H,,CH,+(l-x,-x&H&H, 0.6931 0.4382 0.4765 0.5859 0.6206 0.4913 0.4287 0.6709 0.5690 0.5104 0.4113 0.7203 0.5117 0.5563 0.3702 0.7440
0.3444 0.2720 0.2335 0.2160
0.7592 0.8101 0.8418 0.8547
0.2052 0.1715 0.1508 0.1453
LIQUID-LIQUID
EQUILIBRIA TABLE
VI
Phase I YL
Phase II x1 x2
Xl
IN TERNARY
2. Tie-line
results
739
MIXTURES
at 298.15 K
Phase I Phase II X2 X2 ~~_ _ -Xl __~~-~-.
Phase I xI x2
Xl
Phase II I1
0.7963 0.7638
0.1907 0.2145
0.1614 0.1889
x,CH,OH+x&,H,,+(l-.x,-x,)C,H,Cl 0.8127 0.7330 0.2379 0.2160 0.7724 0.6995 0.2611 0.2602
0.7338 0.6785
0.6647 0.6255
0.2910 0.3239
0.2860 0.3390
0.6484 0.5934
0.8268 0.7989
0.1622 0.1796
0.1986 0.2372
x,CH,OH+x,C,H,,CH,+(l-x,-x2)C6H, 0.7765 0.7770 0.1930 0.2422 0.7197 0.7388 0.2161 0.2740
0.6991 0.6475
0.6969 0.6542
0.2486 0.2840
0.3493 0.4074
0.5662 0.5085
0.7974 0.7481 0.6769
0.1716 0.1936 0.2417
0.1879 0.2110 0.2436
0.2820 0.2969 0.3221
0.6739 0.6498 0.6189
0.5459
0.3562
0.3515
0.5800
0.8239 0.8171 0.7945
0.1659 0.1673 0.1834
0.2034 0.2286 0.2394
0.2622 0.2810 0.3195
0.6780 0.6483 0.6028
0.7052
0.2456
0.3625
0.5523
x,CH,OH+x,C,H,,CH,+(l-s,-xx,)C,H,OH 0.8055 0.7703 0.7230
0.6456 0.6114 0.5959
0.2616 0.2919 0.3058
x,CH,OH+x&H,,CH,+(l-x,-x,)C,H,CH, 0.7702 0.7331 0.7100
0.7839 0.7547 0.7332
0.1891 0.2102 0.2253
obtained:‘r’ methanol, 0.99; ethanol, 0.92; methylcyclohexane, 1.10; for the other components studied here, q* = q”.*. Reduction of vapor-liquid equilibria was performed from the equation:
where p, pi, xi, yi and R are the phase mole fraction, vapor-phase fugacity coefficients, 4i at p and virial equation of state truncated coefficients were estimated using TABLE
pressure, pure-component vapor pressure, liquidmole fraction, and gas constant, respectively. The 4; at ~1, were calculated from the volume-explicit after the second term. Pure and cross second virial the method of Hayden and O’Connell.“” Vapor
3. The results of fitting the extended UNIQUAC equation to vapor-liquid equilibria and root-mean-square deviations 6p, 67: 6x, and 6y, for binary
\-,CH,OH+ x,C,H,CI <,CH,OH +.x&H, r,CH,OH + x,C,H,OH \-,CH,OH +.x&H&H, c-,C,H,OH+x,C,H,,CH, \-,C,H,+x&H,,CH, \-,C,H,CH,+.~*C,H,,CH, \-,C,H,,+.x,C,H,CI \,CH,OH+.x&H,, \-,CH,OH+x,C,H,,CH, ” Obtained from previous paper.“’
58.21 63.45 - 39.80 110.72 211.35 58.90 66.55 133.09 347.73 393.09 mutual
solubilities.
and liquid-liquid mixtures
a,,iK - _ -~.
