Fluid Phase Equilibria 144 Ž1998. 119–129

Prediction of salt effect on vapor–liquid equilibria
Shuzo Ohe )Department of Chemical Engineering, Science UniÕersity of Tokyo, Shinjuku-ku, Tokyo 162, Japan
Received 13 January 1997; accepted 11 August 1997

Abstract
In this paper, a newly proposed model based on solvation between pure solvent and salt for prediction of salt
effect on vapor–liquid equilibria is presented by using only the vapor pressure depression data of puresolventq salt systems that compose the mixed solvent with salt system. The proposed model predictsthermodynamically the salt effect by solvation number between each pure solvent and salt determined from thevapor pressure depression data with an assumption of the vapor pressure depression caused by the solvation.
Three points differ from the originally proposed model by the author wS. Ohe, 1976. Advances in Chemistry
Series, No. 155, American Chemical Society.x. First, it is assumed that each solvent component solvates withsalt instead of the preferential solvation of the original model. It, however, is superficial phenomenon, since thedifference between the solvation numbers is thought to be equivalent to it. Second, it is also assumed that thevapor pressure depression is caused by the solvation. Third, the method predicts the effect from VLE with nosalt and vapor pressure depression data of pure solvent with salt. The salt effect on vapor–liquid equilibria wassatisfactorily predicted for a methanolq ethanolq water q CaCl 2 Ž16.7 wt.%. system from the solvation
numbers determined from vapor pressure depression data of methanolq CaCl 2 , ethanolq CaCl 2 , and water qCaCl 2 system. q 1998 Elsevier Science B.V.
Keywords: Vapor–liquid equilibria; Salt effect; Preferential solvation; Depression of vapor pressure

1. Introduction
A model in which a salt forms preferential solvate with one of the solvents in a binary solvent
system was already proposed to predict salt effect on vapor–liquid equilibrium w1x. For 386
two-solventq 47 single-salt systems, the model was successfully examined w2x. The following two)

Corresponding author.

0378-3812r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved.
PII S 0 3 7 8 - 3 8 1 2 Ž 9 7 . 0 0 2 5 0 - 1

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relations were found: Ž1. preferential solvation number at constant salt molar concentration shows
linear relation with solvated solvent molar concentration; Ž 2. the solvation number extrapolated to theconcentration at 100% of solvated solvent decreases linearly, as the salt concentration increases. The
relations by the model were satisfactory observed over the entire range of solvent concentrations,giving a total mean of the absolute deviation in the vapor phase mole fraction of 0.012.
However, the model should be modified as described below. It is assumed that the salt dissolved in
the solvent mixture solvates with each solvent component. As a result of it, ‘a preferential solvate’ isobserved. The numbers of preferential solvate corresponds to the difference of solvation numbers of
the salt for each solvent molecule.

2. Depression of vapor pressure
Vapor pressure at a given temperature of a solvent is depressed by adding non-volatile substancesthat is salt with the degree of its amount. When the behavior of a single solvent and a salt system isassumed to be non-ideal and complete dissociation of salt, the pressure of the system is given by theEq. Ž1.:

p s Psolvent P asolvent

Ž1.

Since the activity is a product of mean activity coefficient and mole fraction of solvent:"asolvent s gsolvent
P Xsolvent , then the activity coefficient for the pressure is determined from Eq. Ž1.:"gsolvents pr Ž Psolvent P Xsolvent .

Ž2.

It is assumed that depression of vapor pressure of pure solvent system is caused by solvatedmolecule which does not contribute to vaporization. The activity of the solvent becomes:asolvent s Ž n solvent y n salt P So . r  Ž n solvent y n salt P So . q n salt 4Fig. 1. Mean activity coefficients for vapor pressure depression.

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Table 1
Correlation equation parameters for mean activity coefficient of solvent in vapor pressure depression at 101.3 kPaNo.

