Chemistry Reference
In-Depth Information
2
1
ρ
V
xD
22
GkT
=
κ
−
+
11
BT
ρ
1
1
VV
(
ρρ
+
)
12
1
2
GkT
=
κ
−
(1.72)
12
BT
D
2
1
ρ
V
xD
11
GkT
=
κ
−
+
22
BT
ρ
2
2
where
D
is defined by
2
β
E
∂
G
x
Dx x
=+
1
(1.73)
12
2
∂
1
pT
,
and is positive for stable (miscible) solutions.
Similarly, the inversion of Equations 1.56, 1.57, and Equation 1.59 provides the
DCFIs in terms of measurable properties. The expressions for binaries are
V
kT
ρ
2
∂
ln
γ
1
1
C
=−
1
−
N
11
κ
∂
N
BT
1
TpN
,,
2
VV
kT
ρ
∂
∂
ln
γ
12
1
C
=−
1
−
N
(1.74)
12
κ
N
BT
2
TpN
,,
1
2
ρ
V
∂
ln
γ
2
2
C
=−
1
−
N
22
kkT
κ
∂
N
BT
2
TpN
,,
1
where γ
i
is the activity coefficient of component
i.
1.3.3 c
losed
T
ernary
s
ysTems
The explicit expressions for the chemical potential derivatives, partial molar volumes,
and isothermal compressibility become rather cumbersome for ternary systems.
Experimental data are also much less common. However, there are many interesting
effects that involve ternary systems (see Chapter 4). Also, we shall see that consider-
able simplification is obtained when one of the components is at infinite dilution (see
Chapters 10 and 11). If one requires specific expressions for the various properties, it
will prove convenient to define the following set of variables (Smith 2006a),
η
==
M
ρ
AA
+
ρ
AA
+
ρ
AA
123
123
2
13
312
(
)
(
)
(
)
−+
(
)
(
)
ζ
==+
NN
1
N
1
+
N
22
1
+
N
1
N
NN
−+
1
NNN
(1.75)
3
11
33
11
23
32
22
13
31
(
)
−+
1
NNNNNN
+
2
33
12
21
12
23
31
