Modified solvation model for salt effect on vapor liquid equilibria

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1 Fluid Phase Equilibria (2002) Modified solvation model for salt effect on vapor liquid equilibria Hideaki Takamatsu, Shuzo Ohe Department of Chemical Engineering, Graduated School of Engineering, Science University of Tokyo, 1-3 Kagurazaka, Shinjuku-ku, Tokyo , Japan Received 20 May 2001; accepted 29 October 2001 Abstract The prediction method had been presented for salt effect on vapor liquid equilibria by solvation model. This model assumes that salt effect is caused by solvation and solvated solvent molecular cannot contribute to vapor liquid equilibria. The model took into account the vapor pressure depression in mixed solvent. In this work, the solvation model was modified. The relation between solvation number in pure solvent + salt system and correlation error was confirmed. Solvation number was determined by using a new relation. As a result, the model was satisfactory applied for all binary solvents + salt systems. Furthermore, ternary solvents + salt system was predicted by using solvation number in pure solvent determined from binary solvents + salt system. Good accuracy was shown Elsevier Science B.V. All rights reserved. Keywords: Salt effect; Solvation; Vapor liquid equilibria 1. Introduction It is well known that azeotropic mixture cannot be separated by ordinary distillation method and that some kinds of salt are significantly effective to diminish the azeotrope. Therefore, investigators of both of academics and industries have studied salt effect on vapor liquid equlibria. The first method for prediction of salt effect had been proposed by Johnson and Furter [1], which was semi-empirical equation. It is quite important to clarify the mechanism of this effect and to convince the method of correlation and prediction. Although, many investigations have been done for this field, most of them are modification of conventional thermodynamic model for non-electrolyte component system such as activity coefficients model. These models combined extended non-electrolyte activity coefficients model and Debye Hückel term. The activity coefficients model term was used for describing short-range interaction by van der Waals force. Debye Hückel term was used for describing long-range interaction according to Coulomb force. For example, Tan s equation using Wilson equation [2] for describing short-range interaction, electrolyte NRTL model [3 5] using NRTL equation, extended UNIQUAC [6,7] model and LIQUAC Corresponding author. Tel.: ; fax: address: ohe@ms.kagu.sut.ac.jp (S. Ohe) /02/$ see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S (01)

2 702 H. Takamatsu, S. Ohe / Fluid Phase Equilibria (2002) model [8,9] using UNIQUAC equation, Kikic et al. s method [10] using UNIFAC equation, Achard et al. s method [11] using modified UNIFAC equation and Yan et al. s method [12] applying LIQUAC model to atomic group contribution method had been presented. However, most of the mixtures of the salt effect system are composed of non-electrolytes and electrolytes component. Thus, a model, which is capable of explaining contributions of these two different kinds of components, should be introduced. A solvation model had been presented. The alteration of vapor phase composition is thought to be caused by a formation of solvates between solvents and salt. The solvates are also thought to take a part for vapor pressure lowering of the system. A first model in which a salt forms preferential solvate with one of the solvents in a binary solvent system was proposed to predict salt effect on vapor liquid equilibrium [13]. The model was successfully applied to correlate and express the salt effect for 386 binary solvents + 47 single-salt systems [14]. However, this first model has a drawback that the vapor pressure lowering cannot express sufficiently, since the lowering is observed over all the range of liquid composition of solvent. Based on the model, the lowering is zero at the end of composition of the solvent, which is not solvated and increased as the decrease of the component. Then, the modification of the model has been done to overcome this drawback. The model employed a solvation between salt of each of solvent in mixture instead of a preferential solvation. An alteration of vapor phase composition by salt effect thought to be caused by the difference of degree of solvations between solvents. This difference of degree is corresponds to the preferential salvation [15,16]. In this work, relation between solvation number and correlation error is examined. The relation is used to determinate solvation number. And the solvation numbers were used to predict salt effect on vapor liquid equilibria. 2. Lowering of vapor pressure Dissolved salt, which is non-volatile substance, lowers vapor pressure at a given temperature of a solvent. When the behavior of a single solvent and a salt system is assumed to be non-ideal and complete dissociation of salt, the pressure of the system is given by Eq. (1): π = P solvent a solvent. (1) Since the activity is a product of activity coefficient and mole fraction of solvents: a solvent = γ solvent x solvent, then the activity coefficient for the pressure is determined from Eq. (1) as follows: π γ solvent = (P solvent x solvent ). (2) The model assumed salt showed complete disassociation. It is assumed that lowering of vapor pressure of pure solvent system is caused by solvated molecule, which does not contribute to vaporization. The activity of the solvent becomes (n solvent n salt )S 0 a solvent =. (3) (n solvent n salt S 0 ) + n salt Dividing both of the denominator and numerator by n solvent + n salt will give a solvent = (x solvent x salt )S 0, (1 x salt )S 0 where x solvent = 1 x salt. (4)