GplPa
6T/K
lo3 6x
lo3 s,
975.13 1008.86 38.88 827.87 1140.02 85.17 38.36 - 11.97 1349.8 ’ 1247.0”
101.3 226.6 109.3 178.6 181.3 13.3 6.7 108.0
0.00 0.00 0.00 0.10 0.01 0.00 0.00 0.00
0.2 0.6 0.1 0.3 1.2 0.0 0.0 0.8
4.0 4.3 10.1 0.1 0.1 1.5
Parameters
for
(.x,CH,OH+x,C,H,,)
were
taken
from
a
740
I. NAGATA Chlorobenzene
Methanol
Cyclohexane Benzene
Methanol
Methylcyclohexane Ethanol
C
Methanol
Methylcyclohexane Toluene
Methylcyclohexane FIGURE 1. Experimental and calculated liquid-liquid equilibria at 298.15 K. 0, (Solubility) table 1; a-- - -0, (tie-line) table 2; ~ calculated from equation (1). Compositions are expressed as mole fractions. A, {x,CH,OH + x2CiH,,+(l-X, +x,)C,H,,Cl}; B, jx,CH,OH + xrC,H,,CH3 + (1 -x,-x,)C,H,j; C, {x,CH,OH + x&H,,CH, + (I-x,-x,)C,H,OH); D, jx,CH,OH + .x2C,H,,CH, + (1 -x1 -xJC,H,CH,{.
pressures of the pure components were calculated by means of the Antoine equation whose constants were taken from the literature. (l”,r2’ Pure-liquid molar volumes r/; ’ were calculated using the modified Rackett equation.(r3’ The binary parameters, a,, and a,,, were determined using a computer program based on the maximumlikelihood principle as described by Prausnitz et a1.‘14’ Values of the standard deviations in the measured variables, i.e. pressure, temperature, liquid-phase and vapor-phase mole fractions, were 133.3 Pa, 0.05 K, 0.001, and 0.003, respectively. The binary parameters from the mutual binary solubilities were obtained by combining use of the relation (fiXi)’ = (j&f, (3) and a Newton-Raphson iterative method, where I and II refer to two equilibrium liquid pgases. Table 3 gives the binary parameters and the root-mean square deviations between experimental and true values of the measured variables: 6p, pressure; ST, temperature; 6x, liquid-phase mole fraction; 6y, vapor-phase mole fraction.
LIQUID-LIQUID
EQUILIBRIA
IN TERNARY
MIXTURES
741
Ternary tie-line calculations are done by solving equation (3) for three components, X,x: = 1 and C,xf’ = 1 using a Newton-Raphson iterative technique. (14115) For mixtures having a plait point, quantitative calculations for liquid-liquid equilibria are much more difficult. The UNIQUAC equation’14’ reproduced the binary vapor-liquid equilibria listed in table 1 as well as the extended UNIQUAC equation. However, ternary predictions based on the UNTQUAC equation gave bigger two-phase regions for the ternary mixtures studied here than did the extended UNIQUAC equation, so that the ternary predictions from the UNIQUAC equation were not shown here. Figure 1 compares the experimental results with the calculated values obtained from equation (1) having only the binary parameters.
REFERENCES Nagata. I. Thermochim. Acfa 1982, 56, 43. Maher. P. J.: Smith. 9. D. J. Chem. Eng. Dara 1979, 24. 363. Hwang, S. C.; Robinson. R. L. J. Chem. Eng. Data 1977, 22. 319. Hall, D. J.: Mash, C. J.; Pemberton, R. C. NPL Report Chem. 95. January 1979. Benedict, M.: Johnson, C. A.; Solomon, E.: Rubin, L. C. Tram. Am. Chem. Engr.7 1945, 41. 371. Isii, N. J. Sot. Chem. Ind. Jpn 1935, 38, 659. Asmanova. N.; Geral, M. J. Chem. Eng. Darn 1980, 25. 159. Diaz Petia. M.; Compostzo. A.; Crespo Colin. A.; Escudero. I. J. Chem. Thermo&namic.y 1980, (1. 1051. Nagata. I.: Katoh, K. Thermochim. Acta 1980, 39, 45. Riddick. J. A.: Bunger. W. 9. Organic Solvents. 3rd edition. Wiley-Interscience: New York. 1970. Hayden, J. G.: O’Connell, J. P. Ind. Eng. Chem., Proc. Des. Dev. 1975, 14, 221. Boublik, T.: Fried, V.; HBla, E. The Vapour Pressures of Pure Substances. Elsevier: New York. 1973. Spencer, C. F.; Danner. R. F. J. Chem. Eng. Data 1972, 17. 236. Prausnitz. J. M.; Anderson. T. F.; Grens, E. A.; Eckert, C. A.; Hsieh. R.: O’Connell, J. P. Cornpurer Caicuhtions for Multicomponent Vapor- Liquid and Liquid-Liquid Equilibria. Prentice Hall: Englewood Cliffs, N.J. 1980. Null. H. R. Phase Equilibriu in Process Design. Wiley-Interscience: New York. 1970.
