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Infinite dilution activity coefficients for various types of systems
Ililllqitl[
[IlUlIIII ELSEVIER
Fluid Phase Equilibria 112 (1995) 31)7-316
Infinite dilution activity coefficients for various types of systems Jian-Bin Bao, Shi-Jun Han Department of Chemistry, Zhejiang University, Hangzhou, 31002 7, People's Republic of China Received 5 October 1994; accepted 3 June 1995
Abstract
The infinite dilution activity coefficients for various types of systems, one-component solute + one-component solvent, one-component solute + multicomponent solvent, and multicomponent solute + solvent have been studied by use of the gas stripping method. Two techniques, the single-cell technique (SCT) and the double-ccll technique (DCT), are described. The use of them depends mainly on the volatility and nature (one-component or multicomponent) of the solvent. Keywords: Experiments; Method; Infinite dilution activity coefficients; Gas stripping method; Single-cell technique: Double-cell technique
1. Introduction
The infinite dilution is a special state of liquid mixtures. In that state, the concentration of one component, which is usually called the solute, goes to zero, while the mole fraction of the other component or the total mole fraction of the others, i.e. the solvent mole fraction, is close to one. The activity coefficient of the infinitely dilute solute, named as the infinite dilution activity coefficient or the limiting activity coefficient, is a limiting measurement of the nonideality of the solute in this mixture. Alessi et al. (1991) have given the importance of the limiting data both for the development of separation processes and for a better understanding in theories for liquid solutions. In the past forty years, various methods for the direct measurement of infinite dilution activity coefficients have been developed.
1.1. Gas-liquid chromatography method By this method, a solvent is firstly coated on an inert support as a stationary phase for a gas-liquid chromatograph. Little amount (usually only about several microlitres) of a solute is injected to detect the retention time of the solute in the solvent surroundings. By using other properties, such as the column temperature and pressure, the solvent amount in the column and the flow rate of the carrier 0378-3812/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved
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J. oB. Bao, S.-J. Han / Fluid Phase Equilibria 112 (1995) 307-316
gas, the limiting activity coefficient can thereafter be calculated. This method is especially suitable for the limiting values for volatile solutes in nonvolatile or low-volatile solvents because the solvents can be coated easily and steadily. For the same reason, however, it is often unsuitable for the values of the other end, i.e. the limiting activity coefficients for the solvents in the solutes. This means for most of our interested binary systems, it is very difficult to obtain both ends of the limiting values. Nevertheless, possible solute-support interactions or solvent-support interactions instead of solutesolvent interactions would have an effect on the accuracy of these measurements.
1.2. Differential ebulliometry method According to an expression for activity coefficients at infinite dilution derived by Gautreaux and Coates (1955), the limiting values can be obtained by measurements of the limiting slope of boiling temperature with respect to the solute concentration. Thanks to the great work accomplished by Eckert and his co-workers ( Eckert et al., 1981; Thomas et al., 1982; Trampe and Eckert, 1990), this method has been a successful way to get limiting values for many binary systems. But unfortunately, for most highly nonideal systems, it would be difficult to operate.
1.3. Gas stripping method By use of the gas stripping method, a dilute solution in an equilibrium cell is kept initially at the temperature of interest. A constant inert gas flow is introduced into the solution and the components involved are stripped into the vapour phase. If the vapour-liquid equilibrium is established, the limiting activity coefficient can be calculated from the rate of variation of the vapour or liquid solute concentration versus the stripping time. Since the method was established by Leroi et al. (1977), a lot of progress have been made: (a) the Duhem and Vidal (1978) correction for the liquid concentration of the solute for its partition between the vapour phase and the liquid phase in the equilibrium cell; (b) modifications of the structure of the equilibrium cell (Richon et al., 1980; Richon and Renon, 1980); (c) the pre-saturation technique (Dole~al et al., 1981; Dole~al and Holub, 1985) which was proposed for the determination of high-volatile solvent systems; (d) fast expansion of the studying scope, such as for viscous or foaming systems (Richon et al., 1985), and for the mixtures containing food or oil (Lebert and Richon, 1984a; Lebert and Richon, 1984b), etc. These developments showed that this method will have a wider field of application in the future. In this work, to further application of the method, different types of mixtures, i.e. one-component solute + one-component solvent mixtures, one-component solute + multicomponent solvent mixtures, and multicomponent solute + solvent mixtures have been studied.
