Reaction of O2 with the hydrogen atom in water up to 350 °C

Article abstract of DOI:10.1021/jp065140v

The reaction of the H atom with O₂, giving the hydroperoxyl HO₂ radical, has been investigated in pressurized water up to 350 °C using pulse radiolysis and deep-UV transient absorption spectroscopy. The reaction rate behavior is highly non-Arrhenius, with near diffusion-limited behavior at room temperature, increasing to a near constant limiting value of ～5 × 10¹⁰ M^-1 s ^-1 above 250 °C. The high-temperature rate constant is in near-perfect agreement with experimental extrapolations and ab initio calculations of the gas-phase high-pressure limiting rate. As part of the study, reaction of the OH radical with H₂ has been reevaluated at 350 °C, giving a rate constant of (6.0 ± 0.5) × 10⁸ M^-1 s^-1. The mechanism of the H atom reaction with the HO₂ radical is also investigated and discussed.

Full text of DOI:10.1021/jp065140v

J. Phys. Chem. A 2007, 111, 79-88
79
Reaction of O2 with the Hydrogen Atom in Water up to 350 °C
Ireneusz Janik and David M. Bartels*
Notre Dame Radiation Laboratory, Notre Dame, Indiana 46556
Timothy W. Marin
Chemistry Department, Benedictine UniVersity, Lisle, Illinois 60532
Charles D. Jonah
Chemistry DiVision, Argonne National Laboratory, Argonne, Illinois 60439
ReceiVed: August 9, 2006; In Final Form: October 27, 2006
•
•
The reaction of the H atom with O
2
, giving the hydroperoxyl HO
2
radical, has been investigated in pressurized
water up to 350 °C using pulse radiolysis and deep-UV transient absorption spectroscopy. The reaction rate
behavior is highly non-Arrhenius, with near diffusion-limited behavior at room temperature, increasing to a
1
0
-1 -1
near constant limiting value of ∼5 × 10
M
s
above 250 °C. The high-temperature rate constant is in
near-perfect agreement with experimental extrapolations and ab initio calculations of the gas-phase high-
pressure limiting rate. As part of the study, reaction of the OH radical with H has been reevaluated at 350
2
•
8
-1 -1
•
°
C, giving a rate constant of (6.0 ( 0.5) × 10 M s . The mechanism of the H atom reaction with the
•
HO
2
radical is also investigated and discussed.
I. Introduction
Arrhenius behavior above 100 °C, with the rate constant
apparently decreasing above 325 °C. In the discussion below,
we show that the behavior for this reaction is entirely consistent
with the gas-phase high-pressure limit. The mechanism for
•
The reaction of the H atom with aqueous O2, forming the
hydroperoxyl radical,
•
•
reaction of H atom with HO2 radical is also discussed.
•
•
2
H + O f HO
(1)
2
II. Experimental Section
is of central importance in combustion chemistry and has been
1,2
Electron pulse radiolysis/transient absorption experiments
were carried out using 4-20 ns pulses from the Argonne
Chemistry Division’s 20 MeV electron linac accelerator. The
sample cell, flow system, and basic experimental setup and
characteristics were described in previous publications.1
However, for the current measurements some changes were
applied. Analyzing light from a pulsed 150 W xenon lamp
carefully studied both experimentally
chemistry. The reaction in very-high-temperature water is of
importance for supercritical water oxidation processes. In water-
and via quantum
3
4
cooled nuclear reactor chemistry, the reaction is an important
step in “hydrogen water chemistry”, whereby a slight over-
pressure of H2 is used to reduce the radiolytically produced O2
0,11
5
and H2O2 back to water. It is important to be able to predict
(Osram XBO-150W/S) was selected using an ISA-545 double-
the minimum H2 concentration needed to accomplish this kinetic
trick, because excess H2 may result in undesirable hydriding
corrosion.
grating monochromator. With this monochromator, there was
no detectable scattered light from the visible or near-UV to
distort the deep-UV absorption measurements. The detector was
a five-stage Hamamatsu photomultiplier wired to deliver linear
photocurrent up to 2 mA. To minimize the scattering loss of
deep-UV analyzing light encountered over a potentially long
optical path, the detector system was placed roughly 50 cm from
the sample cell and shielded from the linac radiation with lead
bricks.
•
In the gas-phase formation of HO2 , there is no barrier to
•
O-H bond formation for approach of the H atom at about 45
3
degrees with respect to the O-O axis. In room-temperature
water, the measured reaction rate is consistent with nearly
diffusion-limited behavior6
-9
and a barrierless reaction. The
question is whether this remains true at elevated temperature,
and whether the gas-phase potential is strongly perturbed by
the aqueous environment. If not, the gas-phase measurements
can be simply transferred to the aqueous-phase simulation
problem.
The sample was mixed from three separate syringe pumps
(ISCO-260C) working in constant flow mode. The total flow
rate was 4 mL/min. The first pump contained water saturated
with N2O at room temperature, giving an N2O concentration of
•
In the present investigation, the reaction of H atoms and O2
0
.024 molal (m). The N2O (AGA gas, Ultrahigh Purity) was
in pressurized water has been studied at temperatures up to 350
first bubbled through a sparging vessel filled with a highly basic
solution of pyrogallol to remove any traces of oxygen.12 The
second pump contained water saturated with O2 (AGA gas,
Ultrahigh Purity) at room temperature, giving an O2 concentra-
tion of 0.0013 m. The third pump contained water pressurized
°C using pulse radiolysis and transient deep-ultraviolet absorp-
tion spectroscopy. The reaction demonstrates strongly non-
*
Author to whom correspondence should be addressed. E-mail: bartels@
hertz.rad.nd.edu. Phone: (574) 631-5561. Fax: (574) 631-8068.
1
0.1021/jp065140v CCC: $37.00 © 2007 American Chemical Society
Published on Web 12/14/2006

80
J. Phys. Chem. A, Vol. 111, No. 1, 2007
Janik et al.
with H2 (AGA gas, Ultrahigh Purity) at room temperature.
