8 Representation of N H - H S - H O , N H - S O H O, and N H - C O - H O Vapor-Liquid Equilibria 3
2
3
2
2
2
3
2
2
H. RENON
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Group Commun Reacteurs et Processus, ENSTA-Ecole Des Mines, 60, Boulevard St. Michel, 75006 Paris, France
A renewed interest in the behavior of volatile electrolyte solutions appeared around 1975. It was raised by the need of bet ter design of industrial processes , especially pollution control processes, elimination of acid gases from natural gas, removal of sulfur from liquid and solid fuels and more recently coal conver sion processes. VAN AKEN et al. (1) and EDWARDS et al. (2) made clear that two sets of fundamental parameters are useful in describing vaporliquid equilibria of volatile weak electrolytes, (1) the dissocia tion constant(s) Κ of acids, bases and water, and (2) the Henry's constants Η of undissociated volatile molecules. A thermodynamic model can be built incorporating the definitions of these parame ters and appropriate equations for mass balance and electric neu trality. It is complete if deviations to ideality are taken into account. The basic framework developped by EDWARDS, NEWMAN and PRAUSNITZ (2) (table 1) was used by authors who worked on volatile electrolyte systems : the difference among their models are in the choice of parameters and in the representation of deviations to ideality. Table 1. Thermodynamic Framework of Representation of Vapor-Liquid E q u i l i b r i a of Weak E l e c t r o l y t e s Vapor-Liquid E q u i l i b r i u m D i s s o c i a t i o n Balances Mass Balances Electroneutrality D e v i a t i o n s to I d e a l i t y An a p p l i c a t i o n to one b i n a r y mixture of a v o l a t i l e e l e c t r o l y te and water w i l l i l l u s t r a t e the choice of parameters Η and K, an approach i s proposed to represent the v a p o r - l i q u i d e q u i l i b r i u m i n the whole range of c o n c e n t r a t i o n . Ternary mixtures w i t h one a c i d and one base lead to the formation of s a l t s and high i o n i c strengths can be reached. There, i t was found u s e f u l to take i n t o account 0-8412-0569-8/80/47-133-173$05.00/0 © 1980 American Chemical Society
In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.
174
THERMODYNAMICS OF
AQUEOUS
SYSTEMS
WITH
INDUSTRIAL
APPLICATIONS
1
ternary parameters i n PITZER S (3) development and improved r e s u l t s using o r i g i n a l BEUTIER S ideas are presented. 1
A c e t i c Acid-Water M i x t u r e . CRUZ (4) chose t h i s example t o i l l u s t r a t e h i s method of r e p r e s e n t a 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 a of v o l a t i l e weak e l e c t r o l y t e and t o show how t o o b t a i n simply from experimental v a p o r - l i q u i d e q u i l i b r i u m data the s i g n i f i c a n t parameters . He uses the d i s s o c i a t i o n constant g i v e n i n the littérature to represent the d i s t r i b u t i o n of a c e t i c a c i d i n d i l u t e s o l u t i o n from h i s own measurements (mole f r a c t i o n of a c e t i c a c i d between 10"^ and 10~7). Equation (1) where x^ i s the measured apparent mole f r a c t i o n of a c i d i n the l i q u i d phase g i v e s H by p l o t t i n g P y vs.ax^ Downloaded by UNIV LAVAL on May 26, 2014 | http://pubs.acs.org Publication Date: October 29, 1980 | doi: 10.1021/bk-1980-0133.ch008
A
P
ax
?A " < A>
2
Ι
ΪΓ ^ "
00 r^mr^cj>coP a a J
y Downloaded by UNIV LAVAL on May 26, 2014 | http://pubs.acs.org Publication Date: October 29, 1980 | doi: 10.1021/bk-1980-0133.ch008
= m Y H P a a a a
T
φ
(3)
Ρ = a π φ (S) w w w
(4)
Ρ
T
WW
w
D i s s o c i a t i o n E q u i l i b r i u m (5 equations) Χ
(I) Β + Η 0 2
Β
+
+ 0Η~
type of d i s s o c i a t i o n ( I ) , (II) or ( I I I ) i s reported i n t a b l e 2. a. f o r a c i d s and base.
