Kinetic investigation of the reaction Sr(1S) + O2 + He in the temperature range from 303 to 968 K

Article abstract of DOI:10.1021/jp981998b

A kinetic study of the third-order recombination reaction Sr(¹S) + O₂ + He k₁(He)→ SrO₂ + He has been carried out in a fast-flow reactor in the temperature and pressure range of respectively 303-968 K and 6-12 Torr. Strontium atoms were generated by thermal evaporation of strontium metal pellets and then monitored by atomic absorption spectroscopy (AAS). The Arrhenius plot shows a departure from linearity above 500 K. The modified Arrhenius expression taking into account a temperature dependence of the preexponential factor for the entire temperature range results in the expression k_1Sr(He) = [(1.9 ± 0.3) × 10^-23]T^-1.7 exp-[(-12.1 ± 0.8 kJ mol^-1)/RT] cm⁶ molecule^-2 s^-1. The best representation of the temperature dependence is given by the polynomial fit log k_1Sr(He) = -60.83 + 22.44(log T) - 3.89(log T)². A lower limit to the bond energy of the SrO₂(³A₂) reaction product is estimated by means of the method based on the expression of the equilibrium constant and the theory of statistical mechanics. A value of D₀ > 244 kJ mol^-1 was obtained, which is in the range of the values derived from ab initio calculations.

Full text of DOI:10.1021/jp981998b

J. Phys. Chem. A 1998, 102, 8333-8338
8333
1
Kinetic Investigation of the Reaction Sr( S) + O2 + He in the Temperature Range from 303
to 968 K
C. Vinckier* and J. Helaers
Department of Chemistry, KU LeuVen, Celestijnenlaan 200F, 3001 HeVerlee, Belgium
ReceiVed: April 27, 1998; In Final Form: July 14, 1998
k1(He)
1
A kinetic study of the third-order recombination reaction Sr( S) + O
2
+ He
8 SrO + He has been
2
carried out in a fast-flow reactor in the temperature and pressure range of respectively 303-968 K and 6-12
Torr. Strontium atoms were generated by thermal evaporation of strontium metal pellets and then monitored
by atomic absorption spectroscopy (AAS). The Arrhenius plot shows a departure from linearity above 500
K. The modified Arrhenius expression taking into account a temperature dependence of the preexponential
-
23 -1.7
factor for the entire temperature range results in the expression k1Sr(He) ) [(1.9 ( 0.3) × 10 ]T
exp-
-
1
6
-2 -1
[
(-12.1 ( 0.8 kJ mol )/RT] cm molecule s . The best representation of the temperature dependence is
2
given by the polynomial fit log k1Sr(He) = -60.83 + 22.44(log T) - 3.89(log T) . A lower limit to the bond
energy of the SrO ( A ) reaction product is estimated by means of the method based on the expression of the
2 2
equilibrium constant and the theory of statistical mechanics. A value of D > 244 kJ mol was obtained,
which is in the range of the values derived from ab initio calculations.
3
-
1
0
Introduction
Vinckier at al.17,18 used a fast-flow reactor technique with
thermal vaporization of the metal as the source of the Mg and
Ca atoms in the gas phase with atomic absorption spectroscopy
as the detection technique. Excellent agreement has been
observed between both techniques for the determination of the
rate constant of the Mg/O2 reaction.
While the results of the Ca/O2 reaction matched in the
temperature range from 230 to 330 K, a large discrepancy
showed up at higher temperatures. The fast-flow-tube work18
yielded a value for k1Ca(He) which was about a factor of 100
Oxidation reactions of gaseous metal atoms have gained
considerable attention over the past few decades because of a
large variety of possible applications. One of these is situated
in the field of combustion, where metals are added as fuel
additives for the propulsion of rocket engines. It has been
proven that they increase the flame temperature and also the
1
,2
efficiency.
Recently it has been mentioned that metal/N2O
reactions in incinerators may reduce the emission of the
greenhouse gas N2O.3 Atmospheric chemists are also interested
larger at 1100 K than k1 (He) derived from the photolysis-
Ca
in metal atom reactions with molecular oxygen. Different
studies have indicated that in the mesosphere, i.e., at a height
of approximately 90 km, quite high concentrations of neutral
metal atoms are present. Their most important source is the
9
LIF measurements. This was mainly due to the fact that the
activation energy Ea, derived on the basis of the fast-flow-tube
results, was higher than the value derived by means of the
photolysis-LIF method.
The alkaline-earth-metal/O2 reactions will now be extended
with the reaction of strontium atoms. Kinetic data on the Sr/
O2 reaction will be presented covering the temperature range
from 303 to 968 K:
evaporation of meteoroids.4
-6
However, the abundance of the
atoms observed in the mesosphere is quite different from the
relative concentrations present in the meteoroids and their
concentrations also show a totally different seasonal dependence.