Pressurized H2 samples were prepared in our laboratory-built
high-pressure gas-liquid saturator.13 The pressure of hydrogen
in the saturator was constant for given samples of water used
to refill the syringe pump but decreased in the course of several
days of experiment. Typically, the hydrogen pressure ranged
from 82 to 149 bar, giving aqueous hydrogen concentrations
of 0.100-0.055 m.14 The hydrogen concentration in the sample
mix was constant for a given experiment and was always equal
to 50% of the corresponding hydrogen concentration in the
pressurized water saturator. The oxygen concentration in the
sample was changed by changing the flow ratio between pumps
delivering N2O- and O2-saturated water and was in the range
second-order nature. It becomes increasingly important at higher
temperatures where this reaction becomes very fast.17
•
•
H + H f H
(6)
2
The collected UV traces were fitted to a complex water
radiolysis model that includes a set of all the known water
radiolysis reactions and all the extinction coefficients for species
absorbing at the experimental wavelength. The occurrence of
reaction 6 can be nicely accounted for when the dose depen-
dence of the fitted kinetics is included. Therefore, all measure-
ments were carried out using two different doses of roughly 2
and 10 Gy and at least three different oxygen concentrations.
Fits to the experimental data must take into account the
relative dose delivered in each experiment, as well as changes
in the absorbed radiation due to decreasing water density with
increasing temperature. The relative dose delivered by the
accelerator was measured by integrating charge on a thick brass
-
5
-4
2
.5 × 10 to 2.0 × 10 m. Correspondingly, the N2O
-2 -3
concentration was varied between 1.2 × 10 and 5.0 × 10
m. The total pressure in the system was adjusted with a back
pressure regulator to 250 ( 0.1 bar. Normal temperature stability
was (0.3 °C.
Pulse radiolysis of water creates predominantly hydrated
“
shutter” inserted between the beam port and sample cell. It is
-
•
electrons (eaq ) and OH radicals, which are quickly converted
to hydrogen atoms via reactions 2 and 3.
assumed that the absorbed dose is simply proportional to the
water density, as long as the sample is thin enough to avoid
severe scattering of the electrons. The water density was
calculated using the IAPWS-IF97 formulation for light water
eaq- + N O f OH + N + OH
•
-
(2)
(3)
2
2
1
8
PVT relations.
•
•
OH + H f H +H O
2
2
III. Results and Analysis
The presence of more than one absorbing species (HO2 , O2•-,
OH , H , etc.) reacting simultaneously leads to kinetically
complex absorbance-time profiles that can only be resolved
numerically using a computer code. In turn, this means that as
many parameters as possible should be accurately known a
priori; these include molar absorptivities of all species, G values,
rate constants and radiation dose.
In the limit of high oxygen concentration, reaction 1 becomes
pseudo-first-order, and thus the reaction 1 rate constant, k1, can
be established by monitoring the increase of hydroperoxyl
•
•
•
15
radical absorbance at 230 nm. At room temperature, the pKa
•
for the HO2 radical is 4.8, and virtually all of the radical
•-
population converts to the basic O2 form via reaction 4, giving
•
•-
+
HO T O + H
(4,-4)
2
2
A. G Values. G values (escape yield of radicals in moles
per unit energy of radiation absorbed) used in the data analysis
were based on the compilation of previous measurements of
a product that absorbs at 250 nm. Because all of the measure-
ments were performed in water of neutral pH, and the UV
absorption bands are of typical condensed-phase width for both
19
Lin et al., and our unpublished results for the yields of hydrated
•
20
electron, H atom, and H2. From the Lin et al. results we take
•
•-
•
HO2 and O2 , the resulting absorption was a sum of both HO2
-
•
•
the total yield G(eaq + OH + H ) reported up to 350 °C and
and O2 radicals. At elevated temperature, the fraction of O2•-
•-
•
-
by subtraction of our experimental G(H ) + G(eaq ) values we
in the measured signals is lower due to changes in equilibrium
•
estimate G(OH ) numbers in the studied temperature range. The
(
eqs 4,-4) with increasing temperature.16 Above 300 °C, the
G values for H2O2 and H2 were based on previous data supplied
equilibrium lies almost entirely to the left, giving essentially
21,22
by Elliot et al.
•
only HO2 .
•
B. Molar Absorption Coefficients. OH . The product of ꢀG
Measurement of the reaction 1 rate under the chosen
conditions is limited by the lowest oxygen concentration that
can be applied before the oxygen is depleted by repeated electron
pulses. However, with too high an oxygen concentration, the
secondary reaction (5) becomes increasingly important as it
•
for the OH radical in N2O-saturated water was measured in
our apparatus at constant dose at 230 and 250 nm for
temperatures in the range 25-350 °C. Recombination in
oxygen-free water is slow enough that a simple measurement
of absorption at 200 ns after the 4 ns electron pulse is sufficient
for this purpose. We confirmed previous observations that the
eaq- + O f O2
•-
(5)
•
23
2
OH radical spectrum does not change up to 200 °C if a density
correction is applied for the absorbed dose. However, consider-
ing the increase in the spur escape yields of initial transient
generates O2•- without ever reacting with H atoms, thus
obscuring the observed reaction 1 rate. Furthermore, it decreases
the amount of H atoms produced by competition with reactions
•
species with temperature, the absorption coefficient of OH•
radicals at 230 and 250 nm must become lower with temper-
ature. This is apparently related either to the spectrum shifting
toward deeper UV or to depleting of the 230 nm band with the
temperature increase (more detailed analysis of the OH
spectrum is the subject of a future paper ). Applying the
19
2
and 3. The experimental limits placed on the O2 concentration
-
effectively minimized this pathway so that nearly all the eaq
were eventually converted to H . To overcome the limitation
•
•
2
4
of too low an O2 concentration, the doses applied in the
experiment were the lowest possible to obtain usable UV signals
after averaging of 30 consecutive traces. However, even for the
•
measured ꢀG and calculated G(OH ) at a given temperature,
the OH radical extinction coefficients for 230 and 250 nm have
•
•
lowest applied doses, H atom recombination cannot be ignored
been determined. Figure 2 shows the temperature dependence
•
in the overall reaction scheme. Reaction 6 slightly decreases
of these parameters. The OH radical extinction coefficient
•
the H atom concentration, especially at high doses due to its
continuously decreases with temperature from room temperature

Reaction of O2 with the Hydrogen Atom in Water
J. Phys. Chem. A, Vol. 111, No. 1, 2007 81
TABLE 1: Extinction Coefficients as a Function of
-
1
-1
Temperature (M cm ) for the Species Experimentally
Observed (n.d. ) No Data Available)
fit results (av values)
•
•-
Christensen et al.
HO
230 250 230
nm nm nm
1222 717 1760 1890 582 20
n.d. 690 n.d. 1850 n.d. n.d.
1183 673 1735 1813 550 30
n.d. 665 n.d. 1800 n.d. n.d.
