Chemistry Reference
In-Depth Information
exception of (Δ
12
- Δ
23
)
x
2
t
= 0
at infinite dilution of solute (component 2), only solute-
free variables.
The above equation can be applied to the solubility of a gas in various kinds of
binary mixtures, a mixture of two solvents, or a mixture of a solvent and a solute
(salt, polymer, or protein).
The oldest and simplest relationship between the Henry constant in binary solvents
and those in individual solvents is that proposed by Krichevsky (Krichevskii 1937),
b
,
13
−
b
,
13
−
ln
Hx
=
ln
Hx
+
ln
H
23
(10.12)
2, t
21
,
,
1
3
The Krichevsky equation (Equation 10.12) is valid when the binary mixtures 1-2 and
2-3 (gas solute/pure solvents) and the ternary mixture 1-2-3 are ideal (Shulgin and
Ruckenstein 2002b). However, such conditions are often far from reality. Let us con-
sider, for example, the solubility of a hydrocarbon in a water/alcohol solvent (for
instance, water/methanol, water/ethanol, etc.). The activity coefficient of propane
in water at infinite dilution is ≈ 4∙10
3
(Kojima, Zhang, and Hiaki 1997), whereas the
activity coefficients of alcohols and water in aqueous solutions of simple alcohols
seldom exceed 10. It is therefore clear that the main contribution to the nonideality of
the ternary gas/binary solvent mixture comes from the nonideality of the gas solute
in the individual solvents, which are neglected in the Krichevsky equation.
For this reason, in a first step it will be assumed that only the binary solvent (1-3)
behaves as an ideal mixture. One can therefore write that γ
3
b, 1-3
= 1 and
b
,
13
−
b
,
13
−
1
0
3
0
VxVxV
m
=
+
(10.13)
1
3
where
V
m
is the molar volume of the binary mixture 1-3, and
V
1
0
and
V
3
0
are the molar
volumes of the individual pure solvents 1 and 3. Under these conditions, Equation
10.11 becomes,
(
∆∆
12
−
)
∫
23
t
x
=
0
b,
13
−
ln
H
=−
dx
+
A
(10.14)
2
2
(
)
2t
3
b
,
13
−
0
b
,
13
−
0
xVxV
+
1
3
1
3
Equation 10.14 can provide a number of analytical expressions for
H
2
t
with various
assumptions regarding the nonideality term (Δ
12
- Δ
23
)
x
2
t
= 0
. The simplest expression is
obtained by assuming that (Δ
12
)
x
2
t
= 0
= (
G
11
+
G
22
- 2
G
12
)
x
2
t
= 0
and (Δ
23
)
x
2
t
= 0
= (
G
22
+
G
33
- 2
G
23
)
x
2
t
= 0
are independent of the composition of the solvent mixture. Then, Equation
10.14 becomes
(
0
)
b
,
13
−
0
b
,
13
−
BpTx
(, )ln
VxV
+
1
3
1
3
ln
HApT
=
(, )
−
(10.15)
2t
0
0
VV
3
1
where
B
(
p
,
T
) = (Δ
12
- Δ
23
)
x
2
t
= 0
/2.