3 H. Takamatsu, S. Ohe / Fluid Phase Equilibria (2002) Fig. 1. The x y curve for methanol + water + CaCl 2 (4 mol%) at kpa [17]. 3. Effective composition of solvents system containing salt As the concentration of solvent is assumed to be decreased by the number of solvated molecules, the actual solvents composition participating in the vapor liquid equilibrium is changed. Assuming that a salt forms the solvates with each component and that the solvated molecules do not contribute to vapor liquid equilibria, the effective mole fraction x ia for the ith solvent is given by Eq. (5) at salt free basis. Since, the sum of solvent mole fraction is equal to 1 x salt, and the solvation number for the ith solvent is calculated as S i0 x i, and Eq. (5) is obtained. x ia = x i (S i0 x i x salt) 1 x salt S i0 x i x salt (5) Fig. 2. Solvation numbers for methanol + water + CaCl 2 (4 mol%) at kpa [17].

4 704 H. Takamatsu, S. Ohe / Fluid Phase Equilibria (2002) The relation of solvation number S i between that of a singe solvent S i0 and composition of it x i was recognized experimentally. The example for calculation of solvation number is shown in Figs. 1 and 2. From an experimental data shown in Fig. 1, effective mole fraction x ia is able to be calculated from its numerical data. Calculated solvation numbers for each solvent are shown in Fig. 2. It is shown that relation between solvation number S i and the composition of solvent x i has linearity. The relation is caused by a molecular numbers of solvents per salt molecule changing according to stochiometry by changing liquid composition. Therefore, this is one of the strongest pieces of evidence in support of the solvation model. Furthermore, the relation has a physical meaning that solvation number S i depends upon solvent concentration at the condition of capable of making solvates of salt being constant at a given salt concentration in mole fraction, since the number of solvent molecule which can be solvated, increases by the number of itself. 4. Prediction of salt effect from solvation number In the case of mixed solvents system, lowering of vapor pressure may be treated in a similar manner. As total pressure of solvents system, Eq. (6) is given for non-ideal solution, which corresponds to Eq. (1) given for the pure solvent system. P solvent = P i γ i x ia (6) The activity coefficient for vapor pressure lowering is assumed to be average of activity coefficient of each solvent with its mole fraction. Eq. (7) may be derived from the above assumption. γ mix,solvent = γ i,solvent x i (7) Therefore, the basic equation to calculate salt effect on vapor liquid equilibrium corresponds to Eq. (1) is Eq. (8). π = P solvent γ mix,solvent (1 x salt ) (8) Fig. 3. Activity coefficients for methanol + water + CaCl 2 (4 mol%) at kpa [17].

5 H. Takamatsu, S. Ohe / Fluid Phase Equilibria (2002) Since P solvent is determined from Eq. (6), substitution of Eq. (6) into Eq. (8) gives the relation π = P i γ i x ia γ mix,solvent(1 x salt ) (9) The relation between activity coefficient of conventionally defined and that given by Eq. (9) is γ i = γ i γ mix,solvent(1 x salt ) the activity coefficients of each solvent in binary solvents + salt system are shown in Fig. 3. (10) 5. Relation between S i0 and correlation error Solvation number in pure solvent is very important factor in this model. The solvation number was used for calculation of liquid effective mole fraction and activity coefficient of vapor pressure depression in mixed solvent. Therefore, the less accurate of solvation number, the less accurate of the prediction. Then, in order to determine the solvation number more accurately, the relation between the solvation number and correlation error was investigated in binary solvents + salt system. The first, the relation between the solvation number and average of absolute error in vapor phase was investigated. The change of error is shown in Fig. 4. As a result, minimum points of average of absolute error for vapor composition show linear relation between S 10 and S 20. The relation is expressed by following equation: S 10 = ks 20 + S 20,preferential (11) where k is a factor depends on system and S 20,preferential is preferential solvation number of component 2. Fig. 4. Error surface for methanol + water + CaCl 2 (4 mol%) at kpa [17].