2. Theoretical
2.1. Single-cell technique (SCT) By this technique, only one cell is used, just as the original method (Leroi et al., 1977). The basic differential equations relating the variation of the amounts of solute a and solvent b in the dilute
J.-B. Bao, S.-J. Han / F l u i d Phase Equilibria 112 (1995) 307-316
309
solution with time can be written as
dna - -
YapF -
(1)
i
YbpF (l_ ~i yi)RT
dnb
dt-
(2)
Consider Duhem and Vidal's correction (1978), we accordingly use a method similar to that of Leroi et al. (1977) to derive a working expression for SCT: 1
Ins-~l
=
1+~~
1 .In 1 -
pPb b
"t
(3)
2.2. Double-celltechnique (DCT) Two cells, a pre-saturator and a main equilibrium cell, are to be applied for the measurement. In the pre-saturator, a solvent which has the same composition as that in the main equilibrium cell is always added. When an inert stripping gas is introduced, a saturated vapour flow of the solvent is generated firstly, and is used to maintain the composition and amount of the solvent in the main cell. Therefore, for solute in the main cell, the variation of the amount can also be calculated by
dna
YapF -
(4) i
but for each component of the solvent in the main cell dn i
-0, i4:a dt Similarly, the following equation can be derived for the infinite dilution activity coefficient:
(5)
Y'~niRT o-~
i
Y = -
(6)
Pa
+ VG A 1-~.y
i
where
In[S(t)] A
s-~l t
(71
310
J.-B. Bao, S.-J. Han / Fluid Phase Equilibria 112 (1995) 307-316
3. Experimental
The equilibrium cell and the pre-saturator used in this work were the same, as shown in Fig. 1. An important improvement on their structures is that a liquid-conducted-tube (Bao et al., 1990; Bao et al., 1994) was added between stainless-steel capillaries and the cell body to generate a countercurrent of circulating solution to the stripping bubbles while the solution was being stirred by a magnet. The countercurrent could lengthen the retention time of the bubbles in the dilute solution, ensure the compositions uniform both in the upper cell and in the lower cell, and therefore improve mass transfer and make the process of stripping more efficient. The dilute solution under study was introduced quantitatively into the main equilibrium cell by a syringe, the mole fraction of the solute despite one-component or multicomponent always being less than 5 x 10 -4, while only the solvent was added into the pre-saturator if DCT was employed. The cell or cells were then connected on the line of the stripping system and immersed in a thermostat water bath. After about 15 min, the stripping gas N 2 was introduced and kept at a constant flow rate of no more than 0.3 cm 3 s - l . The vapour out of the main cell was periodically sampled to a gas chromatograph for measuring its composition. Other details of the equipment and experiment can be seen in a previous paper (Bao et al., 1994).
It
l 0
E I4
M
ES I
Fig. 1. Equilibrium cell. B, body; C, capillaries; H, small holes; I, insert gas inlet; M, magnet; O, vapour-phase outlet; P, plug; R, PTFE O-ring; S, spacer; T, liquid-conducted-tube.
J.-B. Bao, S.-J. Han / Fluid Phase Equilibria 112 (1995) 307-316
311
All of the organic materials (Analytical Grade, 99.5%, or better) were fractionally distilled and sampled to a gas chromatograph equipped with a flame ionization detector and a thermal conductivity detector, and no impurities were detected. Water used in this work was bidistilled by use of a quartz distillator. NaCI was supplied by Merck (pro analysi) and without further purification.
4. Results and discussion
Using both techniques, SCT and DCT, 23 infinite dilution activity coefficients for various types of systems were newly determined in this work. The details of these measurements will be discussed as below. Either the Eq. (3) or (6), according as which technique was employed, was used to calculate the limiting activity coefficients. Furthermore, each experimental uncertainty of these activity coefficient values was estimated as Legret et al. (1983). 4.1. Type 1. One-component solute + one-component solvent systems For this type of systems, use of SCT or DCT depends mainly on the volatility of the solvent. If it is a nonvolatile or low-volatile substance, it is more convenient to use the former. For example, when the alcohol + n-alkane systems were studied by the gas stripping method (Cori and Delogu, 1986; Bao et al., 1990), it was found that the solutes are always preferentially volatilizable, either an alcohol in an alkane or an alkane in an alcohol. It indicated that only one cell was necessary for the measurements. In this work, some similar systems, such as acetone solvated in methanol, and acrylonitrile in water, etc., have been studied, as listed in Table 1. By contrast, if the solvent is high-volatile, it is best to select the latter. When we measured the limiting activity coefficients for
Table 1
Infinite dilution activity coefficients by the single-cell technique Solute
Solvent
This study
Literature
T (K)
"y~
T (K)
y~
Technique a
Ret.
318.2 318.2 318.15 298.15 333.15 318.0 293.15 298.15 298.15 298.15 298.15 298.15
2.95 2.74 3.00 2.7 2.6 1.92 2.27 2.16 7.5 7.17 6.47 19.8 - 46.2
EB unk ext ext ext EB ext GC ext GC GS ext
Thomas et al., 1982 Thomas et al., 1982 Schreiber and Eckert, 1971 Deal and Derr, 1964 Deal and Derr, 1964 Thomas et al., 1982 Bek~rek, 1968 Landau et al., 1991 Deal and Derr, 1964 Landau et al., 1991 Endler et al., 1985 Lobien and Prausnitz, 1982
313.15
17.6 - 43.6
ext
Lobien and Prausnitz, 1982
benzene
acetonitrile
318.15
2.93+0.1
n-heptane acetone
benzene methanol
318,15 298,15
1.88+0.06 2.28 ___0.03
benzene
methanol
298.15
7.55 + 0 . 2
acrylonitrile
water
303.15 308.15 313.15 318.15
41.8___ 1 41.6 + 1 41.5 + 1 41,4 + l
Techniques: EB, ebulliometric; ext, extrapolated VLE or LLE; GC, gas chromatographic; GS, gas stripping; HS,
headspace chromatographic; unk, unknown.
