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Isothermal vapour-liquid equilibria for binary and ternary mixtures formed by acetonitrile, isobutanol and benzene
Thermochimica Acta, 126 (1988) 107-116 Elsevier Science Publishers B.V., Amsterdam
107 - Printed in The Netherlands
ISOTHERMAL VAPOUR-LIQUID EQUILIBRIA FOR BINARY AND TERNARY MIXTURES FORMED BY ACETONITRILE, ISOBU’I’ANOL AND BENZENE
ISAMU NAGATA Department
of Chemical
Engineering, Kanazawa University, Kanazawa 920 (Japan)
(Received 29 June 1987)
ABSTRACT Isothermal vapour-liquid equilibrium data were measured for the binary acetonitrile-isobutanol and ternary acetonitrile-isobutanol-benzene systems at 60 o C by using a vapour-recirculating equilibrium still. The experimental data were correlated by the extended UNIQUAC and UNIQUAC associated-solution models. The UNIQUAC associated-solution model gives better predicted values for the ternary system.
LIST OF SYMBOLS
A, B, C aLI B IJ
hB h hBC
I,“^;, K
x c4 K BC P pi 41
4; R rI
T
v
acetonitrile, isobutanol and benzene binary interaction parameter second virial coefficient enthalpy of hydrogen-bond formation enthalpies of formation of chemical complexes B,A and B$ components alcohol i-mer association constant, ( @B,,,/@B,@B,)[ i/( i f l)] solvation constant, ( QBJQB,QA,)[i/( ir, + rA)] solvation constant, ( @B,c/Q)B,@c,)[i/( irB + rc)] total pressure saturated vapour pressure of pure component I molecular area parameter of pure component I molecular interaction area parameter of pure component I universal gas constant molecular volume parameter of pure component I absolute temperature true molar volume of alcohol mixture true molar volume of pure alcohol liquid molar volume of pure liquid 1
0040-6031/88/$03.50
0 1988 Elsevier Science Publishers B.V.
108
XI
YJ Z
squid-phase mole fraction of component I vapour-phase mole fraction of component I coordination number equal to 10
Greek letters
Q,Cl
#I
liquid-phase activity coefficient of component I area fraction of component I standard deviations in pressure and temperature standard deviations in liquid-phase and vapour-phase mole fractions exp( - WW segment fraction of component I segment fraction of acetonitrile monomer in mixture segment fraction of isobutanol monomer in mixture segment fraction of isobutanol monomer in pure alcohol solution segment fraction of benzene monomer in mixture vapour-phase fugacity coefficient of component I at system pressure P and system temperature T vapour-phase fugacity coefficient of component 1 at its saturation pressure PI” and system temperature T
INTRODUCTION
The thermodynamic properties of solutions of butanols in acetonitrile and a hydrocarbon are currently the subject of studies in this laboratory. Vapour-liquid equilibria (VLE) for the system l-butanol-aceto~trile-benzene at 60°C [I] and liquid-liquid equilibria for the system acetonitrile-lbutanol-saturated hydrocarbon at 25 OC [2] have been reported. This paper reports VLE data for the binary system acetonitrile-isobutanol and the ternary system acetonitrile-isobutanol-benzene at 60 * C and their correlation by the extended UNIQUAC [3] and UNIQUAC associated-solution model [4].
EXPERIMENTAL
Acetonitrile and isobutanol (Nakarai Pure Chemical Industries Ltd.. analytical reagent grade) were used svithout further purification. C.P. benzene was purified by repeated rec~stall~ation. Some physical properties of the chemicals used for experimental work agree closely with values reported in the literature as shown in Table 1. For measurements of these properties.
109
TABLE 1 Physical properties of chemicals Density at 25 * C (g cme3>
Component
Acetomtrile Isobutanol Benzene
Refractive index at 25’C
Vapour pressure at 60 o C (torr)
Exptl.
Lit. [5]
Exptl.
Lit. [5]
Exptl.
Lit. [5]
0.7766 0.7979 0.8737
0.7766 0.7989 0.87370
1.34161 1.39394 1.49790
1.34163 1.3939 1.49792
368.1 93.0 391.5
368.0 [6] 93.01 391.47
an Anton Paar densimeter (DMA40) and a Shimadzu Pulfrich refractometer were used. Vapour pressures were measured at 60°C with a Boublik vapour-recirculating equilibrium still, the details and operational procedure of which were described in ref. 7. Binary compositions of the liquid-phase and vapour-phase solutions were determined from their refractive index measurements at 25 * C. Ternary compositions of both sample mixtures were analyzed with a gas c~omatograph (Shimadzu GC-8A) connected to an electronic integrator (Shimadzu Chromatopac E-IA). The experimental errors involved in the measured variables were 0.16 torr for pressure, 0.05”C for temperature and 0.002 mole fraction for liquid and vapour compositions, RESULTS AND DISCUSSION
The VLE data at 60 OC for the binary system aceto~trile-isobutanol and the ternary system acetonitrile-isobutanol-benzene are reported in Tables 2 and 3, respectively.
