Kinetic investigation of the reactions of Mg1S, Ca(1S), and Sr(1S) atoms with NO2 over the temperature ranges 303-836, 303-916, and 303-986 K, respectively

Article abstract of DOI:10.1021/jp9920500

The kinetics of the second-order reactions Mg(¹S) + NO₂(X²A₁) →^k1Mg MgO + NO, Ca(¹S) + NO₂(X²A₁) →^k1Ca CaO + NO, and Sr(¹S) + NO₂(X²A₁) →^k1SrSrO + NO have been investigated in a fast-flow reactor in the temperature ranges of, respectively, 303-836, 303-916, and 303-986 K. Solid magnesium, calcium, and strontium pellets were thermally evaporated to generate the corresponding alkaline earth metal atoms in the gas phase. Their decays as a function of the added N0₂ concentration were followed by means of atomic absorption spectroscopy (AAS) at 285.2 nm for magnesium, 422.7 nm for calcium, and 460.7 nm for strontium atoms. All reactions show an Arrhenius behavior and the rate constants are given by k_1Mg = [(1.4 ± 0.2) × 10-¹¹] exp(-3.4 ± 0.6 kJ mol^-1/RT) cm³ molecule^-1 s^-1, K_1Ca = [(1.5 ± 0.6) × 10^-9] exp(-2.9 ± 1.2 kJ mol^-1 RT) cm³ molecule^-1 s^-1, and k_1sr = [(1.2 ± 10^-9] exp(-0.9 ±0.3 kJ mor^-1/RT) cm³ molecule^-1 s^-1. The results will be discussed in terms of the electron jump mechanism. Since the Mg/NO₂ reaction is too slow to proceed via this mechanism, a classical oxygen atom abstraction is suggested. In the case of the Ca/NO₂ and the Sr/NO₂ reactions, the experimental rate constants are too high to be quantitatively explained by the classical electron jump mechanism. The modified electron jump mechanism which takes into account long distance forces between the reagents gives a better agreement with the experimental values.

Full text of DOI:10.1021/jp9920500

J. Phys. Chem. A 1999, 103, 11321-11327
11321
1
1
1
Kinetic Investigation of the Reactions of Mg( S), Ca( S), and Sr( S) Atoms with NO2 over
the Temperature Ranges 303-836, 303-916, and 303-986 K, Respectively
Chris Vinckier,* Jo e1 lle Helaers, Piet Christiaens, and Jan Remeysen
Department of Chemistry, KU LeuVen, Celestijnenlaan 200F, 3001 HeVerlee, Belgium
ReceiVed: June 21, 1999; In Final Form: August 30, 1999
k1Mg
k1Ca
) f
1
2
1
2
The kinetics of the second-order reactions Mg( S) + NO
2
(X A
1
) f MgO + NO, Ca( S) + NO
2
(X A
1
k
1Sr
1
2
2 1
CaO + NO, and Sr( S) + NO (X A ) f SrO + NO have been investigated in a fast-flow reactor in the
temperature ranges of, respectively, 303-836, 303-916, and 303-986 K. Solid magnesium, calcium, and
strontium pellets were thermally evaporated to generate the corresponding alkaline earth metal atoms in the
2
gas phase. Their decays as a function of the added NO concentration were followed by means of atomic
absorption spectroscopy (AAS) at 285.2 nm for magnesium, 422.7 nm for calcium, and 460.7 nm for strontium
atoms. All reactions show an Arrhenius behavior and the rate constants are given by k1Mg ) [(1.4 ( 0.2) ×
-
11
-1
3
-1 -1
-9
1
0
] exp(-3.4 ( 0.6 kJ mol /RT) cm molecule s , k1Ca ) [(1.5 ( 0.6) × 10 ] exp(-2.9 ( 1.2 kJ
-1 3 -1 -1 -9 -1 3 -1
mol /RT) cm molecule s , and k1Sr ) [(1.2 ( 0.1)x 10 ] exp(-0.9 ( 0.3 kJ mol /RT) cm molecule
-
1
s . The results will be discussed in terms of the electron jump mechanism. Since the Mg/NO
2
reaction is too
slow to proceed via this mechanism, a classical oxygen atom abstraction is suggested. In the case of the
Ca/NO and the Sr/NO reactions, the experimental rate constants are too high to be quantitatively explained
2
2
by the classical electron jump mechanism. The modified electron jump mechanism which takes into account
long distance forces between the reagents gives a better agreement with the experimental values.
