+
+
Ind. Eng. Chem. Res. 1996, 35, 2773-2776
2773
Measurements of Infinite-Dilution Ternary Activity Coefficients by Gas Stripping. Acetonitrile-Benzene-n-Heptane at 318.15 K Jian-Bin Bao* and Shi-Jun Han Department of Chemistry, Zhejiang University, Hangzhou 310027, People’s Republic of China
In the measurement of infinite-dilution activity coefficients for a multicomponent system by the gas stripping method, this paper shows a way to obtain more limiting data to improve the study of multicomponent phase equilibria. As an example, the infinite-dilution ternary activity coefficients γ∞A(B,C) for the acetonitrile-benzene-n-heptane system were determined at 318.15 K. Inasmuch as the solvents involved are often composed of two components, the double-cell technique (DCT) was employed to obtain steady solvent surroundings for the dilute solutes, which are apparently an essential condition for reasonable and meaningful measurements of infinite-dilution activity coefficients. The experimental γ∞A(B,C) values were correlated by use of the NRTL and UNIQUAC equations, and the vapor-liquid and liquid-liquid equilibria for the relevant system could be predicted. Introduction Studies on vapor-liquid equilibria (VLE) and liquidliquid equilibria (LLE), especially for multicomponent systems, are time-consuming and sophisticated. For difficulties in the direct measurement of the equilibrium data, many investigators are trying to find a way to estimate them by use of activity coefficient models, such as the Wilson, NRTL, and UNIQUAC equations. For each of them, the most important procedure is the evaluation of the adjustable parameters. According to Schreiber and Eckert (1971) and Nicolaides and Eckert (1978), one of the best ways is to calculate them from infinite-dilution activity coefficients γ∞, actually from infinite-dilution binary activity coefficients γ∞A(B). This is usually simpler and more accurate than other methods, such as from binary VLE or LLE. Therefore, the equilibria for a multicomponent system, theoretically, can be predicted merely from the γ∞A(B) values of the constituent binaries, but such a prediction sometimes may be unsatisfactory. Because the number of γ∞A(B) here is equal to or even less than that of the adjustable parameters in the employed activity coefficient model, the prediction would be unreasonable if one of the original γ∞A(B) values were not accurate enough. Unfortunately, this situation is highly possible since the accuracy of γ∞ values cannot be identified easily. In order to make a reliable estimation for a multicomponent system from the infinite-dilution activity coefficients, not only those of the constituent binaries, which are all composed of one-component solute and onecomponent solvent, but also those of the multicomponent mixtures, which consist of one-component solute and multicomponent solvent, should be available. As an example, a ternary system acetonitrile (1)benzene (2)-n-heptane (3) at 318.15 K is studied in this work. After much care was devoted to experimental methods for the determination of the infinite-dilution activity coefficient, the gas stripping method (Leroi et al., 1977) was employed. In this method, a dilute solution is kept in an equilibrium cell at constant temperature and pressure. A constant inert gas flow is introduced into the solution, and thus the components involved are stripped into the vapor phase. If the vapor-liquid equilibrium is established, the γ∞ value of the solute in the solvent can be calculated directly
Table 1. Densities d and Refractive Indices nD at 293.15 K and the Boiling Points Tb at 101.325 kPa of the Components d/(g‚cm-3) substance
exptl
lit.
nD exptl
Tb/K lit.
exptl
lit.