2
O
2
OH•
H•
•
•-
temp
°C)
HO
2
O
2
250 230 230
nm nm nm
(
at λmax
at λmax
2
5
1251
1274
1290
1306
1314
1322
1330
1338
1346
1354
1892
1950
1988
2027
2046
2066
2085
2105
2124
2143
1
00
50
00
25
50
75
00
25
50
1
2
2
2
2
3
3
3
1160 660 1720 1750 525 106
1121 650 1715 1730 518 112
1075 640 1710 1700 492 134
1050 620 1705 1680 475 176
1020 610 1700 1660 445 208
980
600 1680 1600 409 227
temperature reported by Christensen and Sehested up to 250
C for hydrogenated and oxygenated solutions of variable pH.16
°
To estimate the G values after the 1 µs electron pulse for these
experimental conditions (i.e., H2 and O2 concentrations, and pH),
-
•
•
we applied the total G(eaq + OH + H ) recently obtained from
1
9
methyl viologen measurements by Lin et al. However, from
all our fitting attempts it was evident that the extinction
coefficient values so derived for HO2 and O2 are too high.
The increase of temperature implied an increase of the given
extinction coefficients. Our kinetics observations indicate the
opposite trend.
•
•-
•/O
•-
radical spectrum
Figure 1. Temperature dependence of the HO
2
2
•
•-
Consequently, it was decided to record new HO2 and O2
•
-
at various pH. Circles: O
2
radicals at room temperature (solid) and
•
2
radical at room temperature (solid) and
spectra as a function of temperature. Spectra were measured
using a 50:50 mixture of H2-pressurized water and O2-saturated
water, thus the final room-temperature concentrations of the H2
and O2 solutions upon mixing of the two solutions were
approximately 5.0 × 10 and 6.5 × 10 m, respectively. To
achieve acidic or basic pH, perchloric acid or potassium
hydroxide were respectively added to the O2-saturated water.
Just as in the experiments of Christensen and Sehested, the
chemistry ensures that all the primary OH , e aq, and H radicals
formed upon radiolysis are scavenged to form HO2 or O2
2
00 °C (open). Squares: HO
•
2
00 °C (open). Triangles: effective extinction coefficients of HO /
2
O
•
-
2
at 250 °C (inverse, open), 300 °C (solid), and 350 °C (open). All
spectra shown were acquired using the same applied dose of 9.5 ( 0.5
Gy.
-2
-4
16
•
-
•
•
•-
.
The applied dose was held constant from day to day, varying
on different days by no more than 6%. We were able to register
•
•-
HO2 spectra at pH ) 2 and O2 spectra at pH ) 8 up to 200
•
•-
°
C. Figure 1 shows a comparison of HO2 and O2 spectra
collected at room temperature and at 200 °C. The extinction
coefficients presented in Figure 1 represent the new experimental
-
•
•
19
ꢀ
G divided by G(eaq + OH + H ) obtained by Lin et al.
•
•-
From the results presented in Figure 1 for the HO2 and O2
spectra, one can see that a temperature increase up to 200 °C
•
slightly lowers the HO2 extinction coefficient. This observation
•
•-
agrees with results obtained by Buxton et al., for HO2 /O2
2
5
spectra recorded up to 175 °C. It also roughly agrees with the
behavior of the gas-phase spectrum recorded by Kijewski and
2
6
•-
Troe. In contrast, the O2 spectrum does not change up to
00 °C within experimental error. Though these results con-
tradict Buxton’s report, it agrees with the observations of
2
1
6
•-
Figure 2. Changes of extinction coefficient of species contributing to
the absorption at the experimentally chosen wavelengths. Symbols:
Christensen and Sehested that the product ꢀmaxG for O2
•
increases more than for HO2 with increasing temperature. It
should be noted, however, that the current result is quantitatively
different from either of the previous reports.
extinction coefficients at 230 nm. Symbols and lines: extinction
•
coefficients at 250 nm. Corresponding symbols: squares, HO
2
; filled
•-
•
•
circles, O
2
; triangles, OH ; open circles, H .
Above 200 °C, reliable measurements could not be performed
in acidic conditions as substantial corrosion in the metal flow
system was observed. In addition, hot alkaline solution in the
presence of oxygen etches the sapphire windows and makes
the UV measurements impossible due to excess light scattering.
up to 350 °C. The values used for the data analysis are
summarized in Table 1.
HO2 /O2•-. Initially, the molar absorptivities for O2•- and
•
27
•
HO2 were determined on the basis of the ꢀmaxG changes vs

82
J. Phys. Chem. A, Vol. 111, No. 1, 2007
Janik et al.
Therefore, for temperatures higher than 200 °C, effective
•
•-
combined spectra of HO2 /O2 were recorded at neutral pH.
The spectra recorded at 300 and 350 °C are shown in Figure 1
•
•-
(
triangles). The maximum of the HO2 /O2 effective spectrum
at neutral pH shifts toward deeper UV and the effective
extinction coefficients decrease with increasing temperature. The
•
•-
change in the effective HO2 /O2 spectrum can be correlated
•
with the change of the pKa value of the HO2 radical.
The value of the pKa for equilibrium (4,-4) is 4.8 at room
1
5
temperature and increases to a value of 6.15 at 285 °C,
16
according to the report of Christensen and Sehested. Extrapo-
lating these experimental numbers up to 350 °C, one can expect
a value of pKa ∼ 7, which is above the pH of water at this
temperature (pH350°C ) 5.98), thus suggesting predominance
•
of HO2 . For the whole range of temperatures between 200 and
•
•-
3
2
2
50 °C, we have measured partial spectra of HO2 /O2 between
30 and 250 nm. A sample of a partial spectrum recorded at
50 °C is superimposed in Figure 1 (reversed triangles). The
combined extinction coefficients obtained at 230 and 250 nm
•
were used to estimate separate extinction coefficients for HO2
•
Figure 3. Formation of HO
(
2
at 25 °C for two applied doses, (a) and
•
-
and O2 at these wavelengths by iteration, using the ratio of
b), with (a) being a higher dose. The three traces of each set correspond
•
•-
HO2 and O2 concentrations based on the pKa value at a given
temperature. For temperatures higher than 285 °C, the pKa was
extrapolated using a third-order polynomial function that fits
the experimental pKa values encountered at lower temperatures.
Uncertainty in the extrapolated pKa value is probably (0.2 pK
units at 350 °C. The iteration results were used as initial guesses
in the analysis of the kinetics. During numerical analysis of the
data, the initial guesses were slightly iterated to find the best
fit. The measured combined absorbance applies in any case to
the final product; separate extinction coefficients are only needed
to fit the signal rise for relatively large O2 concentrations, where
the observed signal could be due, in part, to product contribution
from reaction 5. The final best estimates of both extinction
coefficients and their changes with the temperature are shown
in Figure 2.