Introduction
Another source of information on the Mg(Ca,Sr)/NO2 reactions
is coming from molecular beam experiments. Zare et al.1
1,12
This study of the alkaline earth metal atom reactions with
NO2 forms part of a broader kinetic investigation of the reactions
of these metals with several molecules such as O2, N2O, and
Cl2.1 The reason for selecting these compounds is that each
of the reactions with these molecules proceeds according to a
different reaction mechanism.
investigated the luminescence originating from the alkaline earth
metal atom/NO2 reactions in the visible wavelength region.
While the Mg/NO2 reaction did not show any detectable
chemiluminescence, the Ca(Sr)/NO2 reactions showed a broad
continuum which has been assigned to the emission of a not
well-characterized polyatomic species. This emitting species
might be formed in several consecutive collisions between the
vibrational excited ground-state metal oxide molecules or with
NO2. Total reaction cross sections for the Ca(Sr)/NO2 reactions
-7
Indeed the alkaline earth metal atom reactions with oxygen
are third-order reactions showing a positive temperature de-
pendence due to an energy barrier at the intersection of the
covalent and ionic potential energy surface of the reacting
2
12
1
-4,8,9
of, respectively, 93 and 127 Å have been derived. These
values were considered to be in quantitative agreement with
the values calculated in this work (see Discussion section). Herm
species.
All of the very exothermic N2O reactions show a
relatively high activation energy, associated with the closed-
shell character of both reaction partners. The Cl2 reactions are
8
1
3
et al. also studied the Ca(Sr)/NO2 reactions by means of a
crossed beam technique. A “forwardly” orientated product
distribution was observed, indicating that the reaction proceeds
via a direct mechanism and not via a long-living complex. The
fact that most of the observed wide angle scattering was due to
reactive events indicated qualitatively that the cross sections
for the Ca(Sr)/NO2 reactions were large, in agreement with the
very fast and are explained in terms of the electron jump
6
mechanism. A fundamental question is now in how far the
alkaline earth metal atom/NO2 reactions, which also form a
metal oxide, follow the same reaction dynamics as the N2O
reactions.
1
Kinetic data on the Mg(Ca,Sr)( S)/NO2 reactions are very
scarse. The only kinetic measurements available have been
measured in flames in the narrow temperature ranges between
12
results of Zare et al. Contrary to the findings mentioned above,
where a direct mechanism for the Ba(Ca,Sr)/NO2 reactions was
73 and 1100 K.10 All rate constants show a negative temper-
8
1
4
postulated, Parrish and Herm predicted an electron jump
mechanism. This mechanism has been invoked to explain the
large cross sections of the alkali metal/halogen reactions,15 in
which the metal atom throws out its valence electron which is
then captured by the halogen molecule. In this case, the reaction
occurs without a classic collision between the reagents. How-
ature dependence as can be seen in the following expressions:
-8
-1.65 ( 0.03
cm molecule s-1
3
-1
k1Mg ) [(6.6 ( 0.5) × 10 ]T
(1)
-8
-1.65 ( 0.08
cm molecule s-1
3
-1
k1Ca ) [(3.2 ( 1.2) × 10 ]T
-
ever, the NO2 ion formed will not dissociate under the influence
(2)
+
of the Me field (Me ) metal), implying that the intermediate
k1Sr ) [(2.5 ( 0.5) × 10 11]T-0.78 ( 0.02 cm molecule s-1
-
3
-1
+
-
Me NO2 complex remains relatively stable. In the most recent
1
6
(3)
crossed beam study of Davis et al., both reaction channels
1
0.1021/jp9920500 CCC: $18.00 © 1999 American Chemical Society
Published on Web 12/07/1999

11322 J. Phys. Chem. A, Vol. 103, No. 51, 1999
Vinckier et al.
have been put forward for the Ba/NO2 reaction: the first and
most important one proceeds through a long-living Ba /NO2
the reaction time t using the expression t ) zd/Vg. An advantage
of this technique is that relative positions of the metal atom
source and the NO2 inlet remain constant during the experiments.
Reproducible absorbances could be maintained within 10%
when the temperature Ts of the metal pellets was stabilized
within (1%.
