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Solubility of gases in water
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SOLUBILITY
: ..
_,
OF GASES IN WATER
MS. JtiON tid H. EYI&G,
1972
. .
:
‘.
‘1 Febni&
.:
~.’ ,: . .. :_:
:
..’
.,:
.,;
PHYSrCS L&TE’kS
‘.
”
z
Bepartment of ChemsiQ, University of Utah, Solt Lake City, Utah 84112, USA
and ’
Y-K. SUNG
Depa%ent of Chemistry, Dong Guk University. Seoul, Korea’ .. ._ Received 22 Novemder The theory of sgjubility
i!3?1
of gases in liquids proposed
by JhThonand Kihara has been testedand extended to aqueous structure model of liquid waier debeloped by Jhon and Eyring. Besides the usual Kihara potential, the inductive interaction potential is used in the SohIt&-water interaction krms. The calculated values of the volubility and its temperature dependence for the gasep Ar. Kr. Xe. Ne. 02. Nz. and C2H4 show good agreement with experiment-
sqlutions of gases. In the present paper, the theory is discussed in fcrms of the significant
I. InttOdu&jon
In fhe past years, des$te,thk exact experimental
lack of sufficiently data, several-theories have been
molecules in ihe gas phase and in the solution. T is the absolute temperature, k is the Boltzmann constant, and (A 1 + AZ) means the work necessary for tr&sferring one solute molecule from the gas phase to the
solution at co&ant temperature and pressure: The develdped to r;orrelate the solubility data of gases in ft’st term A\, corresponds to the creation of a cavity water: The: solubility problems of gases in liquids were of the shape of the solute molecule against the solvent treated bi Kobadakz and Aider [ 11 , Pierotti [?I, and surface tension. The second t&m A2 .indicates the Choi, Jhoi~ and Eyring [3] with their favorite liquid models, i.e., the celi theory, the scaled particle theory, @tenGal energy between the solute molecule and the surrounding solvent molticules. ., and the significant structure theory, respctively’. All In ‘the present piper, the .au&ors use a different of these methods show some advance over the previous &nsi~~~at$ns of:Uhlig’ [4] and Eley [5] . procedure for calculating the&two terms. First. the Very recently,.Kihara and Jhon [6] ,developed the .’ effective surface boundary foi a hole’is estimated using the domain model of liquid watei developed by Jhon theory df gas Soli+lity in nonpolar liquid; using the : .,and Eyring.‘[7]. Second, Kihara’s core potential [8] core potential df.intermolecular forces, which takes which considers the size and shapes of the molG.les inio‘acc&t the &e id shapes of mol&ulos. hi ail is used to &valuate the solute--water intera&idns, An, thescthqkies, the’free energy df sol\rtion is divided inductive inteiaction is also introduce& into ty& p&ts::The,first is the.work to provide “holes” ,,iqthe solvht,. kd .&the ‘seond is the iolute-solvent inter&ion term.‘~&stw~d-coefficient; C/Q?, is : ,’ ‘. 2.?heory _’... ‘._ ; ., .. ., ‘.th+rLgiiren in i&e foim.:. .’
:
2.1 ;“The cor&&zt&l ofintermqleailarforces j -._. : ‘. : ; ,:. ‘ T@ core giential of inteimolecular~f?rceSwas first ,.. .;.;.,. -:, ._ wli&k: @ aiid. Care the G$rnber den&i&&f solute’: ,,. :piop.osed by Ki&@ -[8! !?nd led to a more’re&tic ._- ~ _ ‘_ ,. :-‘: : -,,: ._, ,‘I‘\ ., i .: 7;. ; _. ., ‘. j ..:.. ‘. ;:-_ : ‘1 : _ ,. : : I~ ._ T _’. : ,,; : -. . .. : : .. ‘..1 ..I
Volume 13, number 1
CHEh@iL
: Table 1
Core measuresand
”
poteniial
,, parameters
PHYUCS
..
,.