acetonitrile 0.7855 0.7857 1.3441 1.34423 354.75 354.75 benzene 0.8765 0.8765 1.5008 1.5011 353.25 353.25 n-heptane 0.6836 0.6837 1.3873 1.3878 371.52 371.55 Table 2. Experimental γ∞A(B,C) Values for the Acetonitrile (1)-Benzene (2)-n-Heptane (3) System at 318.15 K x1
x2
x3
γ∞A(B,C)
solute solute solute solute solute solute solute solute
0.0000 0.1208 0.3255 0.5170 0.6988 0.7951 0.9132 1.0000
1.0000 0.8792 0.6745 0.4830 0.3012 0.2049 0.0868 0.0000
17.4 11.0 6.73 4.59 3.40 3.10 2.85 2.69
1.0000 0.9735 0.9479 0.0911 0.0568 0.0000
solute solute solute solute solute solute
0.0000 0.0265 0.0521 0.9089 0.9432 1.0000
2.88 2.60 2.40 1.34 1.55 1.74
1.0000 0.9022 0.8181 0.7228 0.6211 0.5179 0.3978 0.1814 0.0000
0.0000 0.0978 0.1819 0.2772 0.3789 0.4821 0.6022 0.8186 1.0000
solute solute solute solute solute solute solute solute solute
23.5 15.8 10.5 7.51 5.58 3.93 2.98 2.13 1.90
from the rate of variation of the vapor or liquid solute concentration versus the stripping time. It is vital that the solute have steady solvent surroundings while the dilute solution is being stripped. The method has been proved to be a rapid and useful technique for measuring γ∞A(B) for various binaries (Leroi et al., 1977; Bao and Han, 1995). However, if it is employed for a ternary, the method must be modified. When a dilute ternary solution is stripped by the inert gas flow, the composition of the two-component solvent will be unstable because of the difference between the volatilities of the two components. Thus, the infinite-dilution ternary
+
+
2774 Ind. Eng. Chem. Res., Vol. 35, No. 8, 1996
Figure 1. Experimental and correlated γ∞A(B,C) and predicted tie-line for the acetonitrile (1)-benzene (2)-n-heptane (3) at 318.15 K: O, experimental γ∞A(B,C); 4, experimental LLE (Palmer and Smith, 1972); s, correlated γ∞A(B,C) or predicted tie-line by the UNIQUAC equation; - - -, correlated γ∞A(B,C) or predicted tie-line by the NRTL equation. Table 3. Comparison of the Experimental γ∞A(B) Values of the Three Constituent Binaries with Those in the Literature literature solute acetonitrile
a
solvent benzene
γ∞
A(B)
2.69
acetonitrile benzene
n-heptane acetonitrile
17.4 2.88
benzene n-heptane n-heptane
n-heptane acetonitrile benzene
1.74 23.5 1.90
T/K 318.3 318.2 318.15 318.15 318.15 318.15 318.2 318.2 318.15 318.15 318.15 318.0 318.15
γ∞
A(B)
2.94 3.08 3.20 3.45 23.8 2.94 2.95 2.74 3.00 1.50 28.7 1.92 2.38
techa EB ext ext ext ext EB ext ext ext EB ext
ref Thomas et al., 1982 Thomas et al., 1982 Schreiber and Eckert, 1971 Demirel, 1990 Demirel, 1990 Demirel, 1990 Thomas et al., 1982 Thomas et al., 1982 Schriber and Eckert, 1971 Demirel, 1990 Demirel, 1990 Thomas et al., 1982 Demirel, 1990
Techniques: EB, ebulliometry; ext, extrapolated VLE.
activity coefficient γ∞A(B,C) cannot be obtained from the variation curve of the solute concentration. In this work, the double-cell technique (DCT) (Bao et al., 1993; Bao and Han, 1995) is employed to keep the composition stable. Besides, the amount of the solution in the
equilibrium cell can simultaneously be maintained. This results in a high stripping efficiency. An expression for the calculation of the infinitedilution activity coefficient of a solute in a multicomponent solvent has been derived for DCT (Bao et al.,
+
+
Ind. Eng. Chem. Res., Vol. 35, No. 8, 1996 2775
+ n-heptane or benzene in acetonitrile + rich n-heptane, while the latter, which arranges the peaks in the order of the polarities, was used for n-heptane in acetonitrile + benzene or benzene in rich acetonitrile + n-heptane. Other details of the equipment and experiment can be found in a previous paper (Bao et al., 1994).