+
-
complex, resulting from an electron transfer from the Ba atom
toward the NO2 molecule via the electron jump mechanism; in
the second one, an oxygen abstraction occurs via a direct
mechanism, leading to BaO in an electronic excited state. In
this context, it needs to be pointed out that, in analogy with the
alkaline earth metal atom/N2O reactions, the metal oxides in
the Mg(Sr)/NO2 reactions can be formed in different electronic
states. As will be illustrated in the Discussion section for the
For all the investigated reactions helium (L’Air Liquide) with
a purity of 99.995% was used as a carrier gas as well as in the
gas mixtures. The nitrogen dioxide concentrations were equal
to 0.92% and 0.117% of NO2 for the Mg/NO2 reaction, 0.117%
of NO2 for the Ca/NO2 reaction, and 0.1% of NO2 for the Sr/
NO2 reaction. The magnesium pellets (Alfa Products), the
calcium pellets (Fluka), and the strontium pellets (Aldrich),
respectively, had a purity of about 99.8%, 99.5%, and 99.0%.
As will be pointed out in the next section, adding a mixture
with low NO2 content may lead to rather unstable NO2 flows
and this in view of possible wall adsorption phenomena in the
gas flow controllers, stainless steel and Teflon tubing, etc.
Weighted regressions on all plots were made using the
1
+
Mg/NO2 reaction, the ground state (X Σ ) as well as the triplet
3
excited state ( Π) is energetically accessible while for the Sr/
1
+
3
′1
NO2 reaction SrO can be formed in the X Σ , a Π, and A Π
1
+
states. The Ca/NO2 reaction can only lead to the X Σ ground
state of CaO. In view of the possible occurrence of different
reaction channels, one might expect a non-Arrhenius behavior,
7
,8
as has been observed for the Ca(Sr)/N2O reactions.
1
1
1
Kinetic measurements on the Mg( S), Ca( S), and Sr( S)
atom/NO2 reactions will now be presented covering the tem-
perature ranges from, respectively, 303 to 836 , 303 to 916,
and 303 to 986 K. The experiments were carried out in a fast-
flow reactor using AAS as the detection technique for the
thermally evaporated alkaline earth metal atoms. The results
will be discussed in terms of the electron jump mechanism.
19
statistical SAS package. The quoted errors σ were the standard
deviations.
Results
Determination of the Rate Constants k1Mg, k1 , and k1
Ca
Sr.
The kinetic formalism used in the derivation of the rate constants
Experimental Technique
of the Mg(Ca,Sr) + NO2 reactions has already been described
5
,6
in previous papers,
The experimental setup has been amply described in earlier
publications,2 and only a brief summary will be presented
here. It consists of two major parts: a fast-flow reactor under
low pressure and an AAS detection technique. The reactor is a
quartz tube with an internal diameter of 5.7 cm and a length of
-6
k
[NO2]
1Mg(Ca,Sr)
7.43DMg(Ca,Sr)/He
ln AMg(Ca,Sr) ) -
+
t + B
{
2
}
η
2
r
(4)
1
00 cm. At the upstream end the sample holder contained the
metal pellets which were thermally evaporated at 600-700 K
by means of a kanthal resistance wire. By means of the carrier
gas helium, the alkaline earth metal atoms were transported
downstream in the kinetic zone where they were mixed with
an excess of NO2. In the pressure range from 6 to 12 Torr, the
flow velocity Vg of the carrier gas helium has a constant value
of 320 ( 10 cm s- at 303 K. The temperature in the kinetic
zone could be varied between 303 and 1000 K by means of an
oven, and the temperature was monitored by a chromel-alumel
thermocouple. Magnesium, calcium, and strontium atoms were
detected by AAS at, respectively, 285.2, 422.7, and 460.7 nm.
Assuming that the detection limit corresponds to an absor-
bance of A ) 0.005, one can calculate the detection limit for
the Mg(Ca,Sr) atoms by using a formalism explained in an
in which ln AMg(Ca,Sr) is the natural logarithm of, respectively,
the magnesium, calcium, and strontium absorbance, η is a
correction factor depending on the flow characteristics, DMg(Ca,Sr)/He
is the binary diffusion coefficient of the Mg, Ca, and Sr atoms
in the carrier gas helium, r is the reactor radius, t is the reaction
time, and B is an integration constant. The correction factor η
is related to the flow characteristics, and the determination of
1
20
its magnitude has been amply discussed elsewhere.