-5
-5
-4
to O
2
concentrations 3.2 × 10 , 6.5 × 10 , 1.3 × 10 m, respectively.
-
2
The N O concentration varies between 1.18 and 1.00 × 10 m, and
2
-2
the H
2
concentration is a constant 4.82 × 10 m. Signals were acquired
at 250 nm. Fits are superimposed as solid lines.
our time resolution, and (ii) H2O2 forms in negligible amounts
from OH recombination during the course of the experiment
due to strong scavenging of the radical by reaction 3, and could
exist only as a product of spur reactions with much lower
yields and relatively small extinction coefficients in the range
of interest.
C. Data Analysis. For reaction 1, the change of the total
absorbance with time after an electron pulse was initially
measured for the given temperature range at 250 nm and neutral
pH. A study was carried out as a function of temperature up to
50 °C. All data were collected at a pressure of 250 bar. Typical
data taken at 25 and 200 °C are shown in Figures 3 and 4, with
•
22
3
•
•
H . The H atom absorption spectrum was reported previously
from room temperature up to 200 °C, and no changes in the
spectral shape were found over this temperature range. It is
generally accepted that the absorption must be due to water
molecules in the first solvation shell, because the hydrogen atom
Lyman Alpha line is encountered far into the vacuum ultraviolet.
fitted curves superimposed. The signals track the initial decay
1
7
•
•
•-
of OH radicals and subsequent formation of HO2 /O2 radicals
by their absorption at 250 nm. The different sets of traces
correspond to different doses applied, with larger amplitude
signals representing the higher doses. The different traces
correspond to different oxygen concentrations, where the
•
The shape of the H atom spectrum decreases exponentially
toward the red and somewhat resembles the shape of the water
absorption edge, which also does not change shape with
temperature, although it shifts to the red.28 (For water, the shape
is probably controlled by the Franck-Condon envelope for the
-5
-4
concentration was varied between 1.6 × 10 and 1.3 × 10
m. The concentration of hydrogen was not changed for experi-
ments conducted at a given temperature, and the concentration
of nitrous oxide varied only by 20%, being kept in the range of
28
•
lowest bound-dissociative transition. ) At 250 nm, the H atom
-2
1
.2 × 10 m. An increase of the oxygen concentration causes
-
1
-1 29,30
extinction coefficient is as low as 30 M cm .
For our
• •-
an apparent faster rise of the HO2 /O2 product, in agreement
with pseudo-first-order behavior. At temperatures above 200
•
data analysis at 250 nm, the H atom absorption was very minor.
However, for all data recorded at 230 nm it was necessary to
increase the value of the H atom extinction coefficient,
especially for temperatures higher than 200 °C. The changes
of the H atom extinction coefficient at 230 nm resulting from
fits to the data are summarized in Table 1 and are superimposed
in Figure 2. Given the 0.6 eV red shift of the water absorption
edge between room temperature and 400 °C, it seems quite
°
(
C, the signal amplitude at 250 nm decreases considerably
compare absorption spectra in Figure 1) for the range of applied
•
doses. An increase of the dose at higher temperatures causes
two unwanted effects: (i) increase of contributions from second-
order reactions and (ii) depletion of the oxygen in the system
as a result of the many electron pulses applied to the same
sample. Therefore, the experiment was repeated for the range
of temperatures 150-350 °C at 230 nm where there is a much
•
28
•
reasonable to assume that the H atom spectrum could shift by
a similar amount.
•
•-
higher contribution from the HO2 absorption than from O2
,
-
H2O2 and eaq . Both the hydrogen peroxide and the hydrated
electron extinction coefficients were included in the data analysis
and fits. However, they did not affect the fitted results as (i)
the hydrated electron was converted to OH radicals in tens of
nanoseconds according to reaction 2, basically in the limit of
and higher overall effective absorption. Using these conditions,
we could keep the same range of applied doses for all the desired
temperatures.
The simple pseudo-first-order approach to the kinetics was
not good enough to provide satisfactory fits to the data. We
•

Reaction of O2 with the Hydrogen Atom in Water
J. Phys. Chem. A, Vol. 111, No. 1, 2007 83
Figure 4. Formation of HO •
b), with (a) being a higher dose. The four traces at each dose correspond
at 200 °C and two applied doses (a) and
Figure 5. Decay of the OH absorption after addition of H
•
at 350 °C
concentrations:
(a) 0.0, 3.55 × 10 , 7.16 × 10 , 3.52 × 10 m; (b) 0.0, 3.55 ×
2
2
(
for two applied doses (a ) 8.5 Gy, b ) 17 Gy). H
2
-5
-5
-4
-3
-3
-3
-2
-2
-2
to following O
2
concentrations 1.625 × 10 , 3.25 × 10 , 6.5 × 10
,
-
4
-3
1
.3 × 10 M, where the higher the concentration, the faster the
10 , 7.16 × 10 , 1.42 × 10 , 3.52 × 10 m. A faster decay
observed rise rate. Here, the N
2
O concentration varies between 1.00
corresponds to higher H concentration. The N O concentration varies
2
2
-
2
-2
-2
and 1.18 × 10 m, and the H
2
concentration is 4.82 × 10 M. The
between 2.5 and 1.28 × 10 m. The signals were acquired at 250 nm.
signals are acquired at 250 nm. Fits are superimposed as solid lines.
Fits are superimposed as solid lines.
were forced to build a kinetically complex model that included
many reactions involving all reactive species present. The
observed kinetics can be modeled by a set of some 50 reactions,
-
but in the absence of O2. With these reactants present, the e aq
•
•
are scavenged by the N2O and converted to OH . The OH
subsequently reacts via reaction 3. To fit the experimental traces,
we used the same fitting model described above, but k3 was
fitted instead of k1. The results of this experiment are presented
in Figure 5. With increasing H2 concentrations, a faster decay
of the OH radical is observed as a result of reaction 3. However,
at the same time, reaction 7 restores part of the OH radicals,
giving a contribution to the absorption in the tail of the signal
(a chain reduction of the N2O). For the highest concentration
of H2, the contribution of reaction 7 is less obvious, as the
regenerated OH is quickly removed again by reaction 3. The
H atom does not absorb significantly at this wavelength, and
6
using a model described in previous publications, but adapted
to handle UV-absorbing species. Each rate constant in the model
was tested for sensitivity toward the fit quality. The majority
of the reactions are only minor contributors to the kinetics and
can be ignored. The set of reactions responsible for the observed
kinetics follows:
•
•
eaq- + N O f OH + N
•
(2)
(3)
2
2
•
•
•
OH + H f H + H O
•
2
2
its second-order decay rate via reaction 6 is diffusion-limited.
