Chemistry Reference
In-Depth Information
where
{}
{}
=
HS
0
0
ln
γ
(,,
Tx
ρ
;
ρ
,
x
)
i
2
ξ
σ
ξσ
ξ
(
)
2
i
2
i
ln
ρ
−
ln
1
−
ξ
1
−
32
−
3
ξ
3
3
(9.32)
(
)
−
(
)
3
(
)
2
2
2
3
ξσ
+
ξσ
ξσ
2
−
ξξ
/
HS
3
ξσ
ξ
π
σ
p
RT
2
i
1
i
2
i
3
2
i
3
+
+
+
i
1
−
ξ
ξ
1
−
6
3
3
3
2
−
0
0
i
ξσ
ξ
ξσ
ξ
(
)
0
0
i
ln
ρ
−
ln 1
−
ξ
1
32
−
3
0
0
3
3
−
(
)
−
(
i
(
)
) ()
3
2
2
0
0
02
0
0
0
3
ξσ
+
ξσ
ξσ
2
−
ξ
/ ξ
0
HS
3
ξσ
ξ
π
σ
p
RT
2
i
1
i
2
3
3
2
i
3
+
+
+
i
1
−
ξ
0
ξ
0
1
−
0
6
3
3
3
There are two aspects of this treatment that are significant. First, one or
more binary constants are used in models such as Equation 9.4, for example, in
Equation 9.13. Therefore, when Equation 9.30 is taken to the limit of pure solvent 3,
there is a relation between the Henry's constants,
(
)
(
)
{}
r
{}
0
pure3
1
−
CT
,
ρ
1
−
CT
,
ρ
H
H
=
2R
23
∫
∫
*
2R
limln
γ
=
ln
d
ρ
+
d
ρ
2
R
3
ρ
ρ
x
→
1
3
23
ρ
pureR
0
(9.33)
Therefore, if the binary constant,
k
2R
is set or determined from experiment, Equation
9.33 determines
k
23
. Second, this also means that one can predict solute solubility in
a solvent
i
from that in a convenient reference solvent, R,
(
)
0
f
=−
1
x
γ
f
i
2
i
i
(9.34)
+
f
=
xH
γ
2
2
2
2R
with
+
limln
x
R
→
γ
=
1
(9.35)
2
1
Here,
(
)
(
)
{}
{}
x
ρ
x
ρ
1
−
CT
,
ρ
1
−
CT
ρ
R
3
2R
23
∫
0
+
ln γ
=
d
ρ
+
d
ρ
(9.36)
2
R
3
ρ
ρ
ρ
pureR
