Prediction of Salt Effect on VaporâLiquid Equilibrium: A Method

3 Prediction of Salt Effect on Vapor-Liquid Equilibrium: A Method Based on Solvation II

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SHUZO O H E Ishikawajima-Harima Heavy Ind. Co. Ltd., Research Institute, 1 Shinnakahara Isogoku, Yokohama 235, Japan

The preferential solvation formed between salt and solvent molecules causes a salt effect on vapor-liquid

equilibria.

A

method of prediction of salt effect based on the preferential solvation number was reported previously for the case in which salt was solved below the saturation level. The idea introduced in this chapter applies for salt solved in saturation. The alcohol-ester-calcium

chloride system for which

the preferential solvation was thought to be formed examined.

Specifically, calcium chloride dissolves

was

readily

in alcohol but only sparingly in ester. Thus, when calcium chloride is solved into alcohol-ester mixed solvent, the calcium

chloride will form a preferential

alcohol only. Methanol-methyl tate, and methanol-ethyl

solvation

with

acetate, butanol-butyl

ace-

acetate systems were selected for

the mixed-solvent systems.

W

h e n salt is a d d e d t o a v o l a t i l e s o l v e n t m i x t u r e , t h e r e is a salt effect—a c h a n g e i n t h e v a p o r - l i q u i d e q u i l i b r i u m r e l a t i o n .

This

salt effect occurs b e c a u s e salt forms a p r e f e r e n t i a l solvate w i t h a p a r t i c u l a r c o m p o n e n t o f t h e solvent m i x t u r e , c a u s i n g a d r o p i n p a r t i a l pressure of t h e p a r t i c u l a r c o m p o n e n t w h i c h forms t h e p r e f e r e n t i a l solvate. R e s u l t s of t h e studies c o n d u c t e d b a s e d o n this i d e a are r e p o r t e d b y t h e a u t h o r i n References 1 a n d 2. I n t h e p a s t studies, t h e v a p o r - l i q u i d e q u i l b r i u m r e l a t i o n o f t h e s y s t e m f o r w h i c h f o r m a t i o n o f p r e f e r e n t i a l solvate h a d been expected was observed, preferential solvation n u m b e r was calcul a t e d b a s e d o n t h e a c t u a l l y o b s e r v e d v a l u e s , a n d further, salt effect w a s p r e d i c t e d b a s e d o n t h e p r e f e r e n t i a l solvate n u m b e r .

T h e a u t h o r has

0-8412-0428-4/79/33-177-027$05.00/l © 1979 American Chemical Society In Thermodynamic Behavior of Electrolytes in Mixed Solvents—II; Furter, W.; Advances in Chemistry; American Chemical Society: Washington, DC, 1979.

28

THERMODYNAMIC BEHAVIOR O F ELECTROLYTES

II

d e v e l o p e d t h i s s t u d y f u r t h e r b y e x p a n d i n g t h e c o n c e n t r a t i o n o f t h e salt t o t h e s a t u r a t i o n l e v e l ( i n his f o r m e r studies, i t w a s l i m i t e d t o t h e n o n saturated concentration). Preferential

T h i s c h a p t e r reports o n t h i s m o s t r e c e n t s t u d y .

Solvate System

T h e a u t h o r selected t h e s y s t e m c o n t a i n i n g salt w h i c h is n o t d i s s o l v e d w i t h other c o m p o n e n t s b u t o n l y w i t h a p a r t i c u l a r c o m p o n e n t o f a solvent m i x t u r e as a s y s t e m w i t h w h i c h the p h e n o m e n o n o f p r e f e r e n t i a l solvate c a n b e u n d e r s t o o d easily. C a l c i u m c h l o r i d e is d i s s o l v e d w i t h a l c o h o l b u t Downloaded by UNIV ILLINOIS URBANA on June 11, 2013 | http://pubs.acs.org Publication Date: June 1, 1979 | doi: 10.1021/ba-1979-0177.ch003

i t is n o t d i s s o l v e d w e l l w i t h ester. T h u s , c a l c i u m c h l o r i d e f o r m s a p r e f e r e n t i a l solvate w i t h a l c o h o l a n d does n o t w i t h ester.

