Environmental Engineering Reference
In-Depth Information
governed by
k
0
+
k
1
K
1
/
[
H
+
]
+
k
2
β
2
/
[
H
+
]
2
d
[
Fe
(
II
)
]
d
t
[
Fe
2
+
]
P
O
2
,
r
=−
=
where
K
1
and
β
2
are respectively the equilibrium and stability constants
of the two major hydroxo species, Fe(OH)
+
and Fe(OH)
2
(refer to Sec-
tion 5.8.1); (ii) an abiotic oxidation given by
r
=
k
3
A
[
Fe
(
II
)
][
OH
−
]
2
P
O
2
,
where
A
is the area of the surface to which iron is attached; and (iii) a
biotic oxidation process given by
r
=
k
4
[Bac][Fe(II)][OH
−
]
2
P
O
2
, with
[Bac] measured as grams volatile solids per liter. The rate constants at
298 K were determined to be
k
0
=
1
×
10
−
8
s
−
1
,
k
1
=
3.2
×
10
−
2
s
−
1
,
k
2
=
1
×
10
4
s
−
1
,
k
3
=
4.9
×
10
14
(L/mol)
2
/atm/m
2
/s,
k
4
=
8.1
×
10
16
(L/mol)
2
/atm/s/(gvolatilesolids/L),
K
1
=
10
−
9.5
,
β
2
=
10
−
20.6
,and
A
=
4.2 m
2
/g. Calculate the half-life for Fe(II) in the acidic lake if the pH is
5.2. The sediment showed a 7% loss of weight upon combustion. The
suspended sediment concentration in the lake water was 1 g/L.
5.22
2
Determine the equilibrium constant for the following reactions at 298 K.
Assume unit activities of all species except [H
+
]=
10
−
6
M.
(i) PbO
(
s
)
+
2H
+
(
aq
)
Pb
2
+
(
aq
)
+
H
2
O
(
l
)
.
(ii)
1
4
CH
2
O
+
Fe
(
OH
)
3
(
s
)
+
2H
+
Fe
2
+
+
1
11
4
H
2
O.
The first reaction is of importance in corrosion problems, whereas the
second reaction is an important oxidation reaction occurring in soils and
sediments.
5.23
2
Nitrogen fixation in the environment is mediated by a bacteria called
nitrobacter
. The conversion of N
2
to NH
4
in nature is the primary reduc-
tion reaction at pH 7. This is accompanied by the oxidation of natural
organic matter (designated CH
2
O) to CO
2
. What are the free energy
changes for the two half reactions? What is the total free energy of the
redox process? How is the reaction affected in a slightly acidic lake water
(
pH
=
6
)
?
5.24
2
Assume a linear adsorption constant
K
d
for a nonionic organic pol-
lutant with suspended particles of concentration
ρ
p
. If the pollutant
has an average rate constant of
k
ads
in the sorbed state and
k
aq
in
the aqueous phase for transformation to a product B, obtain the ratio
of the overall reaction rate
k
obs
to
k
aq
. For the following condi-
tions, how is the rate affected: (a) lake waters of
ρ
p
=
10 mg/L; (b)
bottom sediments and soils of
ρ
p
=
10
6
mg/L. Discuss your results
with respect to the two compounds 1,2-DCE and
p
,
p
-DDT.
5.25
2
The oxygen transfer coefficient (
k
l
a)
into a biological fermentor can be
obtained using the sodium sulfite method, where the following reaction is
supposed to occur: Na
2
SO
3
+
4
CO
2
+
Co
2
+
−−−→
Na
2
SO
4
.Co
2
+
catalyzes
the reaction. In a batch fermentor filled with 0.01 m
3
of 0.5 M sodium
sulfite containing 0.002 M Co
2
+
ion, fresh air is bubbled in at a constant
rate. After 10 min of bubbling, an aqueous sample
(
10
×
10
−
6
m
3
)
was
withdrawn and analyzed for sodium sulfite. The final concentration of
sodium sulfite was 0.2 M. Calculate
k
l
a
for oxygen from the above data.
Given that the temperature of the experiment was 298 K and the pressure
was 1 atm, obtain the Henry's constant for oxygen from the text.
(1/2)O
2
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