Chemistry Reference
In-Depth Information
Sharygin, and Wood 1996) manipulated specific combinations of partial molecular
volumetric properties (i.e., compressibility-driven) that led naturally to well-behaved
finite quantities associated with the solvation behavior of infinitely dilute solutes.
These successful isothermal-density correlations suggested an underlying common
mechanism that neutralized the original compressibility-driven contributions to the
mechanical partial molecular properties of the solute at infinite dilution, and rein-
forced the need for its molecular-based interpretation (
vide infra
Section 8.2.2).
The main issue here is to achieve the unambiguous separation between solva-
tion and compressibility-driven phenomena, based on the formal splitting of the
total correlation functions into their corresponding direct and indirect contribu-
tions (Chialvo and Cummings 1994, 1995) according to the Ornstein-Zernike equa-
tion (Hansen and McDonald 1986), and then use the derived rigorous expressions
as zeroth-order approximations, for example, reference systems, in the subsequent
perturbation expansion of the composition-dependent thermodynamics properties of
multicomponent dilute fluid mixtures (
vide infra
Section 8.3).
For that purpose, we can portray the solvation of a single ionic solute
C
z z
νν
+
−
in
a pure solvent at fixed state conditions (constant
T
, and either constant
p
or ρ) as the
formation of an infinitely dilute system in a
thought experiment
involving
N
solvent
molecules in which a number ν of them (ν = ν
+
= ν
-
where ν
+
and ν
-
are the stoichio-
metric coefficients of the salt) can be distinguished by their
solute
labels. Thus, the
initial conditions of the system represent an
ideal solution
in the sense of the Lewis-
Randall rule (O'Connell and Haile 2005), that is
,
the residual properties of the (
N
−ν)
solvent-labeled particles and those of the ν solute-labeled particles are identically
the same (Chialvo 1990b; Chialvo 1993a). To form the desired infinitely dilute
non-
ideal solution
, the solvation process proceeds through the mutation (à la Kirkwood's
coupling-parameter charging [Kirkwood 1936]) of the distinguishable ν solvent mol-
ecules into the final neutral ionic solute
C
z z
νν
+
−
+
−
. The process in which the original
ν
solute
species in the
ideal solution
(i.e., where all solute-solvent interactions are
identical to the solute-solute and the solvent-solvent interactions) are converted into
the neutral ionic species is driven by the free-energy difference, μ
r
,∞
(
T
,
p
) - νμ
r
,o
(
T
,
p
),
where the superscript
r
denotes a residual quantity for a pure (o) or an infinitely dilute
(∞) species at the specified state conditions, respectively. This driving force provides
the sought link between the microstructural changes of the solvent around the mutat-
ing species and the macroscopic (thermodynamic) properties that best characterize
the solvation process.
While this connection can be achieved in essentially four equivalent ways by
interpreting the driving force of the solvation process (Chialvo et al. 2000b), from
either a microscopic or a macroscopic standpoint, it is more instructive to invoke the
one that explicitly illustrates the separation of length scales. To do so, we start from
the exact thermodynamic expression (Modell and Reid 1983),
+
−
(
)
r
,
∞
r
,
o
∞
o
µ
(,)
Tp
−
νµ
(
Tp
,)
=
ν
kT
ln
φφ
2
1
B
21
(8.1)
ρ()
p
ρ
κρ
d
(
)
∫
∞
o
=
V
−
ν
V
2
1
0
T