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J. -B. Bao, S. -J. Han / Fluid Phase Equilibria 112 (1995) 307-316
Table 2 Infinite dilution activity coefficients by the double-cell technique Solute Solvent This study Literature methanol ethanol
acetone acetone
T (K) 298.15 298.15
y2 1.84 + 0.05 2.50 _+0.08
benzene
acetone
298.15
1.62+0.07
benzene n-heptane
acetonitrile 318.15 2.88+0.09 benzene 318.15 1.90 _+0.07
T (K) 293.15 298.3 306.8 298.15 304.0 (see Table 1) (see Table 1)
y~ 1.88 2.44 2.24 1.7 1.59
Techniquea ext EB EB ext EB
Ref. Bekfirek, 1968 Trampe and Eckert, 1990 Thomas et al., 1982 Deal and Derr, 1964 Thomas et al., 1982
a See the footnote to Table 1. solutes in acetone which is obviously a high-volatile solvent (Bao et al., 1993b; Bao et al., 1994; and Table 2), a pre-saturator, that means DCT was employed, was used to maintain the amount of the solution in the main cell and to keep the equilibrium efficiency high. Third, for systems whose solvents have a volatility neither very high nor very low compared with that of the solutes, such as benzene in acetonitrile, and n-heptane in benzene studied here, either SCT or DCT can be used for the determination. As shown in Tables 1 and 2, no obvious differences between both techniques can be found in the limit of the experimental errors. Tables 1 and 2 give comparisons of the limiting activity coefficients measured by the two techniques with those in the literature. As can be seen, agreement is satisfactory, the only exception being the data for acrylonitrile in water. For this system, no other values could be found in the literature, except for those calculated from VLE and solubility data using van Laar or UNIQUAC equation by Lobien and Prausnitz (1982) despite their poor accuracy pointed out by the authors. 4.2. T y p e 2. O n e - c o m p o n e n t solute + m u l t i c o m p o n e n t s o l v e n t s y s t e m s
A multicomponent solvent means that the solvent is composed of two or more substances. For such a system, the measurement will have no physical meaning if SCT is used because the surroundings of the solute, i.e. the solvent, will be changed while stripping. For instance, if we want to measure the limiting activity coefficient for a ketone in 10 mol m -3 NaCl-aqueous solution, the concentration of the salt will be increased for only water is going to be stripped. At this moment, only DCT can be qualified. We can introduce the solvent (NaCI aqueous solution with the same concentration) into the pre-saturator initially. Therefore, the stripping flow out of the pre-saturator and into the main equilibrium cell is the saturated vapour of the multicomponent solvent, and the solvent in the main cell will not be affected (the concentration of NaCl in the pre-saturator increased slightly for the volume of the pre-saturator used here was finite, while that in the main cell was confirmed being constant within the whole experimental period). The limiting values for the systems of this type obtained in this work are shown in Table 3. For the salt concentration of the solvents not very high, Table 3 give s the limiting activity coefficients in pure water for comparison. The same technique has also been employed for the study of a ternary system: methanol + acetone + benzene (Bao et al., 1993a). We measured 4 infinite dilution activity coefficients for methanol in
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Table 3 Infinite dilution activity coefficients in multicomponent solvents Solute acetone
acetone butanone
butanone
3-pentanone
3-pentanone
Solvent
This study
Literature
T (K)
T (K)
y~
10 mol m -3 NaCl-aqueous solution water
298.15
10 molm 3 NaCl-aqueous solution water
298.15
10molm 3 NaCl-aqueous solution water
298.15 108_+3
y~
Technique a Ref.
7 . 7 0 _ + 0 . 2 none
298.15 298.15 2 6 . 4 _ + 0 . 8 none
298.15 298.15 298.15 none
298.15 298.15
7.31 GC 7.56 GC
Landau et al., 1991 Mash and Pemberton, 198(I
27.6 GC 27.8 GC 25.98 HS
Landau et al., 1991 Mash and Pernberton, 1980 Park et al., 1987
113 113
GC GC
Landau et al., 1991 Mash and Pemberton, 1980
a See the footnote to Table 1. acetone + benzene, 2 for acetone in methanol + benzene, 3 for benzene in methanol + acetone. Thus, the estimation of the whole range V L E data f r o m these ternary limiting values would be more accurate than those f r o m the binary limiting data only. 4.3. Type 3. Multicomponent solute + solvent systems
Actually, this is not a new type. If a solute is multicomponent, the system will have more than one limiting values. Each c o m p o n e n t of the solute in the solvent has its o w n activity coefficient at infinite dilution. Obviously, we can measure them separately. On the other hand, if the properties of c o m p o n e n t s c o m p o s e d o f the solute are proper, i.e. their volatilities are close, and the detector (usually a gas chromatograph) can detect their v a p o u r phases accurately, we can determine them simultaneously. T a b l e 4 gives s o m e e x a m p l e s of the measurement. The results are almost equal to those determined separately except for the experimental errors. Thus the efficiency of the determination for limiting activity coefficients would be enhanced (Bao and Han, 1992). 4.4. An overall s c h e m e
An overall s c h e m e to s u m m a r i z e the different possibilities for these m e a s u r e m e n t s is shown in Fig. 2. It can be found that the use of the techniques, S C T or DCT, depends mainly on the volatility and nature ( o n e - c o m p o n e n t or multicomponent) of the solvent o f a solution. I f the solvent is a nonvolatile or low-volatile substance, S C T can usually be employed; but if it is a high-volatile substance or c o m p o s e d of two or m o r e substances, D C T must be applied for a reasonable and accurate measurement.
