8934 J. Phys. Chem. A, Vol. 104, No. 39, 2000
kX ) kXOH[•OH]ss
Destaillats et al.
) kOH - k11[BQ][•OH] - k9[H2O2][•OH] -
d[•OH]
dt
(8)
2k13[•OH]2 - k14[•O2 ][•OH] (17)
-
Table 3 includes the calculated [•OH]ss in the four cases,
employing kiOH values from Table 2. Except for the value of
BQ, which were estimated from the initial data points only, a
good agreement exists in all other cases, thus providing a
reasonable estimation for [•OH]ss. The deviation of BQ from
the assumptions in the simple model of eq 1 becomes even more
evident from the graphical representation (see Figure 5A). In
this case, the process is not pseudo-first-order in [BQ] but rather
zero order. Here, we should also consider the contribution of
reactions of BQ with •HO2(aq) and, particularly at the working
pH, of •O2-(aq). The concentrations of these two species in
solution increase with the irradiation time, since they originate
in the reaction of the two main products of water sonolysis,
•OH and H2O2, in the bulk liquid phase at room temperature:
d[H2O2]
) kH O + k13[•OH]2 - k9 [•OH][H2O2] (18)
2
2
dt
-
d[•O2 ]
-
) k9[H2O2][•OH] - k12[BQ][•O2 ] -
dt
-
- 2
k14[•O2 ][•OH] - k15[•O2 ] (19)
d[BQ]
dt
-
) -k11[BQ][•OH] - k12[BQ][•O2 ]
(20)
Although the reported values for the rate constants were
determined between 20 °C and 25 °C, the temperature depen-
dence of these diffusion-controlled rates is quite small. The
dotted line in Figure 5A represents the calculated BQ depletion
rate, and it shows a good agreement with the experimental
values. The deviation from the simple pseudo-first-order model
from eq 7 can thus be explained simply by the major contribu-
tion of superoxide in the BQ degradation (not observed for the
other three substrates). This fact reveals the importance of
considering, at least in some cases, a more complex scheme of
reactions, considering the particular chemical nature of the
species involved.
•OH(aq) + H2O2(aq) f •HO2(aq) + H2O
k9 ) 2.7 × 107 (9)
-
•HO2(aq) h •O2 (aq) + H+(aq)
pKa ) 4.8 (10)
While •OH(aq) reaches a steady-state concentration, H2O2(aq)
accumulates in the aqueous phase, thus increasing the production
rate of superoxide with reaction time. Given the pH range of
our experiment, the superoxide anion is the prevalent species,
although [•HO2] must also be appreciable.
To assess the role of •HO2(aq) and •O2-(aq) in the depletion
of BQ, a simple kinetic model is postulated in order to reproduce
the experimental observations. The sonochemical production
rates of •OH(aq) and H2O2(aq) under the same ultrasonic
frequency and applied power were previously determined as
Acknowledgment. Financial support provided by the De-
partment of Energy (DOE 1963472402) and the U.S. Navy (N
47408-99-M-5049) is gratefully acknowledged. J.M.J. thanks
the ICSC World Laboratory for a research fellowship.
kOH ) 5.5 × 10-9 M s-1 and kH O ) 2.4 × 10-8 M s-1
,
2
2
References and Notes
respectively.11 The relatively small generation of •HO2 in high-
temperature gas-phase reactions during cavitation was neglected
for simplicity, according to the observations by Hart and
Henglein.25 The model includes the reactions of BQ(aq) with
•OH(aq) and •O2-(aq) (eqs 11-12)
(1) Ince, N. Water Res. 1999, 33, 1080-1084.
(2) Shu, H.; Huang, C.; Chang, M. Chemosphere 1994, 29, 2597-
2607.
(3) Nasr, C.; Vinodgopal, K.; Fisher, L.; Hotchandani, S.; Chatto-
padhyay, A.; Kamat, P. J. Phys. Chem. 1996, 100, 8436-8442.
(4) Vinodgopal, K.; Wynkoop, D.; Kamat, P. EnViron. Sci. Technol.
1996, 30, 1660-1666.
(5) Lagrasta, C.; Bellobono, I.; Bonardi, M. J. Photochem. Photobiol.,
A 1997, 110, 201-205.
BQ(aq) + •OH(aq) f products
k11 ) 1.2 × 109 (11)
k12 ) 1.0 × 109 (12)
-
(6) Chen, L.; Chou, T. J. Mol. Catal. 1993, 85, 201-214.
(7) Tang, W.; Chen, R. Chemosphere 1996, 32, 947-958.
(8) Spadaro, J.; Isabelle, L.; Renganathan, V. EnViron. Sci. Technol.
1994, 28, 1389-1393.
BQ(aq) + •O2 (aq) f products
and the radicals recombination processes of eqs 13-16 as
follows:
(9) Ravishankar, D.; Raju, B. J. Radioanal. Nucl. Chem. 1994, 178,
351-357.
(10) Vinodgopal, K.; Peller, J.; Makogon, O.; Kamat, P. Water Res.
1998, 32, 3646-3650.
2•OH f H2O2
k13 ) 6 × 109
(13)
(11) Joseph, J.; Destaillats, H.; Hung, H.; Hoffmann, M. J. Phys. Chem
A 2000, 104, 301-307.
•OH + •O2- f HO- + O2
k14 ) 1.01 × 1010 (14)
(12) Tseng, T.; Edwards, M. J. AWWA 1999, 91, 159-170.
(13) Colussi, A.; Weavers, L.; Hoffmann, M. J. Phys. Chem. A 1998,
102, 6927-6934.
•HO2 + •O2- + H+ f H2O2 + O2
k15 ) 9.7 × 107
(14) Hua, I.; Hoffmann, M. EnViron. Sci. Technol. 1997, 31, 2237-
(15)
2243.
(15) Kang, J.; Hoffmann, M. EnViron. Sci. Technol. 1998, 32, 3194-
3199.
2•HO2 f H2O2 + O2
k16 ) 8 × 105
(16)
(16) Kang, J.; Hung, H.; Lin, A.; Hoffmann, M. EnViron. Sci. Technol.
1999, 33, 3199-3205.
(17) Sarasa, J.; Roche, M.; Ormad, M.; Gimeno, E.; Puig, A.; Ovelleiro,
J. Water Res. 1998, 32, 2721-2727.
The corresponding differential equations (eqs 17-20) describe
the evolution of the species concentrations in the aqueous phase
during continuous ultrasonic irradiation under O2 saturation. We
assume a complete deprotonation of •HO2(aq) to simplify the
(18) Peralta-Zamora, P.; Kunz, A.; de Moraes, S.; Pelegrini, R.; Moleiro,
P.; Reyes, J.; Duran, N. Chemosphere 1999, 38, 835-852.
(19) Weavers, L.; Hoffmann, M. EnViron. Sci. Technol. 1998, 32, 3941-
3947.
-
reaction scheme (i.e., •O2 is the only species considered in
(20) Mason, T. J. Practical Sonochemistry: User’s Guide to Applications
in Chemistry and Chemical Engineering; Ellis Horwood: London, 1991.
(21) Langlais, B.; Reckhow, D. A.; Brink, D. R. Ozone in Water
Treatment. Application and Engineering; Lewis Pub. Inc.: Denver, 1991.
the calculations). The direct oxidation of BQ by H2O2 is a slow
process that can be neglected under the present experimental
conditions.