Environmental Engineering Reference
In-Depth Information
Hexane
:H
3
C-(CH
2
)
4
-CH
3
. We have six C atoms contributing 6
b
c
and 14 H atoms
contributing 14
b
H
. Therefore
Σ
b
j
=
6
(
0.20
)
+
14
(
0.23
)
=
4.42.
If there are
n
bonds, they contribute to (
n
−
1)
B
b
factors. In this case, there are five C-C
bonds and hence
Σ
B
k
=
(
5
−
1
)(
−
0.12
)
=−
0.48. Hence log
K
ow
=
4.42
−
0.48
=
3.94. The experimental value is 4.11. Hence we have a 4% error in our estimation.
Chlorobenzene
:C
6
H
5
Cl. Since the log
K
ow
value of benzene (C
6
H
6
)
is reported to be
2.13, we only need to subtract the fragment constant for 1H bonded to an aromatic ring
(
b
H
)
and add that for one Cl atom bonded to an aromatic ring (
b
H
)
. Thus log
K
ow
=
2.13
−
0.23
+
0.94
=
2.84. The experimental value is 2.98. The error is 5%.
Cyclopentane
:C
5
H
10
. Fragment factors: 5
b
c
+
10
b
H
=
3.30. Structural factors:
(
5
−
1
)B
b
=−
0.36. Hence log
K
ow
=
2.94. The experimental value is 3.00.
Chlorobiphenyl
:H
5
C
6
-C
6
H
4
Cl.Sinceforbiphenylthevalueis4.09,forchlorobiphenyl
it is 4.09
−
0.23
+
0.94
=
4.8.
3.3.4.2
Linear Free Energy Relationships
It is important to note that other solvent-water partition constants can be related to
K
ow
(Collander, 1951). The partition constant between octanol and water is related
to other partition constants as
log
K
sw
=
a
log
K
ow
+
b
,
(3.53)
where
a
and
b
are constants. This is called a
linear free energy relationship
(LFER).
The slope
a
is a measure of the relative variability of the activity coefficient of the
soluteinthetwosolvents.Theintercept
b
isaconstantandcanberegardedasthevalue
of log
K
sw
for a hypothetical compound whose log
K
ow
is zero.A number of solvent-
water partition constants have been related to
K
ow
. If the solvent is similar in nature
to octanol, a high degree of correlation can be expected. It should be remembered
that using
K
ow
as the reference emphasizes that it is the high activity coefficient
compounds in water that account for the unique partitioning behavior. The changes
in log
K
ow
and log
K
sw
track one another only for homologous series of compounds.
If the compounds vary in their characteristics (polarity and stereochemistry), then the
linear relationship will be less than satisfactory. The situation then calls for separate
LFERs for classes of compounds that resemble one another. In other words, a single
correlation for all types of compounds is untenable.
3.4 NONIDEAL SOLUTIONS
Thissectionisdevotedtononidealbehaviorthatiscommontoenvironmentalsystems.
3.4.1 A
CTIVITY
C
OEFFICIENT FOR
N
ONIDEAL
S
YSTEMS
Mixtures of real fluids (gases or liquids) do not form ideal solutions, although similar
fluids approach ideal behavior. All nonelectrolytes at their infinite dilution limit in
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