•
H + O f HO
(1)
8
-1 -1
2
2
From the fits, a k3 value of (6.0 ( 0.5) × 10 M
s
was
obtained, which is roughly 70% higher than the rate reported
previously. (We should note that the previous value was obtained
at the detection limit of the competition method being used,
•
•-
2
+
HO T O + H
(4,-4)
(6)
2
•
•
13
and a large error bar was admitted. ) The fits were found to
H + H f H
2
have a high sensitivity to k7. It was found that the collected
traces could be fit only using rate constant values between 1.0
•
•
H + N O f OH + N
(7)
2
2
8
-1 -1
and 1.5 × 10 M
s
to give an uncertainty in k3 of (0.5 ×
8
-1 -1
•
•-
f HO -
10 M s . Therefore, the upper limit for k7 was taken to be
H + O2
2
(8)
8
-1 -1
1
.5 × 10 M
s
at 350 °C. On the basis of the reported room-
3
2
6
-1 -1
temperature rate constant of 2.1 × 10 M s , we estimated
•
•
2
H + HO f H O
(9)
2
2
the Arrhenius dependence for reaction 7 with the activation
-
1
9
energy Ea ) 18.5 kJ mol and pre-exponential A ) 3.7 × 10
The temperature dependence of reaction 2 was previously
determined31 and was fixed for the data fitting.
Non-Arrhenius behavior of k3 was reported previously and
these results were used up to 325 °C. However, at 350 °C a
-
1
-1
M
s
over the temperature range studied. Corresponding
rate constants for reaction 7 at given temperatures were included
in the reaction 1 analysis as a minor correction.
1
3
Values for k-4 were calculated assuming diffusion-limited
behavior on the basis of the Debye-Smoluchowski equation
satisfactory fit could not be achieved with the rate constant value
reported previously.13 It appeared that the reported value was
significantly lower than was necessary to fit the present
kdiff ) â4πRDFD
(10)
experimental results. To redetermine k3 at 350 °C, an experiment
•
was performed to directly monitor the OH radical decay at 250
nm in the presence of N2O and various concentrations of H2,
with

84
J. Phys. Chem. A, Vol. 111, No. 1, 2007
Janik et al.
2
z z e
δ
a b
FD )
, δ )
δ-1
4
πꢀ ꢀRk T
e
0 B
where kdiff is written as the Smoluchowski rate times the Debye
factor, FD. The value of e in the definition of δ is the
fundamental electron charge, za and zb are the formal charges
of the reactants, D ) Da + Db is the relative diffusion coefficient
of reactant ions a and b, R is the reaction encounter distance,
kB is Boltzmann’s constant, ꢀ0 is the permittivity of free space,
ꢀ
is the dielectric constant, and â is a statistical factor to account
for spin effects (equal to 1 in this case). The reaction rate was
6
scaled with temperature as proposed previously by Elliot. k4
•
was determined using Ka numbers for HO2 radicals reported
by Christensen and Sehested,16 together with the calculated
values of the reverse reaction (-4).
The reaction 6 rate constant was previously determined up
to 275 °C by Sehested and Christensen,17 and we were able to
extrapolate it up to 350 °C without any dramatic effect on the
fit results, suggesting that this reaction follows Arrhenius
behavior up to 350 °C. There is some uncertainty about these
numbers, as the authors (correctly) reported experimental values
•
of 2k/ꢀ but further assumed that the H atom extinction
coefficient was constant with temperature. The present data
analysis indicates that there is an increase of the H atom
Figure 6. Arrhenius plot for reaction 1 (solid circles). The open circles
represent previously reported data available up to 200 °C, and the
•
8
extinction coefficient with increasing temperature, especially
at shorter wavelengths. It would imply that the 2k numbers
reported by Sehested and Christensen represent a lower limit
for this rate constant. In our analysis, we tested the sensitivity
of the fits by varying this rate constant by (30%. For the highest
values used, we obtained only 5% higher values for the reaction
solid line represents their Arrhenius extrapolation to higher tempera-
tures.
TABLE 2: Fitted Rate Constants (M s-1) for Reactions 1,
-
1
9
, and 14a
-
10
k
1
× 10
1
rate constant, suggesting that our results are only slightly
temp (°C)
using rxn 14
k × 10-10
k14 × 10-10
9
affected by any uncertainty in the reaction 6 rate constant.
2
00
5
1.25
2.9
3.8
4.46
4.78
5.3
5.4
5.7
5.5
5.0
n.d.
n.d.
4.1
4.90
5.12
5.30
5.81
6.11
6.42
6.49
0.96
3.6
7.5
8.5
5.8
3.6
2.4
2.4
1.6
1.0
n.d.
n.d.
Values for k9 as a function of temperature were reported
1
3
3
previously up to 149 °C. To our knowledge, reaction 8 has
150
200
225
1.00
7.55
10.6
16.5
18.1
23.7
26.0
28.0
never been studied above room temperature. Following the
6
example of Elliot, we set k8 equal to k9. Neither reaction is
2
2
3
50
75
00
important to the present analysis for temperatures below 200
°C. However, for higher temperatures it was important to reduce
the extrapolated value of k9 (see below).
An Arrhenius plot of the fitted k1 values is shown in Figure
325
350
6
, and the rate constants are given in Table 2. Data were fitted
a
Two columns of values are shown for k
1
, where the first column
globally for 3-5 oxygen concentrations and two doses. Thus,
a global fit was obtained for 6-10 single experiments at each
temperature. As stated above, sensitivities to various estimated
parameters and different starting values were tested by multiple
least-squares minimizations. The error bars are indicative of the
range of rate constants obtained when the fit was “good”, but
this is a qualitative rather than a quantitative measure. The line
shows results from fits performed without reaction 14, and the second
column includes it in the fitting model. n.d. ) no data available.
rate constant actually decreases. At 350 °C, the rate constant is
more than a factor of 2.5 below the extrapolation of Elliot.6
(Note that we do not advocate an Arrhenius form for kact in
general, as should be made clear below.)
6
in the figure is Elliot’s extrapolation of the Noyes equation
Figure 7 shows changes in k9 as a function of temperature.
