Chemistry Reference
In-Depth Information
and heat capacities at elevated temperatures. Results for Henry's constants are also
quite accurate.
9.3.3 s
oluBiliTies
in
m
ixed
if
liquid
s
olvenTs
While the above treatments are for solutes in single solvents, many applications of
interest involve mixed solvents, especially for gases and pharmaceutical compounds.
FST has been used to develop successful descriptions of such systems. Chapter 10
describes the approach of Shulgin and Ruckenstein. The focus here is on
excess
solubility
, ln
x
Ex
, the difference in solubility in a real solvent mixture and that for the
solvents as an ideal solution (Prausnitz, Lichtenthaler, and Gomes de Azevedo 1999).
For very dilute solutions, the solubility is the reciprocal of the Henry's constant, so
typically the
excess Henry's constant
,
H
2
Ex
, is modeled
n
s
−
∑
Ex
≡
ln
HH xH
m
ln
ln
(9.45)
2
2
if
2
if
if
where the sum is over all solvents. Most measurements and models have been for
binary solvents where the variation of
H
2
Ex
can be positive or negative or both.
Empirical models have been developed, especially because the variation of
H
2
Ex
with
composition is similar for all solutes and is mostly determined by the substances of
the solvent mixture. FST approaches have been among the most successful for both
gaseous and solid solutes in mixed solvents as also described in Chapter 10.
9.3.3.1 Gas Solubility in Mixed Solvents
There have been two FST approaches to gas solubility in mixed solvents. The first
(O'Connell 1971a) expressed
H
2
Ex
in terms of collections of DCFI with simple param-
eterization; details of the relations are given in Section 9.3.3.2. The second (Mathias
and O'Connell 1979; Campanella, Mathias, and O'Connell 1987) used the DCFI
model of Equation 9.4 by integrating the DCFI for the solute from one pure solvent,
identified as reference solvent,
R
, to the mixture composition, which for a binary is
given by
x
R
. Then,
(
)
(
)
+
Ex
*
H
≡−
1
x
ln
HH
2R
/
ln
γ
(9.46)
2
R
23
2
where ln γ
*
is found from Equation 9.30 with ρ
0
being the pure reference solvent
density, and the solution component densities being those for the mixed solvent, ρ
if
=
x
if
ρ
m
for
if
= R, 3. For most systems, the mixture density used can be that for an ideal
solution, though for aqueous systems, the excess volume is large enough that it must
be taken into account (Campanella, Mathias, and O'Connell 1987; O'Connell 1995).
Figure 9.9 shows results for
H
2
Ex
of ethylene in aqueous acetone and aqueous metha-
nol. The complex behavior of the alcohol system is captured reasonably well, and
quantitative agreement for the acetone system is obtained only if the solution excess
