Chemistry Reference
In-Depth Information
where the sets of constants {α} and {β} are
0.65386227
0.16067976
0.807662393
-
=
α
,
β
=
(9.21)
0.22010926
Though the forms of all the other equations are the same, the values used in
Equation 9.11 and Equation 9.21 by Mathias and O'Connell (1981) and Campanella,
Mathias, and O'Connell (1987) differ somewhat from those developed by Abildskov,
Ellegaard, and O'Connell (2009) and Ellegaard, Abildskov, and O'Connell (2011),
which were revised to more successfully correlate the properties of ionic liquids.
Those given here are from Campanella (Campanella, Mathias, and O'Connell 1987).
As in Equation 9.6, the pressure difference is analytic in reduced density and tem-
perature, providing a solution for ρ at a specified
p
or for
p
at a specified ρ
.
9.2.3 P
arTial
m
olar
v
olumes
There is a direct FST connection of partial molar volumes of components in solution
to DCFI,
n
c
∂
∂
β
pV
N
V
kT
j
(
)
{}
i
=
=
x
1
−
CT
,
ρ
(9.22)
j
ij
κ
i
BT
TV N
,,
=
1
ji
≠
This relation has a number of aspects that lead to successful correlations, including
those in the near-critical region where
V
i
∞
may diverge (O'Connell 1994; O'Connell
and Liu 1998; Plyasunov, O'Connell, and Wood 2000; Plyasunov et al. 2000, 2001;
Sedlbauer, O'Connell, and Wood 2000; Plyasunov, Shock, and O'Connell 2006). It
also gives a correction about a misinterpretation of the pressure dependence of gas
solubility (Mathias and O'Connell 1979, 1981; O'Connell 1981), and notes errors in
the values of partial molar volumes of gases from supercritical fluid chromatogra-
phy (Liu and O'Connell 1998). The practical range of dilute solution compositions
where a property is independent of the component's concentration, or is effectively
at infinite dilution, depends on the property and the desired accuracy. Composition
sensitivity is greater for activity coefficients than for partial molar volumes and
enthalpies. This section describes several aspects of partial molar volume modeling,
focusing on infinitely dilute solutions and the near-critical region.
9.2.3.1 Partial Molar Volumes at Infinite Dilution
For dilute solutions, the volume of a dilute binary solution might be approximated as
(
)
o
∞
VTpx
(,,)
≈−
1
xV
+
xV
x
<
0 1
.
(9.23)
m
1
2
1
2
2
2