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J. -B. Bao, S. -J. Han / Fluid Phase Equilibria 112 (1995) 307-316
Table 4 Infinite dilution activity coefficients of multicomponent solutes at 298.15 K Solute methanol + benzene acetone + benzene acetone + butanone + 3-pentanone
Solvent
Technique
acetone
DCT
methanol
Simultaneously
Separately
1.85 ___0.05
1.84 + 0.05
1.61 + 0.06 2.20 + 0.06
1.62 + 0.07 2.28 + 0.03
7.49 + 0.3 7.77 ___0.3
7.55 + 0.2 7.70 + 0.2
26.7 + 0.9
26.4 + 0.8
107 + 3
108 _ 3
SCT
10 moL m-3 NaCl-aqueous solution
DCT
To the solute, however, its volatility is not concerned directly with the use of S C T or D C T , but with the method employed. As indicated by Richon et al. (1980), the solute should have a certain volatility in the dilute solution despite its pure properties if the gas stripping method is applied for the determination o f infinite dilution activity coefficient. H o w e v e r , if the dilute solute is highly volatile, the method is not accurate enough unless s o m e modifications on the sampling technique or detecting equipment are m a d e (Bao et al., 1993c). Further, the nature o f the solute only tells us h o w m a n y limiting activity coefficients the system has. I f it is multicomponent, a valuable attempt is whether these limiting values can be determined simultaneously or not.
/
(.-°,..o
.
/
Fig. 2. An overall scheme to summarize the different possibilities for the use of SCT or DCT.
J.-B. Bao, S.-J. Han /Fluid Phase Equilibria 112 (1995) 307-316
315
5. Conclusions By use of the gas stripping method, infinite dilution activity coefficients for different types of the systems, especially for those containing multicomponent solutes or solvents, have been determined. Thus, applications of the limiting activity coefficients would be more efficient than before.
6. List of symbols A F n
P R S t T V Y Y
desorption rate o f mole fraction of the solute, s flowrate o f pure stripping gas, m 3 s-1 amount o f component, mol pressure, Pa universal gas constant, J m o l - 1 K-1 peak area time, s temperature, K volume, m 3 mole fraction of the vapour phase activity coefficient
6.1.1. Superscripts zc *
infinite dilution properties of pure component
6.1.2. Subscripts a b G i
solute solvent vapour phase in the equilibrium cell component
Acknowledgements W e thank the National Natural Science Foundation o f China and the Natural Science Foundation o f Zhejiang Province for their financial support.
References Alessi, P., Fermeglia, M. and Kikic, I., 1991. Significance of dilute regions. Fluid Phase Equilibria, 70: 239-250. Bao, J.-B., Liu. W.-P. and Han, S.-J., 1990. The measurement of infinite dilution activity coefficients for alcohol-n-alkane systems by gas stripping method. J. Zhejiang Univ., 24: 374-382. Bao, J.-B. and Han, S.-J., 1992. Two developments of gas stripping method for determination of infinite dilution activity coefficients. Natural Gas Chem. Ind. (Ch.), 17(4): 53-56. Bao, J.-B., Chen, G.-H. and Han, S.-J., 1993a. Determination of infinite dilution activity coefficients in multicomponent solvent systems with gas stripping method. J. Chem. Ind. Eng. (Ch.), 44: 542-548.
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J. -B. Bao, S. -J. Han / Fluid Phase Equilibria 112 (1995) 307-316
Bao, J.-B., Hang, L.-L., Ling Y.-P., Chen, G.-H. and Han, S.-J., 1993b. Studies on the determination of infinite dilution activity coefficients of acetone-cycloalkane systems by gas stripping method. Chem. J. Chin. Univ., 14: 1280-1283. Bao, J.-B., Huang, Q., Chen, G.-H. and Han S.-J., 1993c. Determination of large value activity coefficients at infinite dilution. Acta Phys.-Chim. (Ch.), 9: 724-727. Bao, J.-B., Hang, L.-L. and Han, S.-J., 1994. Infinite-dilution activity coefficients of (propanone + an n-alkane) by gas stripping. J. Chem. Thermodynamics, 26: 673-680. Bek~rek, V., 1968. Liquid-vapour equilibrium. XL. Liquid-vapour equilibrium in the systems SO 2-CH3COOCH3-CH3OH and SO2-CH3COCH 3 - CH3OH. Coil. Czech. Chem. Commun., 33: 2608-2619. Cori, L. and Delogu, P., 1986. Infinite dilution activity coefficients of ethanol-n-alkanes mixtures. Fluid Phase Equilibria, 27: 103-118. Deal, C.H. and Derr, E.L., 1964. Selectivity and solvency in aromatics recovery. Ind. Eng. Chem. Process Des. Dev., 3: 394-399. Duhem, P. and Vidal, J., 1978. Extension of the dilutor method to measurement of high activity coefficients at infinite dilution. Fluid Phase Equilibria, 2: 231-235. Dole~al, B. and Holub, R., 1985. Approximate relations for determining the activity coefficients at very low concentration by the method of variation of solute concentration. Coil. Czech. Chem. Commun., 50: 704-711. Dole~al, B., Popl, M. and Holub, R., 1981. Determination of activity coefficients at very low concentrations by the inert gas stripping method. J. Chromatogr., 207: 193-201. Eckert, C.A., Newman, B.A., Nicolaides, G.L. and Long, T.C., 1981. Measurement and application of limiting activity coefficients. AIChE J., 27: 33-40. Endler, I., Hradetzky, G. and Bittrich, H.-J., 1985. Grenzaktivit~itskoeffizienten in bin~iren systemen benzen-alkanol. J. prakt. Chem., 327: 693-697. Gautreaux, M.F. and Coates, J., 1955. Activity coefficients at infinite dilution. AIChE J., 1: 496-500. Landau, I., Belfer, A.J. and Locke, D.C., 1991. Measurement of limiting activity coefficients using non-steady-state gas chromatography. Ind. Eng. Chem. Res., 30: 1900-1906. Lebert, A. and Richon, D., 1984a. Infinite dilution activity coefficients of n-alcohols as a function of dextrin concentration in water-dextrin systems. J. Agric. Food Chem., 32: 1156-1161. Lebert, A. and Richon, D., 1984b. Study of the influence of solute (n-alcohols and n-alkanes) chain length on their retention by purified olive oil. J. Food Sci., 49: 1301-1304. Legret, D., Desteve, J., Richon, D. and Renon, H., 1983. 