Fluid Phase Equilibria 194–197 (2002) 701–715

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 162-8601, 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. © 2002 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 andthat some kinds of salt are significantly effective to diminish the azeotrope. Therefore, investigators ofboth of academics and industries have studied salt effect on vapor–liquid equlibria. The first method forprediction 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 andprediction. 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 coefficientsmodel. 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.: +81-332604282; fax: +81-332673704.
E-mail address: ohe@ms.kagu.sut.ac.jp (S. Ohe).
0378-3812/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved.
PII: S 0 3 7 8 - 3 8 1 2 ( 0 1 ) 0 0 7 8 4 - 1

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H. Takamatsu, S. Ohe / Fluid Phase Equilibria 194–197 (2002) 701–715

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 toatomic group contribution method had been presented. However, most of the mixtures of the salt effectsystem are composed of non-electrolytes and electrolytes component. Thus, a model, which is capableof 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 becaused by a formation of solvates between solvents and salt. The solvates are also thought to take apart for vapor pressure lowering of the system. A first model in which a salt forms preferential solvatewith 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 liquidcomposition 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 themodel has been done to overcome this drawback. The model employed a solvation between salt of eachof 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 ofdegree 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 asolvent. 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 = Psolvent × asolvent .

(1)

Since the activity is a product of activity coefficient and mole fraction of solvents: asolvent = γsolvent ×
xsolvent , then the activity coefficient for the pressure is determined from Eq. (1) as follows:πγsolvent =.
(2)(Psolvent × xsolvent )The model assumed salt showed complete disassociation. It is assumed that lowering of vapor pressureof pure solvent system is caused by solvated molecule, which does not contribute to vaporization. The
activity of the solvent becomes(nsolvent − nsalt )S0
asolvent =.
(3)(nsolvent − nsalt S0 ) + nsalt
Dividing both of the denominator and numerator by nsolvent + nsalt will give
(xsolvent − xsalt )S0
asolvent =,(1 − xsalt )S0
where xsolvent = 1 − xsalt .

(4)

H. Takamatsu, S. Ohe / Fluid Phase Equilibria 194–197 (2002) 701–715

703

Fig. 1. The x–y curve for methanol + water + CaCl2 (4 mol%) at 101.3 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, theactual 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 xia
for the ith solvent is given by Eq. (5) at salt free basis. Since, thesum of solvent mole fraction is equal to 1 − xsalt , and the solvation number for the ith solvent is calculated
as Si0 xi , and Eq. (5) is obtained.
xia=

xi − (Si0 xi xsalt )
1 − xsalt − Si0 xi xsalt

Fig. 2. Solvation numbers for methanol + water + CaCl2 (4 mol%) at 101.3 kPa [17].

(5)

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H. Takamatsu, S. Ohe / Fluid Phase Equilibria 194–197 (2002) 701–715

The relation of solvation number Si between that of a singe solvent Si 0 and composition of it xi wasrecognized 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 xia
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 Si and the composition of solvent xi has linearity. The relation is caused by amolecular numbers of solvents per salt molecule changing according to stochiometry by changing liquidcomposition. 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 Si depends upon solvent concentration at the condition of capable of making solvates of salt being constant at a given salt concentrationin mole fraction, since the number of solvent molecule which can be solvated, increases by the number ofitself.
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.

Psolvent =Pi γi xia(6)
The activity coefficient for vapor pressure lowering is assumed to be average of activity coefficient ofeach solvent with its mole fraction. Eq. (7) may be derived from the above assumption.
γmix,solvent =γi,solvent xi
(7)
Therefore, the basic equation to calculate salt effect on vapor–liquid equilibrium corresponds to Eq. (1)is Eq. (8).
π = Psolvent γmix,solvent (1 − xsalt )Fig. 3. Activity coefficients for methanol + water + CaCl2 (4 mol%) at 101.3 kPa [17].

(8)H. Takamatsu, S. Ohe / Fluid Phase Equilibria 194–197 (2002) 701–715

Since Psolvent is determined from Eq. (6), substitution of Eq. (6) into Eq. (8) gives the relationγmix,solvent (1 − xsalt )π=
Pi γi xia

705

(9)

The relation between activity coefficient of conventionally defined and that given by Eq. (9) is
γi = γi γmix,solvent (1 − xsalt )(10)

the activity coefficients of each solvent in binary solvents + salt system are shown in Fig. 3.
5. Relation between Sii 0 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 ofabsolute error for vapor composition show linear relation between S10 and S20 . The relation is expressedby following equation:
S10 = kS20 + S20,preferential(11)

where k is a factor depends on system and S20,preferential is preferential solvation number of component 2.

