Environmental Engineering Reference
In-Depth Information
The propagation steps are
k
1
R
•
+
O
2
−−→
ROO
•
,
(5.103)
k
2
ROO
•
+
RH
−−→
ROOH
+
R
•
.
Thus the radical
R
•
is reformed in the last propagation step. These steps can be repeated
several times, depending on the light or thermal energies available for initiation. The
only termination steps are radical recombinations such as
k
1
−−→
Pr,
ROO
•
+
R
•
−→
Pr,
R
•
+
R
•
−→
Pr.
ROO
•
+
ROO
•
(5.104)
If the pollutant concentration in the water column is low, the most likely termination
step is the first one listed above. The rate of oxidation of the organic compound is given
by Equation 5.102 above:
d
[
RH
]
d
t
=−
k
2
[
ROO
•
][
RH
]
.
r
=
(5.105)
In natural waters ROO
•
concentration may reach steady-state concentrations of
∼
10
−
9
mol/L.Applying the pseudo-steady-state approximation for the peroxide radical
we obtain.
If we denote the rate of peroxide formation as
r
PER
=
k
1
[R
•
][O
2
], then we can write
r
=−
k
2
r
PER
k
t
1
/
2
[
RH
]=
k
[
RH
]
.
(5.106)
In most natural waters the rate of peroxide formation
r
PER
is constant. Hence
k
is a
pseudo-first-order rate constant. There exist a few classes of compounds (e.g., polyaro-
matic hydrocarbons and nitrosoamines) that are subject to free radical oxidation in both
natural waters and atmospheric moisture (Schnoor, 1992).
5.6 REACTIONS IN SOLUTIONS
5.6.1 E
FFECTS OF
I
ONIC
S
TRENGTH ON
R
ATE
C
ONSTANTS
Reactions in the hydrosphere occur in the presence of many different ions. Hence,
the ionic strength influences the rate of a reaction.
TheACTstatesthattherateofthereactionis
r
k
†
[AB
†
]withthethermodynamic
=
equilibrium constant,
K
†
=
a
(
AB
†
)
/a
(
A
)
a
(
B
)
, where
a
is the activity of a species. Thus
AB
†
AB
†
[
]
γ
AB
†
[
]
K
†
K
†
γ
=
γ
A
γ
B
=
,
(5.107)
[
A
][
B
]
[
A
][
B
]
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