TABLE 2 Vapour-liquid
equilibrium
data for the system acetonitrile (l)-isobutanol
(2) at 60 0 C
Xl
4’1
P (torr)
Yl
Yz
91
G2
0.043 0.078 0.122 0.229 0.343 0.439 0.493 0.521 0.624 0.687 0.737 0.793 0.851 0.952
0.342 0.485 0.570 0.678 0.741 0.775 0.788 0.790 0.828 0.845 0.858 0.885 0.907 0.962
136.8 168.8 196.0 243.0 277.9 296.6 309.0 311.3 327.9 335.2 342.8 347.9 355.3 364.2
3.091 2.962 2.570 2.001 1.659 1.442 1.357 1.296 1.191 1.127 1.089 1.059 1.031 1.001
1.007 1.008 1.025 1.082 1.168 1.268 1.377 1.455 1.600 1.771 1.976 2.065 2.372 3.093
0.983 0.976 0.971 0.962 0.956 0.953 0.951 0.950 0.947 0.946 0.945 0.944 0.943 0.941
0.985 0.984 0.983 0.982 0.981 0.982 0.981 0.981 0.982 0.983 0.983 0.984 0.985 0.988
0.027 0.069 0.077 0.094 0.174 0.260 0.266 0.312 0.330 0.496 0.505 0.590 0.830 0.028 0.073 0.161 0.134 0.402 0.347 0.221 0.299 0.140 0.061 0.565 0.277 0.206
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
0.342 0.612 0.861 0.110 0.476 0.119 0.230 0.504 0.261 0.114 0.213 0.123 0.094 0.285 0.640 0.674 0.600 0.107 0.560 0.574 0.165 0.397 0.237 0.334 0.320 0.322
Yl
0.054 0.158 0.342 0.150 0.283 0.314 0.323 0.478 0.385 0.486 0.519 0.556 0.791 0.055 0.174 0.370 0.275 0.419 0.586 0.395 0.343 0.223 0.105 0.666 0.354 0.282
x3
0.631 0.319 0.062 0.796 0.350 0.621 0.504 0.184 0.409 0.390 0.282 0.287 0.076 0.687 0.287 0.165 0.266 0.491 0.093 0.205 0.536 0.463 0.702 0.101 0.403 0.472
0.145 0.202 0.385 0.071 0.158 0.066 0.099 0.169 0.107 0.057 0.088 0.059 0.059 0.132 0.213 0.222 0.191 0.053 0.197 0.185 0.077 0.138 0.110 0.140 0.117 0.119
YZ 0.801 0.640 0.273 0.779 0.559 0.620 0.578 0.353 0.508 0.457 0.393 0.385 0.150 0.813 0.613 0.408 0.534 0.528 0.217 0.420 0.580 0.639 0.785 0.194 0.529 0.599
Y3
386.7 334.6 221.5 428.5 377.8 452.3 437.2 362.3 428.3 455.8 429.4 449.2 400.2 393.3 326.9 315.4 345.7 461.9 331.6 350.2 447.5 396.9 411.6 370.8 415.9 412.9
P 009
1.738 1.169 1.054 2.928 1.323 2.643 1.981 1.283 1.848 2.400 1.870 2.272 2.671 1.932 1.152 1.099 1.163 2.409 1.236 1.192 2.199 1.456 2.023 1.646 1.602 1.609
(3) at 60 o C a
2.171 2.142 2.762 1.903 1.699 1.497 1.456 1.523 1.366 1.211 1.199 1.145 1.032 2.168 2.178 2.009 1.969 1.309 1.538 1.726 1.405 1.751 1.979 1.191 1.458 1.558
y1
(2)-benzene
’ B,, = - 3475 cm3 mol-‘, B,, = - 2455 cm3 mol-‘, B33= - 1110 cm3 mol-‘, B,, = - 2007 cm3 mol-‘, mol-‘, uk = 55.06 cm3 mol-‘, vi = 97.69 cm3 mol-’ and u$ = 93.32 cm3 mol-‘.
