Chemistry Reference
In-Depth Information
deviations suggest a significant contribution from favorable solute-solute associa-
tions
(G
22
> G
12
)
. FST provides a way to quantify these effects.
In many cases, the solute may appear at low concentrations. Limiting values of
the above expressions are then
∞
∞
∞
∂
∂
βµ
∂
∂
βµ
∂
∂
βµ
ρ
1
1
1
1
=−
1
=−
1
=−
o
m
x
ρ
2
2
2
1
Tp
,
Tp
,
T
,
p
∞
∞
∞
∂
∂
βµ
1
∂
∂
βµ
1
∂
∂
βµ
ρ
1
2
2
2
=
=
=
m
m
x
x
ρ
2
2
2
2
2
2
Tp
,
Tp
,
Tp
,
(1.69)
1
1
+
N
o
−
N
∞
1
1
21
o
∞
o
∞
V
=
V
=
=
kT
κ
−
G
1
2
BT
,
1
12
o
o
ρ
ρ
1
1
1
+
N
o
11
o
kT
κ
=
BT
,
1
o
ρ
1
with
∞
∂
∂
ln
γ
=−
(
)
2
o
o
∞
∞
1
+
ρ
GG G
+
−
2
1111
22
12
m
2
Tp
,
∞
∂
ln
f
(
)
2
o
o
∞
∞
=−
ρ
1111
GG G
+−
2
(1.70)
22
12
∂
x
2
Tp
,
∞
∂
ln
y
2
∞
∞
=−
(
GG
−
)
22
12
∂
ρ
2
Tp
,
and can be used to provide information concerning solute-solute and solute-solvent
affinity at infinite dilution (Henry's law). See Chapters 9 and 10 for more details. The
corresponding DCFI expressions are provided in the literature (O'Connell 1971a).
The inversion of KB theory to provide fluctuating quantities or KBIs in terms of
thermodynamic quantities leads to the following expression for the excess coordina-
tion numbers,
1
ρ
ρ
(
1
−−
φ
)(
1
φ
)
j
i
j
δ
+=
Nk T
ρ
κ
+
(1.71)
ij
ij
jB
T
xx
µ
12
i
ij
Other equivalent expressions involving a single chemical potential derivative (usu-
ally μ
22
) have also appeared. The most common operative form of the inversion
equations for binary mixtures is