The simulation of combustion processes and atmospheric
chemistry requires detailed reaction mechanisms, including the
6
1
3
,7
Sr( S) + O + He f SrO + He
(1)
rate constants of a large number of elementary reactions.
A
2
2
survey of much of the research work in metal atom kinetics
carried out during the last years has been described in ref 8.
While the alkali- and transition-metal atom/O2 reactions have
In the case of the Sr/O2 reaction it needs to be pointed out
1
that the bimolecular reaction path Sr( S) + O2 f SrO + O is
4
,7,9-16
-1 19
been studied extensively over a wide temperature range,
too endothermic (∆H ) 71.6 kJ mol ) to compete with the
much less kinetic information is available on the alkaline-earth-
metal atom/O2 reactions.
third-order reaction in the temperature range from 303 to 1000
K.
Up till now, kinetic measurements for both magnesium and
calcium atom reactions with molecular oxygen in the temper-
ature range from 303 to 1000 K have been carried out by means
The experiments were carried out in a fast-flow reactor using
atomic absorption spectroscopy (AAS) as the detection technique
for the thermally evaporated strontium atoms.
9,17,18
1
of different experimental techniques.
The Mg( S) + O2
This work aims to explore the trend in the activation energies
of the recombination reactions with molecular oxygen, which
appear to decrease according to the series Ea(Mg/O2) > Ea(Ca/
O2) > Ea(Sr/O2). This trend can be understood in relation to
the ionization energy of the metal, since a metal-O2 complex
+
N2 reaction has been investigated by means of a static-flow
technique, in which the Mg atoms were produced by heating
metal chips to 600-700 K and were detected by time-resolved
laser-induced fluorescence (LIF).9 The Ca( S) + O2 + M (M
1
2
0,21
)
N2, He) reaction was studied by the same group of workers,
is formed with a partial ionic character.
using the pulsed laser photolysis of a Ca atom precursor, also
These activation energies leading to a positive temperature
dependence of the rate constant are rather unusual for third-
9
followed by time-resolved LIF of the resulting Ca atoms.
1
0.1021/jp981998b CCC: $15.00 © 1998 American Chemical Society
Published on Web 09/30/1998

8334 J. Phys. Chem. A, Vol. 102, No. 43, 1998
Vinckier and Helaers
order reactions, but they are related to the closed-shell config-
uration of the alkaline-earth-metal atom. This has also been
seen for the Fe + O2 + N2 reaction, in which the iron atom has
6
2
a 3d 4s configuration and which shows an activation energy
-
1 16
of (16.94 ( 0.67) kJ mol .
Finally the occurrence of
activation energies has been confirmed by ab initio calcula-
9
,16,20
tions.
1
It will be pointed out that the Sr( S) + O2 + He reaction
follows an Arrhenius behavior up to about 500 K, after which
the curve flattens out. The bond energy of SrO2 will be esti-
mated using a method based on the expression of the equilibrium
constant in combination with the theory of statistical mechanics.
This experimentally obtained value will be compared with the
values derived by means of ab initio calculations.22
Experimental Technique
The experimental setup has been amply described in earlier
18,20,23,24
Figure 1. Natural logarithm of the Sr atom absorbance as a function
of the reaction time t with various amounts of molecular oxygen
publications,
and only a brief summary will be presented
here. It contains two major parts: a fast-flow reactor under
low pressure and an atomic absorption detection technique
AAS). The reactor consists of a quartz tube with an internal
added: The experimental conditions are T
as carrier gas. [O
g
) 303 K, P
] (10 molecules cm ): (9) 0; (0) 0; ([) 3.5; (])
6.3; (2) 9.1; (4) 15.0; (b) 17.0.
r
) 9 Torr, He
12
-3
2
(
diameter L of 5.7 cm and a length of 100 cm. At the upstream
end a sample holder contained strontium pellets, which were
thermally evaporated at 600-700 K by means of a kanthal
resistance wire. By means of the carrier gas helium, strontium
atoms were transported downstream in the kinetic zone, where
they were mixed with an excess of molecular oxygen. The flow
1
derivation of the rate constant of the Sr( S) + O2 + He reaction
23,24
has already been described in previous papers:
k (He)[O ][He]
7.34DSr/He
1
2
ln A ) -
+
t + B (2)
Sr
{
}
2
velocity Vg of the carrier gas helium is 320 ( 10 cm s- at 303
1
η
2r
K. The temperature in the kinetic zone could be varied between
3
03 and 1000 K by means of an oven, and the temperature was
in which ln ASr is the natural logarithm of the strontium
absorbance, η a correction factor depending on the flow
characteristics, DSr/He the binary diffusion coefficient of Sr atoms
in the carrier gas helium, r the reactor radius, t the reaction
time, and B an integration constant. The correction factor η is
related to the flow characteristics, and the determination of its
monitored by a chromel-alumel thermocouple. Strontium
atoms were detected by atomic absorption spectroscopy (AAS)
at 460.7 nm.