Solute
V(A3) S(A2)
M(A)
a(A)
&cK)
Nea)
0 0 0 0 0
0 0 0 0 3.44
2.75 3.42 3.68 4.07 3.09 2.80 3.75
35.8 0.393 119 1.62'6 167 ,2.456. 225 3.999 124 1.561: 153. I.734 256 3.702
-ha) ma) xea) N@ ozb)
o
CzH.$a)
0
0. 0 0 0 0 o 0
3.4s
4.i8
&Is)
a) Data are taken from ref. [8]. b) Data are taken from ref. 1161.. C) Data are taken from ref. [ 1 l] _
of convex
bodies, the molecular
.’ ,‘1]Fetiruky’.I972 :..;:
dipole mo~ent.ofthe.~water..Thk interaction edergy i -:, between.a nonpolar molecule .tid a pol&moiecule j ::. : :cari.be de&ibed,in ternis oi-& ,re$sion, ‘a dispersion bonding; and an inductive interaction. ,, ,; ,I :- -,, .’ 1 The volume, the’surface area’,.and the mean. ....:. curvature integral of thecore A &m be’den&d by ... &,s,,a@ MA, and the fundamental measures of .the .’ .. core B by.VB-,.Sb,‘an+ MB-Here .’ M = j+(!/rl +‘l/r2)ds; rl and ‘2 are principal radii : “. of curvature’on the surface of the convex core.. Following Kihara [6] , t&i first term,A1 of the activation energy can be expressed
in the form
‘of
one solute molecule
in solution.
treated as convex. The cores to be used in this paper are listed in table 1. The volume V, the surface area S, and the mean curvature integrated over the core’s surface M are also given in table 1. For the potential function U(J), the following form is taken,
liquid water by Jhon and ,Eyring species of solid-like.molecules
for
2.2.
The activation energy of the aqueous solution for the core potential 731: cores are denoted by A for solute mol,ecule and by B for solvent molecule, respectively. The intermolecular potential [9] between the solute gas molecule and a solvent water molecule at the intercore distance p is then
‘where
= 4E~n [(o&/))12 ,.
- (o&P) .6. ] - a,4&~6~ (3)
of.ihe solute gas, and p3 is the
K=
in
[7] , there are two
in equilibrium
in liquid
[Ice-I-likeJ/[Ice-III-like]
= [exp(--CLHIRT)exp(D;TIR)exp(-pAVIRT)]4. Using a formula due to Steiner A1 = Yts,+MA(ofi
[8],
eq.,(4)
+b) •r-n(o&~$+b)~]
(5).
becomes
!(l+K),,
thickness, b, is a function of .. temperature-and-characteristic,of the solvent but.. independent of. the species of solute molecule... The second .term A2 of the activation energy is given, when the summation-is replaced by an integra-- ,.I
in which the additional the
:
CQ is the polarizability
1’/(1+K)
water. The domain containing the numbei.&e-I-like) molecules changes cooperatively into q(Ice-IILlike) molecules and vice versa. The equilibrium constant; K, was accordingly written as
(2)
&&J)
The term
eq. (4) is introduced on the.assumptidn that the energy. of cavity formation is negligible in the (Ice-I-like) part of the liquid structure. K is the.equilib’rium Constant between the voluminous (Ice-I-like) domain and-the ., ’ more dense (Ice-III%ke) domain [7]. According to the significant strucrure theory of
cores are
The potential parameters u and E determined identical molecular pairs are included in table l_
,,
‘. Here 7 is the surface tension;S is the surface area, the parallel body of the core A with the thickness i@AA +b) and-indicz.te,s the effective surface area of
intermolecular potential for which the second virial coefficient can be evaluated analytically [e]. This potential assigns a core to each molecule. The,inter-. molecular potential U is defined for the shortest distance between the cores. In order to apply the geometry
:‘.
L.ETl’TRS.