The use of eq 4 for obtaining kinetic parameters has been
5,21
well-illustrated in our earlier work
summarized here.
and will only briefly be
The values of k1Mg(Ca,Sr) were determined by following first ln
AMg(Ca,Sr) as a function of the reaction time t at various amounts
of NO added. A weighted linear regression of ln A
2
Mg(Ca,Sr)
1
7
-1 1/2
earlier paper, [Mg(Ca,Sr)] ) C1AL Tg , in which C1 is a
proportionality constant, L the optical path length (5.7 cm), and
versus t was carried out using a statistical error for ln AMg(Ca,Sr)
which at average varies between 9 and 11% going from the
highest to the lowest value of ln AMg(Ca,Sr). As an example the
1
0
Tg the gas temperature. With values for C1(Mg) ) 1.820 × 10
-
2
-1/2
10
-2 -1/2
1
cm
K
, C1(Ca) ) 0.663 × 10 cm
K
, and C1(Sr) )
at 500 K, one can calculate the
pseudo-first-order decays of Ca( S) atoms as a function of the
10
-2
-1/2
18
0
.428 × 10 cm
K
reaction time t for various initial NO concentrations at a
2
8
following detection limits: for magnesium, 3.6 × 10 atoms
temperature T ) 303 K and a pressure P equal to 10 Torr are
g
r
-
3
8
-3
cm or 3.11 ppb; for calcium, 1.3 × 10 atoms cm or 1.12
shown in Figure 1.
7
-3
ppb; for strontium, 8.4 × 10 atoms cm or 0.72 ppb at 6 Torr
In the next step the slopes S of these lines were plotted versus
and 500 K.
the added [NO ] and a weighted linear regression results in a
2
Minimum distances between the metal atom source, the NO2
inlet, and the kinetic zone were maintained to allow for sufficient
mixing of the reagents.5,6 Kinetic measurements were made by
following the decay of the alkaline earth metal atom absorbance
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. Decays of the absorbances as a function of the
distance can easily be transformed into decays as a function of
straight line with a slope directly equal to k1Mg(Ca,Sr)/η as is
illustrated in Figures 2-4 for three different temperatures: 303,
665, and 836 K for the Mg/NO2 reaction; 303, 615, and 916 K
for the Ca/NO2 reaction; 303, 662, and 952 K for the Sr/NO2
reaction.
When the magnitude of the intercept is larger than 2 times
2
its standard deviation but smaller than 7.34DMg(Ca,Sr)/He/2r , plug-
flow conditions do not prevail and the factor η is set equal to
2
0
1.3 with an associated systematic error of 10%. In the other

Reactions of Mg(1S), Ca(1S), and Sr(1S) with NO2
J. Phys. Chem. A, Vol. 103, No. 51, 1999 11323
of some individual rate constants measured at a constant
temperature is much larger than stated by their standard
deviations. In this context, it has to be mentioned that in our
recent kinetic studies of the reactions between metal atoms and
other additives such as oxygen, nitrous oxide, methyl halides,
etc., this variation of the rate constants was smaller and in much
better agreement with the stated standard deviations.4
,7,23
While
carrying out the experiments with NO2 as additive gas, it has
been noticed that the quality of the decay curves is much lower
than in the case of the other additives. Sometimes a lower metal
atom decay was observed at presumably a higher but incorrectly
setted NO2 concentration, as is, e.g., the case in Figure 1; the
slope of ln A as a function of t is smaller at the NO2
1
1
-3
concentration of 2.48 × 10 molecules cm than at 1.84 ×
1
1
-3
1
0
molecules cm . This can most probably be explained by
unstable NO2 flows at these low concentrations, due to adsorp-
tion phenomena on various wall surfaces of the whole gas flow
system.
Figure 1. natural logarithm of the Ca atom absorbance as a function
These results can be fitted to the Arrhenius formalism
according to eq 5,
of the reaction time t with various amounts of added NO
experimental conditions are T ) 303 K, P ) 10 Torr, He as carrier
gas; [NO ] (9) 0; (0) 0; ([) 12.0; (]) 18.4; (b) 24.8; (O) 31.2; (2)
7.8; (4) 44.1 expressed in units of 10 molecules cm
2
. The
g
r
2
1
0
-3
3
.
-
RT
Ea
k1Mg(Ca,Sr)
) A exp(
(5)
)
cases, when the magnitude of the intercept is about equal to
2
7
.34DMg(Ca,Sr)/He/2r , a correction factor of 1.6 will be used. The
3
-1 -1
uncertainties σS and σk for the calculated values of the slope S
and the rate constants k1Mg(Ca,Sr) were calculated by combining
the uncertainties of several variables such as the temperature,
flow velocity, and total pressure as well as of the dimension of
the reactor radius according to the method explained in detail
in which A is the pre-exponential factor (cm molecule s ),
-
1
E is the activation energy (kJ mol ), R is the universal gas
a
-
1
-1
constant (8.31 J mol K ), and T is the temperature (K).