Table 4. Experimental Binary VLE for the Acetonitrile (1)-Benzene (2) and Benzene (2)-n-Heptane (3) Systems at 318.15 K acetonitrile (1)-benzene (2)
benzene (2)-n-heptane (3)
x1
y1
x2
y2
0.0000 0.1814 0.3978 0.5179 0.6211 0.7228 0.8181 0.9022 1.0000
0.0000 0.2880 0.4233 0.4972 0.5355 0.6083 0.6879 0.7855 1.0000
0.0000 0.1208 0.3255 0.5170 0.6988 0.7951 0.9132 1.0000
0.0000 0.2858 0.5489 0.6921 0.7986 0.8454 0.9200 1.0000
Results and Discussion Measurements of Infinite-Dilution Ternary Activity Coefficients. By DCT, 23 γ∞A(B,C) values for the acetonitrile (1)-benzene (2)-n-heptane (3) system at 318.15 K were measured, as shown in Table 2 and Figure 1. Actually, 6 of them are γ∞A(B) if their solvents are of one component. The deviations of these measurements, analyzed as in Legret et al. (1983), are not larger than 4%. They were caused mainly by errors in detection of the desorption rates A of the solute concentration. Only the γ∞A(B) values of the three constituent binaries have been found in the literature, as shown in Table 3. Unfortunately, most of them were not measured directly, but extrapolated from VLE. Therefore, probably some of these values are not accurate enough. For example, the maximum differences in Table 3 are of acetonitrile-n-heptane. Two values, 23.8 and 28.7, were obtained by graphical extrapolation of the finiteconcentration VLE (Demirel, 1990). But also according to those data, if extrapolated by use of some activity coefficient models, they became 11.7 and 19.2 (NRTL) and 11.8 and 19.7 (UNIQUAC), respectively (Demirel, 1990). Byproduct from the Measurements. Obviously, when an inert stripping gas passes through a dilute ternary solution, the solvent, with the solute, is also stripped into the vapor phase. Therefore, the equilibrated vapor composition of the binary solvent can be detected simultaneously. Table 4 gives the experimental mole fractions for the acetonitrile-benzene and benzene-n-heptane systems. This means binary VLE, with γ∞A(B,C), have been obtained. We therefore believe the gas stripping method (DCT is necessary) can also be used for the determination of the whole range VLE at a low pressure, such as the subatmospheric. Correlations with the NRTL and UNIQUAC Equations. The experimental γ∞A(B,C) values can be correlated by the NRTL equation (Renon and Prausnitz, 1968) and the UNIQUAC equation (Abrams and Prausnitz, 1975). These correlations are also shown in Figure 1. The deviations between the experimental and the correlated values, together with the parameters obtained, are given in Table 5. Because enough γ∞A(B,C) values have been determined, all adjustable parameters, including the nonrandomness factor R in the NRTL equation, can be obtained by the correlation. Predictions of the VLE and LLE. Since VLE and LLE for the acetonitrile (1)-benzene (2)-n-heptane (3) system at 318.15 K have been measured by Palmer and Smith (1972), the predicted results in this work can be compared directly with the experimental data.