Assuming that the detection limit corresponds to an absor-
bance of A ) 0.005, one can calculate the detection limit for
strontium atoms on the basis of a formalism explained in our
2
8
magnitude has been amply discussed elsewhere.
2
5
-1 1/2
earlier work: [Sr] ) C1AL Tg , in which C1 is a propor-
tionality constant, L the optical path length (5.7 cm), and Tg
The use of eq 2 for obtaining kinetic parameters has been
10,24
well-illustrated in our earlier work
and will only briefly be
1
0
-2
the gas temperature. With a value for C1 ) 0.428 × 10 cm
summarized here. The value of k1(He) is determined by
following first ln ASr as a function of the reaction time t at
various amounts of O2 added. A weighted linear regression of
ln ASr versus t is carried out, taking into account a statistical
error for ln ASr, which at average varies between 10.7 and 13.3%
-1/2
26
K
at 500 K, one can calculate the detection limit for
7
-3
strontium atoms as equal to 8.4 × 10 atoms cm or 0.72 ppb
at 6 Torr and 500 K.
Minimum distances between the Sr atom source, the oxygen
inlet, and the kinetic zone were maintained to allow for sufficient
as one goes from the highest to the lowest value of ln ASr. Figure
shows an example of the pseudo-first-order decays of Sr( S)
23,24
mixing of the reagents.
In the kinetic measurements the
1
1
decay of the strontium absorbance was followed as a function
of the axial distance along the fast-flow reactor. This was
realized by moving the entire reactor assembly along its axis
relative to the detection equipment, which remained at a fixed
position. An advantage of this technique is that relative
positions of the Sr atom source and the O2 inlet remain constant
during the experiments. Reproducible absorbances could be
maintained within 10% when the temperature Ts of the strontium
pellets was stabilized within (1%.
The gases used were helium N4.5, a 1.00% mixture of oxygen
in argon N5.0 and a 5.04% mixture of oxygen in helium N4.5
from UCAR. The strontium pellets (Aldrich) had a purity of
about 99.0%.
atoms as a function of the reaction time at a temperature Tg )
03 K and a pressure Pr of 9 Torr for various initial O2
3
concentrations. In the next step the slopes S of these lines are
plotted versus the added [O2] and a weighted linear regression
results in a straight line with a slope equal to the pseudo-second-
order rate constant k′1 ) k1(He)[He]/η, as is illustrated in Figure
2
for three different temperatures: 303, 600, and 839 K. In
some cases the magnitude of the intercept of this graph is larger
than 2 times its standard deviation, which implies that plug flow
conditions do not prevail. In these cases the factor η is set
equal to 1.3 with an associated systematic error of 10%.28 In
other cases the magnitude of the intercept is about equal to
2
7
.34DSr/He/2r and a correction factor of 1.6 will be used. The
The statistical analysis of the plots, i.e., weighted regressions,
27
uncertainties σ and σ for the calculated values of the slope S
were made using the statistical SAS package. The quoted
S
k
and the rate constant k1(He) are calculated by combining the
uncertainties of several variables such as temperature, flow
velocity, reactor radius, and total pressure according to the
errors σ were the standard deviations.
Results and Discussion
1
29
Determination of the Rate Constant k1(He) of the Sr ( S)
method explained by Howard. Finally, in the case where the
+
O2 + He Reaction. The kinetic formalism used in the
correction factor 1.3 was used, the systematic error of 10% was

1
The Reaction Sr( S) + O2 + He
J. Phys. Chem. A, Vol. 102, No. 43, 1998 8335
TABLE 1: Effect of Initial Absorbance AiSr on k
(He)a
1
AiSr
k
(He) (10-30 cm molecule s-1
6
-2
)
T
g
(K)
P
r
(Torr)
1
303
303
303
511
511
11
9
8
8
8
0.04
0.15
0.26
0.53
1.11
9.1 ( 1.7
9.4 ( 0.7
7.8 ( 1.6
30.5 ( 1.3
36.4 ( 0.7
a
g r
T is the gas temperature and P the reactor pressure.