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., 29: 137-144. Leroi, J.-C., Masson, J.C., Renon, H., Fabries, J.F. and Sannier, H., 1977. Accurate measurement of activity coefficients at infinite dilution by inert gas stripping and gas chromatography. Ind. Eng. Chem. Process Des. Dev., 16: 139-144. Lobien, G.M. and Prausnitz, J.M., 1982. Infinite-dilution activity coefficients from differential ebulliometry. Ind. Eng. Chem. Fundam., 21: 109-113. Mash, C.J. and Pemberton, R.C., 1980. Activity coefficients at very low concentrations for organic solutes in water determined by an automatic chromatographic method. NPL Report Chem. 111; National Physical Laboratory, Teddington, Middlesex, U.K., 24 pp. Park, J.H., Hussam, A., Couasnon, P., Fritz, D. and Carr, P.W., 1987. Experimental reexamination of selected partition coefficients from Rohrschneider's data set. Anal. Chem., 59: 1970-1976. Richon, D., Antoine, P. and Renon, H., 1980. Infinite dilution activity coefficients of linear and branched alkanes from C 1 and C 9 in n-hexadecane by inert gas stripping. Ind. Eng. Chem. Process Des. Dev., 19: 144-147. Richon, D. and Renon, H., 1980. Infinite dilution Henry's constants of light hydrocarbons in n-hexadecane, n-octadecane, and 2,2,4,4,6,8,8-heptamethylnonane by inert gas stripping. J. Chem. Eng. Data, 25: 59-60. Richon, D., Sorrentino, F. and Voilley, A., 1985. Infinite dilution activity coefficients by inert gas stripping method: Extension to the study of viscous and foaming mixtures. Ind. Eng. Chem. Process Des. Dev., 24: 1160-1165. Schreiber, L.B. and Eckert, C.A., 1971. Use of infinite dilution activity coefficients with Wilson's equation. Ind. Eng. Chem. Process Des. Dev., 10: 572-576. Thomas, E.R., Newman, B.A., Nicolaides, G.L. and Eckert, C.A., 1982. Limiting activity coefficients from differential ebulliometry. J. Chem. Eng. Data, 27: 233-240; and references cited therein. Trampe, D.M. and Eckert, C.A., 1990. Limiting activity coefficients from an improved differential boiling point technique. J. Chem. Eng. Data, 35: 156-162.
[IlUlIIII ELSEVIER
Fluid Phase Equilibria 112 (1995) 31)7-316
Infinite dilution activity coefficients for various types of systems Jian-Bin Bao, Shi-Jun Han Department of Chemistry, Zhejiang University, Hangzhou, 31002 7, People's Republic of China Received 5 October 1994; accepted 3 June 1995
Abstract
The infinite dilution activity coefficients for various types of systems, one-component solute + one-component solvent, one-component solute + multicomponent solvent, and multicomponent solute + solvent have been studied by use of the gas stripping method. Two techniques, the single-cell technique (SCT) and the double-ccll technique (DCT), are described. The use of them depends mainly on the volatility and nature (one-component or multicomponent) of the solvent. Keywords: Experiments; Method; Infinite dilution activity coefficients; Gas stripping method; Single-cell technique: Double-cell technique
1. Introduction
The infinite dilution is a special state of liquid mixtures. In that state, the concentration of one component, which is usually called the solute, goes to zero, while the mole fraction of the other component or the total mole fraction of the others, i.e. the solvent mole fraction, is close to one. The activity coefficient of the infinitely dilute solute, named as the infinite dilution activity coefficient or the limiting activity coefficient, is a limiting measurement of the nonideality of the solute in this mixture. Alessi et al. (1991) have given the importance of the limiting data both for the development of separation processes and for a better understanding in theories for liquid solutions. In the past forty years, various methods for the direct measurement of infinite dilution activity coefficients have been developed.
1.1. Gas-liquid chromatography method By this method, a solvent is firstly coated on an inert support as a stationary phase for a gas-liquid chromatograph. Little amount (usually only about several microlitres) of a solute is injected to detect the retention time of the solute in the solvent surroundings. By using other properties, such as the column temperature and pressure, the solvent amount in the column and the flow rate of the carrier 0378-3812/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved
SSDI 0 3 7 8 - 3 8 1 2 ( 9 5 ) 0 2 8 0 0 - 5
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J. oB. Bao, S.-J. Han / Fluid Phase Equilibria 112 (1995) 307-316
gas, the limiting activity coefficient can thereafter be calculated. This method is especially suitable for the limiting values for volatile solutes in nonvolatile or low-volatile solvents because the solvents can be coated easily and steadily. For the same reason, however, it is often unsuitable for the values of the other end, i.e. the limiting activity coefficients for the solvents in the solutes. This means for most of our interested binary systems, it is very difficult to obtain both ends of the limiting values. Nevertheless, possible solute-support interactions or solvent-support interactions instead of solutesolvent interactions would have an effect on the accuracy of these measurements.