x1
Point
Vapour-liquid equilibrium data for the system acetonitrile (1)-isobutanol
TABLE 3
0.972 0.968 0.971 0.963 0.957 0.949 0.949 0.950 0.946 0.939 0.940 0.936 0.937 0.972 0.967 0.959 0.960 0.942 0.951 0.954 0.947 0.959 0.967 0.943 0.949 0.954
0.981 0.986 0.997 0.979 0.986 0.983 0.984 0.995 0.987 0.990 0.993 0.994 1.011 0.980 0.986 0.993 0.988 0.986 1.001 0.992 0.984 0.983 0.980 1.004 0.987 0.984 Ba, = - 906 cm3
0.977 0.975 0.979 0.975 0.972 0.971 0.970 0.973 0.970 0.970 0.971 0.971 0.980 0.977 0.975 0.974 0.973 0.970 0.975 0.973 0.970 0.972 0.975 0.976 0.970 0.971 B,, = - 1057 cm3 mol-‘,
1.256 1.726 2.539 1.071 1.552 1.157 1.287 1.803 1.369 1.379 1.550 1.562 2.082 1.190 1.797 2.020 1.788 1.277 2.021 1.856 1.243 1.405 1.176 1.866 1.405 1.345
t: 0
111
The liquid-phase activity coefficient y and the vapour-phase coefficient (p were derived from the following equations yr = &m+14%~
exp[ f&P
- P,SbW
1
fugacity
0)
(2) where P is the total pressure, y is the vapour-phase mole fraction, x is the liquid-phase mole fraction, u’ is the pure-liquid molar volume estimated by the modified Rackett equation [S], Ps is the pure-~mponent vapour pressure at equilibrium temperature T, R is the universal gas constant and BIJ is the second virial coefficient calculated from the Hayden-O’Connell correlation [9]. The experimental data were correlated by the extended UNIQUAC [4] and UNIQUAC associated-solution models [lo]. Both models give the following forms for the activity coefficient of component 1 in a ternary system. Extended UZVIQUA C model
where the segment fraction a’, the surface fraction 8 and the adjustable parameter 7 are expressed by (P, = xrrrl c XJYJ
71~=
ed -ad’)
(4
(6)
where a, is the binary interaction parameter for the J-I pair and 2 is the coordination number equal to 10. The parameters P, q and q’ are pure-component molecular structure const~ts which depend on the molecular size and the external surface area. UNIQUAC associated-solution model The model assumes that isobutanol self-associates linearly (ISi+ B, = B,+i) and solvates with acetonitrile and benzene (Bj + A, = B,A; B, + C, = B,C).
112 The
activity coefficients of acetonitrile (A), isobutanol (B) and benzene (C) are expressed by
(7)
I
I
1-1n(~eJTJ13)-~ ztKJ
+qB
K
(8)
and In yc is given by changing the subindex A to C in eqn. (7). The overall segment fractions are related to the monomer segment fractions in terms of the equilibrium constants
1 a,=%2[1+$( 1 rAKBA%3
(a,
=
@A,
(9)
1 +
(1
-
h3@Ji,)
&A@A,
(1
-
+
&3C@C,
00)
,]
&%J
(11)
aA,, cPB,and @o, are simult~eous~y solved by iteration using eqns. (9-11). The true molar volume of the ternary mixture is given by &3ArA%3, (1
@
%
-K&$)
+
rB(l
-K~@~I)
I
+
2
KBCrC’B, ”
(1
-
&‘B,)
1
(12) In pure alcohol respectively.
@$ and Vi are obtained
@“B,= [2K, + 1 - (1 + 4KB)“‘j/2K; 1
(l -
KB@i,)/rB
from eqns. (13) and (14), 03) (14)
The method of Vera et al. flO] was used to estimate r and q, which are
113 TABLE 4 Pure component structural parameters for two models Component
Acetonitrile Isobutanol Benzene
UNIQUAC
Extended UNIQUAC 9’
r
4
1.87 3.45 3.19
1.72 3.05 2.40
02
&3 ,b2
associated-solution
r
4
1.50 2.77 2.56
1.40 2.42 2.05
different from those used in the extended UNIQUAC model. Table 4 presents the values of Y and q for both models. The VLE data of other two binary systems constituting the present ternary system have been measured at 45 * C: acetonitrile-benzene [ll] and isobutanol-benzene [12]. In the correlation of the binary VLE data a computer program as described by Prausnitz et al. [13] was used to obtain the optimum binary parameters of both models by along the following objective function
1 05)
+(rrl- *)’ + txli -21i)2+ (Ylj--PIi)* 2 (JT
2
4
uY
where a circumflex denotes the calculated variable and the estimated stan-
0
Mole fraction
of component
1
0.2
0.4
Mole fraction
0.6
0.8
of component
1 1
Fig. 1. Vapour-liquid equilibria for (a) acetonitrile (I)-isobutanol (2) at 60°C and (b) isobutanol (l)-benzene (2) at 45’C: ( -) calculated from the UNIQUAC associatedsolution model; (0) experimental, (a) this work, fb) ref. 12.
a I = extended
14 10
60
45
I II I II I II
Model a
data reduction
associated-solution.
