2001- Modified solvation model for salt effect on vapor–liquid equilibria

7/29/2019 2001- Modified solvation model for salt effect on vaporliquid equilibria

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Fluid Phase Equilibria 194197 (2002) 701715

Modified solvation model for salt effect on vaporliquid 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

Theprediction method hadbeen presentedfor salt effect on vaporliquid equilibria by solvation model. This model

assumes that salt effect is caused by solvation and solvated solvent molecular cannot contribute to vaporliquid

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; Vaporliquid 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 vaporliquid 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 ofconventional thermodynamic model for non-electrolyte component system such as activity coefficientsmodel. These models combined extended non-electrolyte activity coefficients model and DebyeHckel

term. The activity coefficients model term was used for describing short-range interaction by van derWaals force. DebyeHckel term was used for describing long-range interaction according to Coulombforce. For example, Tans equation using Wilson equation [2] for describing short-range interaction,

electrolyte NRTL model [35] using NRTL equation, extended UNIQUAC [6,7] model and LIQUAC

Corresponding author. Tel.: +81-332604282; fax: +81-332673704.

E-mail address: [email protected] (S. Ohe).

0378-3812/02/$ see front matter 2002 Elsevier Science B.V. All rights reserved.PII: S0378-3812(01)00784-1


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702 H. Takamatsu, S. Ohe / Fluid Phase Equilibria 194197 (2002) 701715

model [8,9] using UNIQUAC equation, Kikic et al.s method [10] using UNIFAC equation, Achard et al.smethod [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 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 a

part 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 vaporliquidequilibrium [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 vaporpressure 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 the

model 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 salteffect 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 usedto determinate solvation number. And the solvation numbers were used to predict salt effect on vaporliquid 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):

= Psolvent asolvent. (1)

Since the activity is a product of activity coefficient and mole fraction of solvents: asolvent = solvent xsolvent, then the activity coefficient for the pressure is determined from Eq. (1) as follows:

solvent =

(Psolvent xsolvent). (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. Theactivity of the solvent becomes

asolvent =(nsolvent nsalt)S0

(nsolvent nsaltS0)+ nsalt. (3)

Dividing both of the denominator and numerator by nsolvent + nsalt will give

asolvent =(xsolvent xsalt)S0

(1 xsalt)S0, (4)

where xsolvent = 1 xsalt .


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H. Takamatsu, S. Ohe / Fluid Phase Equilibria 194197 (2002) 701715 703

Fig. 1. The xy 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, the

actual solvents composition participating in the vaporliquid equilibrium is changed. Assuming that a saltforms the solvates with each component and that the solvated molecules do not contribute to vaporliquid

equilibria, the effective mole fraction xia for the ith solvent is given by Eq. (5) at salt free basis. Since, the

sum of solvent mole fraction is equal to 1xsalt , and the solvation number for the ith solvent is calculatedas Si0x

i , and Eq. (5) is obtained.

xia =xi (Si0x

ixsalt)

1 xsalt

Si0xixsalt

(5)

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


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The relation of solvation number Si between that of a singe solvent Si0 and composition of it xi 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 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 relationbetween solvation number Si 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 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 concen-tration 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 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.

Psolvent =

Pii 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.

mix,solvent =

i,solventxi (7)

Therefore, the basic equation to calculate salt effect on vaporliquid equilibrium corresponds to Eq. (1)is Eq. (8).

= Psolventmix,solvent(1 xsalt) (8)

Fig. 3. Activity coefficients for methanol + water + CaCl2 (4 mol%) at 101.3 kPa [17].


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Since Psolvent is determined from Eq. (6), substitution of Eq. (6) into Eq. (8) gives the relation

=

Pii x

iamix,solvent(1 xsalt) (9)

The relation between activity coefficient of conventionally defined and that given by Eq. (9) is

i = i mix,solvent(1 xsalt) (10)

the activity coefficients of each solvent in binary solvents+ salt system are shown in Fig. 3.

5. Relation between SiiiSiiiSiii0 and correlation error

Solvation number in pure solvent is very important factor in this model. The solvation number was usedfor 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 numberand correlation error was investigated in binary solvents+ salt system.

The first, the relation between the solvation number and average of absolute error in vapor phasewas 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 expressed

by following equation:

S10 = kS20 + S20,preferential (11)

where kis 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].