F o r the

component

s y s t e m w h i c h consists o f c a l c i u m c h l o r i d e , a l c o h o l , a n d ester, t h e a u t h o r s e l e c t e d t h e f o l l o w i n g t h r e e systems f o r w h i c h v a p o r - l i q u i d e q u i b r i u m relations have been measured: m e t h a n o l - e t h y l a c e t a t e - c a l c i u m chloride ( I ) ; m e t h y l a c e t a t e - m e t h a n o l - c a l c i u m c h l o r i d e ( 3 ) ; a n d η-butyl a c e t a t e n-butanol-calcium chloride ( 3 ) . Solubility

of Salt into Solvent

Mixture

T h e s o l u b i l i t y o f the salt i n t o a solvent m i x t u r e is d e c i d e d b y t h e concentration of a particular component

i n t h a t m i x t u r e w h e n salt is

readily dissolved only w i t h the particular component i n the solvent m i x t u r e . F i g u r e s 1, 2, a n d 3 s h o w s o l u b i l i t i e s o f c a l c i u m c h l o r i d e few: t h e a b o v e m e n t i o n e d t h r e e systems. F i g u r e 1 shows t h e s o l u b i l i t y o f c a l c i u m

Journal of Chemical Engineering, of Japan

Figure I . Solubility of calcium chloride in boiling methanol-ethyl acetate mixture at 1 atm (3)

In Thermodynamic Behavior of Electrolytes in Mixed Solvents—II; Furter, W.; Advances in Chemistry; American Chemical Society: Washington, DC, 1979.


Figure 2.

Solubility

of calcium chloride in boiling methyl mixture at 1 atm

c h l o r i d e i n t o t h e m e t h a n o l - e t h y l acetate

system.

acetate-methanol

F r o m 0-0.333

mole

f r a c t i o n of m e t h a n o l , t h e s o l u b i l i t y is a l m o s t z e r o . T h e s e s o l u b i l i t y d a t a i n d i c a t e t h a t i f c a l c i u m c h l o r i d e is d i s s o l v e d b y o n l y t h e m e t h a n o l c o n t a i n e d i n t h e m e t h a n o l - e t h y l acetate s o l u t i o n , b o t h solvents exist i n t h e f o r m of c l u s t e r e d m o l e c u l e s c o m p r i s e d of one m e t h a n o l m o l e c u l e t w o e t h y l acetate m o l e c u l e s ( 2 ) .

and

I n m e t h a n o l c o n c e n t r a t i o n s greater t h a n

0.333 m o l e f r a c t i o n , free m o l e c u l e s f o r m i n g n o n c l u s t e r e d m o l e c u l e s present i n t h e system, so t h a t t h e salt is d i s s o l v e d i n t h e free

are

molecules

of m e t h a n o l . F r o m t h e e x t r a p o l a t e d s o l u b i l i t y ( t h e m o l e r a t i o of c a l c i u m c h l o r i d e to m e t h a n o l is — 1 : 6 ) , c a l c i u m c h l o r i d e a n d m e t h a n o l are b e l i e v e d t o f o r m a solvate of C a C l

2

· 6CH OH. 3

F i g u r e 2 shows t h e s o l u

b i l i t y of c a l c i u m c h l o r i d e i n t o t h e m e t h y l a c e t a t e - m e t h a n o l system.

Fig

ure 2 was d r a w n b y the author based on H a s h i t a m s report ( 3 ) .

This

figure

i n d i c a t e s t h a t t h e s o l u b i l i t y changes l i n e a r l y a g a i n s t t h e

concen

t r a t i o n of m e t h a n o l i n t h e same m a n n e r as t h a t d e p i c t e d i n F i g u r e 1. S o l u b i l i t y is a l m o s t z e r o i n t h e r a n g e w h e r e t h e m o l e f r a c t i o n of m e t h a n o l


30

THERMODYNAMIC BEHAVIOR O F ELECTROLYTES

is b e t w e e n 0 a n d 0.15.