12
45
II = UNIQUAC
(B)
(B)
(B)
UNIQUAC,
(A)-benzene
(A)-isobutanol
Acetonitrile
Isobutanol
(A)-benzene
(“C)
No. of data points
equilibrium
Temp.
results of vapour-liquid
Acetonitrile
System
Binary calculated
TABLE 5
(K) 0.02 0.02 0.00 0.00 0.00 0.00
6P (torr) 0.71 0.78 1.21 2.02 1.04 0.84
ST
Root-mean-square
0.4 0.5 0.6 1.5 0.2 0.3
8x (X103)
deviations
3.3 3.6 3.4 5.3 2.4 2.4
7.21 - 10.54 8.40 104.83 133.83 154.38
aAB
Parameters
284.67 258.38 420.34 638.85 465.72 - 8.36
(IBA
(K)
115 TABLE 6 Ternary calculated results for the system acetonitrile (I)-isobutanol(2)-benzene Vapour mole fractions ( X 103)
Model a
Mean deviation Root-mean-square deviation
I II I II
a I = extended UNIQUAC,
Pressure
635
a.Y,
SYs
6P (to=)
5.8 4.6 7.1 5.6
5.5 3.3 6.6 4.0
8.7 3.4 9.8 4.3
8.55 2.48 9.77 3.52
II = UNIQUAC
(3) at 60 * C
SF/P (W 2.25 0.65 2.63 0.90
associated-solution.
dard de~ations for the measured variables were u, = 1 torr for pressure, oz. = 0.05 K for temperature, a, = 0.001 for liquid-phase mole fraction and ur = 0.003 for vapour-phase mole fraction. The equilibrium constants at 50°C and the enthalpies of association and solvation are as follows: KB = 50.6 [14] and ha = -23.2 kJ mol-l [15] for isobutanol; K, = 30 and h,, = - 17 kJ mol-’ for isobutanol-acetonit~le; KBc = 2.5 and h,, = - 8.3 kJ mol-l for isobutano~-benzene. ha, ha, and h,, were assumed to be independent of temperature and fix the temperature-dependence of the equilibrium constants according to the van? Hoff relation. The results of the parameter estimation for the three binary systems are shown in Table 5. Figure 1 compares the calculated values with the measured results for the acetonitrile-isobutanol and isobutanol-benzene systems. Table 6 presents ternary predicted results, indicating that the UN-
BENZENE
A
I
i
*.a
ACETONITRILE
Fig. 2. Equilibrium solution modG1.
Ii
-
”
0.4 0.6 MOLE FRKTION
EXPTL
\
*a
ISOBUTANOL
tie lines: calculated values are obtained from the UNIQUAC
associated-
116
IQUAC associated-solution model gives better results than the extended UNIQUAC model. Figure 2 shows the experimental tie lines and the calculated results derived from the UNIQUAC associated-solution model and suggests that a ternary azeotrope may not exist in the system.
REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13
14 15
I. Nagata, Thermoc~m. Acta, 112 (1987) 187. I. Nagata, Thermochim. Acta, 114 (1987) 227. I. Nagata, Thermochim. Acta, 56 (1982) 43. I. Nagata, Fluid Phase Equilib~a, 19 (1985) 153. J.A. Riddick and W.B. Bunger, Organic Solvents, 3rd edn., Wiley-Interscience, New York, 1970, pp. 107, 154, 399. I. Brown and F. Smith, Amt. J. Chem., 7 (1954) 269. I. Nagata, J. Chem. Eng. Data, 30 (1985) 201. C.F. Spencer and R.P. Danner, J. Chem. Eng. Data, 17 (1972) 236. J.G. Hayden and J.P. O’Connell, Ind. Eng. Chem. Process Des. Dev., 14 (1975) 209. J.H. Vera, S.G. Sayegh and G.A. Ratcliff, Fluid Phase Equilibria, 1 (1977) 113. I. Brown and F. Smith, Aust. J. Chem., 8 (1955) 62. I. Brown, W. Fock and F. Smith, J. Chem. Thermodyn, 1 (1969) 273. J.M. Prausnitz, T.F. Anderson, E.A. Grens, CA. Eckert, R. Hsieh and J.P. O’Connell, Computer Calculations for Multicomponent Vapor-Liquid and Liquid-Liquid Equilibria, Prentice-Hall, Englewood Cliffs, NJ, 1984, Chapters 3, 4 and 6 and Appendices C and D. V. Brandani, Fluid Phase Equilibria, 12 (1983) 87. R.H. Stokes and C. Burfitt, J. Chem. Thermodyn., 5 (1973) 623.