6 706 H. Takamatsu, S. Ohe / Fluid Phase Equilibria (2002) Fig. 5. Relation between solvation number and average of absolute deviation in boiling point for methanol + water + CaCl 2 (4 mol%) at kpa [17]. Next, behavior of average of absolute error for boiling point or total pressure was checked on the relation. The result was shown in Fig. 5. Minimum point of average of absolute error for temperature or total pressure shows on Eq. (11). In this work, the solvation numbers are the points that show minimum point of average of absolute error in boiling point or total pressure on Eq. (11). Fig. 6 shows flow chart for determination of solvation number of each solvent in a mixture from observed data. Fig. 6. Flow sheet for determination of solvation number for each solvent in mixture.

7 H. Takamatsu, S. Ohe / Fluid Phase Equilibria (2002) Fig. 7. Flow sheet for determination of salt effect on vapor liquid equilibria. 6. Procedure of prediction The procedure for predicting the salt effect from the solvation number S i0 of pure solvent is described as follows. (a) Obtain solvation number S i0 determined from procedure shown in Fig. 6. (b) The x ia is calculated from Eq. (5) by using solvation number S i0. (c) Calculate activity coefficients: γ i for each component of solvent system by activity coefficient equation for example, Wilson equation with effective composition x ia. In this work, Wilson equation was used and Wilson coefficients was obtained from Ohe s vapor liquid equilibrium Data Book [18] and DECHEMA s vapor liquid equilibrium data collection [19,20]. (d) Estimate activity coefficients: γ mix,solvent, in Eq. (7), from γ i,solvent of each pure solvent for lowering of vapor pressure of solvents system according to salt concentration. The γ i,solvent is also determined using S i0 with the relation of Eq. (4). (e) Predict vapor phase composition and boiling point or total pressure by Eq. (9). Fig. 7 shows flow chart of procedure of prediction. 7. Result and discussion The correlated results for isobaric and isothermal data with determined solvation number are shown in Tables 1 and 2, respectively. The T x y curve and x y curve are shown in Figs As for isobaric data, 81 data set for binary solvents + salt systems and as for isothermal data, 16 data set were correlated with satisfactory accuracy. As for isobaric system, average error for vapor phase composition calculated was mole fraction and average error for boiling point calculated was 0.72 K. As isothermal system, average error for vapor

