Prediction of Vapor Composition in Isobaric Vapor-Liquid Systems

11 Prediction of Vapor Composition in Isobaric Vapor-Liquid Systems Containing

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Salts at Saturation D. JAQUES and W. F. FURTER Department of Applied Chemistry, Royal Melbourne Institute of Technology, Melbourne, Victoria, Australia, and Department of Chemical Engineering, Royal Military College of Canada, Kingston, Ontario, Canada A method is described for calculating equilibrium vapor compositions from boiling point vs. liquid composition data in ternary systems composed of two liquid components and a salt added to saturation. The procedure is tested on the ethanol-water system containing each of a wide range of inorganic salts at saturation. The results suggest that good quality Τ-Π-x data will yield y values of comparable accuracy.

* T * o o b t a i n 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 b i n a r y systems, i t is n o w w e l l e s t a b l i s h e d that u n d e r

certain circumstances

it can be

more

accurate a n d less t i m e c o n s u m i n g to m e a s u r e the b o i l i n g p o i n t , the t o t a l pressure, a n d the l i q u i d c o m p o s i t i o n a n d t h e n use the G i b b s - D u h e m r e l a t i o n s h i p to p r e d i c t v a p o r c o m p o s i t i o n ( I ) r a t h e r t h a n to m e a s u r e it. T h e d i s a d v a n t a g e is that there is n o w a y o f c h e c k i n g the t h e r m o d y n a m i c consistency o f the e x p e r i m e n t a l data. F o r systems c o m p o s e d o f t w o l i q u i d s a n d a salt at saturation, this p r o c e d u r e is e s p e c i a l l y attractive because there are c o n s i d e r a b l e e x p e r i m e n t a l difficulties i n o b t a i n i n g accurate x - t / - T - I I d a t a a n d the

process

is m o r e t i m e c o n s u m i n g t h a n i n the absence o f salts. A p r o c e d u r e is presented w h i c h is b a s e d u p o n B a r k e r s m e t h o d for c a l c u l a t i n g v a p o r c o m p o s i t i o n s f r o m the

k n o w n temperature

(2) de

p e n d e n c e o f the v a p o r pressure of the p u r e constituents, w i t h s u i t a b l e m o d i f i c a t i o n for the presence o f salt, a n d f r o m the d e p e n d e n c e

o f the

b o i l i n g p o i n t o f the m i x t u r e w i t h c o m p o s i t i o n o f the e q u i l i b r i u m l i q u i d phase.

159 Tassios; Extractive and Azeotropic Distillation Advances in Chemistry; American Chemical Society: Washington, DC, 1974.

160

EXTRACTIVE

AND AZEOTROPIC DISTILLATION

Procedure A c o m p u t e r p r o g r a m is u s e d w h i c h m i n i m i z e s 2 ( Π - Π ) 0

2

where the

t o t a l pressure is g i v e n b y : n

= x p '

c

+ (ΐ-χ)ρ' γ,

m

(1)

2

U s i n g ρ Ί a n d p ' i n s t e a d o f t h e s a t u r a t i o n v a p o r pressures o f t h e p u r e 2

l i q u i d components

a l l o w s f o r t h e presence

o f salt.

F o r salt-saturated


systems i t i s p r o p o s e d t o base t h e a c t i v i t y coefficients o n a s t a n d a r d state of e a c h l i q u i d c o m p o n e n t s a t u r a t e d w i t h salt. T h e a c t i v i t y

coefficients

are r e l a t e d t o t h e l i q u i d c o m p o s i t i o n b y u s i n g t h e two-constant W i l s o n e q u a t i o n ( 3 ) except f o r systems w h i c h s h o w a r e g i o n o f i m m i s c i b i l i t y w h e n t h e three-constant f o r m is necessary. O n e a d v a n t a g e o f t h e W i l s o n e q u a t i o n o v e r other s e m i - e m p i r i c a l a p p r o x i m a t i o n s f o r i n t e g r a t i n g t h e G i b b s - D u h e m e q u a t i o n is t h a t i t h a s a d e g r e e o f b u i l t - i n dependence form

f o r t h e l i q u i d - p h a s e a c t i v i t y coefficients.

temperature

T h e two-constant

gives:

mη -

-W-AM-*))

in y, -

+ (i-x) { - ^

- H i - Α * ,

-

-

W h e n t h e best values o f A i a n d A s i t i o n is c a l c u l a t e d : 2

ln(l-y)

= Ζη((1-χ)ρ' /Π) j(l-x) X

2

j,^}

12

\ 1-A x

(2b)

have been found, the vapor

2 2

A 12

1

ïT^fb)}

(£ -V )(II-p' )/RT -

2

_

-

2

_

2

xA

21

1-A

21

compo

ln(l-A x) 12

)

3

(l-x)f

T h e t e r m i n v o l v i n g t h e m i x e d s e c o n d v i r i a l coefficients

was not used

because o f t h e u n c e r t a i n t i e s i n t h e values o f t h e s e c o n d v i r i a l

coefficients

of t h e p u r e c o m p o n e n t s . Application T h e m e t h o d d e s c r i b e d a b o v e is a p p l i e d t o t h e e t h a n o l - w a t e r

system

w h i c h has b e e n s a t u r a t e d i n t u r n w i t h e a c h of a w i d e r a n g e o f i n o r g a n i c salts. T h e v a p o r pressure o f w a t e r s a t u r a t e d w i t h salts o v e r a t e m p e r a t u r e range is a v a i l a b l e f o r m a n y salts (4).

F o r e t h a n o l these d a t a a r e

u n a v a i l a b l e , a n d a c o r r e c t i o n to t h e saturation v a p o r pressure is a p p l i e d b y m u l t i p l y i n g b y t h e r a t i o o f t h e v a p o r pressure o f e t h a n o l s a t u r a t e d

Tassios; Extractive and Azeotropic Distillation Advances in Chemistry; American Chemical Society: Washington, DC, 1974.

