26 The Solubility of Gases in Water from 350 600 Κ Η. LAWRENCE C L E V E R and C H U L H. H A N
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Department of Chemistry, Emory University, Atlanta, GA 30322
Two recent events allow a more detailed picture of the solubility of hydrogen, nitrogen, oxygen, and the noble gases in water to be given, than could have been given even a year ago. First, a careful compila tion and evaluation of the gas solubility values in water at a gas partial pressure of one atm between the temperatures of 273.15 and about 350 Κ was car ried out by Battino [1-5]. Second, an experimental study of the solubility "of the noble gases in water at moderate pressures and at temperatures up to 561 Κ by a new method was reported by Potter and Clynne [6]. Battino's selected values between 273 and about 350 K, Potter and Clynne's new values, and selected older literature data on the solubility of gases in water at temperatures up to 600 Κ have been combined, and fitted to an equation to give the inverse of the limiting low pressure value of Henry's constant over t h e t e m p e r a t u r e i n t e r v a l o f 273 t o 600 K . Battino's equations [^-5] a r e r e c o m m e n d e d f o r u s e o v e r t h e 273 t o 350 Κ r a n g e a n d t h e e q u a t i o n s o f t h e p r e s e n t w o r k a r e t e n t a t i v e e q u a t i o n s f o r the 350-600 Κ range o f temperature. Henry's constant is defined, H
2,l =
X
2 ^
( P
2/ 2 X
)
" V ? 2 = 02 2 2 2 Ρ
/ Ύ
Χ
(
1
)
w h e r e H2 η i s t h e H e n r y c o n s t a n t , P2 t h e g a s p r e s s u r e , t h e m o l e f r a c t i o n g a s s o l u b i l i t y , ±2 t h e g a s f u g a c i t y , a 2 t h e d i s s o l v e d g a s a c t i v i t y , 02 t h e fugacity coefficient, a n d y2 t h e d i s s o l v e d g a s a c t i v i t y c o e f ficient. In the H e n r y ' s law r e g i o n the d i s s o l v e d gas activity coefficient, 72 = 1/ b y d e f i n i t i o n . For the gases d i s c u s s e d i n t h i s paper the f u g a c i t y c o e f f i c i e n t , 0 , d i f f e r s l i t t l e from u n i t y at the moder ate pressures at which s o l u b i l i t i e s are normally reported. A t u n i t gas p r e s s u r e (atm), t h e mole f r a c 2
0-8412-0569-8/80/47-133-513$06.00/0 © 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.
514
THERMODYNAMICS
OF AQUEOUS SYSTEMS W I T H INDUSTRIAL
APPLICATIONS
t i o n s o l u b i l i t y i s equal to the i n v e r s e of Henry's constant, X = I/H2 assuming u n i t values of 0 and Ύ · A l i n e a r r e g r e s s i o n on a l l o f t h e s e l e c t e d d a t a f o r a g i v e n g a s was r u n t o o b t a i n t h e c o n s t a n t s o f a n equation o f the form 2
2
2
ln A
X +
l
2
= In
1/H
2
A /(T/100) 2
=
±
+ A
3
ln
(T/100)
+ A (T/100)
(2)
4
The u s e o f ( T / 1 0 0 ) a s a v a r i a b l e h a s t h e a d v a n t a g e o f m a k i n g t h e p a r a m e t e r s A - , , A , A 3 , a n d A4 o f s i m i l a r magnitude. The a p p l i c a t i o n o f s t a n d a r d thermodynamic d e f i n i t i o n s to the equation allows the equation p a r a m e t e r s t o be u s e d t o c a l c u l a t e t h e t h e r m o d y n a m i c c h a r a c t e r i s t i c s o f the d i s s o l u t i o n p r o c e s s summarized in Table I. When a l l f o u r p a r a m e t e r s o f t h e e q u a t i o n
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2
Table
I.
In
= A
AG
Χ
λ
C
S o l u b i l i t y equation definitions.
= -RT
1
+ A /(T/100)
= -RA-j^T AS°
= - R T in
λ
100RA
= -OAG°/3T)
2
-
= RA
d / H
RA T 3
1
2
£n
thermodynamic
(T/100) +
+ A3 in
2
In Χ
and
χ
A (T/100) 4
)
(T/100) -• R A T / 1 0 0
+ RA3 £ n
2
4
(T/100) + RA3 +
ΔΗ
c
= -100RA
AC; =
2RA4T/IOO
4- RA3T + R D T / 1 0 0 = AG° + ΤΔ§*° 2
2
(3ΔΗ°/3Τ)
= RA
3
+ 2RA T/100 4
= a + bT
a r e e v a l u a t e d , a h e a t c a p a c i t y change f o r the disso l u t i o n process that i s l i n e a r i n temperature is ob tained. When o n l y t h e f i r s t t h r e e c o n s t a n t s o f t h e e q u a t i o n a r e e v a l u a t e d , a heat c a p a c i t y change i n d e pendent of temperature i s o b t a i n e d . Although a t e m p e r a t u r e d e p e n d e n t h e a t c a p a c i t y change i s more r e a l i s t i c , the s o l u b i l i t y d a t a are o f t e n not a c c u r a t e enough t o j u s t i f y the e v a l u a t i o n o f the f o u r constants. The 273
solubility a n d 350 Κ .
of
gases
between
the
temperature
of
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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26.
