Prediction of Salt Effect in Vapor-Liquid Equilibrium: A Method Based

5

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Prediction of Salt Effect in Vapor-Liquid Equilibrium: A Method Based on Solvation SHUZO OHE Ishikawajima-Harima Heavy Ind. Co. Ltd., Yokohama, Japan 235

A method of prediction of the salt effect of vapor-liquid equi librium relationships in the methanol-ethyl acetate-calcium chloride system at atmospheric pressure is described. From the determined solubilities it is assumed that methanol forms a preferential solvate of CaCl ·6CH OH. The preferential solvation number was calculated from the observed values of the salt effect in 14 systems, as a result of which the solvation number showed a linear relationship with respect to the con centration of solvent. With the use of the linear relation the salt effect can be determined from the solvation number of pure solvent and the vapor-liquid equilibrium relations ob tained without adding a salt. 2

C

alcium

chloride

ethyl acetate.

dissolves

readily

3

in

methanol

but

less

easily

in

A c c o r d i n g l y , it is assumed that the interaction between

methanol and calcium chloride is dominant i n the M e O H - E t O A c - C a C l 2 system. The causes of the salt effect i n the system observed by the author w i l l be discussed

f r o m the standpoint of molecular structure ( F i g u r e 1).

Causes of Salt Effect T h e solubility of c a l c i u m chloride i n the M e O H - E t O A c system ( F i g u r e 2) was obtained f r o m the intersections of the x-y curves obtained at respective constant C a C l concentrations a n d those obtained at saturated concentration. E a c h salt concentration at the intersection of curves of constant salt concentration to salt saturation shows the solubility of c a l c i u m chloride i n the volatile b i n a r y system. T h e solubilities thus obtained ( F i g u r e 2) are linear. F r o m 0 to 0.333 mole fraction of methanol, the solubility is almost zero. These solubility data indicate that if c a l c i u m chloride is dissolved b y o n l y the methanol contained i n 2

53

In Thermodynamic Behavior of Electrolytes in Mixed Solvents; Furter, W.; Advances in Chemistry; American Chemical Society: Washington, DC, 1976.

54

T H E R M O D Y N A M I C BEHAVIOR O F E L E C T R O L Y T E S

the m e t h a n o l - e t h y l acetate solution, both solvents exist i n the f o r m of clustered molecules c o m p r i s i n g one methanol molecule and two e t h y l acetate molecules (Figure 3).

It m a y be assumed that i n methanol concentration over 0.333 mole


fraction, free molecules forming nonclustered molecules are present i n the system,

Figure

1.

MeOH-EtOAc-CaCl

2

system

at

1

atm



5.

OHE

Prediction of Salt Effect Based on

Figure 3. Preferential MeOH-EtOAc-CaClz

55

Solvation

solvation model system at 1 atm

for

so that the salt is dissolved i n the free molecules of methanol. F r o m the extrapolated solubility (mole ratio of c a l c i u m chloride to methanol, ~ 1:6), c a l c i u m chloride and methanol are believed to f o r m a solvate of C a C l 2 * 6 C H 3 0 H . In f o r m i n g this solvate, methanol is trapped b y c a l c i u m chloride a n d cannot easily evaporate. H e n c e the vapor pressure of methanol drops to a corresponding level.

Prediction of Salt Effect from Preferential Solvation Number T h e salt effect i n the M e O H - E t O A c - C a C ^ system can be explained b y preferential solvation. As c a l c i u m chloride dissolves readily i n methanol but only sparingly i n ethyl acetate, it Will be sufficient to consider the interaction between methanol molecules and c a l c i u m chloride molecules only i n the M e O H - E t O A c solution. R e f e r r i n g again to F i g u r e 2, the free methanol molecules w h i c h are not clustered w i t h ethyl acetate increase linearly w h e n the l i q uid-phase composition of methanol is above 0.333 i n mole fraction. T h e solubility


56


of CaCl2 is proportional to the increase i n the n u m b e r of methanol molecules, and calcium chloride is dissolved, forming with methanol a preferential solvation w h i c h m a y be written C a C l 2 * 6 C H O H . Since solvated methanol molecules cannot be evaporated, the composition of methanol p a r t i c i p a t i n g i n the v a p o r l i q u i d e q u i l i b r i u m at the l i q u i d phase is decreased. If it is assumed that the preferential solvates do not exert interaction o n the volatile components i n the l i q u i d phase, the v a p o r - l i q u i d e q u i l i b r i u m relation obtained under the addition of a salt m a y w e l l be considered to be the same as the v a p o r - l i q u i d e q u i l i b r i u m without the salt for a liquid-phase composition f r o m w h i c h the solvents f o r m i n g solvates are excluded. W h e n a salt is expected to f o r m a solvate w i t h alcohol or water as i n the alcohol-water-salt system, that is, when the formation of solvation is not l i m i t e d to a specific component, the above-mentioned p r e d i c t i o n cannot be made unless the solvation n u m b e r of each component is calculated. F o r solvents consisting of ethanol a n d water, however, it has been f o u n d f r o m measurements of W a l d e n constant ( A V * ) of l i t h i u m chloride a n d l i t h i u m f l u o r i d e that preferential h y d r a t i o n of water molecules takes place w h e n the ethanol concentration is less than 25 wt % (I). Therefore we can predict the salt effect i n the alcohol-water-salt system, assuming that the preferential solvation takes place over the entire range of liquid-phase composition although we k n o w that this assumption is very bold.