8 708 H. Takamatsu, S. Ohe / Fluid Phase Equilibria (2002) Table 1 Correlative error of isobaric binary solvents + salt systems Number System Solvation number a This work Reference C 1 C 2 y 1 av T av (K) 1 Methanol + water + CaCl 2 (16.7 wt.%) at kpa [23] 2 Methanol + water + CaCl 2 (2 mol%) at kpa [17] 3 Methanol + water + CaCl 2 (4 mol%) at kpa [17] 4 Methanol + water + CaCl 2 (10 mol%) at kpa [17] 5 Methanol + water + KCl (0.5 M) at kpa [24] 6 Methanol + water + KCl (1 M) at kpa [24] 7 Methanol + water + KCl (2 M) at kpa [24] 8 Methanol + water + LiCl (1 M) at kpa [25] 9 Methanol + water + LiCl (2 M) at kpa [25] 10 Methanol + water + LiCl (4 M) at kpa [25] 11 Methanol + water + NaBr (2 M) at kpa [25] 12 Methanol + water + NaF (0.25 M) at kpa [25] 13 Methanol + water + NaF (0.5 M) at kpa [25] 14 Methanol + water + NaF (1 M) at kpa [25] 15 Methanol + water + NaNO 3 (5 mol%) at kpa [26] 16 Methanol + water + NaNO 3 (7 mol%) at kpa [26] 17 Methanol + water + NaNO 3 (8 mol%) at kpa [26] 18 Ethanol + water + CaCl 2 (16.7 wt.%) at kpa [23] 19 Ethanol + water + CaNO 3 (1.038 M) at 50.7 kpa [27] 20 Ethanol + water + CaNO 3 (2.049 M) at 50.7 kpa [27] 21 Ethanol + water + CH 3 COOK (2.5 mol%) at kpa [28] 22 Ethanol + water + CH 3 COOK (5 mol%) at kpa [28] 23 Ethanol + water + CH 3 COOK (6.6 mol%) at kpa [28] 24 Ethanol + water + CH 3 COOK (8.5 mol%) at kpa [28] 25 Ethanol + water + NH 4 Cl (6 mol%) at kpa [29] 26 Ethanol + water + NH 4 Cl (8 mol%) at kpa [29] 27 2-Propanol + water + CaCl 2 (0.4 M) at kpa [30] 28 2-Propanol + water + CaCl 2 (0.8 M) at kpa [30] 29 2-Propanol + water + CaCl 2 (1.2 M) at kpa [30] 30 2-Propanol + water + CaCl 2 (2.2 wt.%) at kpa [31] 31 2-Propanol + water + CaCl 2 (4.3 wt.%) at kpa [31] 32 2-Propanol + water + CaNO 3 (1.038 M) at 50.7 kpa [27] 33 2-Propanol + water + CaNO 3 (2.049 M) at 50.7 kpa [27] 34 2-Propanol + water + NaCl (5 wt.%) at kpa [32] 35 Methanol + ethanol + CaCl 2 (16.7 wt.%) at kpa [31] 36 Methanol + ethanol + CaCl 2 (16.7 wt.%) at kpa [33] 37 Methanol + ethanol + CaCl 2 (23.1 wt.%) at kpa [33] 38 2-Propanol + 1-propanol + CaCl 2 (10 wt.%) at kpa [23] 39 2-Propanol + 1-propanol + CaCl 2 (13 wt.%) at kpa [23] 40 2-Propanol + 1-propanol + CaCl 2 (16.7 wt.%) at kpa [23] 41 Acetone + methanol + CaCl 2 (5 wt.%) at kpa [34] 42 Acetone + methanol + CaCl 2 (10 wt.%) at kpa [34] 43 Acetone + methanol + CaCl 2 (20 wt.% at kpa [34] 44 Acetone + methanol + KSCN (1 mol%) at kpa [35] 45 Acetone + methanol + KSCN (2 mol%) at kpa [35] 46 Acetone + methanol + KSCN (3 mol%) at kpa [35]

