7 On the Solubility of Volatile Weak Electrolytes in Aqueous Solutions G. MAURER
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Institut für Technische Thermodynamik und Kältetechnik, Universität Karlsruhe (TH), D-7500 Karlsruhe, Fed. Rep. of Germany
The solubility of gaseous weak electrolytes in aqueous solutions is encountered in many chemical and petrochemical processes. In comparison to vapor-liquid equilibria in non reacting systems the solubility of gaseous weak electrolytes like ammonia, carbondioxide, hydrogen sulfide and sulfur dioxide in water results not only from physical (vapor-liquid) equilibrium but also from chemical equilibrium in the liquid phase. This interaction between physical and chemical equilibria complicates considerably the description of vaporliquid equilibria in multicomponent aqueous solutions. The development of thermodynamic correlations for those equilibria is also hindered by the limited experimental material available on that subject. This contribution describes and compares three procedures for representing vapor-liquid equilibria in multicomponent aqueous solutions of volatile weak electrolytes. Starting from the basic thermodynamic relations, the approximations and simplifications applied by van Krevelen, Hoftijzer and Huntjens (1) , Beutier and Renon (2) and Edwards, Maurer, Newman and Prausnitz (3) are discussed; the necessary information for using these correlations is compiled. Results calculated with these procedures are discussed and compared with literature data. Thermodynamic s A s shown i n f i g u r e 1, a v o l a t i l e weak electrolyte i n water a t a g i v e n t e m p e r a t u r e and p r e s s u r e d i s t r i b u t e s i t s e l f between v a p o r and l i q u i d p h a s e . Phase eq u i l i b r i u m d e t e r m i n e s t h e c o n c e n t r a t i o n o f t h e weak e l e c t r o l y t e i n t h e g a s e o u s p h a s e a t a known c o n c e n t r a t i o n of molecular e l e c t r o l y t e i n water. B u t due t o 0-8412-0569-8/80/47-133-139$08.50/0 © 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.
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140
T H E R M O D Y N A M I C S O F AQUEOUS SYSTEMS W I T H INDUSTRIAL APPLICATIONS
Vapor Phase molecular electrolytes —
n
molecular electrolytes^—- ions
Liquid Phase Figure 1.
Vapor-liquid equilibrium in an aqueous system of volatile weak electrolytes
In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.
7.
MAURER
Solubility of Volatile Weak Electrolytes
chemical reactions this concentration of molecular elec t r o l y t e i n l i q u i d w a t e r may b e c o n s i d e r a b l y d i f f e r e n t from i t s t o t a l c o n c e n t r a t i o n . ( T o t a l c o n c e n t r a t i o n i s the a m o u n t o f weak e l e c t r o l y t e i n l i q u i d p h a s e , i f t h e r e w o u l d n o t be d i s s o c i a t i o n ) . In a m u l t i c o m p o n e n t aqueous s y s t e m e n c o u n t e r i n g am monia, c a r b o n d i o x i d e , hydrogen s u l f i d e and s u l f u r d i o x i d e , the vapor phase c o n t a i n s molecules o f o n l y f i v e d i f f e r e n t s p e c i e s , e . g . NH3, C02/ H2S, S 0 and H 0, w h i l e i n t h e l i q u i d p h a s e 15 d i f f e r e n t s p e c i e s a r e p r e sent: b e s i d e s t h e m o l e c u l a r s p e c i e s a l s o 10 i o n i c s p e c i e s , e^_g. N H j , HCO3, H S " , HSO3, O H " , H , NH2COO", S ~ , 003/ SO3. F o r g i v e n t e m p e r a t u r e a n d t o t a l molalities o f t h e weak e l e c t r o l y t e s i n the l i q u i d phase a system of 20 m o s t l y n o n l i n e a r e q u a t i o n s h a s t o b e s o l v e d , i n o r d e r to f i n d the t o t a l p r e s s u r e o f the system and the com p o s i t i o n of the vapor phase. T h e s e e q u a t i o n s i n c l u d e e q u i l i b r i u m - c o n s t a n t s K i (T) f o r n i n e c h e m i c a l r e a c t i o n s , e x p r e s s e d b y a c t i v i t i e s a±z 2
2
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+
F i r s t d i s s o c i a t i o n s o f ammonia ( r e a c t i o n 1), c a r b o n d i o x i d e ( r e a c t i o n 2), hydrogen s u l f i d e ( r e a c t i o n 3), s u l f u r d i o x i d e ( r e a c t i o n 4): = NH^ 0H" NH +H 0 ^ NHj + O H ' K (T) (I) NH w a
3
2
a
1
a
a
3
a
CO2+H2O ^
HCO3 + H
+
HC03
( I D
w
2
a ,HS" l
^
2
HS" + H
+
H
2
co H S
a
K (T)
+
a
T T r
R
+
[HI)
K (T) 3
H S 2
*HS0
S0 +H 0 ^ 2
2
HSO3 + H
+
K (T)
(IV)
4
a
S0
a 9
w
Second d i s s o c i a t i o n s o f carbon d i o x i d e ( r e a c t i o n 5 ) , h y drogen s u l f i d e ( r e a c t i o n 6 ) , s u l f u r d i o x i d e ( r e a c t i o n 7) a
HCO3 ^
CO3 + H+
C0f
Κ (Τ) β
b
(V) HC05
^
SO^ + H
+
K (T) 7
a
S= H =· — HS"
+
(VI)
a
a
HS0~
+
5
a
S" + H+
H
K (T) = a
HS" ^
a
S0f
a
H
= — a
+
(VII)
HS0^
In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.