Solvents

Salts

Parameters of correlation equationa
abc1Ethanol

CaCl 2y5.011

y0.2401.000

2345
6MethanolMethanolMethyl acetate
Propanol
Water

CaCl 2NaSCN
NaSCN
CaCl 2
CaCl 2

4.627
y14.677
y0.1744.888
y16.801

y2.005y0.2980.544
y1.030y3.081

1.000
1.000
1.000
1.000
1.000

a "
gsolvents ax 2 q bx q c, where

AuthorŽs.
Nishi w4x
Ohe et al. w5x
Ohe et al. w5x
Illiuta et al. w6x
Illiuta et al. w6x
Illiuta et al. w6x
Patill et al. w3xx is mole fraction of salt.

Dividing both of the denominator and numerator by n solvent q n salt will give:
asolvent s Ž Xsolvent y Xsalt P So . r Ž 1 y Xsalt P So .

Ž3.

where Xsolvent s 1 y Xsalt .Therefore solvation number So is given as:So s Ž Xsolvent y asolvent . r  Ž yasolvent . P Xsalt 4Ž4.

Mean activity coefficient may be thought to be the function of salt concentration. From observed
data of depression of vapor pressure w3–5x, the relations between mean activity coefficient and salt
concentration at atmospheric pressure are determined by Eq. Ž 2. for two alcohols and water withcalcium chloride as shown in Fig. 1. Table 1 shows correlation equation parameters for puresolventq salt system with the other solvents and salt, over the range from 0 to 0.12 mole fraction ofsalt at isobaric 101.3 kPa, accompanied by the boiling point raising. The solvation numbers between
pure solvent and salt are calculated by Eq. Ž4. for above mentioned system as shown in Fig. 2.

Fig. 2. Solvation number between pure solvent and salt.

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3. Effective composition of solvent system containing salt
As the concentration of solvent is assumed to be decreased by the number of solvated molecules,
the actual solvent composition participating in the vapor–liquid equilibrium is changed. Assumingthat a salt forms the solvates with each component and that the solvated molecules do not contributeto vapor–liquid equilibrium, since the sum of solvent mole fraction is equal to 1 y Xsalt , and thesolvation number for ith solvent is calculated as Si o P X i , the effective mole fraction X i a for thesolvent component is given by:
X i a s Ž X i y Si o P X i P Xsalt . r Ž 1 y Xsalt y ÝSi o P X i P Xsalt .

Ž5.

4. Prediction of salt effect from solvation number
In the case of mixed solvent system, depression of vapor pressure may be treated in a similarmanner. As total pressure of solvent system, Eq. Ž 6. is given for non-ideal solution which corresponds
to the Eq. Ž1. given for the pure solvent system.
Psolvent s Ý Pi P g i P X i aŽ6.

The mean activity coefficient for vapor pressure depression is assumed to be average of mean activity
coefficient of each solvent with its mole fraction. Eq. Ž 7. may be derived from the above assumption.
""gmix,solvent s Ýg i ,solvent P X i

Ž7.

Therefore, the basic equation to calculate salt effect on vapor–liquid equilibrium corresponds to Eq.
Ž1. is Eq. Ž8..
"p s Psolvent P gmix
,solvent P Ž 1 y X salt .

Ž8.

Since psolvent is determined from Eq. Ž6., substitution of Eq. Ž6. into Eq. Ž8. gives the relation:"p s Ž Ý Pi P g i P X i a . P gmix,solvent P Ž 1 y Xsalt .

Ž9.

The relation between activity coefficient of conventionally defined and that given by Eq. Ž9. is:"g i s g i P gmix,solvent P Ž 1 y Xsalt .

Ž 10.

The assumption of Eq. Ž7. was examined with the experimental values for three binary solvent
systems: methanolq ethanolq CaCl 2 , methanolq water q CaCl 2 , and ethanolq water q CaCl 2 system, calculating by Eq. Ž 9. . The comparisons of calculated with observed values w5,2,4x for mean
activity coefficients are shown in Fig. 3.
The activity coefficients predicted for the three binary solvent system containing CaCl 2 are shownS. Ohe r Fluid Phase Equilibria 144 (1998) 119–129

123

Fig. 3. Ža. Mean activity coefficients for vapor pressure depression. Žb. Mean activity coefficients for vapor pressuredepression. Žc. Mean activity coefficients for vapor pressure depression.