9 H. Takamatsu, S. Ohe / Fluid Phase Equilibria (2002) Table 1 (Continued ) Number System Solvation number a This work Reference C 1 C 2 y 1 av T av (K) 47 Acetone + methanol + KSCN (4 mol%) at kpa [35] 48 Acetone + methanol + KSCN (5 mol%) at kpa [35] 49 Acetonev + methanol + LiCl (0.5 mol%) at kpa [36] 50 Acetone + methanol + LiCl (2 mol%) at kpa [36] 51 Acetone + methanol + LiCl (12 mol%) at kpa [36] 52 Acetone + methanol + LiCl (0.5 mol%) at kpa [21] 53 Acetone + methanol + LiCl (0.75 mol%) at kpa [21] 54 Acetone + methanol + LiCl (1 mol%) at kpa [21] 55 Acetone + methanol + LiCl (3 mol%) at kpa [21] 56 Acetone + methanol + LiCl (5 mol%) at kpa [21] 57 Acetone + methanol + NaI (1 mol%) at kpa [37] 58 Acetone + methanol + NaI (1.5 mol%) at kpa [37] 59 Acetone + methanol + NaI (2 mol%) at kpa [37] 60 Acetone + methanol + NaI (3 mol%) at kpa [37] 61 Acetone + methanol + NaI (4 mol%) at kpa [37] 62 Acetone + methanol + NaI (5 mol%) at kpa [37] 63 Acetone + methanol + NaI (6 mol%) at kpa [37] 64 Acetone + methanol + NaI (7 mol%) at kpa [37] 65 Acetone + methanol + NaI (8 mol%) at kpa [37] 66 Acetone + methanol + ZnCl 2 (1.082 M) at kpa [38] 67 Acetone + methanol + ZnCl 2 (1.502 M) at kpa [38] 68 Acetone + methanol + ZnCl 2 (1.751 M) at kpa [38] 69 Acetone + water + KCl (1 mol%) at kpa [39] 70 Acetone + water + KCl (2.5 mol%) at kpa [39] 71 Methanol + ethyl acetate + CaCl 2 (5 wt.%) at kpa [40] 72 Methanol + ethyl acetate + CaCl 2 (10 wt.%) at kpa [40] 73 Methanol + ethyl acetate + CaCl 2 (20 wt.%) at kpa [40] 74 Methanol + THF + CuCl 2 (1 mol%) at kpa [22] 75 Methanol + THF + CuCl 2 (2 mol%) at kpa [22] 76 Methanol + THF + CuCl 2 (3 mol%) at kpa [22] 77 Methanol + THF + CuCl 2 (4 mol%) at kpa [22] 78 Methanol + THF + LiCl (1 mol%) at kpa [22] 79 Methanol + THF + LiCl (2 mol%) at kpa [22] 80 Methanol + THF + LiCl (3 mol%) at kpa [22] 81 Methanol + THF + LiCl (4 mol%) at kpa [22] Average a S 10 : C 1 (1 x 3 )/x 3 ; S 20 : C 2 (1 x 3 )/x 3. phase composition calculated was mole fraction and average error for total pressure calculated was 0.14 kpa. As shown in Tables 1 and 2, in most of the systems containing non-polar solvent, preferential solvation was observed. For example, acetone + methanol + CaCl 2 (Nos. 42, 43) performed preferential solvation. To examine the applicability of modified model for prediction for multi solvents system with a salt, the salt effect of the methanol + ethanol + water + CaCl 2 (16.7 wt.%) system at kpa with 38

10 710 H. Takamatsu, S. Ohe / Fluid Phase Equilibria (2002) Table 2 Correlative error of isothermal binary solvents + salt systems Number System Solvation number a This work Reference C 1 C 2 y 1 av TP av (kpa) 1 Ethanol + water + CaCl 2 (5 wt.%) at K [41] 2 Ethanol + water + CaCl 2 (10 wt.%) at K [41] 3 Ethanol + water + CaCl 2 (15 wt.%) at K [41] 4 Ethanol + water + LiCl (4 M) at K [42] 5 1-Propanol + water + CaCl 2 (5 wt.%) at K [43] 6 1-Propanol + water + CaCl 2 (7 wt.%) at K [43] 7 1-Propanol + water + CaCl 2 (10 wt.%) at K [43] 8 Methanol + ethanol + CaCl 2 (10 wt.%) at K [41] 9 Methanol + ethanol + CaCl 2 (15 wt.%) at K [41] 10 Methanol + ethanol + CaCl 2 (5 wt.%) at K [41] 11 Methanol + 1-propanol + CaCl 2 (10 wt.%) at K [41] 12 Methanol + 1-propanol + CaCl 2 (15 wt.%) at K [41] 13 Methanol + 1-propanol + CaCl 2 (5 wt.%) at K [41] 14 2-Propanol + 1-propanol + CaCl 2 (5 wt.%) at K [44] 15 2-Propanol + 1-propanol + CaCl 2 (10 wt.%) at K [44] 16 2-Propanol + 1-propanol + CaCl 2 (15 wt.%) at K [44] Average a S 10 : C 1 (1 x 3 )/x 3 ; S 20 : C 2 (1 x 3 )/x 3. Fig. 8. The x y curve for methanol + water + CaCl 2 (10 mol%) at kpa [17].