3

T h e for-

Method of Prediction. P R E F E R E N T I A L S O L V A T I O N N U M B E R .

mation of preferential solvation is caused b y the ionization of salt. T h e stability of the i o n i n a solution depends o n the m a g n i t u d e of the dielectric constant of a solvent. D e b y e (2) explained salting out b y the f o r m a t i o n of preferential solvation and f o u n d that the f o l l o w i n g relation exists between salting out a n d the dielectric constant of a solvent. i

,

*2

xi

v i I n — - — vo In — = — vo

Zj ej 2

In E q u a t i o n 1, x i ° a n d x ° are X\ and x at r = 2

I

2

2

0 0

de

(1)

, respectively.

T h e first

component is a nonelectrolyte, while the second component is a n electrolyte such as water.

I n other words, X\ a n d x represent the compositions i n the neigh2

borhood of respective salts and accordingly the solvated compositions. Assuming that changes i n the dielectric constant are i n the linear relationship w i t h changes i n the composition of solvent, this relation is given b y (de/dni) T a b l e I.

= (Ae/Ani).

Effective Factor for Preferential Solvation i n E q u a t i o n l

a

Ae/Ax,

(1/e ) (Ae/Ax,)

-26.61 -45.91 -54.24

-0.0712 -0.0088 -0.0205

2

Systems E t h y l acetate ( l ) - m e t h a n o l (2) Methanol ( l ) - w a t e r (2) Ethanol ( l ) - w a t e r (2) a

e

n

e,

e

6.02 32.63 24.3

32.63 78.54 78.54

2

e : value at 20°C, Ae = e, - e , e: value at x° = x° = 0.5. 2

2


5.

OHE

Prediction of Salt Effect Based on

11

57

Solvation

i-PrOH

10 9 8 7

//


6 5

AO

j — MeOH -HzO

50

60

Figure 4. Difference electric constants and number

70

of disolvation

Therefore we can compare the values of (l/e )(Ae/Axi) i n several solvents (Table 2

i). T h e absolute value of ( l / e ) ( A e / A x i ) is the greatest i n the ethyl acetatemethanol system but becomes smaller i n the ethanol-water system and methanol-water system, i n that order. In solvent systems, the greater the value of the right hand side of E q u a t i o n 1, the greater the value of x /x ° but the smaller the value of xi/xi°. In other words, the preferential solvation due to methanol or water is likely to occur i n such systems. F i g u r e 4 shows the result of plotting the solvation number So of pure solvent, obtained f r o m the measurements of the salt effect, against the difference Ae of dielectric constant of each solvent i n the methanol-water, ethanol-water, and 2-propanol-water systems w h i c h are added w i t h CaCl2. As is apparent f r o m F i g u r e 4, the value of So is greater i n systems w i t h greater value of Ae. T h i s figure shows the same trend as E q u a t i o n 1. T h e n , we can obtain the preferential solvation n u m b e r f r o m the observed values of the salt effect. As the concentration of solvent is decreased b y the n u m b e r of solvated molecules, the actual solvent composition p a r t i c i p a t i n g i n the v a p o r - l i q u i d e q u i l i b r i u m is changed. Assuming that a salt forms the solvate w i t h the first component, the actual composition X i is g i v e n b y 2

2

2

a

(xi - Sx ) + 3

Since xi = x\(l— as follows:

x ), x = x 3

2

x

2

(1 — x ) and x\ + x ' = 1, Equation 2 is rewritten 3

2

,

2

xi' (1 ~ s ) ~ S * 3

(1 - x ) 3

Sx

, *

3

3

Solving E q u a t i o n 3 for S, we obtain g _ 1 ~ * 3 * l ' ~ *la'

^

Therefore, the solvation number can be calculated by determining x ' f r o m the measured values using the v a p o r - l i q u i d e q u i l i b r i u m relation obtained without i a


58


a d d i n g a salt.

W h e n a salt forms the solvation w i t h the second component, the

f o l l o w i n g three equations can be d e r i v e d i n a s i m i l a r manner. *1

* l a ="

*1 +

Xla' =

(1 ~ X ) x / 3

(1 - x ) - S x


3

S =

(5)

(X2 - S x 3 )

(6) 3

1 -xsXiZ-x/ x

(7)

Xla

3

T h e establishment of the m e t h o d of p r e d i c t i o n has been attempted b y the reverse calculation of the preferential solvation n u m b e r f r o m measured values, using Equations 4 a n d 7 w h i c h are based o n the assumption that the salt effect i n the v a p o r - l i q u i d e q u i l i b r i u m is caused b y the preferential solvation f o r m e d between a volatile component and a salt.

T h e observed values were selected f r o m

Ciparis's data book (4), Hashitani's data (5-8), a n d the author's data (9-15).

S

was calculated b y E q u a t i o n 7 w h e n the relative volatility a i n the v a p o r - l i q u i d s

e q u i l i b r i u m w i t h salt is increased w i t h respect to the relative volatility a i n the v a p o r - l i q u i d equilibrium with salt, but b y E q u a t i o n 4 when a is decreased. T h e s

results are shown i n Figures 5 - 1 2 .

F r o m these figures, it w i l l be seen that the

f o l l o w i n g three relations exist:

10 o

;fi =0.02() (3 =0.04

i

i 0

0.2

0.4

0.6

0.8

1.0

Xi Figure 5.