Liquid-liquid equilibria of (methanol + cyclohexane + chlorobenzene) and of (methanol + methylcyclohexane) + benzene, + ethanol, and + toluene at 298.15 ISAMU
K
NAGATA
Department of Chemical Engineering. Kunazawa. Ishikawa 920, Japan
Kanaxwu
University.
i Received 2 February 1984) Liquid-liquid equilibria for (methanol + methylcyclohexane) + benzene, + ethanol, vaporrliquid and liquid-liquid equilibria correlated by the extended UNIQUAC well with those predicted by the equation
cyclohexane + chlorobenzene) and for (methanol + and + toluene at 298.15 K are reported. Binary for 10 mixtures constituting the ternary mixtures are equation. The ternary experimental values compare having only binary parameters.
1. Introduction A program is in progress in this laboratory to measure the liquid-liquid equilibria of ternary methanol-containing mixtures. This paper reports liquid-liquid equilibria for (methanol + cyclohexane + chlorobenzene) and for (methanol + methylcyclohexane) + benzene, + ethanol. and + toluene at 298.15 K and compares observed values with those obtained from the extended UNIQUAC equation.“’ Vapor-liquid equilibria for binary mixtures constituting the ternary mixtures studied here have been reported in the literature: (methanol + chlorobenzene)“’ at 293.15 K; (methanol + benzener3’ at 298.15 K; (methanol + ethanol)‘4’ at 298.15 K: (methanol + toluene)‘5’ at 336.73 to 343.40 K; (ethanol + methylcyclohexane)‘6’ at 298.15 K; (benzene + methylcyclohexane)“’ at 313.15 K; (toluene + methylcyclohexane)“’ at 3 13.15 K; (cyclohexane + chlorobenzene)“’ at 348.15 K.
2. Experimental Points on binodal curves were determined by turbidity titration. Tie lines were obtained by analyzing compositions of the two conjugate phases in equilibrium with a gas chromatograph (Shimadzu model GC4C) connected to an integrator (Shimadzu model ITG-2A). Sample mixtures in an equilibrium cell were maintained at (298.15f0.01) K by use of a water thermostat. Details of the experimental measurements have been reported previously.‘“’ 0021-0614/84/080737+05
%02.00/O
(‘# 1984 Academic
Press Inc. (London)
Limited
I. NAGAT’A
738
S.R. chlorobenzene, cyclohexane, methylcyclohexane, and Spectra-grade methanoi and toluene were used without further purification. C.P. benzene was purified by recrystallization. C.P. ethanol was fractionated after storage over calcium oxide. Densities of the compounds used for the experimental work were measured with an Anton Paar digital densimeter (DMA40) and compared well with literature values.” “) Tables I and 2 list the ternary experimental solubility and tie-line values at 298.15 K, respectively. The mutual binary solubilities for (methanol + cyclohexane) agree well with previous results.‘9’
3. Analysis of results Correlation of the experimental liquid-liquid equilibrium results was carried out using the extended UNIQUAC equation.“’ The activity coefficient fi of any component i in a multicomponent mixture is given by lnf;
=
M4i/xi)+
l -(~ilXi)-:Z4i{1n(~ilei) -4:
where +i = xiri/Cjxjrj and Tij = exp(-aij/T) are pure-component
ln(xjeiTij)
+
1 -(4Jei)} (1)
+ qiCj(qj*/qj)ej-qiCj{(qi*/qi)ejTijlCker’kj),
is the segment fraction, Bi = Xiq,lCjxjqj is the area fraction, is related to the binary adjustable parameter aij; r, q, and q* molecular parameters. Values of q* have been empirically