II

T h e m o l e c u l e s o f m e t h a n o l a n d m e t h y l acetate

f o r m a c l u s t e r o f some k i n d a n d b e c a u s e of this c l u s t e r , n o free m e t h a n o l m o l e c u l e exists. F i g u r e 3 shows the s o l u b i l i t y o f c a l c i u m c h l o r i d e i n t h e b u t y l a c e t a t e - b u t a n o l system. T h i s figure w a s d r a w n also b y t h e a u t h o r b a s e d o n H a s h i t a m s r e p o r t ( 3 ) . T h i s figure shows t h a t t h e s o l u b i l i t y o f c a l c i u m c h l o r i d e reduces l i n e a r l y against t h e r e d u c t i o n o f t h e m o l e f r a c t i o n o f b u t a n o l a n d t h a t t h e existence o f b u t a n o l i n t h e solvent m i x t u r e c o n t r i b u t e s t o d i s s o l v i n g c a l c i u m c h l o r i d e . S i m i l a r l y , i n t h i s s y s t e m also, t h e s o l u b i l i t y o f c a l c i u m c h l o r i d e is a l m o s t z e r o a t t h e r a n g e w h e r e t h e


m o l e f r a c t i o n o f b u t a n o l is b e t w e e n 0 a n d 0.2. T h i s occurs b e c a u s e f o u r m o l e c u l e s o f b u t y l acetate f o r m a c l u s t e r a g a i n s t one m o l e c u l e of b u t a n o l

Ο

ο es ο

3

Journal of Chemical Engineering of Japan

Figure

3.

Solubility

of calcium chloride in boiling mixture at 1 atm (3)

butyl

acetate-butanol


3.

OHÉ

Prediction

of Salt

31

Effect

r e s u l t i n g i n the i n a b i l i t y of a b u t a n o l m o l e c u l e to exist. I t is o b v i o u s f r o m t h e a b o v e d e s c r i b e d three examples t h a t c a l c i u m c h l o r i d e is d i s s o l v e d only b y an alcohol molecule

i n a solvent m i x t u r e .

T h i s indicates that

c a l c i u m c h l o r i d e is r e l a t e d o n l y to a l c o h o l m o l e c u l e s i n t h e solvent m i x t u r e , s u g g e s t i n g t h e existence of a p r e f e r e n t i a l solvate. Preferential

Solvation

Number

W h e n a p r e f e r e n t i a l solvate is f o r m e d across salt a n d a p a r t i c u l a r c o m p o n e n t i n a solvent m i x t u r e , t h e p r e f e r e n t i a l l y s o l v a t e d Downloaded by UNIV ILLINOIS URBANA on June 11, 2013 | http://pubs.acs.org Publication Date: June 1, 1979 | doi: 10.1021/ba-1979-0177.ch003

is a s s u m e d to b e n o n v o l a t i l e .

component

H e n c e , the essential c o n c e n t r a t i o n of t h e

p r e f e r e n t i a l l y s o l v a t e d c o m p o n e n t i n t h e solvent m i x t u r e is r e d u c e d

as

m u c h as t h e s o l v a t e d c o m p o n e n t . T h e v a p o r - l i q u i d e q u i l i b r i u m r e l a t i o n o b t a i n e d u n d e r t h e a d d i t i o n of a salt m a y w e l l b e c o n s i d e r e d to b e t h e same as t h e v a p o r - l i q u i d e q u i l i b r i u m w i t h o u t the salt for composition

from

w h i c h t h e solvents

forming

solvates

liquid-phase

are

excluded.

B a s e d o n this i d e a , the essential c o n c e n t r a t i o n at the t i m e w h e n salt forms a p r e f e r e n t i a l solvate w i t h the p r i m a r y c o m p o n e n t is g i v e n b y E q u a t i o n 1. T h e n w e c a n o b t a i n the 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 f r o m the o b s e r v e d values of the salt effect. A s the c o n c e n t r a t i o n of solvent is d e c r e a s e d b y t h e n u m b e r of s o l v a t e d m o l e c u l e s , the a c t u a l solvent c o m p o s i t i o n 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 c h a n g e d .

par

Assuming that a

salt forms the solvate w i t h t h e first c o m p o n e n t , the a c t u a l

composition

*ia is g i v e n b y

1

Since x

1

=

Xi(l

-

&

(xi-Sxs)+x '