,, :, ~~Volum~:lf,‘nu’rnbkr 1 ,’1. -CHEMICAL PHYSICS‘&T-~ERs 1 February 1972 :. ,. ._’ ., ,:’wher& ‘n ‘~~ihe.number,densities of solvent molecules; ’ Table 2 SolubiIit~ of g&es in water (L-J pottintial) (units:. log of 0s;: ‘:.&thefactoi’f,is the quantitjr which takes account’of the waId coefficient)
.‘fact’th’at,the distributionof soivent molecules at-the :: potential minimum is denser than the.average density. It is a;Qightly~vtiying function of temperature; we negIected,its dependence, on the species of solute mole: cuIe. .. U,&D) is the intermolecular potential of a solute molecule A with a’solvent molecule B, and the ~quaritity (Sx+p+.~) is the average value of the surface areas-as it depends on the orientation of core B. It has been knotin that [$I
._: : ,I I-Joc .::.::
Gases
.-: Ne
AI
20°c
40 Oc
(-6.246)
cdc.
-5.143
-5.198
-5.249
0bs.a).
-4.268
-4.485
-4.5
(-5.484) -3.375
-3.752
-3.981
-2.948
-3.322
-3.556
-2.346
-2.748
-2.311
-2.752
-3.056 -3.045
(-2.951) -1.158
-1.708
-2.138
-1.553.
-2.154
-2.537
CdC.
Obsea)
15
(-3.571) CdC.
Kr
+ (21~)--lMAMB + 2(MA+MB)p
0bs.a)
+ 4rrp2. (8)
Integrating eq. (7), we obtain .’
GIG.
Xe
Ohs.“)
CdC.
(-6.108) -4.959
-5.237
-5.405
-3.018
-3.404
-3.697
(-7.852) -6.179
-6.395
-6.516
-3.767
-4.091
-4.372
0bs.c.d)
ChlC. obs.c,d)
(-4.742)
3. Results and discussion
C2H4
Cal.
-2.299
-3.187
-3.499
ohs.“)
-1.565
-1.970
-2.375
.To. test the applicabiiity of eqs. (6) and (9), the calculated-values
of the solubilitv . of _ gases in water are
compared in tabld 2 and table 3 with the experimental values [13-l 51. The Lennard-Jones (6-l 2) potential [9] for table 2 and the Kihara potential for table 3 are introduced into the equations. In the calculation, the known values of 7 [lo], W[ LO].-and K [7] of liquid water are used. And the empirical parameters, f and B, are chosen as follows:
c)
Data are taken from ref. [ 151_ Estimated value from ref. [ 151.
l/(l+K)
term.
Data are taken from ref. [ 141.
molecule. We chose these parameters’?0 be independent of the solute.species and linearly dependent on the temperature; This is an oversimplification. However,
The dipoie moment of water is taken as l-.84 debye. {9] ;ind the polarizabilitiks of solu~& [ 1 l] are given in table l.‘The potential pa.rameters for water [12]. are t&&n to be ejk_7 167_?K, u = 2.80 A. .; ~4%: Kihara potenrial (table.3) gives much better :., :~8_:~~.:.,.-,::‘::.,__.‘ :-: -. : ‘. ._..‘., _ ‘.-., ,_. ‘,.
without
Data are takenfrom ref. [ 13]_
agreement than the L-J potential. Our theory contains two parameters:.One is concerned with the effective surface ofthe hole and the other involves the spatial .distribution of solvent molecules around a solute
’
t°C.
denotes the values calculated
d)
f = 1.35-G.OO1 t”C, p.= 1.07+0:003
(1 a) b)
with reasonable values for, these parameters, the soIubility of a number,of gases in a solvent are well represented [$I . Neglecting the energy required for cavity formation. mthe.Ice-I-like part of the’liquid, as tie did, markedIy ’
‘_
” :
.-
‘.,
,..,.
.:
,, .;_
.,
; _
;_ :
: ;,
‘.
‘-.
: .. . _
”
:
.