When the rate constants k1Mg(Ca,Sr) were fitted to eq 5 by means
19
of a weighted nonlinear regression using the SAS package,
2
2
by Howard. When the correction factor 1.3 was used, the
systematic error of 10% was taken into account resulting in the
total standard deviation σk. Finally, the observed slopes in
Figures 2-4 need to be multiplied by η to obtain the correct
second-order rate constants k1Mg(Ca,Sr). In the examples mentioned
above, second-order rate constants k1Mg ) 3.8 ( 0.4 (at 303 K),
the following Arrhenius expressions were obtained:
-11
k1Mg ) [(1.4 ( 0.2) × 10 ] ×
-
1
-3.4 ( 0.6 kJ mol
cm molecule s-1 (6)
3
-1
exp
(
)
)
)
RT
6
1
.7 ( 2.1 (at 665 K), and 15.8 ( 3.4 (at 836 K) in units of
-
9
-
12
3
-1 -1
0
cm molecule
s
were derived. In the examples for
k1Ca ) [(1.5 ( 0.6) × 10 ] ×
the Ca/NO2, reaction rate constants k1Ca ) 2.1 ( 0.4 (at 303
K), 11.0 ( 2.0 (at 615 K), and 8.7 ( 1.6 (at 916 K) in units of
-1
-1
-
2.9 ( 1.2 kJ mol
cm molecule s-1 (7)
3
-1
exp
(
-
10
3
-1 -1
RT
1
0
cm molecule
s
were obtained. Finally for the Sr/
NO2 reaction values for k1 were equal to 7.8 ( 1.1 (at 303 K),
-9
Sr
k1Sr ) [(1.2 ( 0.1) × 10 ] ×
9
1
.3 ( 1.4 (at 662 K), and 11.6 ( 0.4 (at 952 K) in units of
cm molecule s .
To confirm the second-order behavior of the reactions, the
-
10
3
-1 -1
0
-0.9 ( 0.3 kJ mol
exp(
cm molecule s-1 (8)
3
-1
RT
pressure dependence of the rate constants k1Mg(Ca,Sr) was examined
in the range between 6 and 12 Torr. It was noticed that at various
temperatures between 303 and 748 K k1Mg(Ca,Sr) was independent
of the pressure. These experiments also confirm that hydrody-
namic effects, as there are the mixing of the reagents or the
wall-loss of Mg(Ca,Sr) atoms, have no systematic effect on the
derived values of the rate constants.
The quoted error margins on both the pre-exponential factors
and the Arrhenius activation energies are at the 1σ level.
The values of ln k1Mg(Ca,Sr) from Table 1 are shown versus 1/T
in Figure 5.
One sees that for all the reactions the rate constants slightly
increase with the temperature, implying the presence of a small
or even negligible activation energy.
Furthermore, the influence of the initial alkaline earth metal
atom concentration on the value of k1
has been checked.
Mg(Ca,Sr)
i
For this purpose, A Mg(Ca,Sr) was varied with a factor of 2-5
and in none of the cases any systematic effect on k1Mg(Ca,Sr) has
been observed. This proves that, as expected at these low initial
metal atom concentrations, mutual reactions between the metal
atoms or consecutive reaction steps involving these metal atoms
were unimportant.
It should be pointed out here that for the calculation of the
Arrhenius parameters of the Ca/NO2 reaction only the weighted
-
10
3
-1 -1
average value of 2.6 × 10 cm molecule
s
at 303 K was
used in view of the large scatter on the data and the unreasonably
high weight of the large number of measurements at 303 K.
Indeed when all the individual values were fitted to the
Arrhenius formalism, including the eight measurements at 303
K, an Arrhenius activation energy of 5.0 ( 1.0 kJ mol was
obtained, which is about 70% higher than our value of 2.9 (
Temperature Dependence of k1Mg, k1 , and k1 The
Ca
Sr.
-
1
experimental conditions together with all the values of k1 , k1 ,
Mg
Ca
and k1Sr determined in the temperature ranges of, respectively,
03-836, 303-916, and 303-986 K are listed in Table 1. Some
attention has to be paid to the fact that the variation in the values
-1
3
1.2 kJ mol . When the same procedure was applied to the Mg/
NO2 and the Sr/NO2 reactions, the calculated Arrhenius

11324 J. Phys. Chem. A, Vol. 103, No. 51, 1999
Vinckier et al.
