Chemistry Reference
In-Depth Information
0.09
0.08
1
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
2
0
0.2
0.4
0.6
0.8
1
x
et
FIGURE 10.5
Comparison between experimental (o) and calculated (solid lines) solubili-
ties of paracetamol (
S
is the mole fraction of paracetamol) in the mixed solvent water/ethanol
(
x
et
is the mole fraction of ethanol) at room temperature. The solubility was calculated using
Equation 10.29. 1-activity coefficients expressed via the Flory-Huggins equation, 2-activity
coefficients expressed via the Wilson equation. (From S. Romero, A. Reillo, B. Escalera,
and P. Bustamante, 1996, The Behavior of Paracetamol in Mixtures of Amphiprotic
and Amphiprotic-Aprotic Solvents. Relationship of Solubility Curves to Specific and
Nonspecific Interactions,
Chemical and Pharmaceutical Bulletin,
44, 1061. Reprinted from
E. Ruckenstein, and I. L. Shulgin, 2003c, Solubility of Drugs in Aqueous Solutions. Part 2:
Binary Nonideal Mixed Solvent,
International Journal of Pharmaceutics,
260, 283, With
permission from Elsevier.)
a minimal number of experimental data. However, our further considerations involve
aqueous multicomponent solvents, because almost all solubility data from literature
(which are used in the examples) are based on aqueous multicomponent solvents.
Let us consider an
n
c
-component mixture containing a solute (component 2),
water, and (
n
c
-2) organic cosolvents. If one considers the (
n
c
-1) mixed solvent as an
ideal mixture, the following expression for the activity coefficient of a solid solute
at infinite dilution in a multicomponent (ternary and higher) solvent can be obtained
(Ruckenstein and Shulgin 2003a, 2004, 2005),
BW
VV
ln
n
,
∞
(ln
γ
2
c
)
=−
+
A
(10.32)
nc
x
0
0
(
−
)
i
≠
13
,
3
1
n
c
x
i
≠
1
,, 3
where γ
2
n
c
,∞
is the activity coefficient of the solid solute at infinite dilution in an
n
c
-component mixture (solute+(
n
c
-1) component solvent),
W
is the molar volume of an
ideal (
n
c
-1)-components solvent,
V
i
0
is the molar volume of the individual cosolvent
i
,
x
i
n
c
is the mole fraction of component
i
in the
n
mixture, and
A
and
B
are composition-
independent constants. The constants
A
and
B
can be determined from the activity
coefficients of the solid solute in two (
n
c
-1)-component mixtures with the mole fraction
of component 1 equal to zero in one of them and the mole fraction of component 3 equal
to zero in the other one. It should be noted that Expression 10.32 is valid on the line
on which the sum of the mole fractions of components 1 and 3 is constant. Of course,
a similar expression can be written for any pair of components of the mixed solvent.