1993; Bao and Han, 1995). For a ternary mixture, which is composed of a dilute solute A and a solvent of two components B and C, C
γ∞A(B,C) ) p*A
∑niRT
[
]
i)A
D
+ VG
C
A(1 -
(1)
∑yi)
i)A
Experimental Section Acetonitrile (Shantou Chemical Co.), benzene (Hangzhou Pharmaceutical Co.), and n-heptane (Hangzhou Oil Refined Co.) of A.P. grade were subjected to fractional distillation. Their final densities, refractive indices, and boiling points, together with their literature values (Lide, 1990-1991), are shown in Table 1. All of them were also sampled to a gas chromatograph (Model GC7A, Shimadzu, installed with a 2 m Porapak Q or 50 m OV-101 capillary column), and no impurity was detected. Two cells, a main equilibrium cell and a presaturator, were employed for DCT. The presaturator here is the same as the main cell (Bao et al., 1994). By test of the vapor composition out of the main cell, our previous work (Bao et al., 1993) proved that such a presaturator is large enough to keep a two-component solvent stable in the main cell. A dilute solution of interest was introduced quantatively into the main cell by a syringe, the mole fraction of the solute always being less than 5 × 10-4, while only the solvent of the same composition as that in the main cell was added into the presaturator. The two cells were then connected and immersed in a thermostated bath. After 15 min, an inert stripping gas N2 was introduced and kept at a constant flowrate of no more than 0.3 cm3‚s-1. The vapors out of the main cell were periodically sent to a gas chromatograph to measure their compositions. Two columns, a 1 m Porapak Q and a 3 m 8% PEG-400 (Shanghai No.1 Reagent Co.)/Chromosorb W NAW (John Manville), were charged alternatively to obtain satisfactory separation of the components. The former, which arranges the peaks in the order of molar masses of the components, was used for the determination of γ∞A(B,C) of acetonitrile in benzene
Table 5. Correlations of the Experimental γ∞A(B,C) Values of the Acetonitrile (1)-Benzene (2)-n-Heptane (3) System binary parameters
AAD
equation
τ12
τ21
τ13
τ31
τ23
τ32
NRTL UNIQUAC
0.8078 0.8972
0.3309 0.6840
2.3398 0.9546
1.9176 0.1695
0.3880 1.5011
0.2288 0.4765
R 0.4100
∆γ∞A(B,C)
100∆γ∞A(B,C)/γ∞A(B,C)
0.27 0.25
4.0 4.2
+
+
2776 Ind. Eng. Chem. Res., Vol. 35, No. 8, 1996 φ ) fugacity coefficient Superscript
Table 6. Predicted Results of VLE and LLE from the Experimental γ∞A(B,C) Values AAD × 100 equation
∆y1
∆y2
∆y3
∆p/p
∆ (xβi /xRi )/(xβi /xRi )a
NRTL UNIQUAC
2.7 1.7
1.1 0.9
2.1 1.1
5.9 3.3
102.9 13.8
a
∆(xβi /xRi )
1 )
(xβi /xRi )
N
[{
|(xβi /xRi )cal - (xβi /xRi )exp|
i)1
(xβi /xRi )exp
∑∑
3N j)1
A ) dilute solute B ) solvent component C ) solvent component i ) component i j ) data point 1 ) acetonitrile 2 ) benzene 3 ) n-heptane
}]
3
The following equation:
yiφip ) γixif*Li exp(pVLi/RT)
(2)
is considered for the prediction of VLE, and another relation:
γRi xRi
)
γβi xβi
R ) conjugate liquid phase β ) conjugate liquid phase Subscripts
(3)