,;
._,:
.,
1
:
:’ ‘.
ir&une 13,:number’1 _Solubiiity
Table 3 of gases in water (core potential) wald coef%ient)
AI
‘.
‘- .’ ‘1 Feb~~J972. - -.: _\’ .-. ‘. : ;. .. : ‘., ,: ‘;. : ..’
The authors
(-6.246) .-5.153.
-5.19s
-5.249
,Obs.a)
-4.268
-4.485
-4.515
Calc.
(-5.484) -3.375
-3.752
-3.981
-3.322
-3.556
,i:948
: ..
wi+ to thank the hionql I&&utes ’ Grati: GM 12862,, National S&tick Founda-. &I, Grant GP 2863 1, and Arti? Retiarch-Duyharqi Contra&t DA-AR01D31-12472Ci5, fqr their support of thiswork. . of Health,
40°C
Ohs.?)
Kr
A++jg&nt
20 “C
CdC.
I
(units: log of Ost-
0°C
Gases
Ne
CHEhfICALPHYSI& LETTERS, ..
-.
Calc.
(-3.571) -2.346
-2.148
-3.056
Ohs.“)
-2.311
-2.752
-3.045
ChlC.
(-2.951) -1.158
”
References [ 1 ] Y. Kobadake
Xe
02
-1.708
-2.138
-2.154
-2.5
37
0bs.a)
-1.593
Calc.
(-4.553) -3.058
-3.436
-3.725
-3.018
-3.404
-3.697
obs.c,d)
(-5.583)
N2
Calc.
-3.917
-4.197
-4.485
obs.c,d)
-3.767
-4.091
-4.372
(-2.952) -1.307
-1.739
-2.156
-1.970
-2.375
CA. C2H4
obs.b)
- 1.565
(1
denotes
a)
Data are taken from ref. [ 131.
the’values calculated
without
b) Cj di
Data are taken from ref. [ 141. Data are taken from ref. [ 15 1. Estimated Value from ref. [ 151..
lj(l+K)
term.
improves agreement between theory and experiment and follows naturally from the theory for water of Jhon and Eyring.
:
and B.J. Alder, J. Phys. Chem. 66 (1962) 645. (21 R.A. Pierotti, J. Phys. Chem: 67 (1963) 1840; 09, (1965) 281. [3] D.S. Choi, MS. Jhon and H. Eyring, J. &em. Phys. 53 (1970) 2608. [4] H.H. Uhlig, J. Phys.Chem.41 (1937) 1215. [5] D.D. Eley,Trans. Faraday Sot. 35 (1939) 1281. [6] T. Kihara and MS. Jhon. Chem. Phys. Letters 7 (1970) 559. [7) M.S. Jhon. J. Grosh, T. Ree and H. Eyring, J. Chem. Phys. 44 (1965) 1465. [S] T. Kihara. Rev. Mod. Phys. 25 (1953) 831; Advan. Chem. Phys. 5 (i963) 147; in: Physical chemistry, vol. V, ed. H. Eyring (Academic Press, New York, 1970). C.F. Chrtiss and R.B. Bird, Molecular 191 J.O..HirschfeIder, theory of gases and liquids.(Wiley, New York; 1967). [IO] N-A. Lange, Handbook of chemistry, 10th ed. (M&rhwHill, New York. 1967). 1111 E.A. hfoelwyn-Hughes. Phykal chemistry (Pergam&
Press, New York,,l964). 1121 J.H. van der Waals and J.C. Platteuw,
Advan. Chem._
Phys. 2 (1959) 1. i131 T.J. Morrison (1954) 3441. T.J. Morrison E. Douglas, J. T. Kihara and 688.
and N.B. Johnstone.
JT Chem.
S&z
and F. Billett, J. Chem; SpL. (1952) 3819. Phys. Chem. 68 (1964) 169. S. Koba, J. Phys. Sot. (Japan) 9 (1954)
: .. .,
.‘.’
,. .:. I : : :: .‘_ ,... ::_ : .,
.‘... I. ..‘.