Fig. 4. Error surface for methanol + water + CaCl2 (4 mol%) at 101.3 kPa [17].

706

H. Takamatsu, S. Ohe / Fluid Phase Equilibria 194–197 (2002) 701–715

Fig. 5. Relation between solvation number and average of absolute deviation in boiling point for methanol + water + CaCl2(4 mol%) at 101.3 kPa [17].

Next, behavior of average of absolute error for boiling point or total pressure was checked on therelation. 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.

H. Takamatsu, S. Ohe / Fluid Phase Equilibria 194–197 (2002) 701–715

707

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 Si 0 of pure solvent is describedas follows.
(a) Obtain solvation number Si 0 determined from procedure shown in Fig. 6.
(b) The xia
is calculated from Eq. (5) by using solvation number Si 0 .
(c) Calculate activity coefficients: γi for each component of solvent system by activity coefficient equation for example, Wilson equation with effective composition xia. In this work, Wilson equation wasused and Wilson coefficients was obtained from Ohe’s vapor–liquid equilibrium Data Book [18] andDECHEMA’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 loweringof vapor pressure of solvents system according to salt concentration. The γ i ,solvent is also determinedusing Si 0 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 shownin Tables 1 and 2, respectively. The T–x–y curve and x–y curve are shown in Figs. 8–13. As for isobaric
data, 81 data set for binary solvents + salt systems and as for isothermal data, 16 data set were correlatedwith satisfactory accuracy.
As for isobaric system, average error for vapor phase composition calculated was 0.018 mole fraction
and average error for boiling point calculated was 0.72 K. As isothermal system, average error for vapor

708

H. Takamatsu, S. Ohe / Fluid Phase Equilibria 194–197 (2002) 701–715

Table 1
Correlative error of isobaric binary solvents + salt systems
Number

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
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46

SystemMethanol + water + CaCl2 (16.7 wt.%) at 101.3 kPa
Methanol + water + CaCl2 (2 mol%) at 101.3 kPa
Methanol + water + CaCl2 (4 mol%) at 101.3 kPa
Methanol + water + CaCl2 (10 mol%) at 101.3 kPa
Methanol + water + KCl (0.5 M) at 101.3 kPa
Methanol + water + KCl (1 M) at 101.3 kPa
Methanol + water + KCl (2 M) at 101.3 kPa
Methanol + water + LiCl (1 M) at 101.3 kPa
Methanol + water + LiCl (2 M) at 101.3 kPa
Methanol + water + LiCl (4 M) at 101.3 kPa
Methanol + water + NaBr (2 M) at 101.3 kPa
Methanol + water + NaF (0.25 M) at 101.3 kPa
Methanol + water + NaF (0.5 M) at 101.3 kPa
Methanol + water + NaF (1 M) at 101.3 kPa
Methanol + water + NaNO3 (5 mol%) at 101.3 kPa
Methanol + water + NaNO3 (7 mol%) at 101.3 kPa
Methanol + water + NaNO3 (8 mol%) at 101.3 kPa
Ethanol + water + CaCl2 (16.7 wt.%) at 101.3 kPa
Ethanol + water + CaNO3 (1.038 M) at 50.7 kPa
Ethanol + water + CaNO3 (2.049 M) at 50.7 kPa
Ethanol + water + CH3 COOK (2.5 mol%) at 101.3 kPa
Ethanol + water + CH3 COOK (5 mol%) at 101.3 kPa
Ethanol + water + CH3 COOK (6.6 mol%) at 101.3 kPa
Ethanol + water + CH3 COOK (8.5 mol%) at 101.3 kPa
Ethanol + water + NH4 Cl (6 mol%) at 101.3 kPa
Ethanol + water + NH4 Cl (8 mol%) at 101.3 kPa
2-Propanol + water + CaCl2 (0.4 M) at 101.3 kPa
2-Propanol + water + CaCl2 (0.8 M) at 101.3 kPa
2-Propanol + water + CaCl2 (1.2 M) at 101.3 kPa
2-Propanol + water + CaCl2 (2.2 wt.%) at 101.3 kPa
2-Propanol + water + CaCl2 (4.3 wt.%) at 101.3 kPa
2-Propanol + water + CaNO3 (1.038 M) at 50.7 kPa
2-Propanol + water + CaNO3 (2.049 M) at 50.7 kPa
2-Propanol + water + NaCl (5 wt.%) at 101.3 kPa
Methanol + ethanol + CaCl2 (16.7 wt.%) at 101.3 kPa
Methanol + ethanol + CaCl2 (16.7 wt.%) at 101.3 kPa
Methanol + ethanol + CaCl2 (23.1 wt.%) at 101.3 kPa
2-Propanol + 1-propanol + CaCl2 (10 wt.%) at 101.3 kPa
2-Propanol + 1-propanol + CaCl2 (13 wt.%) at 101.3 kPa
2-Propanol + 1-propanol + CaCl2 (16.7 wt.%) at 101.3 kPa
Acetone + methanol + CaCl2 (5 wt.%) at 101.3 kPa
Acetone + methanol + CaCl2 (10 wt.%) at 101.3 kPa
Acetone + methanol + CaCl2 (20 wt.% at 101.3 kPa
Acetone + methanol + KSCN (1 mol%) at 101.3 kPa
Acetone + methanol + KSCN (2 mol%) at 101.3 kPa
Acetone + methanol + KSCN (3 mol%) at 101.3 kPa