MeOH-H 0-CaCl2 2

system at 1 atm


5.

OHE

Prediction

of Salt Effect Based on


0

Figure 6.

0.2

0.4

0.6

MeOH-H 0-salt

0.8

system at

2

59

Solvation

1.0

25°C

(a) T h e preferential solvation number S shows the linear relationship w i t h the liquid-phase composition of solvent, X\ or x . 2

(b) W h e n the concentration of salt is not saturated, S increases with increase i n the mole fraction of solvent molecule w h i c h forms the solvate. (c)

S increases w i t h decrease i n salt concentration.

These relations are established i n all cases, regardless of the kinds of solvent systems, kinds of salts, isothermal e q u i l i b r i u m or isobaric e q u i l i b r i u m . It seems that these relations are also independent of salt concentration T o be exact, however, the above-mentioned linear relation (increase or decrease w i t h respect to solvent concentration) is assumed to exist w h e n x is constant. If the range of salt concentration is narrow, the above-mentioned relations are assumed to be established approximately. 3

Let's m a k e a comparison of i n d i v i d u a l cases. Figures 5 - 7 show the cases where C a C ^ was added to the alcohol-water system. F i g u r e 5 shows the values observed by the author when the salt concentration was constant i n terms of mole fraction, a c c o r d i n g to w h i c h the h y d r a t i o n n u m b e r So of salt w i t h water is 11 at x = 0.020, 10 at x = 0.040, a n d 6 at x = 0.100. T h e value of S decreases as the salt concentration increases. T h e reason for this m a y be that the activity of salt decreases a n d the n u m b e r of molecules to be solvated decreases as the salt concentration increases. O u r calculation was m a d e using the data obtained b y Yoshida et al. (16). As we obtained almost the same results as those shown i n F i g u r e 5, graphic representation is omitted. s

3

3

0

F i g u r e 6 shows the results at isothermal e q u i l i b r i u m . T h e observed values in this case were taken f r o m Ciparis's data book (4). The concentration of C a C l ^ *3, is not constant, changing f r o m 0.1009 to 0.155, but the linear relation is shown. T h e salt concentration is higher than i n the case of F i g u r e 5, but So is four, w h i c h is smaller. Figure 7 is based on the values observed by Hashitani et al. (5), where the linear relation is also obtained although x is not constant. In particular, a similar linear relationship is obtained w h e n a salt is dissolved to saturation at the b o i l i n g point. In this case, So is about four, w h i c h is smaller than i n the case i n w h i c h the salt is not saturated. F i g u r e 8 shows the case where C H C O O K was 3

3



60


Figure

7.

EtOH-H 0-CaCl 2

system at 1 atm

2

4 0*3

= 0.065 -0.247

to 2 1

c

0

0.2

Figure 8.

Figure 9.

0.4

0.6

i-PrOH-H 0-CH COOK at 1 atm 2

CH COOH-H Osalt 3

2

s

0.8

1.0 system

system at 1 atm

dissolved to saturation i n the 2-propanol-water system at room temperature. T h e linear relation was also obtained, although the range of composition of was large, 0.065-0.247. A s described above, S was calculated f r o m the observed values of the v a p o r - l i q u i d e q u i l i b r i u m for such cases where a salt is assumed to f o r m the solvation w i t h alcohol or water i n the alcohol-water-salt system, as-


5.

OHE

Prediction

61

of Salt Effect Based on Solvation

suming that the salt forms the preferential solvation w i t h water. As a result, the linear relation was obtained. T h e values of S i n the acetic a c i d - w a t e r system added w i t h S r C ^ , N a C l , and C a C ^ , respectively, are shown i n F i g u r e 9. T h e same results as i n the alcohol-water-salt system were obtained. F i g u r e 10 shows the acetic a c i d - w a t e r system added w i t h C H C O O N a . T h e a d d i t i o n of C H 3 C O O N a forms the solvation w i t h acetic a c i d rather than water. This m a y 3

be because the a f f i n i t y of C H C O O N a for acetic acid is greater than that for water. F i g u r e 11 shows the case of the c h l o r o f o r m - a c e t o n e - Z n C l 2 system; the results obtained were the same as those i n other systems. F i g u r e 12 shows the case of the a l c o h o l - a l c o h o l - C a C l 2 system. I n these three systems, the alcohol of lower b o i l i n g point forms the solvate, and the preferential solvation n u m b e r decreases w i t h increase of the carbon n u m b e r i n the alcohol. T h e effect of the alkyl group is greater and that of the hydroxyl group contributing to the formation


3

U

3

(O

2

1

0 0

0.2

0.6

OA

0.8

1.0

Xi Figure

10.

CH COOH-H 0-CH COONa system at 1 atm s

2

3

5 O 0.051-0.084

A

-

3 2 1 0 0 Figure

0.2 11.

OA

0.6

0.8

Xi Chloroform-acetone-ZnCl at 1 atm

2

1.0 system



62


Figure

12.

k\coho\-alcoho\-CaCl at 1 atm

system

2

of solvate is smaller i n systems having a larger number of carbons i n the alcohol. T h e preferential solvation n u m b e r i n the e t h y l acetate-ethanol-CaCl2 system is shown i n Figure 13. F r o m Figure 13, when the salt is saturated, the preferential solvation n u m b e r becomes constant a n d is independent of the solvent concentration. O n the other hand, this relationship is not observed i n the e t h a n o l -

1 O X3 = 0.(W'M-0.07SI5 * = 0.124•-0.171

A

3

3-0.008 • Xa = 0.29: I

O V

•• 0

I

w 0.2

»

0.4

0.6

S i 0.8

— 1.0

Xf Figure

13.