Figure 2. Slopes S of eq 4 for the Mg/NO
the added NO concentration. The experimental conditions are T
) 8 Torr); 665 K (0) (P ) 12 Torr); 836 K(b) (P
Torr), He as carrier gas, [NO
2
reaction as a function of
2
g
)
)
Figure 4. Slopes S of eq 4 for the Sr/NO
the added NO
303 K ([) (P
2
reaction as a function of
3
8
03 K ([) (P
r
r
r
12
2 g
concentration. The experimental conditions are T )
2
] is expressed in units of 10 molecules
-
3
r
) 10 Torr); 662 K (0) (P
r
) 10 Torr); 952 K (b) (P
r
0
cm
.
1
)
8 Torr), He as carrier gas, [NO
2
] is expressed in units of 10
-
3
molecules cm
.
tions,24 it becomes clear that the NO2 reactions are far less
exothermic. The reason for the higher exothermicity of the
alkaline earth metal atom/N2O reactions is the low bond energy
D0(N2-O) of the O atom in the N2O molecule. This value is
-
1
about equal to 162 kJ mol , which is indeed much lower than
the bond energy of the analogous NO2 molecule, i.e., 310 kJ
-
1 24
mol .
The measured rate constants in this work can only be
compared with the values of Kashireninov et al., derived in the
narrow temperature ranges between 873 and 1100 K.10 Equa-
tions 1-3 all show a small negative temperature dependence,
-
1.65
which for k1Mg and k1 is given by the factor T
by the factor T
and for k1Sr
. However, in this narrow temperature range,
the values of the rate constants will only decrease with about
0% going from 873 to 1100 K. If this calculation is repeated
Ca
-0.78
2
in this same narrow temperature range using our values of
k1Mg(Ca,Sr) from eqs 6-8, the rate constants will increase with less
than 10%. So the effect of the temperature on the values of the
rate constants is far less than one might think on the basis of
the kinetic expressions. However, if one compares the absolute
magnitude of the rate constants at the highest temperatures
covered in our work, one sees a very large difference as is shown
in Table 3.
Figure 3. Slopes S of eq 4 for the Ca/NO
2
reaction as a function of
the added NO concentration. The experimental conditions are T
2
g
)
3
)
03 K ([) (P
r
) 10 Torr); 615 K (0) (P
r
) 10 Torr); 916 K (b) (P
r
] is expressed in units of 1010
8 Torr), He as carrier gas, [NO
2
-
3
molecules cm
.
parameters fell within the error margins quoted in eqs 6 and 8.
One sees that all the reactions are characterized by a small
or even negligible activation energy in the range between 0.9
The values of k1Mg(Ca,Sr) are compared at temperatures of 836,
9
16, and 986 K for, respectively, the Mg, Ca, and Sr/NO2
-
1
and 3.4 kJ mol and a relatively high pre-exponential factor,
which is quantitatively in line with the large cross sections
reaction. One can see that all our values and especially those
of the Ca and Sr/NO2 reactions are much larger. It should be
pointed out here that the determination of kinetic data from
flame studies by means of the TVDF (temperature variation of
12
determined in molecular beam experiments.
Discussion
10
the diffusion flame) technique is strongly complicated through
several interferences as there are the high-temperature gradients
in the reaction zone, the occurrence of secondary reactions, and
the influence of condensation of the gas phase products onto
the thermocouples.
The reaction products of the exothermic Mg(Ca,Sr)/NO2
reactions are summarized in Table 2.24
From Table 2, one sees that the Ca/NO2 reaction can only
1
+
lead to ground-state CaO (X Σ ), while MgO and SrO can be
formed in different electronically excited states. However, it
Our data also allow calculation of the reaction cross sections
Qr for the Mg(Ca,Sr)/NO2 reactions at 303 K as well as at the
highest temperature covered. These values are compared with
the cross sections due to reactive processes, obtained from
molecular beam experiments (see Table 4).
From Table 4, it becomes clear that the values of Qr calculated
from our kinetic constants are in line with those obtained from
molecular beam experiments.
3
3
needs to be pointed out that MgO( Π) and SrO(a Π) are spin-
forbidden reaction products. Since a clear Arrhenius behavior
is observed for all three reactions, the possible occurrence of
two reaction channels with different activation energies is not
likely.