Solvation numbera

This work

C1

C2| y1 |av| T |av(K)

0.54070.57810.62840.67910.31970.00000.00000.00000.00000.00000.05150.25510.00000.00000.00000.5056
0.54190.03040.27840.14470.29910.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.55120.5201
0.63100.19500.00000.00000.21540.00000.00000.22080.16970.24190.70020.64760.77030.87860.43460.18530.31760.09050.26110.26790.21940.28010.08370.14070.29360.74990.8037
0.66150.50130.5964
0.49370.42740.56140.64330.50990.63930.51620.70470.81210.34740.52430.55590.75830.21430.26070.31230.41280.27380.07510.08670.39790.30850.43540.23150.21690.3055

0.009
0.008
0.006
0.015
0.013
0.020
0.026
0.025
0.019
0.029
0.019
0.027
0.016
0.013
0.026
0.010
0.016
0.012
0.024
0.023
0.008
0.018
0.015
0.015
0.014
0.017
0.014
0.013
0.005
0.008
0.009
0.024
0.046
0.015
0.016
0.006
0.010
0.019
0.025
0.016
0.009
0.009
0.018
0.012
0.016
0.019

0.46
0.70
0.56
1.35
0.34
0.48
0.89
1.46
0.80
4.49
0.71
0.72
0.59
0.60
0.66
0.29
0.28
0.70
0.31
0.48
0.34
0.44
1.00
1.53
0.31
1.47
0.44
1.11
2.36
0.23
0.44
0.54
2.15
1.08
0.27
0.30
0.31
0.41
1.28
0.40
0.28
0.28
1.37
0.39
0.29
0.22

Reference

[23]
[17]
[17]
[17]
[24]
[24]
[24]
[25]
[25]
[25]
[25]
[25]
[25]
[25]
[26]
[26]
[26]
[23]
[27]
[27]
[28]
[28]
[28]
[28]
[29]
[29]
[30]
[30]
[30]
[31]
[31]
[27]
[27]
[32]
[31]
[33]
[33]
[23]
[23]
[23]
[34]
[34]
[34]
[35]
[35]
[35]