.. .
:_
.,,
‘.. .,
~.&kMICA&
;:
‘, ..
... . .._
;,_
:
:
:,
SOLUBILITY
: ..
_,
OF GASES IN WATER
MS. JtiON tid H. EYI&G,
1972
. .
:
‘.
‘1 Febni&
.:
~.’ ,: . .. :_:
:
..’
.,:
.,;
PHYSrCS L&TE’kS
‘.
”
z
Bepartment of ChemsiQ, University of Utah, Solt Lake City, Utah 84112, USA
and ’
Y-K. SUNG
Depa%ent of Chemistry, Dong Guk University. Seoul, Korea’ .. ._ Received 22 Novemder The theory of sgjubility
i!3?1
of gases in liquids proposed
by JhThonand Kihara has been testedand extended to aqueous structure model of liquid waier debeloped by Jhon and Eyring. Besides the usual Kihara potential, the inductive interaction potential is used in the SohIt&-water interaction krms. The calculated values of the volubility and its temperature dependence for the gasep Ar. Kr. Xe. Ne. 02. Nz. and C2H4 show good agreement with experiment-
sqlutions of gases. In the present paper, the theory is discussed in fcrms of the significant
I. InttOdu&jon
In fhe past years, des$te,thk exact experimental
lack of sufficiently data, several-theories have been
molecules in ihe gas phase and in the solution. T is the absolute temperature, k is the Boltzmann constant, and (A 1 + AZ) means the work necessary for tr&sferring one solute molecule from the gas phase to the
solution at co&ant temperature and pressure: The develdped to r;orrelate the solubility data of gases in ft’st term A\, corresponds to the creation of a cavity water: The: solubility problems of gases in liquids were of the shape of the solute molecule against the solvent treated bi Kobadakz and Aider [ 11 , Pierotti [?I, and surface tension. The second t&m A2 .indicates the Choi, Jhoi~ and Eyring [3] with their favorite liquid models, i.e., the celi theory, the scaled particle theory, @tenGal energy between the solute molecule and the surrounding solvent molticules. ., and the significant structure theory, respctively’. All In ‘the present piper, the .au&ors use a different of these methods show some advance over the previous &nsi~~~at$ns of:Uhlig’ [4] and Eley [5] . procedure for calculating the&two terms. First. the Very recently,.Kihara and Jhon [6] ,developed the .’ effective surface boundary foi a hole’is estimated using the domain model of liquid watei developed by Jhon theory df gas Soli+lity in nonpolar liquid; using the : .,and Eyring.‘[7]. Second, Kihara’s core potential [8] core potential df.intermolecular forces, which takes which considers the size and shapes of the molG.les inio‘acc&t the &e id shapes of mol&ulos. hi ail is used to &valuate the solute--water intera&idns, An, thescthqkies, the’free energy df sol\rtion is divided inductive inteiaction is also introduce& into ty& p&ts::The,first is the.work to provide “holes” ,,iqthe solvht,. kd .&the ‘seond is the iolute-solvent inter&ion term.‘~&stw~d-coefficient; C/Q?, is : ,’ ‘. 2.?heory _’... ‘._ ; ., .. ., ‘.th+rLgiiren in i&e foim.:. .’
:
2.1 ;“The cor&&zt&l ofintermqleailarforces j -._. : ‘. : ; ,:. ‘ T@ core giential of inteimolecular~f?rceSwas first ,.. .;.;.,. -:, ._ wli&k: @ aiid. Care the G$rnber den&i&&f solute’: ,,. :piop.osed by Ki&@ -[8! !?nd led to a more’re&tic ._- ~ _ ‘_ ,. :-‘: : -,,: ._, ,‘I‘\ ., i .: 7;. ; _. ., ‘. j ..:.. ‘. ;:-_ : ‘1 : _ ,. : : I~ ._ T _’. : ,,; : -. . .. : : .. ‘..1 ..I
Volume 13, number 1
CHEh@iL
: Table 1
Core measuresand
”
poteniial
,, parameters
PHYUCS
..