EtOAc-EtOH-CaCl at 1 atm

2

system


5.

OHE

Prediction

of Salt Effect Based on

w a t e r - C a C k system, as shown i n Figure 7.

63

Solvation

W h e n a salt is dissolved to saturation,

therefore, the same rule cannot be a p p l i e d , thus m a k i n g p r e d i c t i o n impossible. W e can now discuss the solvation number.

In systems such as the metha-

nol-water-CaCl2 system shown i n F i g u r e 5, the hydration number is the greatest, that is, 11 at x = 0.020.

If the h y d r a t i o n n u m b e r of ions is calculated f r o m the

hydration entropy, C a

is seven a n d C l ~ is two (3).

3

2 +

If it is assumed that C a C ^

is completely dissociated a n d both the cation a n d anion forms hydrate, the hy-


dration number becomes:

7 + 2 X 2 = 11, w h i c h agrees w i t h the value obtained

f r o m the salt effect. PREDICTION O F SALT E F F E C T .

The

p r o c e d u r e for

preferential solvation n u m b e r S has been described above.

c a l c u l a t i o n of

the

B y reversing this

procedure, that is, by determining x i ' f r o m S, we can estimate the salt effect using a

the v a p o r - l i q u i d equilibrium without a salt.

W h e n the salt concentration is below

saturation, the preferential solvation number S can be expressed as follows i n cases where the solvation is f o r m e d w i t h the first component. S = Son'

(8)

where So is the solvation n u m b e r of the pure solvent w i t h a salt. W h e n the solvation is f o r m e d w i t h the second component, the solvation n u m b e r is g i v e n b y S = S (l -

(9)

0

A c c o r d i n g l y , Equations 3 a n d 6 are rewritten as follows: / (1 ~ Xs)Xi SQXIXS Xla = (1 - x ) - S o x i ^

(10)

3

U - *3)xi' l a

(

n

)

(l-s )-S (l-xi')x ' 3

0

3

T h e procedure for p r e d i c t i n g the salt effect f r o m the solvation n u m b e r of pure solvent is described below. (a)

D e c i d e w i t h what component the salt forms the preferential solvate

i n the system b e i n g predicted. (b)

O b t a i n the solvation n u m b e r So to be f o r m e d b y a pure solvent.

(c)

C a l c u l a t e X i ' b y E q u a t i o n 10 or 11.

(d)

Set the vapor-phase composition at X i ' i n the absence of salt, at X\ i n

a

a

the presence of salt. E x a m p l e of p r e d i c t i o n : T h e f o l l o w i n g is the p r e d i c t i o n of v a p o r - l i q u i d e q u i l i b r i u m composition w h e n CaCl2 is added i n 7.24 m o l % to the ethyl acetate-ethanol system i n w h i c h the liquid-phase composition of e t h y l acetate is 0.502 i n terms of mole fraction. First, the component that forms the preferential solvation is d e t e r m i n e d a c c o r d i n g to step (a) as described above. Since ethanol is stronger i n polarity and greater i n dielectric constant e than ethyl acetate, we can assume that ethanol


64


Table II.


No.

Systems o f Salt E f f e c t

Systems

Condition

1

Methanol + water + C a C l

2 3 4

Methanol + water + C a C l (No. 33)^ Methanol + water + NaBr (No. 2 9 ) Ethanol + water + CaCl *>

5 6 7 8 9

2-Propanol Acetic acid Acetic acid Acetic acid Acetic acid

2

1 atm

fl

25° C 25° C 1 atm

2

c

2

+ water + water + water + water + water

+ CH COOK« + C a C l (No. 6 1 ) + N a C l (No. A\) + S r C l (No. 6 5 ) + C H C O O N a ( N o . 44)^ 3

c

2

c

c

2

3

1 1 1 1 1

atm atm atm atm atm

10

E t h y l acetate + ethanol + CaCl *>

1 atm

11

Chloroform + acetone + Z n C l

1 atm

12 13

Methanol + ethanol + C a C l Ethanol + f-propanol + C a C l

14

1-Propanol + 1-butanol + C a C l

2

2

2

&

1 atm 1 atm

fl

2

a

2

a

1 atm

Author's data. t> Hashitani's data.

a

Figure

14. Result of prediction for EtOAcEtOH-H 0-CaCl system at 1 atm 2

2


5.