11.

J A Q U E S

A N D

Prediction

F U R T E R

of Vapor

161

Composition

w i t h salt to the v a p o r pressure of p u r e e t h a n o l at the salt s o l u t i o n b o i l i n g T h i s r a t i o , c,

point.

is a s s u m e d to

be

independent

of

temperature.

I n t e r p o l a t i n g l i t e r a t u r e d a t a y i e l d e d the r e q u i r e d v a l u e s of the v o l u m e s of the t w o l i q u i d s ( 5 )

molar

at the a p p r o p r i a t e temperatures a n d the

s e c o n d v i r i a l coefficients of w a t e r ( β )

and ethanol (7).

A n example

of

the fit is s h o w n i n T a b l e I.


Table I. Calculated Vapor Compositions from Fit of Isobaric D a t a Ethanol—Water—Saturated Ammonium Chloride (14)

X .034 .074 .124 .170 .284 .446 .633 .759 .858 .938

G*/RT-x

Τ—χ fit

y

Τ

.495 .595 .646 .674 .696 .720 .752 .807 .869 .936

93.8 87.2 84.2 82.5 81.7 80.8 79.4 78.5 77.7 77.9

fit

(y-y»)

(y-yc)

.000 -.012 -.007 -.005 -.001 -.003 -.019 -.012 -.006 .001

.003 -.007 .000 .004 .009 .005 -.016 -.014 -.011 -.003 .0098

.0098

Sample deviation

A s a n alternative, these d a t a w e r e also fitted to W i l s o n s free e n e r g y equation: (? /RT = E

-x

ln(l-A (l-x)) 21

-

(l-x)

(4)

ln{\-A x) l2

a n d the v a p o r c o m p o s i t i o n w a s a g a i n c a l c u l a t e d b y u s i n g E q u a t i o n 3.

A

d i r e c t c o m p a r i s o n c a n b e m a d e b y e x a m i n i n g the s a m p l e d e v i a t i o n of the v a p o r c o m p o s i t i o n f r o m b o t h

fittings.

T a b l e II presents the t w o sets

of s a m p l e d e v i a t i o n s b a s e d u p o n v a p o r c o m p o s i t i o n s . a n d σο /κτ Ε

T h e values of σπ

i n d i c a t e that some of the d a t a are of d u b i o u s a c c u r a c y — i . e . ,

l o w consistency a n d / o r h i g h e x p e r i m e n t a l scatter. of the o b s e r v e d Ύ-χ

G r a p h i c a l smoothing

d a t a w o u l d have r e d u c e d the values of the s a m p l e

deviations b y r e m o v i n g the e x p e r i m e n t a l scatter c o m p o n e n t , b u t i t w a s c o n s i d e r e d d e s i r a b l e to use the r a w d a t a . T h e v a l i d i t y of the Ύ-χ

e s t i m a t i o n for

the e t h a n o l - w a t e r

binary

w i t h o u t salt was c h e c k e d u s i n g three sets of l i t e r a t u r e d a t a . T h e results are i n c l u d e d i n T a b l e II, a n d O t s u k i s d a t a ( S )

are s h o w n i n F i g u r e 1.

C a l c u l a t e d a n d e x p e r i m e n t a l y-values agree satisfactorily. A d d i t i o n of a salt i n m a n y cases results i n a c o n s i d e r a b l y w i d e r b o i l i n g range, a n d this w o u l d affect the heat of m i x i n g t e r m a n d l e a d to a p o o r e r fit of the d a t a . H o w e v e r , this is u n l i k e l y to be a n i m p o r t a n t factor because

Tassios; Extractive and Azeotropic Distillation Advances in Chemistry; American Chemical Society: Washington, DC, 1974.

162

EXTRACTIVE

AND AZEOTROPIC

DISTILLATION

it has b e e n s h o w n ( 9 ) that a g o o d fit i s o b t a i n e d w i t h i s o b a r i c d a t a f o r the m e t h a n o l - a n i s o l e system w h i c h has a 64 ° C b o i l i n g range.

Comparing

the t w o sets o f results i n T a b l e I I i n d i c a t e s that the G /KT-x

fit

i s gen

e r a l l y superior, b u t f o r t h e better d a t a as i n d i c a t e d b y s m a l l

sample

E

deviations o f pressure a n d free energy, t h e differences c o n c l u s i o n is not u n e x p e c t e d . In y = Ζ τ φ ρ Ί / Π ) -

However, if the following

(Bu-VOffl-p'O/RT

ttl-x)A \ l-A x


l2

+

U

X )

are s m a l l .

12

-

This

equation

ln(l-A {l-x)) 2l

xA ) l-A (l-x)f

5

21

21

is u s e d to c a l c u l a t e the v a p o r c o m p o s i t i o n i n s t e a d o f E q u a t i o n 3, i n every case except f o r b a r i u m nitrate t h e opposite is true. m a r g i n a l , a n d a n e x p l a n a t i o n is offered Table II. Salt — — —

NH CI 4

tNaCl t NaBr t NaN0 tKCl KBr KI K S0 Ca(N0 ) Ba(N0 ) CuCl HgCl HgBr Hgl LiCl" t NaCl » t Na S0 tKCl» ΚΙ" BaCl KN0 (NH ) S(V 3

2

4

3

3

2

2

2

2

2

2

4

2

3

4

d

e

2

6

T h i s effect i s n o t

below.

Comparison of the T - * Fit and the G^/RT-x the Wilson Equation σΠ

«y

Prediction of Vapor Composition in Isobaric Vapor-Liquid Systems

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