1.2. Differential ebulliometry method According to an expression for activity coefficients at infinite dilution derived by Gautreaux and Coates (1955), the limiting values can be obtained by measurements of the limiting slope of boiling temperature with respect to the solute concentration. Thanks to the great work accomplished by Eckert and his co-workers ( Eckert et al., 1981; Thomas et al., 1982; Trampe and Eckert, 1990), this method has been a successful way to get limiting values for many binary systems. But unfortunately, for most highly nonideal systems, it would be difficult to operate.
1.3. Gas stripping method By use of the gas stripping method, a dilute solution in an equilibrium cell is kept initially at the temperature of interest. A constant inert gas flow is introduced into the solution and the components involved are stripped into the vapour phase. If the vapour-liquid equilibrium is established, the limiting activity coefficient can be calculated from the rate of variation of the vapour or liquid solute concentration versus the stripping time. Since the method was established by Leroi et al. (1977), a lot of progress have been made: (a) the Duhem and Vidal (1978) correction for the liquid concentration of the solute for its partition between the vapour phase and the liquid phase in the equilibrium cell; (b) modifications of the structure of the equilibrium cell (Richon et al., 1980; Richon and Renon, 1980); (c) the pre-saturation technique (Dole~al et al., 1981; Dole~al and Holub, 1985) which was proposed for the determination of high-volatile solvent systems; (d) fast expansion of the studying scope, such as for viscous or foaming systems (Richon et al., 1985), and for the mixtures containing food or oil (Lebert and Richon, 1984a; Lebert and Richon, 1984b), etc. These developments showed that this method will have a wider field of application in the future. In this work, to further application of the method, different types of mixtures, i.e. one-component solute + one-component solvent mixtures, one-component solute + multicomponent solvent mixtures, and multicomponent solute + solvent mixtures have been studied.
2. Theoretical
2.1. Single-cell technique (SCT) By this technique, only one cell is used, just as the original method (Leroi et al., 1977). The basic differential equations relating the variation of the amounts of solute a and solvent b in the dilute
J.-B. Bao, S.-J. Han / F l u i d Phase Equilibria 112 (1995) 307-316
309
solution with time can be written as
dna - -
YapF -
(1)
i
YbpF (l_ ~i yi)RT
dnb
dt-
(2)
Consider Duhem and Vidal's correction (1978), we accordingly use a method similar to that of Leroi et al. (1977) to derive a working expression for SCT: 1
Ins-~l
=
1+~~
1 .In 1 -
pPb b
"t
(3)
2.2. Double-celltechnique (DCT) Two cells, a pre-saturator and a main equilibrium cell, are to be applied for the measurement. In the pre-saturator, a solvent which has the same composition as that in the main equilibrium cell is always added. When an inert stripping gas is introduced, a saturated vapour flow of the solvent is generated firstly, and is used to maintain the composition and amount of the solvent in the main cell. Therefore, for solute in the main cell, the variation of the amount can also be calculated by
dna
YapF -
(4) i
but for each component of the solvent in the main cell dn i
-0, i4:a dt Similarly, the following equation can be derived for the infinite dilution activity coefficient:
(5)
Y'~niRT o-~
i
Y = -
(6)
Pa
+ VG A 1-~.y
i
where
In[S(t)] A
s-~l t
(71
310
J.-B. Bao, S.-J. Han / Fluid Phase Equilibria 112 (1995) 307-316
3. Experimental
The equilibrium cell and the pre-saturator used in this work were the same, as shown in Fig. 1. An important improvement on their structures is that a liquid-conducted-tube (Bao et al., 1990; Bao et al., 1994) was added between stainless-steel capillaries and the cell body to generate a countercurrent of circulating solution to the stripping bubbles while the solution was being stirred by a magnet. The countercurrent could lengthen the retention time of the bubbles in the dilute solution, ensure the compositions uniform both in the upper cell and in the lower cell, and therefore improve mass transfer and make the process of stripping more efficient. The dilute solution under study was introduced quantitatively into the main equilibrium cell by a syringe, the mole fraction of the solute despite one-component or multicomponent always being less than 5 x 10 -4, while only the solvent was added into the pre-saturator if DCT was employed. The cell or cells were then connected on the line of the stripping system and immersed in a thermostat water bath. After about 15 min, the stripping gas N 2 was introduced and kept at a constant flow rate of no more than 0.3 cm 3 s - l . The vapour out of the main cell was periodically sampled to a gas chromatograph for measuring its composition. Other details of the equipment and experiment can be seen in a previous paper (Bao et al., 1994).
It
l 0
E I4
M
ES I
Fig. 1. Equilibrium cell. B, body; C, capillaries; H, small holes; I, insert gas inlet; M, magnet; O, vapour-phase outlet; P, plug; R, PTFE O-ring; S, spacer; T, liquid-conducted-tube.
J.-B. Bao, S.-J. Han / Fluid Phase Equilibria 112 (1995) 307-316
311
All of the organic materials (Analytical Grade, 99.5%, or better) were fractionally distilled and sampled to a gas chromatograph equipped with a flame ionization detector and a thermal conductivity detector, and no impurities were detected. Water used in this work was bidistilled by use of a quartz distillator. NaCI was supplied by Merck (pro analysi) and without further purification.