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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 tempera-

ture or total pressure shows on Eq. (11). In this work, the solvation numbers are the points that showminimum point of average of absolute error in boiling point or total pressure on Eq. (11). Fig. 6shows 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.


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Fig. 7. Flow sheet for determination of salt effect on vaporliquid equilibria.

6. Procedure of prediction

The procedure for predicting the salt effect from the solvation number Si0 of pure solvent is describedas follows.

(a) Obtain solvation number Si0 determined from procedure shown in Fig. 6.

(b) The x

ia is calculated from Eq. (5) by using solvation number Si0.(c) Calculate activity coefficients: i for each component of solvent system by activity coefficient equa-tion for example, Wilson equation with effective composition xia. In this work, Wilson equation was

used and Wilson coefficients was obtained from Ohes vaporliquid equilibrium Data Book [18] andDECHEMAs vaporliquid equilibrium data collection [19,20].

(d) Estimate activity coefficients: mix,solvent, in Eq. (7), from i ,solvent of each pure solvent for lowering

of vapor pressure of solvents system according to salt concentration. The i ,solvent is also determinedusing Si0 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 Txy curve and xy curve are shown in Figs. 813. As for isobaricdata, 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 fractionand average error for boiling point calculated was 0.72 K. As isothermal system, average error for vapor


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Table 1

Correlative error of isobaric binary solvents + salt systems

Number System Solvation numbera This work Reference

C1 C2 |y1|av |T|av(K)

1 Methanol + water + CaCl2 (16.7 wt.%) at 101.3 kPa 0.5407 0.7002 0.009 0.46 [23]

2 Methanol + water + CaCl2 (2 mol%) at 101.3 kPa 0.5781 0.6476 0.008 0.70 [17]



5 Methanol + water + KCl (0.5 M) at 101.3 kPa 0.3197 0.4346 0.013 0.34 [24]

6 Methanol + water + KCl (1 M) at 101.3 kPa 0.0000 0.1853 0.020 0.48 [24]

7 Methanol + water + KCl (2 M) at 101.3 kPa 0.0000 0.3176 0.026 0.89 [24]

8 Methanol + water + LiCl (1 M) at 101.3 kPa 0.0000 0.0905 0.025 1.46 [25]



11 Methanol + water + NaBr (2 M) at 101.3 kPa 0.0515 0.2194 0.019 0.71 [25]12 Methanol + water + NaF (0.25 M) at 101.3 kPa 0.2551 0.2801 0.027 0.72 [25]

13 Methanol + water + NaF (0.5 M) at 101.3 kPa 0.0000 0.0837 0.016 0.59 [25]

14 Methanol + water + NaF (1 M) at 101.3 kPa 0.0000 0.1407 0.013 0.60 [25]

15 Methanol + water + NaNO3 (5 mol%) at 101.3 kPa 0.0000 0.2936 0.026 0.66 [26]



18 Ethanol + water + CaCl2 (16.7 wt.%) at 101.3 kPa 0.0304 0.6615 0.012 0.70 [23]

19 Ethanol + water + CaNO3 (1.038 M) at 50.7 kPa 0.2784 0.5013 0.024 0.31 [27]

20 Ethanol + water + CaNO3 (2.049 M) at 50.7 kPa 0.1447 0.5964 0.023 0.48 [27]

21 Ethanol + water + CH3COOK (2.5 mol%) at 101.3 k Pa 0.2991 0.4937 0.008 0.34 [28]

22 Ethanol + water + CH3COOK (5 m ol%) at 101.3 k Pa 0.0000 0.4274 0.018 0.44 [28]

23 Ethanol + water + CH3COOK (6.6 mol%) at 101.3 k Pa 0.0000 0.5614 0.015 1.00 [28]

24 Ethanol + water + CH3COOK (8.5 mol%) at 101.3 k Pa 0.0000 0.6433 0.015 1.53 [28]25 Ethanol + water + NH4Cl (6 mol%) at 101.3 kPa 0.0000 0.5099 0.014 0.31 [29]

26 Ethanol + water + NH4Cl (8 mol%) at 101.3 kPa 0.0000 0.6393 0.017 1.47 [29]

27 2-Propanol + water + CaCl2 (0.4 M) at 101.3 kPa 0.0000 0.5162 0.014 0.44 [30]