U

2

— x ) , *2 — x ' ( l — x ), 3

a n d Xi +

3

2

*2 =

j

1, E q u a t i o n 2

is r e w r i t t e n as f o l l o w s : • -Sx*

* i ' ( l --Χά)

(1-

Xs)

~•Sx3

(2)

obtain

S

m

m

±1 — ^ 3±s±iΧχ'Xs

1 —

( 3 )

Xla

Therefore, the solvation n u m b e r can be calculated b y determining

x ' 1&

f r o m t h e m e a s u r e d values u s i n g t h e v a p o r - l i q u i d e q u i l i b r i u m r e l a t i o n o b t a i n e d w i t h o u t a d d i n g a salt. W h e n a salt forms t h e s o l v a t i o n w i t h the second component, the f o l l o w i n g three equations can be derived i n a similar manner.


32

THERMODYNAMIC

#la =

BEHAVIOR

O F ELECTROLYTES

Xi

II

(4)

X\ + {X2 — Sx ) s

Xla

(l—x )xi (1 — x ) — Sx s

s

s —

1 —

(5) 3

£ 3 X\ ' — X\ &

(6)

Xm

Xs

F i g u r e s 4, 5, a n d 6 i n d i c a t e c a l u c u l a t e d results o f t h e p r e f e r e n t i a l s o l Downloaded by UNIV ILLINOIS URBANA on June 11, 2013 | http://pubs.acs.org Publication Date: June 1, 1979 | doi: 10.1021/ba-1979-0177.ch003

v a t i o n n u m b e r s f o r the t h r e e systems. A s s h o w n b y e a c h figure, 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 s are a l m o s t c o n s t a n t a g a i n s t c o m p o s i t i o n s o f t h e solvent. O n t h e other h a n d , t h e c o n c e n t r a t i o n of salt increases l i n e a r l y a g a i n s t a n increase i n t h e c o n c e n t r a t i o n o f a l c o h o l i n t h e solvent as i n d i c a t e d i n F i g u r e s 1, 2, a n d 3. T h i s f a c t denotes t h a t f o r a n increase of solvent w h i c h forms a p r e f e r e n t i a l solvate i n a solvent m i x t u r e , t h e salt r e q u i r e d t o f o r m a c e r t a i n s o l v a t i o n n u m b e r w i t h t h a t s o l v e n t is d i s s o l v e d . F o r essential c o n c e n t r a t i o n x ' i n E q u a t i o n s 3 a n d 4, w h i c h l2i

are r e q u i r e d i n c a l c u l a t i n g s o l v a t i o n n u m b e r s , t h e d a t a o b s e r v e d b y t h e a u t h o r et a l . ( J ) w e r e u s e d f o r t h e m e t h a n o l - e t h y l acetate

0.2

0.6

0.4

0.8

system;

1.0

χι Journal of Chemical and Engineering Data

Figure 4. Preferential solvation number in the methanol-ethyl acetate sys tem at 1 atm: (O), CaCl : 5 wt %; (Δ), CaCl :10 tot %; (V), CaCl : 20 wt %; (Π), CaCl : 25 wt %; (Φ), CaCl : saturated (I). 2

2

2

2

2



3.

OHÉ

Prediction

33

of Salt Effect

oo

X

1 Journal of Chemical Engineering of Japan

Figure 5. Preferential solvation number in the methyl acetate-methanolcalcium chloride system at 1 atm (0)~CaCl : 6 wt %; (A), CaCl : 15 wt %; (Φ), CaCl : saturated (3). 2