4. Results and discussion
Using both techniques, SCT and DCT, 23 infinite dilution activity coefficients for various types of systems were newly determined in this work. The details of these measurements will be discussed as below. Either the Eq. (3) or (6), according as which technique was employed, was used to calculate the limiting activity coefficients. Furthermore, each experimental uncertainty of these activity coefficient values was estimated as Legret et al. (1983). 4.1. Type 1. One-component solute + one-component solvent systems For this type of systems, use of SCT or DCT depends mainly on the volatility of the solvent. If it is a nonvolatile or low-volatile substance, it is more convenient to use the former. For example, when the alcohol + n-alkane systems were studied by the gas stripping method (Cori and Delogu, 1986; Bao et al., 1990), it was found that the solutes are always preferentially volatilizable, either an alcohol in an alkane or an alkane in an alcohol. It indicated that only one cell was necessary for the measurements. In this work, some similar systems, such as acetone solvated in methanol, and acrylonitrile in water, etc., have been studied, as listed in Table 1. By contrast, if the solvent is high-volatile, it is best to select the latter. When we measured the limiting activity coefficients for
Table 1
Infinite dilution activity coefficients by the single-cell technique Solute
Solvent
This study
Literature
T (K)
"y~
T (K)
y~
Technique a
Ret.
318.2 318.2 318.15 298.15 333.15 318.0 293.15 298.15 298.15 298.15 298.15 298.15
2.95 2.74 3.00 2.7 2.6 1.92 2.27 2.16 7.5 7.17 6.47 19.8 - 46.2
EB unk ext ext ext EB ext GC ext GC GS ext
Thomas et al., 1982 Thomas et al., 1982 Schreiber and Eckert, 1971 Deal and Derr, 1964 Deal and Derr, 1964 Thomas et al., 1982 Bek~rek, 1968 Landau et al., 1991 Deal and Derr, 1964 Landau et al., 1991 Endler et al., 1985 Lobien and Prausnitz, 1982
313.15
17.6 - 43.6
ext
Lobien and Prausnitz, 1982
benzene
acetonitrile
318.15
2.93+0.1
n-heptane acetone
benzene methanol
318,15 298,15
1.88+0.06 2.28 ___0.03
benzene
methanol
298.15
7.55 + 0 . 2
acrylonitrile
water
303.15 308.15 313.15 318.15
41.8___ 1 41.6 + 1 41.5 + 1 41,4 + l
Techniques: EB, ebulliometric; ext, extrapolated VLE or LLE; GC, gas chromatographic; GS, gas stripping; HS,
headspace chromatographic; unk, unknown.
312
J. -B. Bao, S. -J. Han / Fluid Phase Equilibria 112 (1995) 307-316
Table 2 Infinite dilution activity coefficients by the double-cell technique Solute Solvent This study Literature methanol ethanol
acetone acetone
T (K) 298.15 298.15
y2 1.84 + 0.05 2.50 _+0.08
benzene
acetone
298.15
1.62+0.07
benzene n-heptane
acetonitrile 318.15 2.88+0.09 benzene 318.15 1.90 _+0.07
T (K) 293.15 298.3 306.8 298.15 304.0 (see Table 1) (see Table 1)
y~ 1.88 2.44 2.24 1.7 1.59
Techniquea ext EB EB ext EB
Ref. Bekfirek, 1968 Trampe and Eckert, 1990 Thomas et al., 1982 Deal and Derr, 1964 Thomas et al., 1982
a See the footnote to Table 1. solutes in acetone which is obviously a high-volatile solvent (Bao et al., 1993b; Bao et al., 1994; and Table 2), a pre-saturator, that means DCT was employed, was used to maintain the amount of the solution in the main cell and to keep the equilibrium efficiency high. Third, for systems whose solvents have a volatility neither very high nor very low compared with that of the solutes, such as benzene in acetonitrile, and n-heptane in benzene studied here, either SCT or DCT can be used for the determination. As shown in Tables 1 and 2, no obvious differences between both techniques can be found in the limit of the experimental errors. Tables 1 and 2 give comparisons of the limiting activity coefficients measured by the two techniques with those in the literature. As can be seen, agreement is satisfactory, the only exception being the data for acrylonitrile in water. For this system, no other values could be found in the literature, except for those calculated from VLE and solubility data using van Laar or UNIQUAC equation by Lobien and Prausnitz (1982) despite their poor accuracy pointed out by the authors. 4.2. T y p e 2. O n e - c o m p o n e n t solute + m u l t i c o m p o n e n t s o l v e n t s y s t e m s
A multicomponent solvent means that the solvent is composed of two or more substances. For such a system, the measurement will have no physical meaning if SCT is used because the surroundings of the solute, i.e. the solvent, will be changed while stripping. For instance, if we want to measure the limiting activity coefficient for a ketone in 10 mol m -3 NaCl-aqueous solution, the concentration of the salt will be increased for only water is going to be stripped. At this moment, only DCT can be qualified. We can introduce the solvent (NaCI aqueous solution with the same concentration) into the pre-saturator initially. Therefore, the stripping flow out of the pre-saturator and into the main equilibrium cell is the saturated vapour of the multicomponent solvent, and the solvent in the main cell will not be affected (the concentration of NaCl in the pre-saturator increased slightly for the volume of the pre-saturator used here was finite, while that in the main cell was confirmed being constant within the whole experimental period). The limiting values for the systems of this type obtained in this work are shown in Table 3. For the salt concentration of the solvents not very high, Table 3 give s the limiting activity coefficients in pure water for comparison. The same technique has also been employed for the study of a ternary system: methanol + acetone + benzene (Bao et al., 1993a). We measured 4 infinite dilution activity coefficients for methanol in
313
J. -B. Bao, S.-J. Han / Fluid PhaseEquilibria 112 (1905)307-316
Table 3 Infinite dilution activity coefficients in multicomponent solvents Solute acetone
acetone butanone
butanone
3-pentanone
3-pentanone
Solvent
This study
Literature
T (K)
T (K)
y~
10 mol m -3 NaCl-aqueous solution water
298.15
10 molm 3 NaCl-aqueous solution water
298.15
10molm 3 NaCl-aqueous solution water
298.15 108_+3
y~
Technique a Ref.
