Chemistry Reference
In-Depth Information
(
)
(
)
(
)
r
r
,
∞
2
2
2
Hxx
(,)
=
H kT
−
05
.
∂∂
kTx
+∂
05
.
k
∂
Tx
+∂
kTxx
∂
−
323
3
B
22
2
3
3
3
23
23
p
p
p
(
)
(
)
∂∂
kTx
−∂
k
∂
Tx
23
2
33
3
p
p
Alternatively, we can express the solute partial molecular enthalpy in the same
form as Equation 8.40 and Equation 8.43, that is,
(
)
(
)
r
r
,
∞
2
r
r
,o
Hxx
(,)
=
H kT
+
∂∂
kTx
+∂
k
∂
Tx
+
HxxH
(,)
−
223
2
B
22
2
23
3
1
23
1
p
p
(8.46)
(
)
(
)
r
r
∞
+
2
r
xH
r
,
o
Hxx
(,)
=
H
kT
∂
kTx
∂
+∂
k
∂
Tx
+
Hx
(
,)
−
323
3
B
23
2
33
3
1
223
1
p
p
Similar to the case of the other residual properties, the quadratic-dependent term
[
H
-
1
r
(
x
2
,
x
3
) -
H
1
r
,o
]
T,p
and (∂
k
23
/∂
T
)
p
link the two expressions for the residual partial
molecular properties in Equation 8.46, so that the system's residual molar enthalpy
becomes,
r
r
hTpx x
(,,,)
=
HpT NN NNNN
(
,, ,
,
)(
+
+
)
23
123
1
2
3
(
)
(
)
r
,
o
r
,
∞
r
,
o
r
,
∞
r
,
o
=
H
+
xH
−
H
+
x
HH
−
+
(8.47)
1
2
2
1
3
3
1
Tp
,
Tp
,
(
)
(
)
(
)
kT
2
05
.
∂∂
kTx
2
+∂∂
05
.
k
Tx
2
+∂
k
∂
Txx
p
B
22
2
33
3
23
23
p
p
Obviously, the entropic contributions are simply obtained by substituting Equation 8.38
and Equation 8.45 into the definition of the species residual partial molecular entropy
as illustrated in Appendix D of Chialvo et al. (2008).
8.3.2 m
icroscoPic
i
inTerPreTaTion
oF
The
e
xPansion
c
oeFFicienTs
Now we make contact between the macroscopic coefficients
k
ij
(
T
,
p
), defined by
Equation 8.39, and the microstructural details of the reference system, that is, the
solvation behavior of the species in the infinitely dilute system, by invoking the sol-
vation formalism discussed in Section 8.2 (and references therein) from which we
have that
(
)
o
∞
∞
∞
o
kTpGGGGVi j
ij
(,)
=
+−−
,
=
2
,, 3
(8.48)
11
ij
1
i
1
j
1
Moreover, as discussed extensively elsewhere (Chialvo and Cummings 1994, 1999;
Chialvo et al. 2000c), and according to the argument developed previously in
Section 8.2, we can split the TCFI of an infinitely dilute solution into direct (DCFI)
and indirect (ICFI) contributions as follows (Chialvo 1993b),