,.
Solute
V(A3) S(A2)
M(A)
a(A)
&cK)
Nea)
0 0 0 0 0
0 0 0 0 3.44
2.75 3.42 3.68 4.07 3.09 2.80 3.75
35.8 0.393 119 1.62'6 167 ,2.456. 225 3.999 124 1.561: 153. I.734 256 3.702
-ha) ma) xea) N@ ozb)
o
CzH.$a)
0
0. 0 0 0 0 o 0
3.4s
4.i8
&Is)
a) Data are taken from ref. [8]. b) Data are taken from ref. 1161.. C) Data are taken from ref. [ 1 l] _
of convex
bodies, the molecular
.’ ,‘1]Fetiruky’.I972 :..;:
dipole mo~ent.ofthe.~water..Thk interaction edergy i -:, between.a nonpolar molecule .tid a pol&moiecule j ::. : :cari.be de&ibed,in ternis oi-& ,re$sion, ‘a dispersion bonding; and an inductive interaction. ,, ,; ,I :- -,, .’ 1 The volume, the’surface area’,.and the mean. ....:. curvature integral of thecore A &m be’den&d by ... &,s,,a@ MA, and the fundamental measures of .the .’ .. core B by.VB-,.Sb,‘an+ MB-Here .’ M = j+(!/rl +‘l/r2)ds; rl and ‘2 are principal radii : “. of curvature’on the surface of the convex core.. Following Kihara [6] , t&i first term,A1 of the activation energy can be expressed
in the form
‘of
one solute molecule
in solution.
treated as convex. The cores to be used in this paper are listed in table 1. The volume V, the surface area S, and the mean curvature integrated over the core’s surface M are also given in table 1. For the potential function U(J), the following form is taken,
liquid water by Jhon and ,Eyring species of solid-like.molecules
for
2.2.
The activation energy of the aqueous solution for the core potential 731: cores are denoted by A for solute mol,ecule and by B for solvent molecule, respectively. The intermolecular potential [9] between the solute gas molecule and a solvent water molecule at the intercore distance p is then
‘where
= 4E~n [(o&/))12 ,.
- (o&P) .6. ] - a,4&~6~ (3)
of.ihe solute gas, and p3 is the
K=
in
[7] , there are two
in equilibrium
in liquid
[Ice-I-likeJ/[Ice-III-like]
= [exp(--CLHIRT)exp(D;TIR)exp(-pAVIRT)]4. Using a formula due to Steiner A1 = Yts,+MA(ofi
[8],
eq.,(4)
+b) •r-n(o&~$+b)~]
(5).
becomes
!(l+K),,
thickness, b, is a function of .. temperature-and-characteristic,of the solvent but.. independent of. the species of solute molecule... The second .term A2 of the activation energy is given, when the summation-is replaced by an integra-- ,.I
in which the additional the
:
CQ is the polarizability
1’/(1+K)
water. The domain containing the numbei.&e-I-like) molecules changes cooperatively into q(Ice-IILlike) molecules and vice versa. The equilibrium constant; K, was accordingly written as
(2)
&&J)
The term
eq. (4) is introduced on the.assumptidn that the energy. of cavity formation is negligible in the (Ice-I-like) part of the liquid structure. K is the.equilib’rium Constant between the voluminous (Ice-I-like) domain and-the ., ’ more dense (Ice-III%ke) domain [7]. According to the significant strucrure theory of
cores are
The potential parameters u and E determined identical molecular pairs are included in table l_
,,
‘. Here 7 is the surface tension;S is the surface area, the parallel body of the core A with the thickness i@AA +b) and-indicz.te,s the effective surface area of
intermolecular potential for which the second virial coefficient can be evaluated analytically [e]. This potential assigns a core to each molecule. The,inter-. molecular potential U is defined for the shortest distance between the cores. In order to apply the geometry
:‘.