CLEVER AND HAN
515
Solubility of Gases in Water
B a t t i n o has used the above e q u a t i o n i n h i s e v a l u a t i o n o f the s o l u b i l i t y o f gases i n water a t one atmosphere gas p r e s s u r e a t temperatures between 2 7 3 and about 3 5 0 K. T a b l e s I I and I I I and F i g u r e 1 summarize h i s e v a l u a t i o n o f the s o l u b i l i t y d a t a . T a b l e I I g i v e s the temperature i n t e r v a l , the number o f l a b o r a t o r i e s t h a t B a t t i n o judges have p u b l i s h e d r e l i a b l e s o l u b i l i t y d a t a , the number o f e x p e r i m e n t a l v a l u e s used i n the l i n e a r r e g r e s s i o n , the l i n e a r r e g r e s s i o n s t a n d a r d d e v i a t i o n a t the m i d p o i n t tempera t u r e , and the temperature o f minimum mole f r a c t i o n s o l u b i l i t y (maximum v a l u e o f Henry's c o n s t a n t ) a t one atmosphere p a r t i a l p r e s s u r e o f the gas. For a l l o f the gases except oxygen o n l y a t h r e e c o n s t a n t e q u a t i o n was used. The temperature o f minimum mole f r a c t i o n solubi l i t y a t one atmosphere gas p a r t i a l p r e s s u r e was c a l c u l a t e d from the t h r e e c o n s t a n t e q u a t i o n . The d i f f e r e n t i a t i o n o f e q u a t i o n ( 2 ) w i t h r e s p e c t t o tempera t u r e g i v e s T ^ = 1 0 0 A2/A3. The v a l u e s t h a t f a l l o u t s i d e the temperature range o f the e x p e r i m e n t a l d a t a used i n the r e g r e s s i o n must be l o o k e d on as o n l y t e n t a t i v e v a l u e s o f the temperature o f minimum s o l u b i lity. T a b l e I I I g i v e s v a l u e s o f the changes i n Gibbs energy, e n t h a l p y , e n t r o p y , and heat c a p a c i t y o f the s o l u t i o n p r o c e s s as c a l c u l a t e d from the e q u a t i o n s o f T a b l e I . F i g u r e 1 shows the recommended n o b l e gas mole f r a c t i o n s o l u b i l i t i e s a t u n i t gas p a r t i a l p r e s sure (atm) as a f u n c t i o n o f temperature. The tempera t u r e o f minimum s o l u b i l i t y i s marked. The o r d e r o f i n c r e a s e i n the s o l u b i l i t y o f the gases a t any g i v e n temperature i n the 2 7 3 - 3 5 0 Κ range p a r a l l e l s , t o a f i r s t a p p r o x i m a t i o n , the p o l a r i z a b i l i t y o f the gas. T a b l e IV summarizes the p o l a r i z a b i l i t i e s and the molar volumes a t 2 7 3 . 1 5 Κ and 1 atm o f the gases. The gases are l i s t e d i n the o r d e r o f de c r e a s i n g molar volume which g i v e s some i n d i c a t i o n o f t h e i r n o n - i d e a l c h a r a c t e r . The p o l a r i z a b i l i t y i n d i c a t e s the magnitude o f the London d i s p e r s i o n energy between the gas and a g i v e n s o l v e n t . m
n
The
s o l u b i l i t y o f the gases i n water from
600
K.
350 to
The l i t e r a t u r e was s e a r c h e d , and the d a t a on the s o l u b i l i t y o f gases i n water between the temperatures of 3 5 0 and 6 0 0 Κ were c o m p i l e d . The measurements i n the 3 5 0 t o 6 0 0 Κ temperature range were u s u a l l y made at moderate gas p a r t i a l p r e s s u r e s . The s o l u b i l i t y a t
In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.
In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.
273 278
273
273
273
273
Ar
Kr
Xe
Rn
2
2
H
N
four
348
348
-
5/73
9/74
9/69
3/40
5/20
3/30
11/42 3/13
9/59
9/59
Labs/Exp. Values
equation
348
348
348
373
348
353
318
_ 348
constant
273
273
273
Ne
-
Temperature Range/K
273
°2*
II
0.34
0.72
0.52
1.02
0.35
0.32
0.26 0.69
0.47
0.54
Standard Deviation a t M i d T/%
365.2
348.1
327.6
371.5
383.0
375.8
-
371.2
322.7
304.1
Temperature o f Minimum S o l y / K
t h e E v a l u a t i o n o f Gas S o l u b i l i t y i n Water a t 101.325 kPa (1 Atm) a n d Low T e m p e r a t u r e s ( B a t t i n o , [1-5])
He
Gas
Summary o f
Table
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26.
CLEVER
AND HAN
517
Solubility of Gases in Water
rH I
1
0 rH g rH 1
vo
h)
rH rH
\
o Çh U
LO rH
vo rH
rH
O
CN
00 CN CN
vo
ro
rH CT> CN
00 ro rH
vo o
o
CN rH
CN rH
o
vo o
o
rH 1
CN rH 1
CN
O
o
CN
•
00
σ\
CN 0 •Η +J
rH 0 W Of
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rH 1
rH 1
σ»
ro ro
σ\
rH CN 1
1
CN
vo in
σ\ vo
CN rH
00
rH CN
CN
00 CN
vo
l
l