These data also demonstrate non-Arrhenius behavior that is even
more extreme than for reaction 1. The effect of reaction 9 at
high temperature was very obvious as its rate affects both the
(11) fit to the previously available data obtained from room
temperature up to 200 °C:
kobs- ) kdiff + kact
1
-1
-1
(11)
•
•-
time profile and the final amplitude of the HO2 /O2 product
absorption, therefore affecting the fitted k1 value. We have no
disagreement with the previous measurements by Lundstrom
where rate constant, kact, was calculated on the basis of Arrhenius
equation
3
3
et al., up to 150 °C. In this range of temperatures, reaction 9
•-
is of little importance because the O2 absorption prevails. We
assumed Arrhenius behavior for reaction 8, using parameters
-Ea/RT
kact ) Ae
(12)
6
suggested by Elliot over the entire temperature range studied.
-
1
11
with the parameters Ea ) 7.75 kJ mol and A ) 5.71 × 10
In fact, neither reaction 8 nor 9 was very important below 200
°C. Above 200 °C, it was necessary to decrease the value for
k9 in comparison to the Arrhenius behavior reported previ-
-1
-1
M
s
, and kdiff is defined by eq 10 with FD ) 1, as the
reactants are non-ionic. Within error limits, our data agree with
6
-8
33
previous reports
up to 100 °C but then undershoot the
ously. Above 225 °C, k9 even started to decrease. The solid
extrapolation at higher temperatures. Above 300 °C, the fitted
circles in Figure 7 represent the values obtained from this

Reaction of O2 with the Hydrogen Atom in Water
J. Phys. Chem. A, Vol. 111, No. 1, 2007 85
Figure 7. Arrhenius plot for reaction 9 (solid circles) and alternative
reaction 14 (open circles). The dashed line represents Arrhenius
extrapolation of previously reported data for reaction 9 available up to
1
50 °C to higher temperatures.
1
Figure 8. Comparison of experimental results of k (solid circles) with
1
the high-pressure limit data (solid line) and kdiff determined from eq
10 with â(T) calculated from eq 13. Open circles represent values of
analysis. As one can see, the reaction rate constant decreases
dramatically with increasing temperature, and above 300 °C,
the reaction is not required. The numbers plotted in Figure 7
represent upper limits for this rate constant.
kact inferred from the Noyes equation.
splitting magnitude produces a 7.6 ps oscillation period,35 which
means that the reaction probability will oscillate on the time
scale of a diffusive encounter. This problem of an oscillatory
reaction probability during a diffusive encounter has been solved
IV. Discussion
3
6
The discovery that reaction 1 is not diffusion-limited in high-
temperature water comes as a surprise, given that there is no
barrier to O-H bond formation in the gas phase. Both species
are hydrophobic, so there is no reason to expect a strong
perturbation of the water solvent on either reactant, or particular
involvement of a water molecule in the transition state. Standard
ab initio density functional calculations confirm that the reaction
path is essentially unaffected by a dielectric continuum environ-
by Green et al., who provide the solution
2 1 + R
x
ω/D
ω/D
â )
(13)
3
[
]
2
+ R
x
where ω is 2π divided by the oscillation period. The 2/3
prefactor removes from consideration the unreactive
|Q((3/2)〉 spin states. Thus, the value of â will lie between 1/3
and 2/3 depending on the diffusion rate, and therefore the
temperature.
•
ment, though the product HO2 radical is stabilized by solvation
and hydrogen bonding.34 However, to say that there is no barrier
to the reaction is incorrect, because there are large barriers in
In Figure 8 we plot our measured rate constants and the
estimated diffusion limit based on eq 10. The diffusion
•
the potential for approach of the H atom at 0° or 90° with
respect to the O-O axis. Only for an approach along roughly
4
coefficient for O is 2.4 × 10 m s at 25 °C and the H•
-
9
2
-1
37
2
3
-9
2 -1 38
5° is there no barrier. Thus, in expecting a diffusion-limited
atom diffusion coefficient is 7.5 × 10 m s . We estimate
the higher-temperature diffusion rates by scaling with T/viscos-
ity, as suggested by Stokes-Einstein behavior. Equation 13
yields a spin factor closer to 2/3 than to 1/3 for the entire
temperature range. With this estimate of the diffusion limit, the
activated barrier reaction rate kact is deduced from the Noyes
equation as the open circles in Figure 8. The rate constant kact
is the rate of reaction that would apply if diffusional transport
reaction rate, we were assuming that the solvent cage effect
would provide sufficient angular averaging in recollisions so
that the proper angle of approach would always be found. This
is apparently not the case because of the very high diffusion
rates of both reactants at high temperatures.
We can use eq 11 to interpolate between the diffusion limit
and a barrier-limited reaction rate. Because of the presence of
two “spin-active” reactants, the spin statistical factor, â, in eq
3
9
were no constraint. As we expected, the reaction is nearly
diffusion-limited at room temperature but is almost entirely
limited by some barrier above 200 °C.
1
0 now necessitates consideration.35 In the present case of a
doublet H atom reacting with a triplet O2 molecule we could
expect one-third of initial encounter pairs to be reactive doublets
According to classical statistical mechanics, the (Maxwell-
Boltzmann) velocity distribution function for collisions of the
two reactants in a solvent will be exactly the same as in gas-
phase collisions of the same molecules. Then the overall reaction
probability per collision will also be the same, if the solvent
|
D((1/2)〉, and two-thirds to be unreactive quartet |Q((1/2)〉,
|
Q((3/2)〉 states. But the presence of zero field splitting in the
triplet O2 molecule means that doublet and quartet are not true
eigenstates of the encounter pair spin Hamiltonian, and the
doublet/quartet character will oscillate in time. Spin quantization
along the O-O axis is conserved, but the |Q((1/2)〉 sublevels
mix with the |D((1/2)〉 sublevels. The |Q((3/2)〉 sublevels do
not mix and remain unreactive. Solution of the time-dependent
Schr o¨ dinger equation and substitution of the O2 zero field
4
0
does not modify the potential surfaces. The appropriate gas-
phase quantity for comparison is the so-called high-pressure
limiting rate constant, where a third body is always available
39
to carry away or supply excess energy. The high-pressure limit
•
for H + O2 has been estimated by extrapolation of pressure

86
J. Phys. Chem. A, Vol. 111, No. 1, 2007
Janik et al.
