Environmental Engineering Reference
In-Depth Information
2.4.1 Reaction rate Constants by Functional Group Contribution
Method
•
Recently, it has been possible to determine the aqueous phase HO
reaction rate con-
stants by the functional GCM, which can be applied to the photoinduced degradation
of a given organic compound in aqueous media (Minakata et al.
2009
). The GCM is
based on Benson's thermochemical group additivity (Benson
1976
). Under the princi-
ple of group additivity, it is hypothesized that an observed experimental rate constant
for a given organic compound is the combined rate of all elementary reactions involv-
ing HO
•
, which can be estimated using Arrhenius activation energy
E
a
and frequency
factor
A
. Each reaction mechanism defines a base activation energy,
E
a
º, and a func-
tional group contribution of activation energy,
E
a
Ri
. The latter results from the neigh-
boring (i.e.,
α
-position) and/or the next-nearest neighboring (i.e.,
β
-position) functional
group (i.e., Ri). The GCM considers four reaction mechanisms that can be initiated by
HO
•
•
in the aqueous phase, which include (1) H-atom abstraction, (2) HO
addition to
•
C C doble bond(s) on alkenes, (3) HO
addition to C
=
C doble bond(s) on aromatic
•
compounds, and (4) HO
interaction with sulfur (S)-, nitrogen (N)-, or phosphorus
(P)-atom-containing compounds (Minakata et al.
2009
). Accordingly, an overall reac-
tion rate constant,
k
overall
, can be given by Eq.
2.5
k
overall
=
k
abs
+
k
add
−
alkene
+
k
add
−
aromatic
+
k
int
(2.5)
where,
k
abs
,
k
add-alkene
,
k
add-aromatic
, and
k
int
are the rate constants for the aforemen-
tioned reaction mechanisms (1)-(4), respectively.
Rate constant for hydrogen-atom abstraction
(Minakata et al.
2009
): For
H-atom abstraction, the active bond is a C-H bond. In general, molecules are catego-
rized based on the number of C-H bond(s) (i.e., CH
3
R
1
, CH
2
R
1
R
2
, and CHR
1
R
2
R
3
,
where R
i
is a functional group (
i
=
1
−
3)). Each of the fragments corresponds to a
partial rate constant
k
CH
3
R
1
,
k
CH
2
R
1
R
2
, and
k
CHR
1
R
2
R
3
, respectively. The C-H bond
itself and adjacent functional group(s) contributes to the overall
E
a
as the base activa-
tion energy,
E
a
0
, and group contribution parameter,
E
a,abs
R
i
, due on the functional
group R
i
, respectively. For example, the base activation energy for H-atom abstraction
from one of the primary C-H bonds is
E
a,prim
0. The
E
a,abs
R
i
indicates the electron-
donating and—withdrawing ability of the functional group. An electron-donating
functional group decreases the
E
a
and, hence, increases the overall reaction rate con-
stant, and vice versa. Accordingly, the partial rate constant for the fragmented parts
such as CH
3
R
1
, CH
2
R
1
R
2
and CHR
1
R
2
R
3
can be written as below (Eqs.
2.6
-
2.8
)
k
CH
3
R
1
=
3
A
prim
e
−
E
a
,prim
+
E
R
1
a
,abs
(2.6)
RT
k
CH
2
R
1
R
2
=
2
A
sec
e
−
E
a
,sec
+
E
R
1
a
,abs
+
E
R
2
a
,abs
RT
(2.7)
k
CHR
1
R
2
R
3
=
A
tert
e
−
E
a
,tert
+
E
R
1
a
,
abs
+
E
R
2
a
,
abs
+
E
R
3
a
,
abs
(2.8)
RT