H. Takamatsu, S. Ohe / Fluid Phase Equilibria 194–197 (2002) 701–715

709

Table 1 (Continued )Number

SystemAcetone + methanol + KSCN (4 mol%) at 101.3 kPa
Acetone + methanol + KSCN (5 mol%) at 101.3 kPa
Acetonev + methanol + LiCl (0.5 mol%) at 101.3 kPa
Acetone + methanol + LiCl (2 mol%) at 101.3 kPa
Acetone + methanol + LiCl (12 mol%) at 101.3 kPa
Acetone + methanol + LiCl (0.5 mol%) at 101.3 kPa
Acetone + methanol + LiCl (0.75 mol%) at 101.3 kPa
Acetone + methanol + LiCl (1 mol%) at 101.3 kPa
Acetone + methanol + LiCl (3 mol%) at 101.3 kPa
Acetone + methanol + LiCl (5 mol%) at 101.3 kPa
Acetone + methanol + NaI (1 mol%) at 101.3 kPa
Acetone + methanol + NaI (1.5 mol%) at 101.3 kPa
Acetone + methanol + NaI (2 mol%) at 101.3 kPa
Acetone + methanol + NaI (3 mol%) at 101.3 kPa
Acetone + methanol + NaI (4 mol%) at 101.3 kPa
Acetone + methanol + NaI (5 mol%) at 101.3 kPa
Acetone + methanol + NaI (6 mol%) at 101.3 kPa
Acetone + methanol + NaI (7 mol%) at 101.3 kPa
Acetone + methanol + NaI (8 mol%) at 101.3 kPa
Acetone + methanol + ZnCl2 (1.082 M) at 101.3 kPa
Acetone + methanol + ZnCl2 (1.502 M) at 101.3 kPa
Acetone + methanol + ZnCl2 (1.751 M) at 101.3 kPa
Acetone + water + KCl (1 mol%) at 101.3 kPa
Acetone + water + KCl (2.5 mol%) at 101.3 kPa
Methanol + ethyl acetate + CaCl2 (5 wt.%) at 101.3 kPa
Methanol + ethyl acetate + CaCl2 (10 wt.%) at 101.3 kPa
Methanol + ethyl acetate + CaCl2 (20 wt.%) at 101.3 kPa
Methanol + THF + CuCl2 (1 mol%) at 101.3 kPa
Methanol + THF + CuCl2 (2 mol%) at 101.3 kPa
Methanol + THF + CuCl2 (3 mol%) at 101.3 kPa
Methanol + THF + CuCl2 (4 mol%) at 101.3 kPa
Methanol + THF + LiCl (1 mol%) at 101.3 kPa
Methanol + THF + LiCl (2 mol%) at 101.3 kPa
Methanol + THF + LiCl (3 mol%) at 101.3 kPa
Methanol + THF + LiCl (4 mol%) at 101.3 kPa

47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
Averagea

Solvation numbera

This work

C1

C2| y1 |av| T |av(K)

0.26840.31790.00000.00000.00000.20860.01710.05990.00000.00000.50310.40990.35710.36990.37370.36100.35180.35310.3806
0.16500.13740.03070.00000.00000.52240.51340.65190.81110.64810.50380.39140.81110.6516
0.51100.39140.34380.40020.12340.20230.81480.27150.13560.20690.27230.39830.5721
0.53190.51480.56690.58980.5876
0.58280.59570.61930.41870.42090.42540.6496
0.6816
0.29490.00000.00000.78310.57580.37200.18000.78310.5766
0.37310.1800

0.023
0.026
0.021
0.021
0.034
0.012
0.012
0.011
0.006
0.009
0.016
0.017
0.020
0.024
0.026
0.034
0.033
0.037
0.041
0.028
0.020
0.029
0.020
0.023
0.005
0.012
0.022
0.014
0.014
0.018
0.021
0.014
0.014
0.018
0.021

0.21
0.23
0.38
0.42
6.49
0.48
0.42
0.36
0.31
0.57
0.23
0.21
0.17
0.17
0.15
0.35
0.51
0.55
0.69
0.21
0.21
0.28
0.69
2.60
0.23
0.65
2.36
0.14
0.21
0.27
0.35
0.14
0.20
0.26
0.35

0.018

0.72

Reference

[35]
[35]
[36]
[36]
[36]
[21]
[21]
[21]
[21]
[21]
[37]
[37]
[37]
[37]
[37]
[37]
[37]
[37]
[37]
[38]
[38]
[38]
[39]
[39]
[40]
[40]
[40]
[22]
[22]
[22]
[22]
[22]
[22]
[22]
[22]

S10 : C1 (1 − x3 )/x3 ; S20 : C2 (1 − x3 )/x3 .

phase composition calculated was 0.009 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 + CaCl2 (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 + CaCl2 (16.7 wt.%) system at 101.3 kPa with 38