+
A X A
(II)
(III) A" X (IV)
Β + A
(V)
H0
X
2
7
Ύ
+ Η A
=
+ H
Χ H
ΒΑ
+
Mass Balance +
A = m
A
+
V mA
2
. . . . ι* components on the l e f t side of d i s s o c i a t i o n e q u i l i b r i u m , j , components on the r i g h t side of the same. (5)
m
- «Έ
+ H 0 , f o r example, formation of carbamate
+ OH"
m
ΐ i Κ = —^~γ" j j j
B
+
+
+
(2 equations)
(
"BA"
m = A
+
6
)
(7)
V
E l e c t r o n e u t r a l i ty
V
+
V
-V
+
2
M
+
A=
( 8 )
"OH"
Given (Ρ, Τ, Α, Β ) , the 10 equations (3) to (8) y i e l d the ten unknown ( n y m - , m= , m , m^- , m , m^- , y , γ ) i f the expressions of φ. , Y. , a are known. ι ι w Deviations to I d e a l i t y A
A
B+
H+
A
β
Vapor Phase. The f u g a c i t y c o e f f i c i e n t s are taken for NOTHNAGEL et a l . (5) c o r r e l a t i o n .
In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.
182
THERMODYNAMICS
OF
AQUEOUS
SYSTEMS
WITH
INDUSTRIAL
APPLICATIONS
L i q u i d Phase. Ύ and a are derived from the f o l l o w i n g s i o n of the excess Gibbs energy. G
E
= G
E
(PITZER) + G
E
(BORN) + G
E
expres
(EDWARDS)
I n t e r a c t i o n s Between Ions. P I
M
n RT
E R )
°
&
\
m
l\
h L \ k l%
+
l
"k " l ^
i o n s )
( 9 )
L
WW
*"
E l e c t r i c Work of Charge. /
G (BORN), Μ η RT w w
,/V
+ 0,5 V
f
D
V. +0,5 V \ ions) (10)
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=
J
J
J
\
f
c
η
I n t e r a c t i o n Between Neutral G (EDWARDS) M n RT w w
ι
c '
Species.
2 2 Σλ m + Σ μ m a aa a a aaa a
(a n e u t r a l
solute)
(11)
A c t i v i t y C o e f f i c i e n t s of Ions (molality s c a l e ) l n γ. =
\ 3ni
l n Ύ. =
RT / η
_J_ 2 3
+
M + 2 Σ λ. _ dl k jk k m
ki
L.
, η, , η
V
+ _J_ Σ _ k l 2 kl dl \ ™ 1
ra
"k i
w
ν. + ν il ι c Vi - V 7** V j
a V £w
1.5 ν V c ( V i - V )a (V, C
c v
c
D, n
(v
vr
-
f
A c t i v i t y C o e f f i c i e n t s of Neutral
(Vi - v ) c
c
Solutes
:
J
(12)
8 l
l n
n
Y
a
\
=
'
a *
8 n
L
- (k k V
V η
T
' vV' n , n"a_ ' "k' ~ 1.5 v , V k
Ό lr V
L
n
a
(Vf - V )
c
c
D
+ 2λ
/ n
aa
n
a
+3y
n
m 2 aaa a
(13)
A c t i v i t y of Water -»
ln a = w
M w
_ Σ m. j J
+
_ L f J _ É_\ M V3n RT/
(?
n
n
]=-M φ m. +Σ m ) w \ j j a a/
In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.
8.