30 2-Propanol + water + CaCl2 (2.2 wt.%) at 101.3 kPa 0.0000 0.3474 0.008 0.23 [31]

31 2-Propanol + water + CaCl2 (4.3 wt.%) at 101.3 kPa 0.0000 0.5243 0.009 0.44 [31]

32 2-Propanol + water + CaNO3 (1.038 M) at 50.7 kPa 0.0000 0.5559 0.024 0.54 [27]

33 2-Propanol + water + CaNO3 (2.049 M) at 50.7 kPa 0.0000 0.7583 0.046 2.15 [27]

34 2-Propanol + water + NaCl (5 wt.%) at 101.3 kPa 0.0000 0.2143 0.015 1.08 [32]

35 Methanol + ethanol + CaCl2 (16.7 w t.%) at 101.3 kPa 0.5512 0.2607 0.016 0.27 [31]

36 Methanol + ethanol + CaCl2 (16.7 w t.%) at 101.3 kPa 0.5201 0.3123 0.006 0.30 [33]37 Methanol + ethanol + CaCl2 (23.1 w t.%) at 101.3 kPa 0.6310 0.4128 0.010 0.31 [33]

38 2-Propanol + 1-propanol + CaCl2 (10 w t.%) at 101.3 kPa 0.1950 0.2738 0.019 0.41 [23]

39 2-Propanol + 1-propanol + CaCl2 (13 w t.%) at 101.3 kPa 0.0000 0.0751 0.025 1.28 [23]

40 2-Propanol + 1-propanol + CaCl2 (16.7 wt.%) at 101.3 k Pa 0.0000 0.0867 0.016 0.40 [23]

41 Acetone + methanol + CaCl2 (5 wt.%) at 101.3 kPa 0.2154 0.3979 0.009 0.28 [34]

42 Acetone + methanol + CaCl2 (10 wt.%) at 101.3 kPa 0.0000 0.3085 0.009 0.28 [34]

43 Acetone + methanol + CaCl2 (20 wt.% at 101.3 kPa 0.0000 0.4354 0.018 1.37 [34]

44 Acetone + methanol + KSCN (1 mol%) at 101.3 kPa 0.2208 0.2315 0.012 0.39 [35]




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Table 1 (Continued)


C1 C2 |y1|av |T|av(K)

47 Acetone + methanol + KSCN (4 m ol%) at 101.3 k Pa 0.2684 0.3438 0.023 0.21 [35]

48 Acetone + methanol + KSCN (5 m ol%) at 101.3 k Pa 0.3179 0.4002 0.026 0.23 [35]

49 Acetonev + methanol + LiCl (0.5 mol%) at 101.3 k Pa 0.0000 0.1234 0.021 0.38 [36]

50 Acetone + methanol + LiCl (2 m ol%) at 101.3 k Pa 0.0000 0.2023 0.021 0.42 [36]


52 Acetone + methanol + LiCl (0.5 mol%) at 101.3 k Pa 0.2086 0.2715 0.012 0.48 [21]

53 Acetone + methanol + LiCl (0.75 mol%) at 101.3 k Pa 0.0171 0.1356 0.012 0.42 [21]




57 Acetone + methanol + NaI (1 mol%) at 101.3 kPa 0.5031 0.5721 0.016 0.23 [37]

58 Acetone + methanol + NaI (1.5 m ol%) at 101.3 kPa 0.4099 0.5319 0.017 0.21 [37]59 Acetone + methanol + NaI (2 mol%) at 101.3 kPa 0.3571 0.5148 0.020 0.17 [37]







66 Acetone + methanol + ZnCl2 (1.082 M) at 101.3 k Pa 0.1650 0.4187 0.028 0.21 [38]

67 Acetone + methanol + ZnCl2(1.502 M ) at 101.3 kPa 0.1374 0.4209 0.020 0.21 [38]

68 Acetone + methanol + ZnCl2 (1.751 M) at 101.3 k Pa 0.0307 0.4254 0.029 0.28 [38]

69 Acetone + water + KCl (1 mol%) at 101.3 kPa 0.0000 0.6496 0.020 0.69 [39]

70 Acetone + water + KCl (2.5 mol%) at 101.3 kPa 0.0000 0.6816 0.023 2.60 [39]71 Methanol + ethyl acetate + CaCl2 (5 wt.%) at 101.3 k Pa 0.5224 0.2949 0.005 0.23 [40]