710

H. Takamatsu, S. Ohe / Fluid Phase Equilibria 194–197 (2002) 701–715

Table 2
Correlative error of isothermal binary solvents + salt systems
Number

SystemEthanol + water + CaCl2 (5 wt.%) at 298.15 K
Ethanol + water + CaCl2 (10 wt.%) at 298.15 K
Ethanol + water + CaCl2 (15 wt.%) at 298.15 K
Ethanol + water + LiCl (4 M) at 298.15 K
1-Propanol + water + CaCl2 (5 wt.%) at 298.15 K
1-Propanol + water + CaCl2 (7 wt.%) at 298.15 K
1-Propanol + water + CaCl2 (10 wt.%) at 298.15 K
Methanol + ethanol + CaCl2 (10 wt.%) at 298.15 K
Methanol + ethanol + CaCl2 (15 wt.%) at 298.15 K
Methanol + ethanol + CaCl2 (5 wt.%) at 298.15 K
Methanol + 1-propanol + CaCl2 (10 wt.%) at 298.15 K
Methanol + 1-propanol + CaCl2 (15 wt.%) at 298.15 K
Methanol + 1-propanol + CaCl2 (5 wt.%) at 298.15 K
2-Propanol + 1-propanol + CaCl2 (5 wt.%) at 298.15 K
2-Propanol + 1-propanol + CaCl2 (10 wt.%) at 298.15 K
2-Propanol + 1-propanol + CaCl2 (15 wt.%) at 298.15 K

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Averagea

Solvation numbera

This work

C1

C2| y1 |av| TP|av(kPa)

0.46400.61680.11320.69660.00000.00000.00000.18170.46370.12410.63640.67190.65930.00000.00000.00000.68530.85420.77310.89530.56290.75860.84540.00000.27270.00000.49940.48270.59380.12130.20580.2716

0.006
0.006
0.006
0.005
0.028
0.014
0.014
0.007
0.004
0.003
0.012
0.010
0.012
0.003
0.002
0.002

0.03
0.15
0.16
1.10
0.36
0.16
0.11
0.07
0.11
0.29
0.09
0.04
0.11
0.12
0.12
0.11

0.009

0.14

S10 : C1 (1 − x3 )/x3 ; S20 : C2 (1 − x3 )/x3 .

Fig. 8. The x–y curve for methanol + water + CaCl2 (10 mol%) at 101.3 kPa [17].

Reference

[41]
[41]
[41]
[42]
[43]
[43]
[43]
[41]
[41]
[41]
[41]
[41]
[41]
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[44]
[44]

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711

Fig. 9. The T–x–y curve for methanol + water + CaCl2 (10 mol%) at 101.3 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 systemwith 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 0.021 for methanol and 0.020 for ethanol,
respectively.

Fig. 10. The x–y curve for acetone + methanol + LiCl (5 mol%) at 101.3 kPa [21].

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Fig. 11. The T–x–y curve for acetone + methanol + LiCl (5 mol%) at 101.3 kPa [21].

Fig. 12. The x–y curve for methanol + THF + LiCl (1 mol%) at 101.3 kPa [22].

Fig. 13. The T–x–y curve for methanol + THF + LiCl (1 mol%) at 101.3 kPa [22].

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713

Fig. 14. Comparison between observed data and predicted data (bubbling point) for methanol + ethanol + water + CaCl2 at
101.3 kPa [45].

Fig. 15. Predicted vapor compositions for methanol + ethanol + water + CaCl2 (16.7 wt.%) at 101.3 kPa [45]; (䊊), liquidcomposition; (䊏), predicted vapor composition; (䊐), 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

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error were examined and from this relation, solvation number was determined. It was satisfactory torepresent 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
asolvent
activity for lowering of vapor pressure of pure solvent systemci
constant for solvation numberkcoefficient in Eq. (11)nsaltmole number of salt
nsolvent
mole number of solventP
total pressure of system (kPa)
Psolvent
total pressure of system as solvent system (kPa)Pi
vapor pressure of pure component i (kPa)S0solvation number between solvent and salt
Si 0solvation number of salt with pure component of mixed solvent systemximole fraction of ith solvent existing saltxi
mole fraction of ith solvent at salt free basisxiaeffective mole fraction of ith solvent at salt free basis
xsalt
mole fraction of salt
xsolvent
mole fraction of solvent
Greek symbols
γi
activity coefficient of conventionally defined
γiactivity coefficient for effective mole fraction of ith solvent
γ i ,solvent
activity coefficient for lowering of vapor pressure of ith solvent
γ mix,solvent activity coefficient for lowering of vapor pressure of mixed solvent system
Subscriptiith solvent

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