Environmental Engineering Reference
In-Depth Information
The generic remediation reaction takes the form
a
A +
b
B =
d
D +
e
E. If
C
t
= 0
= the contaminant at time,
t
= 0, then the observed
rate of reaction (
k
observed
), between
t
= 0, and
t
= m, can be determined [130, 131] as
=
(
)
CC
tm
/
(1.1)
tm t
=
=
0
k
observed
(
=
( ))
s
C
C
=
[
]
Ln
t
=
0
k
t
(1.2)
observed
tm
=
Equations 1.1, 1.2 apply to each remediation model.
1.3.1
catalyst model
The hypothesis [48] that ZVM acts as a catalyst will result in decreasing particle size, increasing particle surface area, and/or
increasing the quantity of ZVM, automatically increasing the observed rate of reaction (
k
observed
) [48, 55, 129-131]:
k
ap
k
=
observed
[
Normalised ReactionRate
]
(1.3)
sa
(
)
m
st n
=
−
E
RT
()
asa
kA
=
exp
(1.4)
sa
sa
−
E
(
)
a
observed
k
=
A
exp
(1.5)
(
)
observed
observed
RT
(
)
=
[][][]
k
mn
p
−−
11
Reactionratemol ls ABC
,
v
(1.6)
a
It is commonly assumed that if a plot of ln(
k
sa
or
k
observed
) vs. time and pollutant concentration can be interpreted as a negative,
or positive, zero-, first-, second- or third-order reaction [130, 131], then the ZVM must be acting as a catalyst. However, the
primary interaction of the ZVM is with water (e.g., n-Fe
0
+ H
2
O = HFeOH
2+
+ 2e
−
), and this interaction generates e
−
[103]
(Appendix 1.C). e
−
is a powerful catalyst (used in electron shuttle reactions) [130]. It is therefore possible that much of the
catalytic activity attributed to n-Fe
0
(and other ZVM) has been misattributed, and the actual catalytic activity/remediation
reactions are undertaken by e
−
[10] (as the availability of e
−
is directly linked to the corrosion of ZVM (Appendix 1.B, 1.C)).
The catalytic model assumes that the remediation reactions may take the form, A + ZVM = {A[ZVM]} = products, or
A + ZVM hydride, oxide, hydroxide, peroxide = {A[ZVM hydride, oxide, hydroxide, peroxide]} = products, The associated
reaction rates are [130]:
k
d
= A + ZVM = {A[ZVM]};
k
−
d
= {A[ZVM]} = A + ZVM;
k
r
= {A[ZVM]} = products. The overall rate of
reaction (
v
) =
k
r
[{A[ZVM]}] =
k
d
k
r
[A{ZVM}]/(
k
−
d
+
k
r
) [130] and the overall rate coefficient
k
observed
=
v
/{A[ZVM]} =
k
d
k
r
/
(
k
−
d
+
k
r
) [130]. The equilibrium constant (
K
{A[ZVM]}
) for the encounter pair {A[ZVM]} is
k
d
/
k
−
d
and
k
observed
=
k
r
K
{A[ZVM]}
[130].
In groundwater, the ZVM diffusion environment results in
k
observed
(m
3
s
−1
) = 4
πr
{A[ZVM]}
D
{A[ZVM]}
[130]. Transition state theory
(absolute rate theory) [130] defines:
k
observed
=
k
B
T
/
h
exp(−Δ
G
ǂ
/
RT
). The concentration of dissolved ions in the water impacts
directly on the reaction rate (
k
), that is,
k
observed
= (
k
B
T
/
h
) K
ǂ
(γ
A
γ
ZVM
/γ
{A[ZVM]}
) [130]. These interactions are rarely accounted for
in studies that suggest that ZVM acts as a remediation catalyst.
1.3.2
redox model
In groundwater [103, 104, 131]:
RT
nF
∆
G
nF
RT
nF
()
= −
[]
=
()
=− °−
[]
∆
E
Eh
∆
E
ln
Q
∆
E
ln
K
(1.7)
RT
nF
°
()
∆
G
nF
°=
[]
=
∆
E
ln K
(1.8)
