Chemistry Reference
In-Depth Information
The constants
A
(
p
,
T
) and
B
(
p
,
T
) can be obtained using the following extreme
expressions,
(ln)
H
=
ln
H
(10.16)
2t
b
1
,
13
0
−
23
,
x
=
and
(ln)
H
=
ln
H
(10.17)
2t
b
3
,
13
0
−
21
,
x
=
Combining Equation 10.15 through Equation 10.17 yields the final result,
(
)
+
(
)
0
0
ln
HVV
ln
−
ln
ln
HVV
ln
−
ln
21
,
3
23
,
1
ln
H
=
(10.18)
2t
0
0
ln
VVV
1
− ln
3
Equation 10.18 provides the Henry constant for a binary solvent in terms of those for
the individual solvents and their molar volumes. This simple equation was obtained
using less restrictive approximations than those involved in the Krichevsky equation,
but assuming that only the binary solvent 1-3 is an ideal mixture. Such an assump-
tion is reasonable because the nonideality of the binary solvent is much lower than
those of the solute gas and each of the constituents of the solvent.
Equation 10.11 can be, however, integrated using any of the analytical expressions
available for the activity coefficient ln γ
3
b, 1-3
, such as the Van Laar, Margules, Wilson,
NRTL, and so forth. To take into account the nonideality of the molar volume, one
can use the expression,
b
,
13
−
b
,
13
−
0
0
E
VxVxVV
m
=
+
+
(10.19)
1
1
3
3
m
where the last term is the excess molar volume.
When the integration in Equation 10.11 cannot be performed analytically, one can
first integrate it numerically between 0 <
x
3
b, 1-3
< 1 to obtain the expression
1
b
,
13
−
1
∂
ln
γ
∫
b
,
13
−
b
,
13
−
3
ln
HHB
−
ln
= −
1
+
x
dx
23
,
21
,
3
3
b
,
1
−
3
V
∂
x
3
pT
,
(10.20)
0
1
2
(
)
∞
∞
+
ln
γ−
ln
γ
31
13
,
,
b
.
Equation 10.20 allows one to determine the constant
B
. Further, Equation 10.11
can be integrated between 0 <
x
3
b, 1-3
<
x
, to obtain the Henry constant for a mole
fraction
x
in a binary solvent,
b
,
13
−
,
13
−
∞
∞
where
γ
=
x
lim
γ
and
γ
=
x
lim
γ
13
,
1
31
,
3
→
0
→
0
1
3