OHE

65

Prediction of Salt Effect Based on Solvation

Predicted b y the Solvation


X

3

0.020 0.040 0.0887-0.175 0.0563-0.1247 0.159-0.179 0.0636-0.1052 0.066-0.247 0.128-0.228 0.0035-0.1025 0.028-0.077 0.0552-0.1397 0.0375-0.0960 0.0471-0.0848 0.124-0.171 0.051-0.084 0.115-0.169 0.192-0.268 0.0561-0.0765 0.050 0.110 0.089-0.105

S 11.0 10.0 4.0 4.0 4.5 8.0 3.0 3.0 6.4 11.0 3.5 3.5 6.0 4.0 3.3 2.7 2.3 5.0 4.0 3.0 1.0 0

Error (%)

Figure

Table

1.2 0.5 1.4 8.6 5.2 7.1 6.3 10.2 2.9 6.4 1.2 9.8 1.1 3.6 3.3 2.7 2.3 2.5 3.8 3.6 2.8

5 5 6 6 7 7 8 9 9 9 10 10 13 13 11 11 11 12 12 12 12

III III IV V VI VI VII VIII IX X XI XI XII XII XIII XIII XIII XIV XV XV XVI

Tdb\e No. in Ciparis' data book.

c


66


and CaCl2 f o r m the solvate. T h e n the solvation n u m b e r is d e t e r m i n e d as described i n step (b). As the solvation number of ethanol and C a C ^ is not available i n the literature, w e c a n use So = 6 obtained f r o m the observed values shown i n F i g u r e 13. F o r step (c), w e c a n obtain x\ ' = 0.655 b y substituting x\ = 0.502, x = 0.8724 a n d So = 6 i n E q u a t i o n 11. F i n a l l y w e c a n determine the vaporphase composition as described i n step (d). W h e n the liquid-phase composition of ethyl acetate is 0.655 mole fraction, the vapor-phase composition i n the absence of C a C l is 0.613 mole fraction. Accordingly, when the liquid-phase composition of ethyl acetate is 0.502 mole fraction, the vapor-phase composition i n the presence of CaCl2 i n 7.24 m o l % w i l l be 0.655 mole fraction. Since the observed value is 0.620 mole fraction, the error is 1.1%. a

3


2

T h e results of prediction over the entire range of liquid-phase composition are given i n T a b l e X I I .

T h e comparison of the p r e d i c t i o n results w i t h the ob-

served values shown i n the x-y d i a g r a m is shown i n F i g u r e 14. R E S U L T S O F P R E D I C T I O N A N D DISCUSSION.

given i n Table II together w i t h error.

T h e systems p r e d i c t e d are

T h e results of p r e d i c t i o n of each system

are given i n Tables I I I - X V I . T h e values of So obtained f r o m the observed values shown i n Figures 4 - 1 2 were used as the preferential solvation n u m b e r for prediction. As So is the solvation number between a pure solvent and a salt, it should not be obtained f r o m T a b l e III.

Salt Effect Predicted f r o m the Preferential Solvation f o r Methanol—Water—CaCl

2

S y s t e m at 1 a t m

S = 11.0 0

X

y\ calc.

y\ obs.

0.020 0.020 0.020 0.020 0.020 0.020 0.020 0.020 0.020

0.463 0.616 0.700 0.760 0.806 0.850 0.892 0.931 0.968

0.478 0.594 0.702 0.757 0.810 0.849 0.890 0.920 0.955

3

0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900

Error (%) 3.1 3.7 0.3 0.4 0.5 0.1 0.2 1.2 1.4 av. 1.2%

S = 10.0 0

*»' 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900

x

3

0.040 0.040 0.040 0.040 0.040 0.040 0.040 0.040 0.040

3^1 calc.

y\ obs.

0.529 0.667 0.743 0.794 0.841 0.881 0.915 0.948 0.975

0.530 0.655 0.737 0.794 0.843 0.884 0.914 0.944 0.966

Error (%) 0.2 1.8 0.8 0 0.2 0.3 0.1 0.4 0.9 av. 0.5%


5.

OHE

67


Table I V .

Salt Effect Predicted f r o m the Preferential Solvation for Methanol-Water-CaCI

2

S y s t e m at 2 5 ° C

S = 4.0 0


X

0.2633 0.2909 0.2941 0.3791 0.3977 0.6626 0.6895 0.7257 0.7542

3

0.155 0.175 0.150 0.1464 0.1532 0.1171 0.1242 0.0887 0.1009

^1 calc.

0.867 0.920 0.872 0.896 0.910 0.942 0.953 0.945 0.956

y\ obs. 0.866 0.866 0.877 0.893 0.901 0.956 0.960 0.962 0.962

Error (%) 0.1 6.2 0.6 0.3 1.0 1.5 0.7 1.8 0.6 av. 1.4%

Table V .

Salt E f f e c t Predicted f r o m the Preferential S o l v a t i o n f o r M e t h a n o l - - W a t e r - N a B r S y s t e m at 25° C S = 4.0 0

*/

x 0.1247 0.1118 0.0909 0.0722 0.0563 3

0.148 0.292 0.500 0.700 0.900

^1 calc.

^1 obs.

0.575 0.725 0.840 0.915 0.970

0.756 0.820 0.884 0.932 0.979

Error (%) 23.9 11.5 5.0 1.8 0.9 av.

8.6%

the v a p o r - l i q u i d e q u i l i b r i u m relations. A t present, however, data are not available. In each table, the comparison of prediction results of each system and observed values is shown as the error. The mean error was 0.5% m i n i m u m and 10.2% m a x i m u m . A general trend is that the error is great w h e n the value of S is large. F o r example, i n the m e t h a n o l - w a t e r - N a B r system shown i n T a b l e V , S decreases w i t h the increase i n x\ as shown i n Figure 6. W h i l e the error is 23.9% at X\ = 0.148, it decreases to 0.9% at ae/ = 0.900. T h e same trend is observed i n all systems given i n Tables V I - X I , X I V - X V I . T h e cause of this m a y be that the difference between the calculated value of S and the measured value of S is large where the value of S is great. A n example of p r e d i c t i o n results is shown i n F i g u r e 15 i n the f o r m of a n x-y d i agram. T h e errors i n this method of p r e d i c t i o n are assumed to result f r o m : (a) (b)

the degree of linearity of values of S to X\, a n d the amount of scatter of values of S f r o m the above-mentioned line.