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S. Ohe r Fluid Phase Equilibria 144 (1998) 119–129

Fig. 4. Activity coefficients for binary solvent and salt system.

Fig. 5. Activity coefficients for binary solvent and salt system.

Fig. 6. Activity coefficients for binary solvent and salt system.

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Table 2
Wilson parameters for solvent binary system used for prediction of salt effect at 101.3 kPa
No.

Solvent binary system

Wilson parameters

12
3
4
5
6

AcetonitrileŽ1.qwaterŽ2.
EthanolŽ1.qwaterŽ2.
Ethyl acetateŽ1.qethanolŽ2.
MethanolŽ1.qethanolŽ2.
MethanolŽ1.qwaterŽ2.
Methyl acetateŽ1.qmethanolŽ2.

L12

L21

0.311510.18165
0.623672.30756
0.551480.327350.19027
0.78386
0.667360.20397
0.897810.71155

System numbers forparameters from Ohe w7x220
431713120
189550as the conventional coefficient in Figs. 4–6. The activity coefficient of each solvent component at its
own zero mole fraction does not approach to unity because of depression of its vapor pressure.
5. Procedure of prediction
The procedure for predicting the salt effect from the solvation number So pure solvent is described
below.
Ža. Obtain the solvation number So to be formed by pure solvent. So is obtained on Eq. Ž 4. , by"using correlation equation and its parameters in Table 1.
estimating gsolvent
Žb. Calculate effective compositions: X i a of solvent system by solvation number and salt
concentration using corresponding Eq. Ž5..
Žc. Calculate activity coefficients: g i for each component of solvent system by activity coefficientequation for example, Wilson Equation using effective composition X i a.
""
Žd. Estimate mean activity coefficients: gmix,solvent, in Eq. Ž7., from g i,solventof each pure solvent
component for depression of vapor pressure of solvent system according to salt concentration.
Že. Predict vapor phase composition and boiling point or total pressure by Eq. Ž 9. . Wilson
Table 3Predicted result for salt effect on vapor–liquid equilibria
No.

SystemSaltSalt
concentration

Datapoints

D < yi < aav.
wyxb
D < T < av.
wKx

AuthorŽs.

12345678910

Acetoneqmethanol
Acetonitrileqwater
Ethyl acetateqethanol
Methanolqwater
Methyl acetateqmethanol
Methyl acetateqmethanol
Methyl acetateqmethanol
Propanolqwater
Propanolqwater
Methanolqethanolqwater

CaCl 2
CaCl 2
CaCl 2
CaCl 2
CaCl 2NaSCN
NaSCN
CaCl 2
CaCl 2
CaCl 210 wt.%
10 wt.%
10 wt.%
16.7 wt.%
15 wt.%
2 mole%4 mole%2 mole%4 mole%16.7 wt.%

7599412121313
38

0.112
0.039
0.024
0.019
0.032
0.036
0.038
0.019
0.031
0.023

1.02
0.49
0.87
0.62
0.92
1.01
1.13
0.95
1.62
0.44

Ohe w8x
Sada et al. w9x
Hashitani and Hirata w10x
Nishi w4x
Hashitani and Hirata w10x
Illiuta et al. w6x
Illiuta et al. w6x
Illiuta et al. w6x
Illiuta et al. w6x
Ohe w11x

aD < yi < av.s S < yi,calcd y-yi,exptl <rno. of data point s.
D < T < av.s S < Tcalcd yTexptl <rno. of data point s.

b

S. Ohe r Fluid Phase Equilibria 144 (1998) 119–129

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Fig. 7. Comparison between methanol vapor composition observed and predicted by the presented method.

parameters for solvent binary system used to predict salt effect at 101.3 kPa are shown in Table 2.
The parameters at 101.3 kPa were taken from Ohe w7x, shown with system numbers in the reference.
6. Results and discussions
The predicted results are shown in Table 3. Nine binary solventq salt and one ternary q saltsystems were predicted by the proposed method. Systems of number 1, 2, 3, and 5 were calculated byassuming that each component of methanol, water, ethanol was solvated with salt. Three-solvent–
one-salt system was examined in order to confirm the applicability of newly proposed model for
prediction of a multi-component solvent–one-salt system, using only the solvation numbers of theFig. 8. Comparison between ethanol vapor composition observed and predicted by the presented method.

