Environmental Engineering Reference
In-Depth Information
•
the following points are considered: (i) Probability for the symmetrical HO
addi-
tion to the benzene ring is identical (ii) Addition to the
ipso
-position is negligible
for the aromatic compounds with single functional groups (e.g., <8 % for phenol
and <1 % for chloro benzene) due to the significant steric effect (Raghavan and
Steenken
1980
; Merga et al.
1996
; Mvula et al.
2001
). Therefore, only when all
positions on the aromatic ring are filled with functional groups, HO
•
adds to the
ipso
-position with identical probability for all the available positions.
For the determination of the reaction rate constant, the E
a
is a sum of two parts:
(i) a base part, Eº
a
, resulting from the HO
•
addition to the aromatic ring depending
on the number(s) and position(s) of the functional groups and (ii) group contribu-
tion parameter(s), E
a,add-aromatic
Rm, due to the functional group(s), R
m
(where
m
is the number of functional group(s),
m
=
1-6), on the aromatic ring. To reduce
the number of group contribution factors to calibrate, it is assumed that
A
dif-
fers not by the type of the functional groups but by their number and position.
Accordingly, the group rate constant,
k
º
(i-name)-j
, and the group contribution factor,
Z
Rm
, may be expressed as below (Eqs.
2.19
,
2.20
)
k
(
i-name
)
-
j
=
A
(
i-name
)
-
j
e
−
[
(
E
o
a
(
i-name
)
]
RT
(2.19)
Z
Rm
=
e
−
E
a
,add-aromatic
Rm
RT
(2.20)
where
A
º
(
i
-name)-
j
denotes the Arrhenius frequency factor;
E
º
a(
i
-name)
denotes a
base part of
E
a
; the name (benz, pyr, fur, imid, or triaz) denotes a compound that
has a base structure of benzene, pyridine, furan, imidazole, or triazine, respec-
tively;
i
denotes position(s) of the functional group, and
j
denotes position(s) for
HO
•
•
to add. The rate constant for the HO
addition to aromatic compounds can
be expressed by (Eq.
2.21
)
nk
o
(
i-name
)
-
j
Z
Rm
k
add-aromatic
=
(2.21)
where
n
indicates the number of available position(s) to add. The rate constant for
1,4-
tert
-butylphenol [(CH
3
)
3
C-C
6
H
4
-OH] can be depicted as a typical example
(Eq.
2.22
)
2
k
o
(
1,4
-
benz
)−
2,6
+
2
k
o
(
1,4
-
benz
)
-
3,5
k
=
Z
−
OH
Z
-
alkane
+
3
×
3
×
k
prim
X
>
C
<
+
k
−
OH
(2.22)
•
The group contribution factors for the HO
addition to aromatic compounds,
+
against electrophilic substituent constants
σ
are depicted in Fig
2
b for benzene
(
r
=
0.89), pyridine (
r
=
0.93), and furan (
r
=
0.65) compounds (EPI
2007
). The
figure shows that the group contribution factors that are empirically derived from
the experimental rate constants linearly correlate with the general electron-donat-
ing and -withdrawing property. It is shown that a total of 64 % of the rate con-
stants for 64 compounds from the prediction is within the error goal.
Rate constants for HO
•
interactions with S-, N-, or P-atom containing
compounds
(Minakata et al.
2009
): The HO
•
radical reacts with the S-, N-, or