T h e amount of scatter must be smaller if observed values are accurate.

The

linearity of values of S affects the validity of this method of prediction. T o discuss


68

THERMODYNAMIC

Table V I .

BEHAVIOR

OF

ELECTROLYTES

Salt E f f e c t P r e d i c t e d f r o m the Preferential S o l v a t i o n f o r Ethanol—Water—CaCl

2


S = 4.5 0

x


Xl

v

3

0.106 0.233 0.385 0.482 0.666 0.860 0.907 0.917 0.929 0.962

0.168 0.161 0.159 0.170 0.179 0.164 0.171 0.167 0.160 0.165

l

calc.

0.678 0.745 0.814 0.819 0.988 0.977 0.990 0.988 0.986 0.995

obs.

0.785 0.830 0.860 0.868 0.908 0.952 0.960 0.973 0.973 0.989

Error (%) 13.6 10.2 5.4 5.9 8.8 2.6 3.1 1.5 1.3 0.6 av.

5.2%

S = 8.0 0

y\ calc.

0.105 0.426 0.457 0.583 0.791

0.0636 0.0952 0.0970 0.1052 0.0919

0.525 0.805 0.863 0.954 0.938

obs.

Error (%) 19.9 3.7 2.7 8.4 0.8

0.655 0.836 0.840 0.880 0.931 av.

Table V I I .

7.1%

Salt E f f e c t Predicted f r o m the Preferential S o l v a t i o n f o r 1 - P r o p a n o l - - W a t e r - C H C O O K S y s t e m at 1 a t m 3

S = 3.0 0

X

3

0.024 0.090 0.190 0.390 0.485 0.592 0.682 0.896 0.952

0.247 0.240 0.239 0.237 0.235 0.222 0.200 0.120 0.066

calc.

0.641 0.662 0.762 0.860 0.880 0.865 0.850 0.900 0.936

obs.

Error (%)

0.672 0.801 0.853 0.891 0.889 0.894 0.906 0.959 0.975

4.6 17.4 10.7 3.5 1.0 3.2 6.2 6.2 4.0 av.


6.3%

5.

OHE

Table VIII.

69


Salt Effect Predicted f r o m the Preferential S o l v a t i o n f o r Acetic Acid—Water—CaCl

2


S = 3.0 0

x 0.22 8 0.227 0.212 0.199 0.197 0.195 0.186 0.136 0.128


3

0.016 0.044 0.146 0.274 0.297 0.544 0.558 0.732 0.739

3

l obs. 0.086 0.250 0.414 0.536 0.547 0.655 0.646 0.719 0.708

y\ calc.

v

0.085 0.193 0.346 0.460 0.480 0.715 0.695 0.745 0.740

Error (%) 1.2 22.8 16.4 14.2 12.2 9.2 7.6 3.6 4.5 av. 10.2%

Table I X .

Salt E f f e c t P r e d i c t e d f r o m t he Preferential S o l v a t i o n f o r A c e t i c A c i d- W a t e r - N a C l S y s t e m at 1 a t m S = 6.4 0

x 0.033 0.071 0.114 0.232 0.412 0.745 0.994

0.1025 0.0934 0.0863 0.0642 0.0384 0.0129 0.0035

y 1 obs. 0.068 0.121 0.167 0.252 0.382 0.641 0.985

calc.

3

0.075 0.123 0.165 0.250 0.360 0.645 0.986

Error (%) 10.3 1.6 1.2 0.8 5.8 0.6 0.1 av.

Table X .

2.9%

Salt E f f e c t Predicted f r o m the Preferential S o l v a t i o n f o r A c e t i c A c i d - W a t e r - S r C l S y s t e m at 1 a t m 2

S = 11.0 0

x

3

0.025 0.031 0.051 0.059 0.150 0.161 0.229 0.319 0.445 0.449 0.527 0.529 0.696 0.707

0.077 0.073 0.075 0.070 0.061 0.058 0.056 0.049 0.039 0.038 0.033 0.034 0.024 0.028

calc.

0.162 0.130 0.235 0.183 0.273 0.267 0.351 0.389 0.466 0.465 0.504 0.512 0.643 0.667

y\

obs.

Error (%) 26.6 9.1 11.4 16.8 7.8 9.5 2.3 0.8 3.8 3.8 0.4 6.0 1.6 4.5

0.128 0.143 0.211 0.220 0.296 0.295 0.343 0.386 0.449 0.448 0.502 0.483 0.633 0.638 av.


6.4%

70

THERMODYNAMIC BEHAVIOR OF ELECTROLYTES

Table X I .

Salt E f f e c t P r e d i c t e d f r o m the Preferential S o l v a t i o n f o r

A c e t i c A c i d - W a t e r - C H C O O N a S y s t e m at 1 a t m 3

S = 3.5 0

X


Xl

3

0.035 0.074 0.130 0.268 0.488 0.863

0.0552 0.0597 0.0657 0.0809 0.1037 0.1397

y\ calc.

^ i obs.