107 - Printed in The Netherlands
ISOTHERMAL VAPOUR-LIQUID EQUILIBRIA FOR BINARY AND TERNARY MIXTURES FORMED BY ACETONITRILE, ISOBU’I’ANOL AND BENZENE
ISAMU NAGATA Department
of Chemical
Engineering, Kanazawa University, Kanazawa 920 (Japan)
(Received 29 June 1987)
ABSTRACT Isothermal vapour-liquid equilibrium data were measured for the binary acetonitrile-isobutanol and ternary acetonitrile-isobutanol-benzene systems at 60 o C by using a vapour-recirculating equilibrium still. The experimental data were correlated by the extended UNIQUAC and UNIQUAC associated-solution models. The UNIQUAC associated-solution model gives better predicted values for the ternary system.
LIST OF SYMBOLS
A, B, C aLI B IJ
hB h hBC
I,“^;, K
x c4 K BC P pi 41
4; R rI
T
v
acetonitrile, isobutanol and benzene binary interaction parameter second virial coefficient enthalpy of hydrogen-bond formation enthalpies of formation of chemical complexes B,A and B$ components alcohol i-mer association constant, ( @B,,,/@B,@B,)[ i/( i f l)] solvation constant, ( QBJQB,QA,)[i/( ir, + rA)] solvation constant, ( @B,c/Q)B,@c,)[i/( irB + rc)] total pressure saturated vapour pressure of pure component I molecular area parameter of pure component I molecular interaction area parameter of pure component I universal gas constant molecular volume parameter of pure component I absolute temperature true molar volume of alcohol mixture true molar volume of pure alcohol liquid molar volume of pure liquid 1
0040-6031/88/$03.50
0 1988 Elsevier Science Publishers B.V.
108
XI
YJ Z
squid-phase mole fraction of component I vapour-phase mole fraction of component I coordination number equal to 10
Greek letters
Q,Cl
#I
liquid-phase activity coefficient of component I area fraction of component I standard deviations in pressure and temperature standard deviations in liquid-phase and vapour-phase mole fractions exp( - WW segment fraction of component I segment fraction of acetonitrile monomer in mixture segment fraction of isobutanol monomer in mixture segment fraction of isobutanol monomer in pure alcohol solution segment fraction of benzene monomer in mixture vapour-phase fugacity coefficient of component I at system pressure P and system temperature T vapour-phase fugacity coefficient of component 1 at its saturation pressure PI” and system temperature T
INTRODUCTION
The thermodynamic properties of solutions of butanols in acetonitrile and a hydrocarbon are currently the subject of studies in this laboratory. Vapour-liquid equilibria (VLE) for the system l-butanol-aceto~trile-benzene at 60°C [I] and liquid-liquid equilibria for the system acetonitrile-lbutanol-saturated hydrocarbon at 25 OC [2] have been reported. This paper reports VLE data for the binary system acetonitrile-isobutanol and the ternary system acetonitrile-isobutanol-benzene at 60 * C and their correlation by the extended UNIQUAC [3] and UNIQUAC associated-solution model [4].
EXPERIMENTAL
Acetonitrile and isobutanol (Nakarai Pure Chemical Industries Ltd.. analytical reagent grade) were used svithout further purification. C.P. benzene was purified by repeated rec~stall~ation. Some physical properties of the chemicals used for experimental work agree closely with values reported in the literature as shown in Table 1. For measurements of these properties.
109
TABLE 1 Physical properties of chemicals Density at 25 * C (g cme3>
Component
Acetomtrile Isobutanol Benzene
Refractive index at 25’C
Vapour pressure at 60 o C (torr)
Exptl.
Lit. [5]
Exptl.
Lit. [5]
Exptl.
Lit. [5]
0.7766 0.7979 0.8737
0.7766 0.7989 0.87370
1.34161 1.39394 1.49790
1.34163 1.3939 1.49792
368.1 93.0 391.5
368.0 [6] 93.01 391.47
an Anton Paar densimeter (DMA40) and a Shimadzu Pulfrich refractometer were used. Vapour pressures were measured at 60°C with a Boublik vapour-recirculating equilibrium still, the details and operational procedure of which were described in ref. 7. Binary compositions of the liquid-phase and vapour-phase solutions were determined from their refractive index measurements at 25 * C. Ternary compositions of both sample mixtures were analyzed with a gas c~omatograph (Shimadzu GC-8A) connected to an electronic integrator (Shimadzu Chromatopac E-IA). The experimental errors involved in the measured variables were 0.16 torr for pressure, 0.05”C for temperature and 0.002 mole fraction for liquid and vapour compositions, RESULTS AND DISCUSSION
The VLE data at 60 OC for the binary system aceto~trile-isobutanol and the ternary system acetonitrile-isobutanol-benzene are reported in Tables 2 and 3, respectively.