TABLE 1. Mutual solubilities at 298.15 K
0.8288 0.8069 0.7760 0.7526
0.1712 0.1845 0.2061 0.2220
0.7192 0.6841 0.6478 0.5998
0.2482 0.2764 0.3073 0.3489
0.5595 0.3856 0.4155 0.5219 0.4197 0.3630 0.4987 0.4408 0.3098 0.4796 0.4587 0.2346
0.5212 0.5712 0.6208 0.7058
0.2230 0.1775 0.1684 0.1544
0.7209 0.1430 0.8508 0.7867 0.1251 0.8749 0.8034 0.8329
x,CH30H+x&H,,CH,+(l-x,-.x2)ChH6 0.1739 0.8261 0.2498 0.6808 0.3700 0.5443 0.5940 0.3389 0.6750 0.2698 0.8027 0.1784 0.1806 0.8006 0.2764 0.6431 0.4519 0.4664 0.6256 0.3115 0.7151 0.2379 0.8386 0.1554 0.2095 0.7479 0.3169 0.6000 0.5147 0.4087 0.6484 0.2919 0.7622 0.2036 0.8547 0.1453 x,CH,OH+.U,C,H,,CH,+(I-x,-YJC,H,OH 0.1739 0.8261 0.3735 0.5493 0.5071 0.4013 0.5789 0.3243 0.7183 0.2131 0.8299 0.1533 0.2695 0.6891 0.3965 0.5187 0.5239 0.3812 0.6602 0.2530 0.7620 0.1865 0.8547 0.1453 0.3368 0.5956 0.4203 0.4885 0.5586 0.3445 0.6929 0.2297 0.7807 0.1772 0.1739 0.1860 0.2054 0.2268
0.8261 0.7901 0.7537 0.7176
0.2420 0.2979 0.3443 0.4009
x,CHJOH+x,C,H,,CH,+(l-x,-x&H&H, 0.6931 0.4382 0.4765 0.5859 0.6206 0.4913 0.4287 0.6709 0.5690 0.5104 0.4113 0.7203 0.5117 0.5563 0.3702 0.7440
0.3444 0.2720 0.2335 0.2160
0.7592 0.8101 0.8418 0.8547
0.2052 0.1715 0.1508 0.1453
LIQUID-LIQUID
EQUILIBRIA TABLE
VI
Phase I YL
Phase II x1 x2
Xl
IN TERNARY
2. Tie-line
results
739
MIXTURES
at 298.15 K
Phase I Phase II X2 X2 ~~_ _ -Xl __~~-~-.
Phase I xI x2
Xl
Phase II I1
0.7963 0.7638
0.1907 0.2145
0.1614 0.1889
x,CH,OH+x&,H,,+(l-.x,-x,)C,H,Cl 0.8127 0.7330 0.2379 0.2160 0.7724 0.6995 0.2611 0.2602
0.7338 0.6785
0.6647 0.6255
0.2910 0.3239
0.2860 0.3390
0.6484 0.5934
0.8268 0.7989
0.1622 0.1796
0.1986 0.2372
x,CH,OH+x,C,H,,CH,+(l-x,-x2)C6H, 0.7765 0.7770 0.1930 0.2422 0.7197 0.7388 0.2161 0.2740
0.6991 0.6475
0.6969 0.6542
0.2486 0.2840
0.3493 0.4074
0.5662 0.5085
0.7974 0.7481 0.6769
0.1716 0.1936 0.2417
0.1879 0.2110 0.2436
0.2820 0.2969 0.3221
0.6739 0.6498 0.6189
0.5459
0.3562
0.3515
0.5800
0.8239 0.8171 0.7945
0.1659 0.1673 0.1834
0.2034 0.2286 0.2394
0.2622 0.2810 0.3195
0.6780 0.6483 0.6028
0.7052
0.2456
0.3625
0.5523
x,CH,OH+x,C,H,,CH,+(l-s,-xx,)C,H,OH 0.8055 0.7703 0.7230
0.6456 0.6114 0.5959
0.2616 0.2919 0.3058
x,CH,OH+x&H,,CH,+(l-x,-x,)C,H,CH, 0.7702 0.7331 0.7100
0.7839 0.7547 0.7332
0.1891 0.2102 0.2253
obtained:‘r’ methanol, 0.99; ethanol, 0.92; methylcyclohexane, 1.10; for the other components studied here, q* = q”.*. Reduction of vapor-liquid equilibria was performed from the equation:
where p, pi, xi, yi and R are the phase mole fraction, vapor-phase fugacity coefficients, 4i at p and virial equation of state truncated coefficients were estimated using TABLE
pressure, pure-component vapor pressure, liquidmole fraction, and gas constant, respectively. The 4; at ~1, were calculated from the volume-explicit after the second term. Pure and cross second virial the method of Hayden and O’Connell.“” Vapor
3. The results of fitting the extended UNIQUAC equation to vapor-liquid equilibria and root-mean-square deviations 6p, 67: 6x, and 6y, for binary
\-,CH,OH+ x,C,H,CI <,CH,OH +.x&H, r,CH,OH + x,C,H,OH \-,CH,OH +.x&H&H, c-,C,H,OH+x,C,H,,CH, \-,C,H,+x&H,,CH, \-,C,H,CH,+.~*C,H,,CH, \-,C,H,,+.x,C,H,CI \,CH,OH+.x&H,, \-,CH,OH+x,C,H,,CH, ” Obtained from previous paper.“’
58.21 63.45 - 39.80 110.72 211.35 58.90 66.55 133.09 347.73 393.09 mutual
solubilities.