1
TABLE 2: Rate Constant k
2
1
(He) of the Reaction Sr( S) +
a
O
+ He as a Function of Temperature T
g
AiSr
k
1
(He) (10-30 cm molecule s-1
)
6
-2
T
g
(K)
P
r
(Torr)
3
3
3
3
3
3
3
4
03
03
03
03
03
03
60
01
6
8
9
0.17
0.26
0.15
0.13
0.04
0.14
0.21
0.25
0.38
1.11
0.53
0.52
0.78
0.62
0.32
0.69
0.57
0.48
0.54
0.34
0.59
0.89
0.57
6.8 ( 1.0
7.8 ( 1.6
9.4 ( 0.7
9
10.8 ( 0.7
9.1 ( 1.7
7.8 ( 1.3
11
12
8
8
8
8
8
8
6
8
9
11
12
9
8
8
9
9
2
Figure 2. Slopes S (Figure 1) as a function of the added O con-
11.7 ( 0.9
16.7 ( 2.1
25.9 ( 1.8
36.4 ( 0.7
30.5 ( 1.3
28.7 ( 4.2
30.0 ( 4.1
35.7 ( 1.6
33.1 ( 1.4
41.2 ( 1.1
30.6 ( 1.0
35.1 ( 1.5
26.1 ( 3.6
34.3 ( 3.8
34.6 ( 1.9
33.1 ( 3.1
42.4 ( 2.2
centration. The experimental conditions are P
r
) 9 Torr, He as carrier
2
gas, T : (9) 303 K; (0) 600 K; ([) 839 K. [O
g
] is expressed in units
1
2
-3
455
of 10 molecules cm
.
5
5
5
6
6
6
6
6
6
6
7
8
8
9
11
11
41
00
00
00
00
00
62
97
38
39
99
68
9
a
P
r
is the reactor pressure and AiSr the initial absorbance.
Figure 3. Pseudo-second-order rate constant k′
1
as a function of the
pressure at T ) 303 K ([) and 600 K (0). k′ is expressed in units of
g
1
-
12
3
-1 -1
1
0
cm molecule
s .
taken intoaccount, resulting in the total standard deviation σk.
The third-order rate constant k1(He) is then obtained by dividing
k′1η by the helium concentration. In the example mentioned
above, at 9 Torr of He and with η ) 1.6, third-order rate
constants k1(He) ) 10.8 ( 0.7, 33.1 ( 1.4, and 34.6 ( 1.9 in
-
30
6
-2 -1
units of 10
03, 600, and 839 K.
To illustrate the third-order behavior of the Sr/O2 reaction,
cm molecule
s
are derived at, respectively,
3
the pressure dependence between 6 and 12 Torr of the pseudo-
second-order rate constant k′1 is examined as shown in Figure
3
. The lines were forced through the origin, because the values
Figure 4. Plots of ln k1Sr(He) versus 1/T according to the T- fit
1.7
of the intercepts I are smaller than or of the same order as 2
times their standard deviations. It is clear that k′1 indeed linearly
increases when the pressure is raised, which confirms that
Sr( S) + O2 + He is a third-order reaction and is still at its
low-pressure limit.
(- - -) (eq 5) and the polynomial fit (- - -) (eq 7).
Temperature Dependence of k1(He). The experimental
conditions together with the values of k1(He) determined in the
temperature range from 303 to 968 K are listed in Table 2.
1
Finally, the effect of the initial Sr atom concentration on the
value of k1(He) has been examined. For this purpose, A Sr is
As can be seen from Table 2, k (He) increases with increasing
1
i
temperatures and analogous to the Mg/O and Ca/O reactions
2
2
varied by a factor of 6 and 2 at 303 and 511 K, respectively.
Table 1 shows that A Sr has no systematic effect on k1(He), which
the Sr/O reaction will be characterized by an activation energy.
2
i
The experimental values for k (He) are shown in Figure 4.
1
proves that, as expected at these low Sr atom concentrations,
complex reactions were unimportant.
One clearly sees that the points flatten out at temperatures above
500 K.

8336 J. Phys. Chem. A, Vol. 102, No. 43, 1998
Vinckier and Helaers
Below 500 K, the Arrhenius expression is given by
third-order rate constants as a function of the temperature
3
1-33
is based on the so-called Tro e¨ formalism.
ism calculates the strong collision rate constant k
This formal-
for the
diss,0
-28
sc
k (He) ) [(2.7 ( 0.5) × 10 ] ×
1
Sr
-
1
reverse unimolecular decomposition reaction
-
8.7 ( 0.6 kJ mol
cm molecule s-1 (3)
6
-2
exp
(
)
RT
krec
Sr + O + M y z SrO + M:
2
2
kdiss
It should be mentioned here that eq 3 is slightly different from
the Arrhenius expression when all the data over the entire
temperature range are taken into account.30
Z F(E )RT exp(-E /RT)F F F Frot,intF
corr
sc
diss,0
LJ
0
0
anh
E
rot
k
)
(8)
Qvib
To fit the rate constants k1(He) over the entire temperature
range, the following three-parameter expression was tried:
in which ZLJ is the collision frequency for a bimolecular collision
between the complex SrO2 and He, F(E0) is the density of
harmonic vibrational energy levels of SrO2 at the dissociation
threshold energy E0, Qvib is the vibrational partition function of
SrO2 and Fanh, FE, and Frot are correction factors which are
related to the anharmonicity, the energy, and the rotation
dependence of F.
-
RT
Ea
n
k ) AT exp
(4)
(
)
with A being the preexponential factor, T the temperature, n
the temperature dependence of A, Ea the activation barrier, and
R the universal gas constant.