falloff behavior by Troe and co-workers,1,41 and calculated with
high level ab initio methods by Harding et al. Their high-
pressure gas-phase limit for this reaction is also plotted as the
solid line in Figure 8. Thus our measured aqueous-phase rate
constants are in virtually perfect agreement with the calculated
high-pressure limit between 200 and 300 °C.
constants made by Percival and co-workers.47,48 They studied
several different reactions of muonium “atom” with aromatic
systems, both diffusion-limited and non-diffusion-limited, and
3
2+
also spin exchange with Ni ion. In nearly all cases they found
a decrease or plateau in apparent reaction rate above 250 °C
and decided that the common thread was the decrease of
collision frequencies per encounter because of the increased
diffusion rate and reduced caging effect. A number of other
Although we can justify equivalent reaction probability per
collision in this case by the hydrophobic nature of the reactants
•
•
-
free radical reactions involving OH radicals, H atoms, and e aq
are known to be diffusion-limited near room temperature but
(i.e., the entrance channel for reaction is hardly perturbed), it is
also necessary to have equivalent encounter frequency in both
liquid and gas phase to obtain the same reaction rates. The
general picture is that solvent caging produces many collisions
and recollisions within a short time, separated by very long
periods of solvent isolation of the reactants. But the time
averaged number of collisions is nearly the same in both phases.
If we identify a “collision” by the contact distance between
reactants, then to a first approximation the relative probability
8
deviate from the diffusion limit in hot pressurized water. On
the basis of their analysis of collision frequencies, Percival and
4
9
co-workers suggested this should be a general theme of
virtually all of the small free radicals involved in water radiation
5
0
chemistry.
As we now consider the behavior of reaction 9 as illustrated
in Figure 7, we can appreciate that there probably is a strong
orientational preference for the reaction to form hydrogen
peroxide. At room temperature, the rate constant is at least near
(or volume density) of collisions can be obtained by comparing
H...O2 radial distribution functions g(r) for the dense fluid and
the dilute gas at the contact distance R. It is well-established
that for small hydrophobic species in water molecular dynamics
simulations, the short-range solute-solute radial distribution
•
the diffusion limit. The fast diffusion of the H atom may
contribute to the slowing of the reaction at higher temperature,
causing the rate to reach a “high-pressure limit.” Unlike the H•
42,43
+ O case, the hydroperoxyl radical should be hydrogen bonded,
functions deviate very little from unity (the dilute gas limit).
2
and this might strongly affect the potential and the orientational
Even so, we find the agreement between our aqueous-phase
result and the calculated high-pressure limit of ref 3 to be
remarkably good.
averaging, to change the nature of the reaction relative to the
gas phase. However, the magnitude of the rate constant decrease
shown in Figure 7 is difficult to rationalize.
Below 200 °C the value of kact is apparently larger than the
gas-phase high-pressure rate. Although there is large error in
the estimate of kact at room temperature where kdiff dominates,
a larger value of the reaction rate in water relative to gas phase
In the gas phase, reaction 9 is practically not observed and
•
•
the result of H atom reaction with HO2 leads to products via
three different reaction channels (13)-(15). Among all channels,
might be expected on the basis of the phenomenon of “hydro-
•
•
H + HO f H + O
2
(13)
(14)
phobic attraction”.44 When both hydrophobes are confined
2
2
within the same solvent cage, some of the unfavorable solvation
free energy of the reactants is recovered. This means that the
actual number of collisions of H and O2 is larger in water than
in the gas phase, and the g(R) “at contact” for H...O2 will be
slightly larger than unity. The hydrophobic acceleration of the
•
•
•
H + HO f 2OH
2
•
•
•
H + HO f H O + O
(15)
2
2
•
reaction 14 was found to contribute more than 90% in the H
1
3,44
rate is expected to be more pronounced at low temperature,
•
51-54
+
HO2 process at room temperature.
Reaction 13 would
consistent with the behavior of kact in Figure 8. However, the
apparent (3x) hydrophobic acceleration would imply an as-
sociation free energy on the order of kT. This is probably too
large to be consistent with the extreme linearity of Henry’s law
be nearly indistinguishable from reaction 9 in our experiment,
and the oxygen atom product of reaction 15 would react with
water to form peroxide, making it kinetically equivalent to
reaction 9. To our knowledge, reaction 14 was never reported
in the condensed phase. We decided to extend the reaction set
by addition of reaction 14 and refit our data. The k1 value was
constrained to be equal to the gas-phase high-pressure limit as
suggested above (i.e., kact was constrained). The results of the
fitting for reaction 14 are included in Figure 7 as open circles.
The fit is good, giving an Arrhenius activation energy Ea )
4
5,46
constants for small hydrophobic gas molecules like O2.
There is a small discrepancy for the data points above 300
C, in that we have no mechanism to explain the apparent slight
°
decrease in rate constants. However, attention should be given
to the larger error bars in these data points. Numerous
uncertainties exist in the fitting of these data. The pKa for the
•
•-
HO2 /O2 system is not actually known, nor are the actual
separate extinction coefficients for these species. The rate of
approach to equilibrium has an effect on the fitting. In addition,
there is the issue of actual oxygen concentration in the
experiments. We flow a mixture of O2- and H2-saturated water
through metal tubing at high temperature. It could well be that
we reduce a fraction of the O2 on the way into our radiolysis
cell. In this case, the fitted rate constants will be low due to the
error in concentrations. Still another explanation is discussed
-1
12
-1 -1
1
6.3 kJ mol and preexponential A ) 6.6 × 10
M
s
for
reaction 14.
•
As reaction 14 recreates the initial substrate (i.e., the H atom
via reaction 3), the oxygen uptake in 30 consecutive and
averaged electron shots is much larger than one would expect
from only reaction 1. It would cause a gradual decrease in the
•
apparent risetime of HO2 signal after each consecutive electron
shot for the lowest oxygen concentration used in the experiment.
Indeed we observed such an effect, especially above 300 °C.
Initially, we thought that it was caused by the reactions on the
metal walls in our high-temperature preheater/cell system.
However, it can also be explained by the occurrence of the chain
reaction where concentration of HO2 and the H atom are
suitable to propagate the chain at the lowest O2 concentra-
tion. That is the only positive evidence for reaction 14 in our
system.
•
•
below in the context of the H + HO2 cross reaction. Given all
of these uncertainties of the highest-temperature points, and the
superb agreement with the high-pressure limit at lower tem-
peratures, we advise use of the high-pressure limit rate constant
in water above 300 °C as well.