7 . 7 0 _ + 0 . 2 none
298.15 298.15 2 6 . 4 _ + 0 . 8 none
298.15 298.15 298.15 none
298.15 298.15
7.31 GC 7.56 GC
Landau et al., 1991 Mash and Pemberton, 198(I
27.6 GC 27.8 GC 25.98 HS
Landau et al., 1991 Mash and Pernberton, 1980 Park et al., 1987
113 113
GC GC
Landau et al., 1991 Mash and Pemberton, 1980
a See the footnote to Table 1. acetone + benzene, 2 for acetone in methanol + benzene, 3 for benzene in methanol + acetone. Thus, the estimation of the whole range V L E data f r o m these ternary limiting values would be more accurate than those f r o m the binary limiting data only. 4.3. Type 3. Multicomponent solute + solvent systems
Actually, this is not a new type. If a solute is multicomponent, the system will have more than one limiting values. Each c o m p o n e n t of the solute in the solvent has its o w n activity coefficient at infinite dilution. Obviously, we can measure them separately. On the other hand, if the properties of c o m p o n e n t s c o m p o s e d o f the solute are proper, i.e. their volatilities are close, and the detector (usually a gas chromatograph) can detect their v a p o u r phases accurately, we can determine them simultaneously. T a b l e 4 gives s o m e e x a m p l e s of the measurement. The results are almost equal to those determined separately except for the experimental errors. Thus the efficiency of the determination for limiting activity coefficients would be enhanced (Bao and Han, 1992). 4.4. An overall s c h e m e
An overall s c h e m e to s u m m a r i z e the different possibilities for these m e a s u r e m e n t s is shown in Fig. 2. It can be found that the use of the techniques, S C T or DCT, depends mainly on the volatility and nature ( o n e - c o m p o n e n t or multicomponent) of the solvent o f a solution. I f the solvent is a nonvolatile or low-volatile substance, S C T can usually be employed; but if it is a high-volatile substance or c o m p o s e d of two or m o r e substances, D C T must be applied for a reasonable and accurate measurement.
314
J. -B. Bao, S. -J. Han / Fluid Phase Equilibria 112 (1995) 307-316
Table 4 Infinite dilution activity coefficients of multicomponent solutes at 298.15 K Solute methanol + benzene acetone + benzene acetone + butanone + 3-pentanone
Solvent
Technique
acetone
DCT
methanol
Simultaneously
Separately
1.85 ___0.05
1.84 + 0.05
1.61 + 0.06 2.20 + 0.06
1.62 + 0.07 2.28 + 0.03
7.49 + 0.3 7.77 ___0.3
7.55 + 0.2 7.70 + 0.2
26.7 + 0.9
26.4 + 0.8
107 + 3
108 _ 3
SCT
10 moL m-3 NaCl-aqueous solution
DCT
To the solute, however, its volatility is not concerned directly with the use of S C T or D C T , but with the method employed. As indicated by Richon et al. (1980), the solute should have a certain volatility in the dilute solution despite its pure properties if the gas stripping method is applied for the determination o f infinite dilution activity coefficient. H o w e v e r , if the dilute solute is highly volatile, the method is not accurate enough unless s o m e modifications on the sampling technique or detecting equipment are m a d e (Bao et al., 1993c). Further, the nature o f the solute only tells us h o w m a n y limiting activity coefficients the system has. I f it is multicomponent, a valuable attempt is whether these limiting values can be determined simultaneously or not.
/
(.-°,..o
.
/
Fig. 2. An overall scheme to summarize the different possibilities for the use of SCT or DCT.
J.-B. Bao, S.-J. Han /Fluid Phase Equilibria 112 (1995) 307-316
315
5. Conclusions By use of the gas stripping method, infinite dilution activity coefficients for different types of the systems, especially for those containing multicomponent solutes or solvents, have been determined. Thus, applications of the limiting activity coefficients would be more efficient than before.
6. List of symbols A F n
P R S t T V Y Y
desorption rate o f mole fraction of the solute, s flowrate o f pure stripping gas, m 3 s-1 amount o f component, mol pressure, Pa universal gas constant, J m o l - 1 K-1 peak area time, s temperature, K volume, m 3 mole fraction of the vapour phase activity coefficient
6.1.1. Superscripts zc *
infinite dilution properties of pure component
6.1.2. Subscripts a b G i
solute solvent vapour phase in the equilibrium cell component
Acknowledgements W e thank the National Natural Science Foundation o f China and the Natural Science Foundation o f Zhejiang Province for their financial support.
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J. -B. Bao, S. -J. Han / Fluid Phase Equilibria 112 (1995) 307-316
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