In the case of a plain bimolecular reaction, normal Arrhenius
behavior is expected, giving positive values for n. In most cases
third-order reactions will show a negative temperature depen-
dence, and thus n becomes negative. The latter is not surprising
in view of the RRKM theory, which predicts that the rate
constant indeed decreases when the temperature is being
Frot,int takes into account internal rotations, and Fcorr is the
correction factor to account for the coupling between different
degrees of freedom and is usually taken as unity.
3
1,32
To take into account the barrier in the entrance channel Ea,
9
the following expression can be used:
3
1-33
E ) D (Sr-O ) + E
a
(9)
raised.
To determine the best value for n, we allowed n to
0
0
2
vary between -2.5 and -1.0 with increments of 0.1. The
smallest residual sum of squares was obtained when n was set
equal to -1.7. This results in the following expression for k1-
where D0(Sr-O2) represents the bond energy of SrO2. In this
calculation the value of D0(Sr-O2) was respectively set equal
-
1
to 190 and 255 kJ mol , as determined by different ab initio
(He):
22
calculation methods (see further in the text). For Ea the value
k (He) ) [(1.9 ( 0.3) × 10 23]T-1.7
-
-1
of 8.7 kJ mol derived from the temperature dependence of
×
6
1
Sr
k1 (He) below 500 K was used (eq 3).
Sr
-1
-
12.1 ( 0.8 kJ mol
cm molecule s-1 (5)
-2
The rate constant for the strong collision recombination
reaction is obtained by means of eq 10, in which Keq is the
equilibrium constant of the reaction.
exp
(
)
RT
This is also illustrated in Figure 4, which shows that eq 5 fits
the experimental results reasonably well.
sc
rec,0
sc
diss,0
k
) Keqk
(10)
The behavior of k1(He) observed in this work is quite different
from the expression obtained by Kashireninov et al. by means
of the diffusion flame technique.34 These authors have proposed
the following second-order rate constant for the Sr/O2 reaction
between 1040 and 1215 K:
The weak collision rate constant krec,0 can be calculated by
introducing the collision efficiency for energy transfer âc
sc
rec,0
krec,0 ) âck
(11)
-
10
k
) [(3.2 ( 0.5) × 10 ] ×
1Sr
in which âc varies between 0 and 1. Its value as a function of
the temperature is given by
-
1
-
59.8 ( 7.9 kJ mol
cm molecule s-1 (6)
3
-1
exp
(
)
RT
âc
〈∆E〉
FERT
)
-
(12)
At the highest temperature at which we measured, i.e., 968 K,
1 - âc
x
the value of k1 in eq 6 leads to a second-order rate constant of
Sr
-
13
3
-1 -1
1
.9 × 10 cm molecule s . This value is about 20 times
in which 〈∆E〉 is the average energy transferred per collision
lower than the pseudo-second-order rate constant measured in
which in this case was temperature-dependent according to 〈∆E〉
-
12
3
-1 -1
1.04(0.05
our work, which is 3.8 × 10
cm molecule s . In that
≈ T
.
sc
diss,0
3
case the third-order recombination rate constant with He as a
third body is more important than the second-order oxygen atom
abstraction process.
The parameters for calculating k
for the SrO ( A )
2
2
1
molecule are listed in Table 3. The ground state A of SrO
1
2
should not be used, because its formation in reaction 1 is spin-
forbidden and such reactions are too slow within the time scale
Finally the experimental values for k1(He) could also be fitted
to the second-degree polynomial
1
1
of these experiments. The second reason the A state will not
be formed is that its formation requires a second electron transfer
2
2
2
log k (He) ) -60.83 + 22.44(log T) - 3.89(log T) (7)
from the metal toward the oxygen, which is normally a step
with a high energy barrier.
1
Sr
2
1
Figure 4 shows that this fit is a very good representation of the
temperature dependence. A polynomial, however, does not
provide any kinetic information.