2

2

N a g a t a ' s d a t a (4) w e r e u s e d f o r the m e t h y l a c e t a t e - m e t h a n o l

system;

a n d f o r t h e b u t y l a c e t a t e - b u t a n o l system, d a t a o b s e r v e d b y B r u n j e s et a l . ( 5 ) w e r e u s e d . F i g u r e 4 shows t h a t the 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 i s a b o u t 5.5 i n t h e m e t h a n o l - e t h y l a c e t a t e - c a l c i u m c h l o r i d e system, a n d i t is constant at t h e r a n g e w h e r e t h e m o l e f r a c t i o n o f m e t h a n o l is b e t w e e n 0.333 a n d 1.000. A t t h e r a n g e w h e r e the m o l e f r a c t i o n o f m e t h a n o l is less t h a n 0.333, the c o n c e n t r a t i o n o f c a l c i u m c h l o r i d e is z e r o a n d c o n s e q u e n t l y t h e 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 is also zero. F i g u r e 5 i n d i c a t e s t h a t f o r t h e m e t h y l a c e t a t e - m e t h a n o l - c a l c i u m c h l o r i d e system, t h e 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 is a b o u t 5, a n d i t i s constant a t t h e r a n g e w h e r e t h e m o l e f r a c t i o n o f m e t h y l acetate is b e t w e e n 0 a n d 0.85. A t t h e r a n g e w h e r e t h e m o l e f r a c t i o n o f m e t h y l acetate is 0.85 t o 1.0, t h e c o n c e n t r a t i o n o f c a l c i u m c h l o r i d e is zero, a n d c o n s e q u e n t l y ,

t h e preferential solvation

n u m b e r is also zero. F o r t h e b u t y l a c e t a t e - b u t a n o l - c a l c i u m c h l o r i d e sys-


34

THERMODYNAMIC

3.0

BEHAVIOR

OF ELECTROLYTES

II

2.0

GO


1.0

0.2

Figure

6.

Preferential

0.4

0-8

0.6

solvation number in the butyl cium chloride system at 1 atm

1.0

acetate-butanol-cal-

tern, t h e 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 is a b o u t 2 a n d i t is constant at t h e r a n g e w h e r e t h e m o l e f r a c t i o n of b u t y l acetate is b e t w e e n 0 a n d as s h o w n i n F i g u r e 6.

0.8

A t t h e r a n g e w h e r e the m o l e f r a c t i o n of b u t y l

acetate is 0.8 to 1.0, the c o n c e n t r a t i o n of c a l c i u m c h l o r i d e is zero, a n d the 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 is also zero.

Prediction

of Salt Effect

A m e t h o d to p r e d i c t salt effect o n v a p o r - l i q u i d e q u i l i b r i u m i n w h i c h salt is d i s s o l v e d i n a s a t u r a t e d state is i n t r o d u c e d .

I n this m e t h o d , salt

effect is p r e d i c t e d b y u s i n g 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 s , t h e c o n c e n t r a t i o n of t h e salt, a n d t h e v a p o r - l i q u i d e q u i l i b r i u m d a t a for w h i c h salt is n o t i n v o l v e d . I t is p o s s i b l e to p r e d i c t salt effect c o m p l e t e l y w i t h o u t u s i n g a c t u a l l y m e a s u r e d d a t a i f the 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 c a n b e p r e d i c t e d . P r e s e n t l y , h o w e v e r , i t is i m p o s s i b l e to c o m p l e t e l y p r e d i c t p r e f e r ential solvation number.

H e n c e , the preferential solvation numbers

are

o b t a i n e d t h r o u g h a c t u a l measurements, a n d these n u m b e r s are u s e d f o r the prediction.

If preferential solvation number can be predicted inde

pendently i n the future, this method w i l l be a n extremely hopeful

one.

T h e salt effect p r e d i c t i o n m e t h o d is e n t i r e l y i n reverse s e q u e n c e of t h a t u s e d to o b t a i n 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 .

S p e c i f i c a l l y , i t is c a r r i e d

o u t i n t h e f o l l o w i n g sequence. ( 1 ) T h e c o m p o n e n t s w h i c h f o r m p r e f e r e n t i a l solvate i n a m i x e d solvent system are d e t e r m i n e d .


3.