142
THERMODYNAMICS O F AQUEOUS SYSTEMS W I T H INDUSTRIAL
Carbamate r e a c t i o n
(reaction
8) a
NH COO~ 2
NH +HC0~ = ^ NH C00"+H 0 o
o
3
3
Dissociation
of
8
(VIII)
^
2
H
+
(reaction
+ OH*
1
a
a
aH C O- ~
3
H C 0
9) a
H 0
w
Q
2
water
a
K (T)=
o
2
APPLICATIONS
H
+
A
0H"
K (T) =
(IX)
9
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w F u r t h e r m o r e , 5 v a p o r - l i q u i d phase e q u i l i b r i a a r e involved, e.g. f o r m o l e c u l a r NH3, C 0 , H S a n d S0 and for water. Applying the concept of Henry's constant H i f o r t h e s o l u t i o n o f a gas i i n p u r e water and f u g a c i t y coefficient for d e s c r i b i n g the influence of i n t e r molecular forces i n the vapor phase, the r e s u l t i n g equations are : 2
2
a
H
i
= Ρ y
±
(X)- ( XIII)
ι
= NH3, C0 2 , H S , S0 2
i and
φ
±
2
2
a
f = P y ψ (XIV) W W W (P, y^ and f d e s i g n a t e the t o t a l p r e s s u r e , the mole f r a c t i o n o f component i i n v a p o r phase and the f u g a c i t y of pure water). The mass b a l a n c e i n t h e l i q u i d p h a s e r e s u l t s i n four a d d i t i o n a l equations: J
w
m
m
=
tot,NH
3
tot,C0
2
m
=
M
m
=
tot,H S
C0 m
2
m
tot,S0
N H
+
+
m
2
H S
+
m
"
m
so
2
+
m
""NB^COO-
+
HCO-
2
2
+
" W J
3
^HsCOO" +
HS"
m
+
HSO-
(XV)
+
m
C0=
(XVI)
S
(XVII)
^03
(XVIII)
(m^ d e s i g n a t e s t h e m o l a l i t y o f s p e c i e s i i n l i q u i d phase). T h e r e m a i n i n g two e q u a t i o n s r e s u l t f r o m t h e c o n d i t i o n o f b u l k e l e c t r o n e u t r a l i t y i n the l i q u i d phase and t h e mole b a l a n c e i n t h e g a s e o u s p h a s e : +
" N H J =
M
0 H "
+
M
+
% H
+ 3
Y
C 0
+ 2
y
H S 2
+
+
HC03
2(m
Y
S 0
HSÛ3
+ m
s =
+ 2
M
*w
c o
=
=
1
+
M
+ m
H S s o
+
^ C O O "
=)
(
(
χ
X
In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.
ι
X
χ
)
)
7. M A U R E R
143
Solubility of Volatile Weak Electrolytes
In p r i n c i p l e , t h i s system o f 20 e q u a t i o n s c a n be solved provided the e q u i l i b r i u m constants, a c t i v i t i e s , H e n r y - c o n s t a n t s and f u g a c i t i e s a r e a v a i l a b l e . While some r e s u l t s f o r most o f t h e s e p r o p e r t i e s a r e a v a i l a b l e , t h e r e e x i s t s no approved method f o r c a l c u l a t i n g a c t i v i t i e s i n c o n c e n t r a t e d aqueous s o l u t i o n s o f weak e l e c trolytes; t h e r e f o r e , s e v e r a l a p p r o x i m a t i o n s were de veloped.
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Method by van K r e v e l e n ,
Hoftijzer
and H u n t j e n s
(1) (KHH)
T h i s method a p p l i e s v e r y r e s t r i c t i v e approxima tions, resulting i na limited applicability. The me thod cannot be a p p l i e d t o t h e complete multicomponent system d e s c r i b e d above; i t i s s u i t a b l e o n l y f o r am monia r i c h subsystems o f NH -C0 -H 0 tot,NH tot,C0 NH -H S-H 0 tot,NH ^ " tot,H S and NH -C0 -H S-H 0 tot,NH > tot,C0 tot, H S). As t h e model i s r a t h e r s i m p l i f i e d , i t was based on ex p e r i m e n t a l r e s u l t s which c o v e r t h e t e m p e r a t u r e range from 20 t o 60 oc a t t h e f o l l o w i n g m o l a l i t i e s : 3
2
m
2
>
m
3
3
2
2
2
l
3
3
2
2
2
m
2
( m
+
3
NH^-C0 -H 0: 0.5 < m. ^ tot,NH 9
3
2
9
NH^-H.S-H.O: 3 2 2
2