Extrapolation of k1(He) between 303 and 2000 K. A
method to fit and extrapolate the experimental values of
The interatomic distances rSr-O and rO-O as well as the
2
2
vibrational frequencies were values obtained from ab initio
calculations, since no experimental values are available. An
estimation for the Lennard-Jones parameter ꢀ(SrO2-He) was
9
based on the value for ꢀ(CaO2-He). For the characterization

1
The Reaction Sr( S) + O2 + He
J. Phys. Chem. A, Vol. 102, No. 43, 1998 8337
+ He: Input Parameters Used in the Troe1
1
TABLE 3: Extrapolation of Rate Data for the Reaction Sr( S) + O
2
Formalism3
1-33 a
Input Parameters for the SrO
) ) 190 kJ mol- (B3LYP(RECP))b
(3A
) Molecule
2 2
1
(Sr-O
) ) 255 kJ mol-1 (MP2)b
D
0
(Sr-O
2
D
0
2
r
Sr-O ) 2.349 Å; rO-O )2 1.340 Å
r
Sr-O ) 2.349 Å; rO-O )2 1.340 Å
-
45
-45
I
I
I
A
) 2.23 × 10 kg m
I
I
I
A
) 2.23 × 10 kg m2
-
46
2
2
-46
B
C
) 2.39 × 10 kg m
B
C
) 2.39 × 10 kg m
-
45
) 1.99 × 10 kg m2
-45
) 1.99 × 10 kg m
-
1
-1
ν
ν
ν
E
E
1
2
3
) 339 cm
) 360 cm
ν
ν
ν
E
E
1
2
3
) 1726 cm
-
1
-1
) 358 cm
-
1
-1
) 1182 cm
) 1074 cm
-
1
-1
a
) 8.7 kJ mol
) 199 kJ mol
a
) 8.7 kJ mol
-
1
-1
0
0
) 264 kJ mol
Data for Sr +O
2
+ He at 303 K
σ(SrO -He) ) 3.25 Å; ꢀ(SrO
LJ ) 7.12 × 10 cm molecule
s ) 3; m ) 2; r ) 0
σ(SrO
2
-He) ) 3.25 Å; ꢀ(SrO
2
-He)/k ) 350 K
2
2
-He)/k ) 350 K
-1 -1
-
10
3
-1 -1
-10
3
Z
LJ ) 7.12 × 10 cm molecule
s
Z
s
s ) 3; m ) 2; r ) 0
Q
vib ) 1.531
) 1.024; Fanh ) 1.78; Frot )-137.69; Fcorr ) 1; Felec ) 1
Q
vib ) 1.231
) 1.018; Fanh ) 1.78; Frot ) 50.30; Fcorr ) 1; Felec ) 1
F
K
E
F
K
E
9
3
20
3
-1
eq ) 2.0 × 10 cm molecule
eq ) 2.5 × 10 cm molecule
sc
) 4.0 × 10 cm molecule s-1
-40
3
-1
sc
) 1.6 × 10 cm molecule s-1
-51 3
-1
k
k
k
k
k
k
diss,0
sc
rec,0
exp
diss,0
) 7.8 × 10 cm molecule s-1
-31
6
-2
sc
rec,0
exp
rec,0
) 4.1 × 10 cm molecule s-1
-31
6
-2
) 9.2 × 10 cm molecule s-1 c
-30
6
-2
) 9.2 × 10 cm molecule s-1 c
-30
6
-2
rec,0
-
1
-1
â
c
) 11.8; 〈∆E〉 ) 12.50 kJ mol
â
c
) 22.6; 〈∆E〉 ) 15.43 kJ mol
a
For the definition of symbols not in the present text, see refs 31-33. b For the meaning of the symbols, see refs 21 and 22. c Weighted mean
value at 303 K.
of the SrO2( A2) state Andrews et al.22 provided different values
for both D0(Sr-O2) as well as the vibrational frequencies
depending on the ab initio method used. The various input
parameters are shown in Table 3.
3
Comparison between the Alkaline-Earth-Metal/O2 Reac-
tions. It is well-known that the third-order reaction of closed-
shell metal atoms with molecular oxygen is characterized by
an energy barrier. This barrier is located in the entrance channel
at the crossing of the covalent and ionic potential energy
surfaces.
When this modified Tro e¨ formalism was used to calculate
the rate constant krec,0 with the input parameters from Table 3,
collision efficiencies âc of about 13 were obtained when D0-
As has already been mentioned, both the Mg + O2 and the
Ca + O2 reactions previously studied at our laboratory1
showed Arrhenius expressions for their rate constants:
7,18
Sr-O2) was set equal to 190 kJ mol-1 (B3LYP(RECP)
(
-
1
method). With a D0(Sr-O2) value of 255 kJ mol (MP2
method), together with the vibrational frequencies calculated
with the same method, âc values of the order of about 25 were
obtained. With the helium atom as collision partner for the
stabilization of the SrO2 molecule one normally expects values
for âc of the order of 0.1. Lower values for âc could only be
obtained by increasing the bond energy D0(Sr-O2) to values
of about 1000 kJ mol , which is not a realistic value. Another
way to reduce âc when keeping D0(Sr-O2) at 190 or 255 kJ
mol is by introducing an additional correction factor Felec into
eq 8. This factor takes into account that several low-lying
electronic excited states of the SrO2 molecule might participate
in the reaction. A similar procedure has also been followed by
-31
k1Mg(He) ) [(5.5 ( 1.1) × 10 ] ×
-1
-
16.8 ( 0.8 kJ mol
cm molecule s-1 (13)
6
-2
exp(
)
RT
-28
k (He) ) [(1.5 ( 0.2) × 10 ] ×
1
-1
Ca
-1
-10.2 ( 0.4 kJ mol
cm molecule s-1 (14)
6
-2
exp
-1
(
)
RT
While for both the Mg and Ca/O2 reactions an Arrhenius
behavior was observed over the entire temperature range
1
6,35,36
between 303 and 1000 K, the rate constant of the Sr/O reaction
several authors
to fit the experimental data to the RRKM
2
starts to level off at temperatures above 500 K and probably
decreases from 1000 K and higher. When only the rate
calculation. This led to values for Felec between 75 and 100,
which is of course completely out of range.