1
2
If one compares the reaction enthalpies from Table 2 with
those of the analogous alkaline earth metal atom/N2O reac-

Reactions of Mg(1S), Ca(1S), and Sr(1S) with NO2
TABLE 1: Rate Constants k1Mg(Ca,Sr) of the Reactions Mg( S) + NO
J. Phys. Chem. A, Vol. 103, No. 51, 1999 11325
1
1
1
2
, Ca( S) + NO
2
, and Sr( S) + NO
2
as a Function of the
a
Temperature T
g
-
12
-10
-10
-1
k
1Mg (× 10
k
1Ca (× 10
k
1Sr (× 10
3
-1
(Torr) AiCa cm molecule s-1
3
-1
(Torr) AiSr cm molecule s-1
3
T
g
(K)
P
r
(Torr) AiMg cm molecule s-1
)
T
g
(K)
P
r
)
T
g
(K)
P
r
)
303
303
303
303
386
390
400
478
481
482
544
550
550
550
550
552
552
616
620
620
665
665
665
665
748
748
748
748
833
836
8
8
8
8
8
8
8.5
7
8
8
6
6
6
9
9
12
12
8
8
0.17
0.22
0.22
0.32
0.20
0.45
0.54
0.37
0.25
0.42
0.45
0.45
0.58
0.77
0.70
0.61
1.05
0.62
0.21
0.54
0.10
0.85
0.10
0.18
0.60
0.85
0.96
0.32
1.10
0.60
3.8 ( 0.4
3.1 ( 0.1
3.0 ( 0.5
3.2 ( 0.7
3.6 ( 0.4
4.9 ( 0.3
5.9 ( 0.4
7.9 ( 0.4
3.8 ( 0.5
8.6 ( 1.0
11.3 ( 1.8
10.2 ( 1.4
7.5 ( 1.3
14.6 ( 2.2
12.0 ( 1.5
11.5 ( 1.6
12.2 ( 2.0
7.9 ( 1.0
8.5 ( 0.8
7.3 ( 0.3
6.7 ( 1.6
7.9 ( 2.7
7.6 ( 2.4
6.7 ( 2.1
8.2 ( 0.9
8.9 ( 0.3
6.9 ( 0.2
9.1 ( 3.9
15.9 ( 1.8
15.8 ( 3.4
303
303
303
303
303
303
303
303
381
388
390
390
447
456
498
509
566
576
591
602
602
615
624
700
721
736
840
916
8
8
8
0.46
0.66
0.54
0.19
0.87
0.97
0.25
0.30
0.14
0.67
0.29
0.11
0.49
0.57
0.42
0.27
0.60
0.28
0.65
0.14
0.29
0.53
0.44
0.18
0.37
0.56
0.63
0.27
2.2 ( 0.3
2.5 ( 0.5
2.4 ( 0.4
3.2 ( 0.6
2.5 ( 0.4
2.1 ( 0.4
4.7 ( 0.7
3.2 ( 0.5
8.5 ( 0.3
8.7 ( 1.2
3.6 ( 0.6
6.6 ( 1.1
4.5 ( 0.6
8.7 ( 2.0
10.0 ( 2.0
5.4 ( 0.9
10.0 ( 2.0
8.4 ( 1.7
6.7 ( 1.0
11.0 ( 3.0
10.0 ( 3.0
11.0 ( 2.0
6.8 ( 1.7
17.0 ( 6.0
10.0 ( 2.0
10.0 ( 3.0
7.4 ( 3.1
8.7 ( 1.6
303
303
303
303
303
303
303
357
407
454
499
508
508
542
662
662
662
662
662
681
764
798
798
848
893
952
986
6
8
9
0.09
0.50
0.34
0.25
0.31
0.23
0.42
0.25
0.35
0.39
0.25
0.73
0.21
0.34
0.28
0.21
0.08
0.17
0.42
0.26
0.31
0.13
0.51
0.31
0.19
0.23
0.16
9.0 ( 0.9
6.0 ( 0.9
10.3 ( 1.4
9.4 ( 1.5
7.8 ( 1.1
6.2 ( 0.7
11.8 ( 0.9
7.7 ( 1.4
9.6 ( 0.4
7.3 ( 1.1
10.4 ( 0.7
10.8 ( 0.2
11.5 ( 0.6
10.4 ( 0.7
9.4 ( 1.9
8.3 ( 1.3
9.2 ( 0.3
9.3 ( 1.4
8.6 ( 1.4
8.4 ( 1.0
11.9 ( 0.6
10.7 ( 0.3
10.3 ( 0.5
10.5 ( 1.0
12.5 ( 1.0
11.6 ( 0.4
11.7 ( 1.4
10
10
10
12
12
12
10
8
10
8
10
10
8
10
8
12
8
8
10
8
9
10
11
12
8
8
8
8
8
8
8
6
7
8
10
12
8
8
8
8
6
8
10
12
6
8
8
8
8
12
10
8
8
8
8
10
12
8
8
8
a
P
r
Is the Reactor Pressure and AiMg(Ca,Sr) Are the Initial Absorbances
R
TABLE 2: Reaction Enthalpy ∆H of the Exothermic
Mg(Ca,Sr)/NO Reactions Leading to Various Electronic
2
24
