Chemistry Reference
In-Depth Information
As mentioned above, the solubility can be calculated in two different ways:
1. From solubilities in individual constituents of the solvent and their molar
volumes. The molar volume of a ternary mixed solvent (
W
) in Equation
10.37 can be obtained from the molar volumes of water, methanol, and
1-propanol as an ideal molar volume,
t
0
t
0
t
0
WxVx
=
+
V
+
x
V
(10.38)
HO
HO
MeOH
MeOH
PrOH
PrOH
2
2
where
x
t
H
2
O
,
x
t
MeOH
, and
x
PrOH
are the mole fractions of water, methanol, and
1-propanol in the mixed solvent and
V
H
2
O
,
V
MeOH
, and
V
PrOH
are the molar vol-
umes of the pure water, methanol, and 1-propanol. There are three options
for selecting the binary subsystems I and II: (1) water/methanol and water/1-
propanol, (2) water/methanol and methanol/1-propanol, or (3) water/1-pro-
panol and methanol/1-propanol. One can show that all these selections lead
to the same result. For our calculations, we will select the aqueous binary
subsystems (water/methanol and water/1-propanol), because the solubili-
ties of naphthalene in binary aqueous mixed solvents are available in the
same references as those for ternary data (Morris 1988; Dickhut, Andren,
and Armstrong 1989). Hence, the binary subsystem I is the binary system
water/1-propanol with the mole fractions of components:
y
b,I
PrOH
=
x
t
MeOH
+
x
PrOH
and
y
b,
H
2
O
= 1 -
y
b,I
PrOH
and molar volume,
b, I
b, I
()
I
0
0
Vy
=
Vy
+
V
(10.39)
m
HO
HO
PrOH
PrOH
2
2
The binary subsystem II is water/methanol with the mole fractions of com-
ponents:
z
b, II
t
t
b, II
b, II
=
x
+
x
and
z
=
1-
y
and molar volume,
MeOH
MeOH
PrOH
HO
MeOH
2
()
II
b, II
0
b, II
0
V
=
z
Vz
+
V
(10.40)
m
HO
HO
MeOH
MeOH
2
2
The solubilities of naphthalene in the binary subsystems I and II can be
calculated using Equation 10.37 for binary mixed solvents, which requires
only solubilities in the individual constituents of the solvent.
2. From the experimental solubilities in binary solvents and molar volumes of
the individual constituents, the calculation procedure is the same as above,
with the exception that the solubilities of naphthalene in the binary subsys-
tems I and II are obtained from experiment. The calculation of the solubili-
ties in binary aqueous solvents was described in previous sections. It should
be noted that the water/methanol/1-butanol mixed solvent and the binary
subsystem water/1-butanol are not completely miscible. Only the homoge-
neous regions of mixed solvents are considered here.
The solubilities of naphthalene and anthracene in ternary aqueous mixed solvents
are predicted and compared with experiment in Table 10.2.