TABLE 2 Vapour-liquid
equilibrium
data for the system acetonitrile (l)-isobutanol
(2) at 60 0 C
Xl
4’1
P (torr)
Yl
Yz
91
G2
0.043 0.078 0.122 0.229 0.343 0.439 0.493 0.521 0.624 0.687 0.737 0.793 0.851 0.952
0.342 0.485 0.570 0.678 0.741 0.775 0.788 0.790 0.828 0.845 0.858 0.885 0.907 0.962
136.8 168.8 196.0 243.0 277.9 296.6 309.0 311.3 327.9 335.2 342.8 347.9 355.3 364.2
3.091 2.962 2.570 2.001 1.659 1.442 1.357 1.296 1.191 1.127 1.089 1.059 1.031 1.001
1.007 1.008 1.025 1.082 1.168 1.268 1.377 1.455 1.600 1.771 1.976 2.065 2.372 3.093
0.983 0.976 0.971 0.962 0.956 0.953 0.951 0.950 0.947 0.946 0.945 0.944 0.943 0.941
0.985 0.984 0.983 0.982 0.981 0.982 0.981 0.981 0.982 0.983 0.983 0.984 0.985 0.988
0.027 0.069 0.077 0.094 0.174 0.260 0.266 0.312 0.330 0.496 0.505 0.590 0.830 0.028 0.073 0.161 0.134 0.402 0.347 0.221 0.299 0.140 0.061 0.565 0.277 0.206
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
0.342 0.612 0.861 0.110 0.476 0.119 0.230 0.504 0.261 0.114 0.213 0.123 0.094 0.285 0.640 0.674 0.600 0.107 0.560 0.574 0.165 0.397 0.237 0.334 0.320 0.322
Yl
0.054 0.158 0.342 0.150 0.283 0.314 0.323 0.478 0.385 0.486 0.519 0.556 0.791 0.055 0.174 0.370 0.275 0.419 0.586 0.395 0.343 0.223 0.105 0.666 0.354 0.282
x3
0.631 0.319 0.062 0.796 0.350 0.621 0.504 0.184 0.409 0.390 0.282 0.287 0.076 0.687 0.287 0.165 0.266 0.491 0.093 0.205 0.536 0.463 0.702 0.101 0.403 0.472
0.145 0.202 0.385 0.071 0.158 0.066 0.099 0.169 0.107 0.057 0.088 0.059 0.059 0.132 0.213 0.222 0.191 0.053 0.197 0.185 0.077 0.138 0.110 0.140 0.117 0.119
YZ 0.801 0.640 0.273 0.779 0.559 0.620 0.578 0.353 0.508 0.457 0.393 0.385 0.150 0.813 0.613 0.408 0.534 0.528 0.217 0.420 0.580 0.639 0.785 0.194 0.529 0.599
Y3
386.7 334.6 221.5 428.5 377.8 452.3 437.2 362.3 428.3 455.8 429.4 449.2 400.2 393.3 326.9 315.4 345.7 461.9 331.6 350.2 447.5 396.9 411.6 370.8 415.9 412.9
P 009
1.738 1.169 1.054 2.928 1.323 2.643 1.981 1.283 1.848 2.400 1.870 2.272 2.671 1.932 1.152 1.099 1.163 2.409 1.236 1.192 2.199 1.456 2.023 1.646 1.602 1.609
(3) at 60 o C a
2.171 2.142 2.762 1.903 1.699 1.497 1.456 1.523 1.366 1.211 1.199 1.145 1.032 2.168 2.178 2.009 1.969 1.309 1.538 1.726 1.405 1.751 1.979 1.191 1.458 1.558
y1
(2)-benzene
’ B,, = - 3475 cm3 mol-‘, B,, = - 2455 cm3 mol-‘, B33= - 1110 cm3 mol-‘, B,, = - 2007 cm3 mol-‘, mol-‘, uk = 55.06 cm3 mol-‘, vi = 97.69 cm3 mol-’ and u$ = 93.32 cm3 mol-‘.