Vapor-Liquid
RENON
Equilibria
183
In a = M w w
1 1
d
w (
v -v ) f
2
c
w 'n c 1 2 3Ί 1.5 V — I- Σ λ m - 2 Σ μ m (14) __ ^ 2 J a aa a a aaa a J 5
D w
V
Ν
D n
d (V w
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L i s t of Symbols a A A
activity i n solution apparent m o l a l i t y of a c i d (mole/kg of water) DEBYE - HUCKEL constant / 2ττ N d J / 2 2 3/2 =
V looo
/
(D~TT) w
( 1 5 )
b = 1.2 Β apparent m o l a l i t y of base (mole/ kg water) Cj to c o e f f i c i e n t s i n equations (20) (22) C
MV MX
p T
-
T Z E R
(29)
ternary i n t e r a c t i o n parameter f o r s a l t MX
3 d^ D
d e n s i t y of water (kg/dm ) d i e l e c t r i c constant of n e u t r a l s o l u t i o n (without ions)
11
D = D i l+ Σ 5Ça_) n w \ a V /
(
1
6
)
n
D w
d i e l e c t r i c constant of water D
e f°
w
= 305.7 exp (-exp (-12.741 + 0.01875 T) - T/219) ( 1 7 )
charge of e l e c t r o n (4,8029 . 1 0 ~ reference f u g a c i t y
f(I)=
df dl E G H
=
4I_ 3 b 2A DH 3 Ll
l
n
( 1
+
1
b
/
I
l /
2
I ±—r-pr + b l 1
/
2
1 0
esu)
)
(
2 1/2 + I l n (1 + b I ) 1 / Z
2
b
1
8
)
(19)
J
excess GIBBS energy i n the d e f i n i t i o n of e l e c t r o c h e m i s t s by r e f e r e n c e to the " i d e a l " s o l u t i o n i n m o l a l i t y s c a l e . _j Henry's constant of u n d i s s o c i a t e d a c i d o r base (atm. kg/mole ) l n H = C, + C / T + C l n Τ + C, Τ (20) a 1 2 3 4 0
I
i o n i c strengh I =
k
\
Σ
m. z?
BOLTZMANN'S constant k = 1.38045 . 1 θ "
(21) 1 6
erg κ"
1
In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.
184
THERMODYNAMICS
Κ
OF
AQUEOUS
SYSTEMS
WITH
INDUSTRIAL
APPLICATIONS
e q u i l i b r i u m constant i n m o l a l i t y s c a l e l n Κ = Cj + C /T + C I n Τ + C Τ 2
L. J
3
(22)
4
dimensionless constant ( r . en A) 2 ο J e ζ· j _ . 10 (23) L j 2 r. kTD J w molecular weight of water 0.018 kg/mole m o l a l i t y mol/kg number of mole oo _ i AV0GADR0 S number Ν = 6.0232 . 10 mol pressure (atm) Combination of PITZER b i n a r y i o n i c i n t e r a c t i o n parameter Q = β(0)/(β(0) ( 1 ) ) POYNTING c o r r e c t i o n ζ
6
Z
8
-
M m η N Ρ Q
1
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+
Ρ
β
ο
r, R S Τ ν v^
i o n i c c a v i t y r a d i u s (A) gas constant ^ / j \ sum of PITZER b i n a r y i o n i c i n t e r a c t i o n parameters Q=B +β temperature (Κ) p a r t i a l molar volume, dm^/mol volume of i o n i c c a v i t i e s f o r i o n j per equivalent(dm /mol) r . en A J 3
0
v? = 3
V
c
43
π
3
Ν
r . . 10" j
2 7
(24)
3 volume of a l l i o n i c c a v i t i e s (dm /kg of water) V c
= ? v? J J
m. J
(25)
volume of r e a l s o l u t i o n V
= -i- + ? m. v. + Σ f d j j j a w
m
ο (dm /kg water) a
γ
(26)
a
V\ volume of i o n i c s o l u t i o n excluding n e u t r a l s o l u t e s (dnP /kg water) V. = -1 + ? m. v. w volume of n e u t r a l s o l u t i o n excluding J
V η
J
(27)
J
ions (dm3/kg of water)
V = -L + Σ γ n d a a a w y mole f r a c t i o n i n vapor phase z. number of charges of i o n j . 3 - 1 α d i e l e c t r i c c o e f f i c i e n t (dm /mol ) a
(28)
m
a J =
2
ÉS'k^iS'k^ parameters i n PITZER b i n a r y term f o r i n t e r a c t i o n b e t ^ ^ ween ions of opposite s i g n j and k obtained from S and Q. γ a c t i v i t y c o e f f i c i e n t (molality scale) λ EDWARDS extended PITZER b i n a r y c o e f f i c i e n t f o r i n t e r a c t i o n aa _ι of n e u t r a l spec i e s (B i n EDWARDS(IO) ( k g / m o l ) -1
In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.