L.ETl’TRS.
,, :, ~~Volum~:lf,‘nu’rnbkr 1 ,’1. -CHEMICAL PHYSICS‘&T-~ERs 1 February 1972 :. ,. ._’ ., ,:’wher& ‘n ‘~~ihe.number,densities of solvent molecules; ’ Table 2 SolubiIit~ of g&es in water (L-J pottintial) (units:. log of 0s;: ‘:.&thefactoi’f,is the quantitjr which takes account’of the waId coefficient)
.‘fact’th’at,the distributionof soivent molecules at-the :: potential minimum is denser than the.average density. It is a;Qightly~vtiying function of temperature; we negIected,its dependence, on the species of solute mole: cuIe. .. U,&D) is the intermolecular potential of a solute molecule A with a’solvent molecule B, and the ~quaritity (Sx+p+.~) is the average value of the surface areas-as it depends on the orientation of core B. It has been knotin that [$I
._: : ,I I-Joc .::.::
Gases
.-: Ne
AI
20°c
40 Oc
(-6.246)
cdc.
-5.143
-5.198
-5.249
0bs.a).
-4.268
-4.485
-4.5
(-5.484) -3.375
-3.752
-3.981
-2.948
-3.322
-3.556
-2.346
-2.748
-2.311
-2.752
-3.056 -3.045
(-2.951) -1.158
-1.708
-2.138
-1.553.
-2.154
-2.537
CdC.
Obsea)
15
(-3.571) CdC.
Kr
+ (21~)--lMAMB + 2(MA+MB)p
0bs.a)
+ 4rrp2. (8)
Integrating eq. (7), we obtain .’
GIG.
Xe
Ohs.“)
CdC.
(-6.108) -4.959
-5.237
-5.405
-3.018
-3.404
-3.697
(-7.852) -6.179
-6.395
-6.516
-3.767
-4.091
-4.372
0bs.c.d)
ChlC. obs.c,d)
(-4.742)
3. Results and discussion
C2H4
Cal.
-2.299
-3.187
-3.499
ohs.“)
-1.565
-1.970
-2.375
.To. test the applicabiiity of eqs. (6) and (9), the calculated-values
of the solubilitv . of _ gases in water are
compared in tabld 2 and table 3 with the experimental values [13-l 51. The Lennard-Jones (6-l 2) potential [9] for table 2 and the Kihara potential for table 3 are introduced into the equations. In the calculation, the known values of 7 [lo], W[ LO].-and K [7] of liquid water are used. And the empirical parameters, f and B, are chosen as follows:
c)
Data are taken from ref. [ 151_ Estimated value from ref. [ 151.
l/(l+K)
term.
Data are taken from ref. [ 141.
molecule. We chose these parameters’?0 be independent of the solute.species and linearly dependent on the temperature; This is an oversimplification. However,
The dipoie moment of water is taken as l-.84 debye. {9] ;ind the polarizabilitiks of solu~& [ 1 l] are given in table l.‘The potential pa.rameters for water [12]. are t&&n to be ejk_7 167_?K, u = 2.80 A. .; ~4%: Kihara potenrial (table.3) gives much better :., :~8_:~~.:.,.-,::‘::.,__.‘ :-: -. : ‘. ._..‘., _ ‘.-., ,_. ‘,.
without
Data are takenfrom ref. [ 13]_
agreement than the L-J potential. Our theory contains two parameters:.One is concerned with the effective surface ofthe hole and the other involves the spatial .distribution of solvent molecules around a solute
’
t°C.
denotes the values calculated
d)
f = 1.35-G.OO1 t”C, p.= 1.07+0:003
(1 a) b)
with reasonable values for, these parameters, the soIubility of a number,of gases in a solvent are well represented [$I . Neglecting the energy required for cavity formation. mthe.Ice-I-like part of the’liquid, as tie did, markedIy ’
‘_
” :
.-
‘.,
,..,.
.:
,, .;_
.,
; _
;_ :
: ;,
‘.