x1
Point
Vapour-liquid equilibrium data for the system acetonitrile (1)-isobutanol
TABLE 3
0.972 0.968 0.971 0.963 0.957 0.949 0.949 0.950 0.946 0.939 0.940 0.936 0.937 0.972 0.967 0.959 0.960 0.942 0.951 0.954 0.947 0.959 0.967 0.943 0.949 0.954
0.981 0.986 0.997 0.979 0.986 0.983 0.984 0.995 0.987 0.990 0.993 0.994 1.011 0.980 0.986 0.993 0.988 0.986 1.001 0.992 0.984 0.983 0.980 1.004 0.987 0.984 Ba, = - 906 cm3
0.977 0.975 0.979 0.975 0.972 0.971 0.970 0.973 0.970 0.970 0.971 0.971 0.980 0.977 0.975 0.974 0.973 0.970 0.975 0.973 0.970 0.972 0.975 0.976 0.970 0.971 B,, = - 1057 cm3 mol-‘,
1.256 1.726 2.539 1.071 1.552 1.157 1.287 1.803 1.369 1.379 1.550 1.562 2.082 1.190 1.797 2.020 1.788 1.277 2.021 1.856 1.243 1.405 1.176 1.866 1.405 1.345
t: 0
111
The liquid-phase activity coefficient y and the vapour-phase coefficient (p were derived from the following equations yr = &m+14%~
exp[ f&P
- P,SbW
1
fugacity
0)
(2) where P is the total pressure, y is the vapour-phase mole fraction, x is the liquid-phase mole fraction, u’ is the pure-liquid molar volume estimated by the modified Rackett equation [S], Ps is the pure-~mponent vapour pressure at equilibrium temperature T, R is the universal gas constant and BIJ is the second virial coefficient calculated from the Hayden-O’Connell correlation [9]. The experimental data were correlated by the extended UNIQUAC [4] and UNIQUAC associated-solution models [lo]. Both models give the following forms for the activity coefficient of component 1 in a ternary system. Extended UZVIQUA C model
where the segment fraction a’, the surface fraction 8 and the adjustable parameter 7 are expressed by (P, = xrrrl c XJYJ
71~=
ed -ad’)
(4
(6)
where a, is the binary interaction parameter for the J-I pair and 2 is the coordination number equal to 10. The parameters P, q and q’ are pure-component molecular structure const~ts which depend on the molecular size and the external surface area. UNIQUAC associated-solution model The model assumes that isobutanol self-associates linearly (ISi+ B, = B,+i) and solvates with acetonitrile and benzene (Bj + A, = B,A; B, + C, = B,C).
112 The
activity coefficients of acetonitrile (A), isobutanol (B) and benzene (C) are expressed by
(7)
I
I
1-1n(~eJTJ13)-~ ztKJ
+qB
K
(8)
and In yc is given by changing the subindex A to C in eqn. (7). The overall segment fractions are related to the monomer segment fractions in terms of the equilibrium constants
1 a,=%2[1+$( 1 rAKBA%3
(a,
=
@A,
(9)
1 +
(1
-
h3@Ji,)
&A@A,
(1
-
+
&3C@C,
00)
,]
&%J
(11)
aA,, cPB,and @o, are simult~eous~y solved by iteration using eqns. (9-11). The true molar volume of the ternary mixture is given by &3ArA%3, (1
@
%
-K&$)
+
rB(l
-K~@~I)
I
+
2
KBCrC’B, ”
(1
-
&‘B,)
1
(12) In pure alcohol respectively.
@$ and Vi are obtained
@“B,= [2K, + 1 - (1 + 4KB)“‘j/2K; 1
(l -
KB@i,)/rB
from eqns. (13) and (14), 03) (14)
The method of Vera et al. flO] was used to estimate r and q, which are
113 TABLE 4 Pure component structural parameters for two models Component
Acetonitrile Isobutanol Benzene
UNIQUAC
Extended UNIQUAC 9’
r
4
1.87 3.45 3.19
1.72 3.05 2.40
02
&3 ,b2
associated-solution
r
4
1.50 2.77 2.56
1.40 2.42 2.05
different from those used in the extended UNIQUAC model. Table 4 presents the values of Y and q for both models. The VLE data of other two binary systems constituting the present ternary system have been measured at 45 * C: acetonitrile-benzene [ll] and isobutanol-benzene [12]. In the correlation of the binary VLE data a computer program as described by Prausnitz et al. [13] was used to obtain the optimum binary parameters of both models by along the following objective function
1 05)
+(rrl- *)’ + txli -21i)2+ (Ylj--PIi)* 2 (JT
2
4
uY
where a circumflex denotes the calculated variable and the estimated stan-
0
Mole fraction
of component
1
0.2
0.4
Mole fraction
0.6
0.8
of component
1 1
Fig. 1. Vapour-liquid equilibria for (a) acetonitrile (I)-isobutanol (2) at 60°C and (b) isobutanol (l)-benzene (2) at 45’C: ( -) calculated from the UNIQUAC associatedsolution model; (0) experimental, (a) this work, fb) ref. 12.
a I = extended
14 10
60
45
I II I II I II
Model a
data reduction
associated-solution.