0.020 0.040 0.070 0.137 0.257 0.606

0.020 0.041 0.070 0.140 0.262 0.610

Error (%) 0 2.4 0 2.1 1.9 0.7 av. 1.2%

S = 3.5 0

x

3

0.034 0.073 0.122 0.264 0.468 0.835

0.0375 0.0405 0.0447 0.0551 0.0702 0.0960

^1 obs.

^1 calc. 0.020 0.043 0.052 0.143 0.284 0.644

Error (%) 9.1 6.5 31.6 9.5 0.4 1.9

0.022 0.046 0.076 0.158 0.285 0.632 av.

Table X I I .

9.8%

Salt E f f e c t Predicted f r o m the Preferential S o l v a t i o n for E t h y l A c e t a t e — E t h a n o l - C a C l S y s t e m at 1 a t m 2

S - 6.0 0

x 0.049 0.123 0.240 0.401 0.403 0.502 0.629 0.741 0.797

3

y\ calc.

^1 obs.

0.0471 0.0535 0.0631 0.0743 0.0720 0.0724 0.0848 0.0824 0.0795

0.124 0.265 0.417 0.560 0.558 0.613 0.713 0.781 0.815

0.123 0.266 0.407 0.558 0.550 0.620 0.710 0.789 0.830

Error (%) 0.8 0.4 2.5 0.4 1.5 1.1 0.4 1.0 1.8 av.

1.1%

S = 4.0 0

Xi

X

0.149 0.290 0.442 0.604

0.124 0.148 0.161 0.171

3

^1 calc. 0.373 0.563 0.696 0.824

y\ obs. 0.363 0.543 0.673 0.789

Error (%) 2.8 3.7 3.4 4.4 av.


3.6%

5.

OHE

71


Table XIII.

Salt E f f e c t Predicted f r o m the Preferential S o l v a t i o n for

Chloroform—Acetone—ZnCl

2


S = 3.3 Downloaded by UNIV OF SOUTHERN CALIFORNIA on June 9, 2013 | http://pubs.acs.org Publication Date: June 1, 1976 | doi: 10.1021/ba-1976-0155.ch005

0

calc.

y\ obs.

Error (%)

0.0235 0.108 0.169 0.267 0.406 0.615 0.804 0.922 0.972

0.0325 0.0725 0.167 0.267 0.408 0.640 0.812 0.948 0.981

0 50.0 1.2 0 0.5 3.9 1.0 2.7 0.9

x

3

0.0497 0.102 0.198 0.295 0.398 0.549 0.689 0.838 0.951

0.0511 0.0562 0.0622 0.0628 0.0683 0.0757 0.0803 0.0836 0.0254

av7~3.3% S = 2.7 0

Jt,'

0.0497 0.102 0.198 0.295 0.398 0.549 0.689 0.838

0.1147 0.1187 0.1303 0.1519 0.1465 0.1619 0.1694 0.1088

y\ calc.

0.0439 0.097 0.212 0.385 0.515 0.755 0.870 0.925

Error (%) 0 0.7 3.2 0.5 2.8 1.3 3.8 4.7

y\ obs. 0.0439 0.0963 0.219 0.383 0.530 0.765 0.904 0.971

av. 2.7% S = 2.3 0

Xi'

0.0497 0.102 0.198 0.398 0.549 0.689

x 0.1018 0.1914 0.2098 0.2345 0.2541 0.2679 3

3^ calc.

0.0620 0.135 0.309 0.715 0.896 0.958

y\ obs. 0.0663 0.137 0.313 0.672 0.883 0.946

Error (%) 6.5 1.5 1.3 6.4 1.5 1.3 av. 2.3%


72

THERMODYNAMIC BEHAVIOR OF ELECTROLYTES

Table X I V .

Salt E f f e c t Predicted f r o m the Preferential S o l v a t i o n f o r Methanol-Ethanol-CaCl

2


S = 5.0 0

X

y 1 calc.

0.077 0.071 0.069 0.066 0.064 0.062 0.058 0.056

0.099 0.285 0.407 0.522 0.620 0.715 0.864 0.934


3

0.098 0.265 0.382 0.490 0.590 0.684 0.852 0.928

obs.

Error (%)

0.100 0.310 0.437 0.530 0.627 0.705 0.864 0.934

1.0 8.1 6.9 1.5 1.1 0.4 0 0 av.

Table X V .

2.5%

Salt E f f e c t Predicted f r o m the Preferential S o l v a t i o n f o r Ethanol—1-Propanol—CaCl

2


S = 3.0 0

Xi

x

y\ calc.

^1 obs.

0.056 0.112 0.225 0.339 0.449 0.562 0.674 0.786 0.899

0.110 0.110 0.110 0.110 0.110 0.110 0.110 0.110 0.110

0.040 0.082 0.175 0.274 0.377 0.485 0.602 0.732 0.873

0.046 0.082 0.171 0.269 0.401 0.509 0.607 0.749 0.881

3

Error (%) 13.0 0 2.3 1.9 6.0 4.7 0.8 2.3 0.9 av.

3.6%

S = 4.0 0

X

3

0.053 0.105 0.210 0.316 0.421 0.526 0.632 0.737 0.842 0.947

0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050

y\ calc.

0.046 0.095 0.198 0.298 0.403 0.505 0.613 0.724 0.837 0.948

^I obs.

0.044 0.090 0.182 0.274 0.385 0.508 0.624 0.741 0.844 0.948

Error (%) 4.6 5.6 8.8 8.8 4.7 0.6 1.8 2.3 0.8 0 av.


