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
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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.
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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
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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