constants k1 (He) below 500 K are considered (eq 3), one sees
3
Sr
Using the molecular parameters of SrO2( A2) taken from the
various ab initio methods, one thus arrives at âc values which
are unrealistically high. When the calculations were performed
with the other triplet state SrO2( B2), âc values in the same range
were obtained. However, as can be seen from Table 3, the
problem is that there are large uncertainties on the value of D0-
Sr-O2) ranging from 190 to 255 kJ mol . In addition, one
should notice a very large discrepancy between the calculated
that the Arrhenius activation energies decrease according to the
series Ea(Mg) ) 16.8, Ea(Ca) ) 10.2, and Ea(Sr) ) 8.7 (each
-
1
expressed in kJ mol ). Since the reaction most probably
proceeds through a partial charge transfer between the metal
atom and the oxygen molecule, it is logical to establish a
qualitative correlation between the Arrhenius activation energy
Ea and the ionization energy (IE) of the metal, which indeed
shows the trend IE(Mg) ) 7.64 eV > IE(Ca) ) 6.11 eV >
IE(Sr) ) 5.69 eV.
3
-
1
(
-
1
values of ν1: 339 and 1726 cm when, respectively, the
B3LYP(RECP) or the MP2 method was used.22
The preexponential factor for the Mg/O2 reaction is much
lower than for the other two reactions. This implies that the
probability for redissociation of the CaO and SrO transition
In view of the foregoing, a fit based on the Tro e¨ formalism
is inappropriate and thus the extrapolation over a broader
temperature range should not be made.
2
2
states is much lower than for MgO2. This can be understood

8338 J. Phys. Chem. A, Vol. 102, No. 43, 1998
Vinckier and Helaers
in terms of the magnitudes of the dissociation energies for the
is a Research Director of the National Fund for Scientific
Research (Belgium). J.H. is grateful to the Institute for Science
and Technology (IWT) for granting her a doctoral fellowship.
3
ground-state metal-O2 molecules. For MgO2 in either the A2
3
-
g
or the Σ state dissociation energies in the range from 82 to
-
1
3
3
1
06 kJ mol were derived, while for CaO2( A2) and SrO2( A2)
-
1
References and Notes
ranges from respectively 156-204 kJ mol and 190-255 kJ
mol were obtained, depending on the ab initio method used.
-1
22
(
1) Grosse, A. V.; Conway, J. B. Ind. Eng. Chem. 1958, 50, 663.
3
Bond Energy of the SrO2 ( A2) Molecule. Up until now
no experimental values have been available for the bond energy
of the SrO2 molecule. Our results allow us to derive a minimal
value for this bond energy, based on the expression for the
equilibrium constant Keq for the reaction Sr + O2 + He h SrO2
(2) Gordon, A. S.; Drew, C. M.; Prentice, J. L.; Knipe, R. H. AIAA J.
1
968, 6, 577.
(3) Perry, R. A.; Miller, J. A. Int. J. Chem. Kinet. 1996, 28, 217-234.
4) Plane, J. M. C. In Gas-Phase Metal Reactions; Fontijn, A., Ed.;
(
Elsevier: Amsterdam, 1992.
(5) Murad, E.; Swider, W. Geophys. Res. Lett. 1979, 6, 929.
(
(
(
6) Swider, W. Planet. Space Sci. 1984, 32, 307.
7) Plane, J. M. C. Int. ReV. Phys. Chem. 1991, 10, 1, 55.
8) Gas-Phase Metal Reactions; Fontijn, A., Ed.; Elsevier: Amsterdam,
+
He:
[
SrO2]t
(A - A )
0
t
1
992.
(9) Nien, C. F.; Rajasekhar, B.; Plane, J. M. C. J. Phys. Chem. 1993,
7, 6449.
10) Vinckier, C.; Corthouts, J.; De Jaegere, S. J. Chem. Soc., Faraday
Trans. 2 1988, 84, 1951.
11) Ritter, D.; Weisshaar, J. C. J. Am. Chem. Soc. 1990, 112, 6425.
K )
)
(15)
eq
[
Sr] [O ]
A [O ]
t
2
t
2
9
(
with A0 being the initial absorbance at a reaction time t ) 0 ms
and At the absorbance at time t. In this expression the SrO2
concentration is set equal to the amount of Sr atoms which
reacted.
