Environmental Engineering Reference
In-Depth Information
where
r
P
is the photo-formation rate of phenol obtained experimentally
(M s
-1
),
F
B,HO
is the fraction of HO radicals that react with benzene [i.e.,
k
HO/
Ph
×
C
HO
×
C
Ph
/(
k
HO/Ph
×
C
HO
×
C
Ph
+
∑
k
i
C
HO
C
i
), where
i
is scaven-
ger], and
Y
P
is the yield of phenol formed per benzene oxidized by HO
•
. It is
Y
P
=
0.75
±
0.07 in natural waters (Arakaki and Faust
1998
). The
F
B,OH
values
are much variable for a variety of natural waters, also depending on the concen-
tration of added benzene and on the amount of the natural HO
•
scavengers. For
addition of 1.2 mM benzene it has been found
F
B,HO
=
0.94 for cloud waters
(Arakaki and Faust
1998
), 0.92 and 0.99 for rivers, and 0.68 for seawaters (Takeda
et al.
2004
). The high values of
F
B,HO
in rivers and cloud suggest that most of
the HO radicals formed photolytically reacts with benzene. In contrast, the low
value in seawater samples suggests the 32-34 % of photolytically formed HO rad-
icals reacts with various scavengers of HO radical other than benzene. There are
many scavengers, DOM components, HCO
3
-
, CO
3
2-
, NO
2
-
, halides (X
−
, but chlo-
ride only in acidic medium) etc. that can interact with HO
•
in aqueous solution
(Zafiriou
1974
; Mopper and Zhou
1990
; Vione et al.
2006
; Zepp et al.
1987
;
Voelker and Sulzberger
1996
; Minakata et al.
2009
). In seawater, the bromide ion
(Br
−
) alone scavenges approximately 93 % of photo-generated HO
•
(Mopper and
Zhou
1990
).
To mathematically derive the terms in Eq.
2.2
for any added benzene concen-
tration, one requires a kinetic model where the scavengers and benzene simultane-
ously react with photogenerated HO
•
at the rates R
SC
and R
B
, respectively (Takeda
et al.
2004
). Under the steady-state condition, the formation rate of HO
•
is equal
to the consumption rate as follows (Takeda et al.
2004
):
(2.3)
r
HO
=
r
SC
+
r
B
r
SC
=
k
SC
[
SC
][
HO
]
SS
=
k
′
SC
[
HO
]
SS
(2.4)
r
S
=
k
B
[
B
][
HO
]
SS
(2.5)
where
k
SC
is the reaction rate constant of HO radicals with various scavengers in the
water sample,
k
′
SC
=
k
SC
[SC]
is the apparent scavenging rate constant of the HO
radical,
k
B
is the reaction rate constant of HO
•
with benzene (i.e., 7.8
×
10
9
M
-1
s
-1
), [B] is the concentration of benzene added to the water sample (e.g. ~1 mM),
and [HO]
SS
is the steady-state concentration of HO
•
. Under conditions where ben-
zene is in excess (i.e.,
r
B
>>
r
SC
), most of the photo-generated HO
•
react with ben-
zene, thus
F
B,HO
≈
1. In contrast, in the most general case it is:
r
B
r
B
+
R
SC
[
B
]
[
B] +
k
′
SC
/
k
B
F
B,HO
=
=
(2.6)
From Eqs.
2.3
-
2.6
, the phenol formation rate (
r
P
) can be expressed as:
1
r
P
1
r
HO
+
Y
P
+
[
k
sc
]
r
HO
+
Y
P
×
k
B
[
B]
(2.7)
=