S. Ohe r Fluid Phase Equilibria 144 (1998) 119–129

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Fig. 9. Comparison between water vapor composition observed and predicted by the presented method.

pure solvent–salt systems that compose the multi-component system. The salt effect on isobaric
vapor–liquid equilibrium was satisfactorily predicted for a methanol–ethanol–water–calcium chlorideŽ16.7 wt.%. system.
The comparisons between observed w11x and predicted vapor compositions and boiling point are
shown in Figs. 7–10. The average of the absolute deviations in the vapor phase mole fractions with38 data sets for each component were 0.025 for methanol, 0.031 for ethanol and 0.012 for water,respectively. The mean of the absolute deviations in the boiling point was 0.44 K. The agreement of
the mentioned ternary solvent system with one salt with observed values was as good as in thebinaries: methanolq water q CaCl 2 , methanolq ethanolq CaCl 2 and ethanolq water q CaCl 2 system. The accuracy of boiling point predicted by this work were slightly better than those of theoriginally proposed method Žmean deviation 0.95 K. by author.

Fig. 10. Comparison between observed and predicted temperatures by the presented method.

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7. Conclusions
A newly developed model based on solvation between each solvent and salt to predict and toanalyze salt effect on vapor–liquid equilibria was proposed and successfully applied to binary andternary solvent systems with salt.
Ž1. It is found that the prediction method of salt effect based on solvation is applicable tomulti-component solvent–salt system as well as binary solvent–salt system.
Ž2. The required data for the prediction is only the solvation number So which is determined fromthe data of depression of vapor pressure in pure solvent–salt system. Another data required is thevapor–liquid equilibrium data of the corresponding solvent system without salt. The applicability ofthe proposed model is thought almost all of the system including salt. However, lacking of the vapor
pressure depression data for organic solvent and salt systems, the systems to be able to be predicted
limited. Therefore, the data of depression vapor pressure pure organic solvent with salt are expected
to be observed in the near future.

8. List of symbol
asolventn saltn solvent
PPsolvent
SoSi oXi
Xi aXsalt
Xsolvent
gi"
g i,solventgi"
gmix,solvent
pi

Activity for depression of vapor pressure of pure solvent system wyx
Mole number of salt wyx
Mole number of solvent wyx
Vapor pressure wkPax
Vapor pressure of solvent wkPax
Solvation number between solvent and salt wyx
Solvation number of salt with pure component of mixed solvent system wyx
Mole fraction of ith solvent component existing salt wyx
Effective mole fraction of ith solvent component existing salt wyx
Mole fraction of salt wyx
Mole fraction of solvent wyx
Activity coefficient of conventionally defined wyx
Mean activity coefficient for depression of vapor pressure of ith solvent wyx
Activity coefficient of solvent with no salt wyx
Mean activity coefficient for depression of vapor pressure of mixed solvent system wyx
Total pressure of the system wkPax
ith solvent wyx

References
w1x S. Ohe, 1976. Advances in Chemistry Series, No. 155, Am. Chem. Soc.
w2x S. Ohe, 1991. Vapor–Liquid Equilibrium Data—Salt Effect, Elsevier, New York.
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w4x Y. Nishi, J. Chem. Eng. Jpn. 8 Ž1975. 187.
w5x S. Ohe, K. Yokoyama, S. Nakamura, Kagaku Kogaku 34 Ž1970. 325.

S. Ohe r Fluid Phase Equilibria 144 (1998) 119–129

w6x M.C. Illiuta, F.C. Thyrion, O.M. Landauer, J. Chem. Eng. Data 41 Ž1996. 402.
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