Environmental Engineering Reference
In-Depth Information
where
k
′
1
=
k
[
H
2
O
2
]
. The reaction is quite fast at high temperature and pH, and
it becomes quite difficult to be examined at 25 °C and pH 8. The reaction at 5 °C
and pH 3.5 followed first-order kinetics with respect to Fe(II) for seawater sam-
ples, giving
k
′
=
0.0385
±
0.0009 min
−
1
and log
k
=
1.50
±
0.02 (
k
in M
−
1
s
-1
)
(Millero and Sotolongo
1989
). At higher pH and temperature, the second-order
reaction rate constants have been determined at the stoichiometric ratio [Fe(II)]/
[H
2
O
2
]
=
2, following Eq. (
4.29
) (Benson
1960
)
(4.29)
1
/[
Fe(II)
]=
1
/[
Fe(II)
]
o
+ (
k
/
2
)
t
where [Fe(II)]
o
is the initial concentration of Fe(II).
The rate constant
k
(M
-1
s
-1
) for Eq. (
4.29
) is independent of pH below pH
4, and increases significantly at high pH values. It is a linear function of [H
+
] or
[HO
-
] from pH 6 to 8 in seawater. The effect of pH is not affected by a variation
of the temperature
The effects of temperature (T) and ionic strength (
I
) on
k
at pH 6 can be
expressed as (Eq.
4.30
) (Millero and Sotolongo
1989
):
log
K
=
13. 73
−
2, 948
/
T
−
1. 70
I
1
/
2
(4.30)
+
1. 20
I
The reaction rates can be depicted as (Eq.
4.31
) (Millero and Sotolongo
1989
):
d
[
Fe(II)
]/
dt
=−
k
2
[
Fe(II)
][
H
2
O
2
][
HO
−
]
(4.31)
where the values of
k
2
are independent of temperature. This is attributed to the
fact that the activation energy is of the same order of magnitude as the heat of ion-
ization of water (
Δ
H
w
*
). The effect of the ionic strength on log
k
2
can be depicted
as (Eq.
4.32
) (Millero and Sotolongo
1989
):
log
K
2
=
11. 72
−
2. 14
I
1
/
2
+
1. 38
I
(4.32)
The overall reaction rate
k
over the entire range of pH, temperature and ionic
strength can be expressed by (Eq.
4.33
) (Millero and Sotolongo
1989
):
(4.33)
k
=
k
o
α
Fe
+
k
1
α
FeOH
where
α
Fe
and
α
FeOH
,
k
o
and
k
1
are the fractions of the two Fe(II) species and the
rate constants for the oxidation of Fe
2
+
and FeOH
+
, respectively. The values of
k
o
and
k
1
can be expressed by (Eqs.
4.34
,
4.35
) (Millero and Sotolongo
1989
):
(4.34)
log
K
0
=
8. 37
−
1, 866
/
T
log
k
1
=
17. 26
−
2. 948
/
T
−
1. 70
I
1
/
2
+
1. 20I
(4.35)
The addition of HCO
3
-
at constant pH linearly increases the reaction rate, inde-
pendently of the temperature and salinity. This result can be attributed to FeCO
3
0
reacting faster than FeOH
+
with H
2
O
2
. At a given pH and ionic strength, the reac-
tion rates in seawater are almost the same as in NaCl. These results can explain