and liquid-liquid mixtures
a,,iK - _ -~.
GplPa
6T/K
lo3 6x
lo3 s,
975.13 1008.86 38.88 827.87 1140.02 85.17 38.36 - 11.97 1349.8 ’ 1247.0”
101.3 226.6 109.3 178.6 181.3 13.3 6.7 108.0
0.00 0.00 0.00 0.10 0.01 0.00 0.00 0.00
0.2 0.6 0.1 0.3 1.2 0.0 0.0 0.8
4.0 4.3 10.1 0.1 0.1 1.5
Parameters
for
(.x,CH,OH+x,C,H,,)
were
taken
from
a
740
I. NAGATA Chlorobenzene
Methanol
Cyclohexane Benzene
Methanol
Methylcyclohexane Ethanol
C
Methanol
Methylcyclohexane Toluene
Methylcyclohexane FIGURE 1. Experimental and calculated liquid-liquid equilibria at 298.15 K. 0, (Solubility) table 1; a-- - -0, (tie-line) table 2; ~ calculated from equation (1). Compositions are expressed as mole fractions. A, {x,CH,OH + x2CiH,,+(l-X, +x,)C,H,,Cl}; B, jx,CH,OH + xrC,H,,CH3 + (1 -x,-x,)C,H,j; C, {x,CH,OH + x&H,,CH, + (I-x,-x,)C,H,OH); D, jx,CH,OH + .x2C,H,,CH, + (1 -x1 -xJC,H,CH,{.
pressures of the pure components were calculated by means of the Antoine equation whose constants were taken from the literature. (l”,r2’ Pure-liquid molar volumes r/; ’ were calculated using the modified Rackett equation.(r3’ The binary parameters, a,, and a,,, were determined using a computer program based on the maximumlikelihood principle as described by Prausnitz et a1.‘14’ Values of the standard deviations in the measured variables, i.e. pressure, temperature, liquid-phase and vapor-phase mole fractions, were 133.3 Pa, 0.05 K, 0.001, and 0.003, respectively. The binary parameters from the mutual binary solubilities were obtained by combining use of the relation (fiXi)’ = (j&f, (3) and a Newton-Raphson iterative method, where I and II refer to two equilibrium liquid pgases. Table 3 gives the binary parameters and the root-mean square deviations between experimental and true values of the measured variables: 6p, pressure; ST, temperature; 6x, liquid-phase mole fraction; 6y, vapor-phase mole fraction.
LIQUID-LIQUID
EQUILIBRIA
IN TERNARY
MIXTURES
741
Ternary tie-line calculations are done by solving equation (3) for three components, X,x: = 1 and C,xf’ = 1 using a Newton-Raphson iterative technique. (14115) For mixtures having a plait point, quantitative calculations for liquid-liquid equilibria are much more difficult. The UNIQUAC equation’14’ reproduced the binary vapor-liquid equilibria listed in table 1 as well as the extended UNIQUAC equation. However, ternary predictions based on the UNTQUAC equation gave bigger two-phase regions for the ternary mixtures studied here than did the extended UNIQUAC equation, so that the ternary predictions from the UNIQUAC equation were not shown here. Figure 1 compares the experimental results with the calculated values obtained from equation (1) having only the binary parameters.
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