8.
Vapor-Liquid
RENON
X
C
aa "
l
+
C
2
/
Equilibria
185
T
PITZER b i n a r y i n t e r a c t i o n c o e f f i c i e n t f o r ions j . k . of d i f f e r e n t signs (kg/mol |)
- ? ? - [ * · ' ( a l l other X j ^ are zero, ^aaa PITZER ternary c o e f f i c i e n t ,
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e
x
t
e
n
d
e
β
Λ
,
X
+
F
3Γ
=
^MXX
C μ
ΜΜχ
P
MXY
- »mx =
+
ί ψ »
( 3 2 )
ïëb>
PITZER t e r n a r y i n t e r a c t i o n c o e f f i c i e n t s =
Λ
d
^aaa = " 55TT < aa
^MMX
* "
T
S
"
A
L
T
S
«
/2 f
* ψ -
% X X
R
°
2 -2 (kg mol )
+
o
r
]
2
~
s
a
W
l
t
s
*«
( 3 4 )
( 3 5 )
a l l other μ are zero π
vapor pressure of water w log
Φ
3
I 0
π, - 7.96681
fugacity coefficient
-
(36) φ
osmotic c o e f f i c i e n t
Subscripts a neutral solute h i j k l i o n i c species w water Superscript 00
infinite dilution
Literature Cited
1. 2. 3.
VAN AKEN, A.B. ; DREXHAGE, J.J. ; de SWAAN ARONS, J. Ind. Eng. Chem. Fundam., 1975, 14(3), 154. EDWARDS, T.J. ; NEWMAN, J. ; PRAUSNITZ, J.M. ; A.I.Ch.E.J., 1975, 21(2), 248. PITZER, K.S. ; J. Phys. Chem., 1973, 77(19), 268 ; J. Am. Chem. Soc., 1974, 96(18) , 5701.
In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.
186
THERMODYNAMICS
4.
CRUZ, J. ; RENON, H. ; Ind. Eng. Chem. Fundam., 1979, 18(2), 168. NOTHNAGEL, K.H. ; ABRAMS, D.S. ; PRAUSNITZ, J.M., Ind. Eng. Chem. Proc. Des. Devt., 1973, 12(1), 25. BROWN, I. ; EWALD, A.H. ; Austr. J. Sci. Res. Phys. Ser., 1950, 3, 306. CRUZ, J. ; RENON, H. ; A.I.Ch.E. E. Journal, 1978, 24(5),817. BEUTIER, D. ; RENON, H. ; Ind. Eng. Chem. Proc. Des. Devt., 1978, 17(3), 220. BROMLEY, L.A. ; J. Chem. Therm. , 1973, 4, 669. EDWARDS, T.J. ; MAURER, O. ; NEWMAN, J. ; PRAUSNITZ, J.M. ; A.I.Ch.E. Journal, 1978, 24(6), 966.
5. 6. 7. 8.
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9. 10.
RECEIVED
OF
AQUEOUS
SYSTEMS
WITH
INDUSTRIAL
APPLICATIONS
January 31, 1980.
In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.
