Environmental Engineering Reference
In-Depth Information
where
K
†
is the ratio of activity coefficients. The overall rate expression in terms
γ
of
K
†
is
γ
r
=
k
†
K
†
K
†
[
A
][
B
]=
k
[
A
][
B
]
.
(5.108)
γ
0
)
as
k
0
, then
If we denote the rate constant at zero ionic strength
(I
=
K
0
K
†
=
k
.
(5.109)
γ
In Section 3.4, we noted that the activity coefficient of a solute
i
in a dilute elec-
trolyte solution is given by the Debye-Huckel limiting law, ln
Az
i
z
j
I
1
/
2
, where
I
is the ionic strength. For the present case, we have two components A and B and
hence
γ =−
ln
K
†
z
A
+
z
B
−
1
/
2
2
z
A
z
B
I
1
/
2
γ
=
A
[
(z
A
+
z
B
)
]
=−
(5.110)
where (
z
A
+
z
B
)
is the charge of the activated complex, AB
†
. Hence
ln
k
k
0
2
z
A
z
B
I
1
/
2
.
=
(5.111)
If
z
A
and
z
B
are of the same charge, then increasing
I
increases the rate constant,
whereas for ions of opposite charge, the rate constant decreases with increasing
I
.If
either of the species is uncharged,
I
will have no effect on the rate constant. These
effects are called
kinetic salt effects
. Using the value of A
0.51 derived in Section
3.4., the approximate dependence of
I
on the rate constant can be readily estimated
using the following equation:
=
ln
k
k
0
1.02
z
A
z
B
I
1
/
2
.
=
(5.112)
Hence a slope of the plot of ln
k
versus
I
1
/
2
should give a slope of 1.02
z
A
z
B
.
Note that one can also substitute other relationships for
as given in Table 3.2 and
obtain the appropriate relationship between rate constant and ionic strength that are
applicable at higher values of
I
.
The ionic strength effect on rate constants will become significant only for
I >
0.001 M. For rainwater
I
is small, whereas for lakes and rivers it is close to the above
value. For atmospheric moisture (fog and cloud) and for seawater
I
exceed 0.001 M.
Wastewater also has values of
I >
0.001 M. Only for these latter systems does the
dependence of
I
on
k
become significant.
γ
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