Environmental Engineering Reference
In-Depth Information
Considering all of the chain reactions for the loss of ozone, we have
1
k
9
k
12
.
1
g
d
[
O
3
]
d
t
=
k
9
k
12
OH
−
]+
OH
−
]
−
k
1
[
2
k
1
[
+
+
k
13
[
M
]
(6.114)
[
O
3
]
Including the total ozone consumption via nonchain reactions as well, we can write
the above equation as
1
k
9
k
12
1
g
d
[
O
3
]
d
t
=
k
9
k
12
OH
−
]+
OH
−
]
−
k
1
[
2
k
1
[
+
+
k
13
[
M
]
+
k
14
[
M
]
.
[
O
3
]
(6.115)
At constant [OH
−
] (or pH) and constant [M], we can write
d
[
O
3
]
d
t
=−
k
tot
[
O
3
]
tot
.
(6.116)
Thus, the rate is pseudo-first-order with a rate constant
k
tot
. A plot of ln[O
3
] versus
t
should yield a straight line with slope
k
tot
for a specified [OH
−
] and [M]. For a
batch reactor, the above equation will give the rate of disappearance of ozone in the
presence of different substrates. The identity of solute M may be different at different
points along the chain. Thus, for example, the species M undergoing oxidation and
forming radicals that start the chain reaction with the rate constant
k
13
is called an
initiator
(represented by I). Those that terminate the chain by reacting with OH
•
are called
terminators
or
suppressors
(represented by S). Those species that react
with OH
•
to reform O
−
2
with rate constant
k
9
are called
propagators
(represented
by P). The
direct
reaction of M with ozone characterized by the rate constant
k
14
is designated
k
d
. Staehelin and Hoigne (1985) have identified different species in
water that perform the above functions. These are listed in Table 6.2 along with the
respective rate constants. To differentiate these species correctly in the rate equation,
they also generalized the above rate constant to give
)
1
k
p
[
]
M
OH
−
]+
OH
−
]+
k
tot
=
k
I
[
(
2
k
I
[
k
I
[
M
]
+
+
k
d
[
M
]
,
(6.117)
k
s
[
S
]
where
k
I
=
k
12
. For most hard wastewaters where
bicarbonate is the predominant scavenger of OH
•
,wehave
k
I
[
k
13
,
k
d
=
k
14
,
k
P
=
k
9
, and
k
S
=
OH
•
]
M
]
2
k
1
[
, and
hence
1
k
p
[
M
]
k
tot
=
k
I
[
M
]
+
+
k
d
[
M
]
.
(6.118)
k
s
[
S
]
Now that we have gained an understanding of the kinetics of ozone oxidation pro-
cesses, we shall next see how this information can be utilized in analyzing ozonation
reactors.
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