11 H. Takamatsu, S. Ohe / Fluid Phase Equilibria (2002) Fig. 9. The T x y curve for methanol + water + CaCl 2 (10 mol%) at kpa [17]. data sets was estimated by solvation number in pure solvent + salt system determined from binary solvent + salt system. Systems used for determination of solvation number of each solvent in ternary system are No. 1 of Table 1 for methanol and water, and No. 35 for ethanol, respectively. Values of C for prediction are methanol (0.5407), ethanol (0.2607) and water (0.7002), respectively. The results are shown in Figs. 14 and 15. Fig. 14 shows the predicted result of bubble point of the system with average absolute deviation 0.85 K. Fig. 15 shows the predicted result of vapor composition of the system in mole fraction with average absolute deviation for methanol and for ethanol, respectively. Fig. 10. The x y curve for acetone + methanol + LiCl (5 mol%) at kpa [21].

12 712 H. Takamatsu, S. Ohe / Fluid Phase Equilibria (2002) Fig. 11. The T x y curve for acetone + methanol + LiCl (5 mol%) at kpa [21]. Fig. 12. The x y curve for methanol + THF + LiCl (1 mol%) at kpa [22]. Fig. 13. The T x y curve for methanol + THF + LiCl (1 mol%) at kpa [22].

13 H. Takamatsu, S. Ohe / Fluid Phase Equilibria (2002) Fig. 14. Comparison between observed data and predicted data (bubbling point) for methanol + ethanol + water + CaCl 2 at kpa [45]. Fig. 15. Predicted vapor compositions for methanol + ethanol + water + CaCl 2 (16.7 wt.%) at kpa [45]; ( ), liquid composition; ( ), predicted vapor composition; ( ), observed vapor composition. 8. Conclusion The modified model of Ohe et al. has been proposed for representing salt effect on vapor liquid equilibria. In this work, a relation between solvation number in pure solvent + salt system and correlation

14 714 H. Takamatsu, S. Ohe / Fluid Phase Equilibria (2002) error were examined and from this relation, solvation number was determined. It was satisfactory to represent salt effect on vapor liquid equilibria by using the modified model. And ternary solvents + salt system was predicted by using solvation number determined from binary solvents + salt system. Good accuracy was shown in the system. The modified model based on solvation between each solvent and salt to predict and to analyze salt effect on vapor liquid equilibria was proposed and successfully applied to the binary and ternary solvents systems with salt. List of symbols a solvent activity for lowering of vapor pressure of pure solvent system c i constant for solvation number k coefficient in Eq. (11) n salt mole number of salt n solvent mole number of solvent P total pressure of system (kpa) P solvent total pressure of system as solvent system (kpa) P i vapor pressure of pure component i (kpa) S 0 solvation number between solvent and salt S i0 solvation number of salt with pure component of mixed solvent system x i mole fraction of ith solvent existing salt x i mole fraction of ith solvent at salt free basis x ia effective mole fraction of ith solvent at salt free basis x salt mole fraction of salt mole fraction of solvent x solvent Greek symbols γ i activity coefficient of conventionally defined γ i activity coefficient for effective mole fraction of ith solvent γ i,solvent activity coefficient for lowering of vapor pressure of ith solvent activity coefficient for lowering of vapor pressure of mixed solvent system γ mix,solvent Subscript i ith solvent References [1] A.I. Johnson, W.F. Furter, Can. J. Chem. Eng. 38 (1960) [2] T.C. Tan, Chem. Eng. Res. Des. 65 (1987) [3] C.-C. Chen, H.I. Britt, J.F. Boston, L.B. Evans, AIChE J. 28 (1982) [4] C.-C. Chen, L.B. Evans, AIChE J. 32 (1986) [5] B. Mock, L.B. Evans, C.-C. Chen, AIChE J. 32 (1986) [6] B. Sander, A. Fredenslund, P. Rasmussen, Chem. Eng. Sci. 41 (1986) [7] E.A. Macedo, P. Skovborg, P. Rasmussen, Chem. Eng. Sci. 45 (1990) [8] J. Li, H. Polka, J. Gmehling, Fluid Phase Equilib. 94 (1994) [9] H. Polka, J. Li, J. Gmehling, Fluid Phase Equilib. 94 (1994)

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