‘-.
: .. . _
”
:
.
,;
._,:
.,
1
:
:’ ‘.
ir&une 13,:number’1 _Solubiiity
Table 3 of gases in water (core potential) wald coef%ient)
AI
‘.
‘- .’ ‘1 Feb~~J972. - -.: _\’ .-. ‘. : ;. .. : ‘., ,: ‘;. : ..’
The authors
(-6.246) .-5.153.
-5.19s
-5.249
,Obs.a)
-4.268
-4.485
-4.515
Calc.
(-5.484) -3.375
-3.752
-3.981
-3.322
-3.556
,i:948
: ..
wi+ to thank the hionql I&&utes ’ Grati: GM 12862,, National S&tick Founda-. &I, Grant GP 2863 1, and Arti? Retiarch-Duyharqi Contra&t DA-AR01D31-12472Ci5, fqr their support of thiswork. . of Health,
40°C
Ohs.?)
Kr
A++jg&nt
20 “C
CdC.
I
(units: log of Ost-
0°C
Gases
Ne
CHEhfICALPHYSI& LETTERS, ..
-.
Calc.
(-3.571) -2.346
-2.148
-3.056
Ohs.“)
-2.311
-2.752
-3.045
ChlC.
(-2.951) -1.158
”
References [ 1 ] Y. Kobadake
Xe
02
-1.708
-2.138
-2.154
-2.5
37
0bs.a)
-1.593
Calc.
(-4.553) -3.058
-3.436
-3.725
-3.018
-3.404
-3.697
obs.c,d)
(-5.583)
N2
Calc.
-3.917
-4.197
-4.485
obs.c,d)
-3.767
-4.091
-4.372
(-2.952) -1.307
-1.739
-2.156
-1.970
-2.375
CA. C2H4
obs.b)
- 1.565
(1
denotes
a)
Data are taken from ref. [ 131.
the’values calculated
without
b) Cj di
Data are taken from ref. [ 141. Data are taken from ref. [ 15 1. Estimated Value from ref. [ 151..
lj(l+K)
term.
improves agreement between theory and experiment and follows naturally from the theory for water of Jhon and Eyring.
:
and B.J. Alder, J. Phys. Chem. 66 (1962) 645. (21 R.A. Pierotti, J. Phys. Chem: 67 (1963) 1840; 09, (1965) 281. [3] D.S. Choi, MS. Jhon and H. Eyring, J. &em. Phys. 53 (1970) 2608. [4] H.H. Uhlig, J. Phys.Chem.41 (1937) 1215. [5] D.D. Eley,Trans. Faraday Sot. 35 (1939) 1281. [6] T. Kihara and MS. Jhon. Chem. Phys. Letters 7 (1970) 559. [7) M.S. Jhon. J. Grosh, T. Ree and H. Eyring, J. Chem. Phys. 44 (1965) 1465. [S] T. Kihara. Rev. Mod. Phys. 25 (1953) 831; Advan. Chem. Phys. 5 (i963) 147; in: Physical chemistry, vol. V, ed. H. Eyring (Academic Press, New York, 1970). C.F. Chrtiss and R.B. Bird, Molecular 191 J.O..HirschfeIder, theory of gases and liquids.(Wiley, New York; 1967). [IO] N-A. Lange, Handbook of chemistry, 10th ed. (M&rhwHill, New York. 1967). 1111 E.A. hfoelwyn-Hughes. Phykal chemistry (Pergam&
Press, New York,,l964). 1121 J.H. van der Waals and J.C. Platteuw,
Advan. Chem._
Phys. 2 (1959) 1. i131 T.J. Morrison (1954) 3441. T.J. Morrison E. Douglas, J. T. Kihara and 688.
and N.B. Johnstone.
JT Chem.
S&z
and F. Billett, J. Chem; SpL. (1952) 3819. Phys. Chem. 68 (1964) 169. S. Koba, J. Phys. Sot. (Japan) 9 (1954)