72 Methanol + ethyl acetate + CaCl2 (10 wt.%) at 101.3 k Pa 0.5134 0.0000 0.012 0.65 [40]

73 Methanol + ethyl acetate + CaCl2 (20 wt.%) at 101.3 k Pa 0.6519 0.0000 0.022 2.36 [40]

74 Methanol + THF + CuCl2 (1 mol%) at 101.3 kPa 0.8111 0.7831 0.014 0.14 [22]




78 Methanol + THF + LiCl (1 mol%) at 101.3 kPa 0.8111 0.7831 0.014 0.14 [22]




Average 0.018 0.72a 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


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Table 2

Correlative error of isothermal binary solvents + salt systems


C1 C2 |y1|av |TP|av(kPa)

1 Ethanol + water + CaCl2 (5 wt.%) at 298.15 K 0.4640 0.6853 0.006 0.03 [41]



4 Ethanol + water + LiCl (4 M) at 298.15 K 0.6966 0.8953 0.005 1.10 [42]

5 1-Propanol + water + CaCl2 (5 wt.%) at 298.15 K 0.0000 0.5629 0.028 0.36 [43]



8 Methanol + ethanol + CaCl2 (10 wt.%) at 298.15 K 0.1817 0.0000 0.007 0.07 [41]

9 Methanol + ethanol + CaCl2 (15 wt.%) at 298.15 K 0.4637 0.2727 0.004 0.11 [41]

10 Methanol + ethanol + CaCl2 (5 wt.%) at 298.15 K 0.1241 0.0000 0.003 0.29 [41]11 Methanol + 1-propanol + CaCl2 (10 w t.%) at 298.15 K 0.6364 0.4994 0.012 0.09 [41]

12 Methanol + 1-propanol + CaCl2 (15 w t.%) at 298.15 K 0.6719 0.4827 0.010 0.04 [41]

13 Methanol + 1-propanol + CaCl2 (5 wt.%) at 298.15 K 0.6593 0.5938 0.012 0.11 [41]

14 2-Propanol + 1-propanol + CaCl2 (5 wt.%) at 298.15 K 0.0000 0.1213 0.003 0.12 [44]

15 2-Propanol + 1-propanol + CaCl2 (10 w t.%) at 298.15 K 0.0000 0.2058 0.002 0.12 [44]

16 2-Propanol + 1-propanol + CaCl2 (15 w t.%) at 298.15 K 0.0000 0.2716 0.002 0.11 [44]

Average 0.009 0.14

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

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


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Fig. 9. The Txy 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 binarysolvent + 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 re-sults 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 0.021 for methanol and 0.020 for ethanol,respectively.

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


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

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

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


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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]; (), 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 vaporliquidequilibria. 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 vaporliquid 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 vaporliquid equilibria was proposed and successfully applied to the binary and ternary solventssystems with salt.

List of symbols

asolvent activity for lowering of vapor pressure of pure solvent system

ci constant for solvation number

k coefficient in Eq. (11)

nsalt mole number of salt

nsolvent mole number of solvent

P total pressure of system (kPa)Psolvent total pressure of system as solvent system (kPa)

Pi vapor pressure of pure component i (kPa)

S0 solvation number between solvent and salt

Si0 solvation number of salt with pure component of mixed solvent system

xi mole fraction ofith solvent existing salt

xi mole fraction ofith solvent at salt free basis

xia effective mole fraction ofith solvent at salt free basis

xsalt mole fraction of salt

xsolvent mole fraction of solvent

Greek symbols

i activity coefficient of conventionally defined

i activity coefficient for effective mole fraction ofith solvent

i ,solvent activity coefficient for lowering of vapor pressure ofith solvent

mix,solvent activity coefficient for lowering of vapor pressure of mixed solvent system

Subscript

i ith solvent

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2001- Modified solvation model for salt effect on vapor–liquid equilibria

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Transcript of 2001- Modified solvation model for salt effect on vapor–liquid equilibria