12
45
II = UNIQUAC
(B)
(B)
(B)
UNIQUAC,
(A)-benzene
(A)-isobutanol
Acetonitrile
Isobutanol
(A)-benzene
(“C)
No. of data points
equilibrium
Temp.
results of vapour-liquid
Acetonitrile
System
Binary calculated
TABLE 5
(K) 0.02 0.02 0.00 0.00 0.00 0.00
6P (torr) 0.71 0.78 1.21 2.02 1.04 0.84
ST
Root-mean-square
0.4 0.5 0.6 1.5 0.2 0.3
8x (X103)
deviations
3.3 3.6 3.4 5.3 2.4 2.4
7.21 - 10.54 8.40 104.83 133.83 154.38
aAB
Parameters
284.67 258.38 420.34 638.85 465.72 - 8.36
(IBA
(K)
115 TABLE 6 Ternary calculated results for the system acetonitrile (I)-isobutanol(2)-benzene Vapour mole fractions ( X 103)
Model a
Mean deviation Root-mean-square deviation
I II I II
a I = extended UNIQUAC,
Pressure
635
a.Y,
SYs
6P (to=)
5.8 4.6 7.1 5.6
5.5 3.3 6.6 4.0
8.7 3.4 9.8 4.3
8.55 2.48 9.77 3.52
II = UNIQUAC
(3) at 60 * C
SF/P (W 2.25 0.65 2.63 0.90
associated-solution.
dard de~ations for the measured variables were u, = 1 torr for pressure, oz. = 0.05 K for temperature, a, = 0.001 for liquid-phase mole fraction and ur = 0.003 for vapour-phase mole fraction. The equilibrium constants at 50°C and the enthalpies of association and solvation are as follows: KB = 50.6 [14] and ha = -23.2 kJ mol-l [15] for isobutanol; K, = 30 and h,, = - 17 kJ mol-’ for isobutanol-acetonit~le; KBc = 2.5 and h,, = - 8.3 kJ mol-l for isobutano~-benzene. ha, ha, and h,, were assumed to be independent of temperature and fix the temperature-dependence of the equilibrium constants according to the van? Hoff relation. The results of the parameter estimation for the three binary systems are shown in Table 5. Figure 1 compares the calculated values with the measured results for the acetonitrile-isobutanol and isobutanol-benzene systems. Table 6 presents ternary predicted results, indicating that the UN-
BENZENE
A
I
i
*.a
ACETONITRILE
Fig. 2. Equilibrium solution modG1.
Ii
-
”
0.4 0.6 MOLE FRKTION
EXPTL
\
*a
ISOBUTANOL
tie lines: calculated values are obtained from the UNIQUAC
associated-
116
IQUAC associated-solution model gives better results than the extended UNIQUAC model. Figure 2 shows the experimental tie lines and the calculated results derived from the UNIQUAC associated-solution model and suggests that a ternary azeotrope may not exist in the system.
REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13
14 15
I. Nagata, Thermoc~m. Acta, 112 (1987) 187. I. Nagata, Thermochim. Acta, 114 (1987) 227. I. Nagata, Thermochim. Acta, 56 (1982) 43. I. Nagata, Fluid Phase Equilib~a, 19 (1985) 153. J.A. Riddick and W.B. Bunger, Organic Solvents, 3rd edn., Wiley-Interscience, New York, 1970, pp. 107, 154, 399. I. Brown and F. Smith, Amt. J. Chem., 7 (1954) 269. I. Nagata, J. Chem. Eng. Data, 30 (1985) 201. C.F. Spencer and R.P. Danner, J. Chem. Eng. Data, 17 (1972) 236. J.G. Hayden and J.P. O’Connell, Ind. Eng. Chem. Process Des. Dev., 14 (1975) 209. J.H. Vera, S.G. Sayegh and G.A. Ratcliff, Fluid Phase Equilibria, 1 (1977) 113. I. Brown and F. Smith, Aust. J. Chem., 8 (1955) 62. I. Brown, W. Fock and F. Smith, J. Chem. Thermodyn, 1 (1969) 273. J.M. Prausnitz, T.F. Anderson, E.A. Grens, CA. Eckert, R. Hsieh and J.P. O’Connell, Computer Calculations for Multicomponent Vapor-Liquid and Liquid-Liquid Equilibria, Prentice-Hall, Englewood Cliffs, NJ, 1984, Chapters 3, 4 and 6 and Appendices C and D. V. Brandani, Fluid Phase Equilibria, 12 (1983) 87. R.H. Stokes and C. Burfitt, J. Chem. Thermodyn., 5 (1973) 623.