3.8%

5.

OHE

73


this point i n detail, it is necessary to establish an elaborate theory f r o m the standpoint of physical chemistry. It was possible for various systems, however, to obtain the linear relation e m p i r i c a l l y f r o m the measured values as described above. A c c o r d i n g l y , we are of the o p i n i o n that the f a i t h f u l utilization of such results is m e a n i n g f u l as the first step toward the establishment of this type of prediction method since there is no prediction method of salt effect available at


present.

Table X V I .

Salt E f f e c t P r e d i c t e d f r o m the Preferential S o l v a t i o n f o r 1-Propanol—1-Butanol—CaCl

2


S = 1.0 0

X

3>l calc.

0.136 0.141 0.156 0.187 0.176 0.180 0.177 0.134

0.168 0.458 0.553 0.627 0.715 0.795 0.878 0.945

3

0.100 0.300 0.400 0.500 0.600 0.700 0.800 0.900

obs.

Error (%)

0.183 0.451 0.566 0.662 0.736 0.807 0.873 0.944

8.2 1.6 2.3 5.3 2.9 1.5 0.6 0.1 av.

2.8%

Conclusion The salt effect is attributable to the formation of preferential solvation f r o m the standpoint of molecular structure. In other words, w h e n c a l c i u m chloride, w h i c h dissolves readily i n methanol but very little i n ethyl acetate, was a d d e d to the methanol-ethyl acetate system to saturation, calcium chloride formed with methanol the preferential solvate which may be written C a C ^ - O C H ^ O H . It was also shown f r o m the observation of solubility that the solvated methanol molecules d i d not participate i n the v a p o r - l i q u i d e q u i l i b r i u m . T h e preferential solvation number was calculated f r o m the observed values of salt effect i n 14 systems, as a result of w h i c h the solvation number showed the linear relationship with respect to the concentration of solvent. It has been made clear that the solvation n u m b e r increases w i t h increase i n the concentration of a solvent f o r m i n g the solvation w h e n the salt concentration is not saturated, but is kept constant w h e n the salt concentration is saturated. T h u s the salt effect was predicted w i t h the use of the above-mentioned relationship. A c c o r d i n g to this prediction method, the salt effect can be d e t e r m i n e d f r o m the solvation n u m b e r of pure solvent a n d the v a p o r - l i q u i d e q u i l i b r i u m relations without a salt.


74



Nomenclature e

= electric charge of electron

k

= B o l t z m a n n constant

n

= n u m b e r of nonelectrolyte molecule

r

= distance between ions

S

= preferential solvation n u m b e r

T

= Absolute temperature

t

= temperature

v

[1.6018 X 1 0 ~ [(1.38044 ± 0.00007) X 1 0 "

coulomb]

1 9

erg/deg]

1 6

[ ] —

[10~ cm] 8

[H [°K] [°C]

molar v o l u m e

[cc/mol]

x

l i q u i d phase composition

[mole fraction]

y

= vapor phase composition

[mole fraction]

z

= electric charge n u m b e r

e

= dielectric constant

7r = ratio of the c i r c u m f e r e n c e to its diameter

Superscript '

= salt free

Subscripts 1 = first component 2 = second component 3 = t h i r d component a

= free solvent molecule not solvated

i

= ion

Literature Cited 1. Wada, G., Itoh, C., J. Chem. Soc. Jpn. Pure Chemistry Section (1956) 77, 391. 2. Debye, P., Z. Phys. Chem. (Leipzig) (1927) 130, 55. 3. Harned, H. S., Owen, B. B., "Physical Chemistry of Electrolytic Solutions," 3rd ed., Reinhold, N.Y., 1957, p 546. 4. Ciparis, J. N., "Data of Salt Effect in Vapour-Liquid Equilibrium," Lithuanian Ag ricultural Academy, Kaunas, USSR, 1966. 5. Hashitani, M., Hirose, Y., Hirata, M., Kagaku Kogaku (1968) 32, 182. 6. Hashitani, M., Hirata, M., J. Chem. Eng. Jpn (1968) 1, 116. 7. Hashitani, M., Hirata, M., J. Chem. Eng. Jpn (1969) 2, 149. 8. Hashitani, M., Ph.D. Thesis, Tokyo Metropolitan University, Tokyo, Japan (1970). 9. Ohe, S., Yokoyama, K., Nakamura, S., Kogyo Kagaku Zasshi (1969) 72, 313. 10. Ohe, S., Yokoyama, K., Nakamura, S.,J.Chem. Eng. Jpn (1969) 2, 1. 11. Ohe, S., Yokoyama, K., Nakamura, S., J. Chem. Eng. Data (1971) 16, 70. 12. Ohe, S., Yokoyama, K., Nakamura, S., Kogyo Kagaku Zassni (1970) 73, 1647. 13. Ohe, S., Yokoyama, K., Nakamura, S., Kagaku Kogaku (1970) 34, 325. 14. Ohe, S., Yokoyama, K., Nakamura, S., Kagaku Kogaku (1970) 34, 1112. 15. Ohe, S., Yokoyama, K., Nakamura, S., Kagaku Kogaku (1971) 35, 104. 16. Yoshida, F., Yasunishi, A., Hamada, Y., Kagaku Kogaku (1964) 28, 133. RECEIVED July 6, 1975.


Prediction of Salt Effect in Vapor-Liquid Equilibrium: A Method Based

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