•
•
•
The results of our study of the H + O2 reaction confirm to
a large extent the analysis of high-temperature muonium rate

Reaction of O2 with the Hydrogen Atom in Water
J. Phys. Chem. A, Vol. 111, No. 1, 2007 87
On the other hand, there is no proof that reaction 9 is present
in our system either. In the presence of reaction 14, the rate of
(11) Takahashi, K.; Bartels, D. M.; Cline, J. A.; Jonah, C. D. Chem.
Phys. Lett. 2002, 357, 358.
(
12) Williams, D. D.; Blachly, C. H.; Miller, R. R. Anal. Chem. 1952,
10
-1
-1
reaction 9 was varied between 1.0 and 5.0 × 10
M
s
,
2
4, 1819.
showing no important effect on the analysis, but the fitting was
slightly better where the reaction 9 rate was kept at the lower
end. It is not the intention of this work to prove or disprove
(13) Marin, T. W.; Jonah, C. D.; Bartels, D. M. Chem. Phys. Lett. 2003,
371, 144.
(
(
14) Wiebe, R.; Gaddy, V. L. J. Am. Chem. Soc. 1934, 56, 76.
15) Bielski, B. H. J.; Cabelli, D. E.; Arudi, R. L.; Ross, A. B. J. Phys.
•
whether reaction 9 or 14 is the predominant channel for the H
Chem. Ref. Data 1985, 14, 1041.
16) Christensen, H.; Sehested, K. J. Phys. Chem. 1988, 92, 3007.
(17) Sehested, K.; Christensen, H. Radiat. Phys. Chem. 1990, 36, 499.
18) Wagner, W.; Kruse, A. Properties of Water and Steam: The
•
+
HO2 process in aqueous solution, as both lead to a similar
(
answer about the reaction 1 temperature dependence. Neverthe-
less, the model including reaction 14 removes the inexplicable
decrease in rate at elevated temperature for both reactions 1
and 9, provides reasonable numbers for the reaction 14 rate
constant, and is consistent with gas-phase data. It should be
strongly considered in future experiments and modeling.
(
Industrial Standard IAPWS-IF97 for the Thermodynamic Properties of
Water; Springer: Berlin, 1998.
(
19) Lin, M. Z.; Katsumura, Y.; Muroya, Y.; He, H.; Wu, G. Z.; Han,
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(
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This work has yielded measurements of the reaction rate of
(
•
H atom with O2 in pressurized water up to 350 °C and allows
8
8, 2465.
one of the first direct comparisons of a free radical association
reaction in water with the corresponding gas-phase reaction over
a wide temperature range. Perhaps not surprisingly because of
the hydrophobic character of the reactants, the aqueous-phase
rate constants agree very well with the gas-phase high-pressure
limit once diffusion-limit effects are removed. On the other hand,
it has not been generally recognized in the past that the rate of
diffusion-limited radical reactions in water may plateau or even
decrease at temperatures above 200 °C.49 It has been implicitly
assumed that solvent caging would remain effective to much
higher temperature. Therefore, this work has major implications
for modeling of free radical processes in water, such as in
nuclear reactors or supercritical water oxidation systems.
(24) Janik, I.; Bartels, D. M.; Jonah, C. D. J. Phys. Chem., submitted.
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8
0, 2482.
(
30) Janata, E. Proc. Indian Acad. Sci. Chem. Sci. 2002, 114,
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31.
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4
(
(
33) Lundstrom, T.; Christensen, H.; Sehested, K. Radiat. Phys. Chem.
2
004, 69, 211.
Acknowledgment. We thank Dr. Sergey Chemerisov for
maintaining and operating the linac used in this work. We thank
Dr. Daniel M. Chipman at the Notre Dame Radiation Laboratory
for his density functional calculation of the H + O2 reaction
channel under the dielectric continuum approximation. We thank
Dr. Chipman as well as Dr. Larry Harding at Argonne National
Laboratory, and Dr. Nick Green of Oxford University for useful
conversations. Work at Argonne National Laboratory was
performed under the auspices of the Office of Science, Division
of Chemical Science, US-DOE under contract number W-31-
(34) Chipman, D. M. Unpublished work, 2006.
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(
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40) For the purpose of qualitative discussion here we consider the
1
(
(
(
reaction rate to be a product of collision frequency and reaction probability
per collision. More rigorous treatments as in ref 3 consider in detail the
conversion of translational degrees of freedom into rotational modes of the
product. The capture probability becomes a function of the energy and the
angular momentum J, so that the “collision radius” can only be defined in
terms of a distribution. The point here is that this distribution should be the
same regardless of third body density, so long as the dense fluid does not
change the binary interaction potential of the reactants.
109-ENG-38. Additional support has been provided by US-DOE
NERI grant 02-060. The Notre Dame Radiation Laboratory is
supported by the Office of Basic Energy Sciences at the United
States Department of Energy. This is document number NDRL-
4
675 from the Notre Dame Radiation Laboratory.
(
41) Cobos, C. J.; Hippler, H.; Troe, J. J. Phys. Chem. 1985, 89, 342.
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9
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(
(
(
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2
000, 2, 631.
(
(
(
(
(
(
4) Brock, E. E.; Savage, P. E. AIChE J. 1995, 41, 1874.
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(
50) On this point we agree with Percival and co-workers for those
recombination reactions of radicals where there is some angular dependence
of the reaction channel, like the H• + O reaction. Most OH• radical reactions
2
Chem. Soc. Faraday Trans. 1990, 86, 1539.
9) Roduner, E.; Tregennapiggott, P. L. W.; Dilger, H.; Ehrensberger,
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will fall into this category, and we might expect to find that the high-pressure
limiting rate constant applies if solvation is not a large effect. The reduction
(
+
of spin exchange rate between muonium and Ni2 ions at high temperature
may also be explained by the reduced caging effect, on the assumption
that spin exchange is weak in this system. However, we disagree with
(

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Janik et al.
Percival in applying this collision frequency analysis to hydrated electron
reactions. These are essentially a special type of electron-transfer reaction,
and a modified version of the Marcus theory must apply. Therefore, several
quantities such as the ∆G for the reaction and reorganization energy may
account for a non-Arrhenius or decreased rate constant at elevated
temperatures.
(51) Hack, W.; Preuss, A. W.; Wagner, H. G. Ber. Bunsen-Ges. Phys.
Chem. Chem. Phys. 1979, 83, 212.
(
7.
52) Thrush, B. A.; Wilkinson, J. P. T. Chem. Phys. Lett. 1981, 84,
1
(
53) Sridharan, U. C.; Qiu, L. X.; Kaufman, F. J. Phys. Chem. 1982,
8
6, 4569.
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