OHÉ

Prediction

of Salt

35

Effect

(2) T h e 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 across salt a n d solvent is determined. (3) S o l u b i l i t y o f salt i n t o t h e solvent m i x t u r e is d e t e r m i n e d . (4) T h e essential c o m p o s i t i o n (*i ') is c a l c u l a t e d b y a p p l y i n g E q u a t i o n 2 o r 5. a

(5) V a p o r c o m p o s i t i o n f o r t h e x ' is r e a d o u t b y u s i n g the vaporl i q u i d e q u i l i b r i u m d a t a f o r w h i c h salt is n o t i n v o l v e d , a n d this v a p o r c o m p o s i t i o n is u s e d as t h e v a p o r c o m p o s i t i o n f o r t h e a c t u a l c o n c e n t r a t i o n (Xi). 1&

F i g u r e s 7, 8, a n d 9 i n d i c a t e t h e p r e d i c t i o n results f o r t h e f o l l o w i n g


three systems:

m e t h a n o l - e t h y l acetate,

methyl acetate-methanol, a n d

b u t y l acetate-butanol w i t h saturated c a l c i u m chloride, respectively. T h e a b s o l u t e v a l u e of m e a n errors \Ay\ w e r e 0.018 a n d 0.014 f o r e a c h system, w h i l e the m a x i m u m a n d m i n i m u m errors w e r e 0.047 a n d 0, 0.039 a n d 0.005, a n d 0.039 a n d 0.005, r e s p e c t i v e l y .

0.2

Figure

7.

0.4

0.6

Result of prediction for methanol-ethyl ride system at 1 atm: (O), observed; (—),

0.8

acetate-calcium calculated.


1.0

chlo-



OHÉ

Prediction


3.

37

of Salt Effect

X !

Figure

9.

Result of prediction for butyl acetate-butanol-calcium ride system at 1 atm: (O), observed; (—), calculated.


chlo-

38

THERMODYNAMIC

BEHAVIOR

OF ELECTROLYTES

II

Conclusion A s a cause of salt effect, t h e existence of a p r e f e r e n t i a l solvate f o r m e d across salt a n d p a r t i c u l a r c o m p o n e n t i n a s o l v e n t m i x t u r e is c o n s i d e r e d . 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 w a s c a l c u l a t e d for t h e a l c o h o l - e s t e r - c a l c i u m c h l o r i d e s y s t e m i n w h i c h f o r m a t i o n of p r e f e r e n t i a l b e l i e v e d to exist.

solvate

was

T h e preferential solvation number was found to

constant regardless of c o m p o s i t i o n s of a s o l v e n t m i x t u r e .

O n the

be

other

h a n d , t h e s o l u b i l i t y o f salt i n t o m i x e d s o l v e n t i n c r e a s e d l i n e a r l y a g a i n s t a n increase of c o m p o s i t i o n of t h e c o m p o n e n t w h i c h d i s s o l v e d salt.

This


f a c t i n d i c a t e s t h a t t h e e n t i r e d i s s o l v e d salt c o n t r i b u t e s t o t h e f o r m a t i o n of s o l v a t i o n w i t h t h e p a r t i c u l a r c o m p o n e n t i n t h e m i x e d solvent.

The

a u t h o r feels t h a t t h e s t u d y s h o u l d b e c o n t i n u e d i n o r d e r t o m a k e t h e salt effect c l e a r so t h a t i t w i l l b e p o s s i b l e to a p p l y t h e a b o v e d e s c r i b e d i d e a t o o t h e r systems also.

Glossary

of Symbols

S = preferential solvation number ( — ) χ = liquid-phase composition (mole fraction) y = vapor-phase composition (mole fraction) Superscript ' = salt free Subscripts 1 = first c o m p o n e n t 2 = second component 3 = third component a = free s o l v e n t m o l e c u l e n o t s o l v a t e d

Literature Cited 1. 2. 3. 4. 5.

Ohe, S., Yokoyama, K., Nakamura, S., J. Chem. Eng. Data (1971) 16(1), 70. Ohe, S., Adv. Chem. Ser. (1976) 155, 53. Hashitani, M., Mirata, M., J. Chem. Eng. Jpn. (1969) 1(2), 116. Nagata, I., J. Chem. Eng. Data (1969) 14(4), 418. Brunjes, A. S., Furnas, C. C., Ind. Eng. Chem. (1935) 27, 396.

RECEIVED March 1,

1978.


Prediction of Salt Effect on VaporâLiquid Equilibrium: A Method

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