for the prediction of LLE. In both equations, the activity coefficients γi of each component can be calculated conveniently by use of the NRTL or UNIQUAC equation since the adjustable parameters involved have been obtained from the experimental γ∞A(B,C) values. Table 6 shows the results of these predictions. It is found that the UNIQUAC equation gives better results than the NRTL equation does. Acknowledgment We thank the National Natural Science Foundation of China (No. 29406048) and the Natural Science Foundation of Zhejiang Province (No. 293051) for their financial support, as well as Miss Qiu-Hong Zhou and Mr. Ang Li for some experimental work. Nomenclature A ) desorption rate of the vapor-phase mole fraction of solute, which is defined as before (Bao et al., 1993; Bao and Han, 1995), s-1 d ) density, g‚cm-3 D ) flowrate of the stripping gas, cm3‚s-1 f*L ) fugacity of pure liquid at zero pressure, MPa n ) amount of substance, mol nD ) refractive index N ) number of liquid-liquid equilibrium data p ) total pressure, MPa p*A ) vapor pressure of pure solute, MPa R ) universal gas constant, 8.314 MPa‚cm3‚mol-1‚K-1 T ) absolute temperature, K Tb ) boiling temperature, K VG ) volume of the gaseous space in the main equilibrium cell, cm3 VL ) liquid molar volume, cm3 x ) liquid-phase mole fraction y ) vapor-phase mole fraction Greek Letters R ) nonrandomness factor in the NRTL equation γ ) activity coefficient γ∞ ) infinite-dilution activity coefficient τ ) binary parameters of the NRTL or UNIQUAC equation
Author-Supplied Registry Nos. Acetonitrile, 7505-8; benzene, 71-43-2; n-heptane, 142-82-5. Literature Cited Abrams, D. S.; Prausnitz, J. M. Statistical Thermodynamics of Liquid Mixtures: A New Expression for the Excess Gibbs Energy of Partly or Completely Miscible Systems. AIChE J. 1975, 21, 116-128. Bao, J.-B.; Han, S.-J. Infinite Dilution Activity Coefficients for Various Types of Systems. Fluid Phase Equilib. 1995, 112, 307316. Bao, J.-B.; Chen, G.-H.; Han, S.-J. Determination of Infinite Dilution Activity Coefficients in Multicomponent Solvent Systems with Gas Stripping Method. J. Chem. Ind. Eng. (Ch.) 1993, 44, 542-548. Bao, J.-B.; Hang, L.-L.; Han, S.-J. Infinite-Dilution Activity Coefficients of (Propanone + an n-Alkane) by Gas Stripping. J. Chem. Thermodyn. 1994, 26, 673-680. Demirel, Y. Calculation of Infinite Dilution Activity Coefficients by the NRTL and UNIQUAC Models. Can. J. Chem. Eng. 1990, 68, 697-701. Legret, D.; Desteve, J.; Richon, D.; Renon, H. Vapor-Liquid Equilibrium Constants at Infinite Dilution Determined by a Gas Stripping Method: Ethane, Propane, n-Butane, n-Pentane in the Methane-n-Decane System. AIChE J. 1983, 29, 137-144. Leroi, J.-C.; Masson, J.-C.; Renon, H.; Fabries, J.-F.; Sannier, H. Accurate Measurement of Activity Coefficients at Infinite Dilution by Inert Gas Stripping and Gas Chromatography. Ind. Eng. Chem. Process Des. Dev. 1977, 16, 139-144. Lide, D. R. CRC Handbook of Chemistry and Physics, 71st ed.; CRC Press: Boca Raton, FL, 1990-1991. Nicolaides, G. L.; Eckert, C. A. Optimal Representation of Binary Liquid Mixture Nonidealities. Ind. Eng. Chem. Fundam. 1978, 17, 331-340. Palmer, D. A.; Smith, B. D. Thermodynamic Excess Property Measurements for Acetonitrile-Benzene-n-Heptane System. J. Chem. Eng. Data 1972, 17, 71-76. Renon, H.; Prausnitz, J. M. Local Compositions in Thermodynamic Excess Functions for Liquid Mixtures. AIChE J. 1968, 14, 135144. Schreiber, L. B.; Eckert, C. A. Use of Infinite Dilution Activity Coefficients with Wilson’s Equation. Ind. Eng. Chem. Process Des. Dev. 1971, 10, 572-576. Thomas, E. R.; Newman, B. A.; Nicolaides, G. L.; Eckert, C. A. Limiting Activity Coefficients from Differential Ebulliometry. J. Chem. Eng. Data 1982, 27, 233-240 and references cited therein.
Received for review November 8, 1995 Revised manuscript received May 7, 1996 Accepted May 8, 1996X IE950679T X Abstract published in Advance ACS Abstracts, July 1, 1996.
