Chemistry Reference
In-Depth Information
where the elements of the matrix
K
are
[
]
K
ij
=+′
W
νξ
n
(9.61)
ij
o
ij
and, the elements of the matrix
ξ
are
∂
∂
ξ
[]
=
i
ξ
(9.62)
ij
n
o
j
TV
,,
µ
o
kj
≠
Ultimately obtaining the desired properties such as density differences and activ-
ity coefficients would be complicated, but feasible. This seems not to have been
attempted. A much simpler case for complete reactions, such as dissociation of
strong electrolytes, is shown in the next section.
9.4.2 F
lucTuaTion
s
oluTion
T
heory
oF
s
Trong
e
lecTrolyTe
s
oluTions
Equations 9.60, 9.61, and 9.62 above can be used directly for FST properties of solu-
tions with fully ionized salts (Perry and O'Connell 1984). In this case, the projection
of the extent of reaction terms in Equation 9.62 is null and
(
)
−
1
T
−
1
AWxCW
=
−
(9.63)
For dissociation of a salt
a
ab
νν
into ions, the FST derivatives are
∂
∂
βµ
o1
=−
xC
−
1
1
11
n
o1
TVn
,,
o2
∂
∂
βµ
∂
∂
βµ
o1
o2
=−
ν
Cv C
=−
=
(9.64)
aa
1
bb
n
n
o2
o1
TVn
,,
TV
,
n
o1
o2
∂
∂
βµ
νν
+
o2
a
b
2
2
=
−
ν
C
+
2
νν
CC
+
ν
a a
ab ab
b b
n
x
o2
2
TVn
,,
o1
where
x
1
=
N
o1
/[
N
o1
+ (ν
a
+ ν
b
)
N
o2
] and
x
2
= 1 -
x
1
.
Models for the species DCFI can
be used in Equations 9.64 to obtain solution thermodynamic properties in the same
manner as was done with nonelectrolytes above.
However, examination of the Debye-Hückel limiting law (Perry, Cabezas, and
O'Connell 1988) shows a major complication in that the long-range electrostatic
interactions lead to divergences of the ion-ion correlation functions,
c
aa
,
c
ab
, and
c
bb
in the limit of infinite dilution. Analysis of the long-range contributions (Stell, Patey,
and Høye 1981) leads to rigorous formulas for the limiting law DCFIs, while more