(
(12) Belyung, D. P.; Hranisavljevic, J.; Kashireninov, O. E.; Santana,
G. M.; Fontijn, A.; Marshall, P. J. Phys. Chem. 1996, 100, 17835.
(
(
13) Campbell, M. L.; McClean, R. E. J. Phys. Chem. 1993, 97, 7942.
14) Campbell, M. L.; Hooper, K. L.; Kolsch, E. J. Chem. Phys. Lett.
Since the decay curves of ln ASr as a function of time at the
highest temperature and lowest O2 concentration still remain
linear, the equilibrium is far from being reached and thus the
calculated equilibrium constant is a lower limit. Kmin is now
1
9
9
997, 274.
(15) Brown, C. E.; Mitchell, S. A.; Hackett, P. A. J. Phys. Chem. 1991,
5, 1062.
(16) Helmer, M.; Plane, J. M. C. J. Chem. Soc., Faraday Trans. 1994,
1
2
3
calculated at 968 K and at an O2 concentration of 4.3 × 10
molecules cm , resulting in the value Kmin ) 7.4 × 10 cm
molecule .
0, 395.
-
3
-11
(17) Vinckier, C.; Christiaens, P. Bull. Soc. Chim. Belg. 1992, 101, 10.
(18) Vinckier, C.; Remeysen, J. J. Phys. Chem. 1994, 98, 10535.
-
1
(
(
19) Sullivan, H. F.; Glassman, I. Combust. Sci. Technol. 1972, 4, 241.
20) Vinckier, C.; Christiaens, P.; Hendrickx, M. In Gas-Phase Metal
On the other hand, the equilibrium constant can also be
calculated on the basis of statistical mechanics, according to
eq 16, with QSrO , QSr, and QO being the partition functions of
Reactions; Fontijn, A., Ed.; Elsevier: Amsterdam, 1992; p 52.
(21) Bauschlicher, C. W.; Partridge, H.; Sodupe, M.; Langhoff, S. R. J.
Phys. Chem. 1992, 96, 9259-9264.
2
2
3
respectively SrO2( A2), Sr, and O2; D0 is the bond energy of
3
(22) Andrews, L.; Bauschlicher, C. W.; Chertihin, G. V.; Thompson,
C. A.; Dillon, J.; Byrne, S. J. Phys. Chem. 1996, 100, 10088-10099.
SrO2. In the calculation of the partition function of SrO2( A2)
the vibrational frequencies from the B3LYP(RECP) method
(23) Vinckier, C.; Christiaens, P. J. Phys. Chem. 1992, 96, 8423.
were used.22
(24) Vinckier, C.; Christiaens, P. J. Phys. Chem. 1992, 96, 2146.
25) De Jaegere, S.; Willems, M.; Vinckier, C. J. Phys. Chem. 1982,
86, 3569.
(
QSrO2
D0
(
26) Brouwers, H. Ph.D. Thesis, Faculty of Science, KU Leuven, 1984.
K )
exp
(16)
eq
( )
Q Q
RT
(27) SAS Statistical Package, SAS Institute Inc., Cary, NC, 1989.
Sr O2
(
28) Fontijn, A.; Felder, W. In ReactiVe Intermediates in the Gas-
-
11
cm3
Phase: Generation and Monitoring; Setser, W., Ed.; Academic Press: New
After Keq was set equal to Kmin ) 7.4 × 10
York, 1979; p 59.
-
1
molecule , a minimal value for the bond energy of the
(
29) Howard, C. J. J. Phys. Chem. 1979, 83, 3.
-
1
SrO2 molecule D0 > 244 kJ mol was obtained. This result
lies between the values of 190 and 255 kJ mol obtained by
means of the ab initio calculations mentioned above. Incor-
porating the vibration frequencies from the MP2 method only
resulted in a slightly higher minimal value for D0 of 251 kJ
(30) Vinckier, C.; Helaers, J. 14th International Symposium on Gas
-
1
Kinetics, University of Leeds, 1996.
(31) Tro e¨ , J. J. Chem. Phys. 1977, 66, 4745.
2
2
(
(
32) Tro e¨ , J. J. Chem. Phys. 1977, 66, 4758.
33) Tro e¨ , J. J. Phys. Chem. 1979, 83, 114.
(34) Kashireninov, O. E.; Manelis, G. B.; Repka, L. F. Russ. J. Phys.
Chem. (Engl. Transl.) 1982, 56, 630.
-
1
mol .
(
35) Mitchell, S. A. In Gas-Phase Metal Reactions; Fontijn, A., Ed.;
Elsevier: Amsterdam, 1992.
36) Bauschlicher, C. W.; Langhoff, S. R.; Partridge, J.; Sodupe, M. J.
Phys. Chem. 1993, 97, 856.
Acknowledgment. We thank the Fund for Joint Basic
Research (FKFO), Brussels, Belgium, for a research grant. C.V.
(