States of the Corresponding Metal Oxide
possible excited states of the metal oxide
∆H
R
(kJ mol-1)
1
2
1
+
2
Mg( S) + NO
2
(X A
1
) f MgO(X Σ ) + NO(X Π)
-31.8
-4.2
1
2
3
2
Mg( S) + NO
2
(X A
1
) f MgO( Π) + NO(X Π)
1
2
1
+
2
Ca( S) + NO
2
(X A
1
) f CaO(X Σ ) + NO(X Π)
-76.7
1
2
1
+
2
Sr( S) + NO
2
(X A
1
1
1
) f SrO(X Σ ) + NO(X Π)
-120.2
-11.8
-3.0
1
2
3
2
Sr( S) + NO
2
2
(X A
) f SrO(a Π) + NO(X Π)
1
2
′1
2
Sr( S) + NO
(X A
) f SrO(A Π) + NO(X Π)
TABLE 3: Rate Constants on the Basis of Ref 10 (Eqs 1-3)
and Our Values (Eqs 6-8), Both Calculated at the Highest
Temperature Covered in Our Work
highest Texp (K)
from our work (cm molecule
k
1
(Kashireninov)
1
k (this work)
3
-1
-1) (cm molecule s-1
3
-1
s
)
-
-
-
12
13
13
-12
Mg
Ca
Sr
836
916
986
1.0 × 10
4.2 × 10
1.2 × 10
8.6 × 10
-9
1.0 × 10
-9
1.0 × 10
Figure 5. Plot of ln k Mg(Ca,Sr)
nonlinear regression method: Mg/NO
Sr/NO (2) (eq 8).
1
versus 1/T according to the weighted
2
([) (eq 6); Ca/NO (O) (eq 7);
2
TABLE 4: Comparison between Our Calculated Values of
2
the Cross Sections Q
r
and the Values Obtained in Ref 12
2
2
T (K)
Q
r
(Å ) (this work)
Q
r
(Å ) (ref 12)
From a mechanistic point of view, it is worthwhile to check
if the alkaline earth metal atom/NO2 reactions are governed by
the electron jump mechanism. As already mentioned in the
Mg
Ca
Sr
303
36
303
16
303
986
0.5
1.5
47.5
91.5
178.0
140.8
8
93
14,16
Introduction, a few authors have postulated this mechanism
in view of the large cross sections observed in molecular beam
9
127
1
2
experiments. According to this electron jump mechanism the
rate constant kej for the reaction is given by eq 9,
0
.5
πµ) , with µ the reduced mass of the reagents; rc is the distance
between the metal atom and NO2 at which the electron jumps
from the metal toward the NO2 molecule. The value of rc is
2
k ) πr V
(9)
ej
c
r
1
5
in which Vr is the average molecular velocity, equal to (8RT/
given by

1
1326 J. Phys. Chem. A, Vol. 103, No. 51, 1999
Vinckier et al.
TABLE 5: Comparison between the Calculated Values of r
1
4.35
c
rc )
Å
(10)
c
(eq 10), kej (eq 9), and kmej (eq 14) with the Value of r (exp)
IEMg(Ca,Sr) - EA (NO )
v
2
Derived from kexp and the Experimental Value kexp at Room
Temperature as well as At the Highest Temperature
in which IEMg(Ca,Sr) is the ionization energy of the Mg, Ca, or
Sr atom, respectively, equal to 7.64, 6.10, and 5.69 eV, EAv-
3
kexp (cm3
-1
3
rc
kej (cm
rc(exp)
kmej (cm
(
Å) molecule s-1
-
1
)
(Å) molecule s-1) molecule-1 s-1
)
(NO2) is the vertical electron affinity of the NO2 molecule. In
Mg/NO2 2.7 1.5 × 10-
10
0.4
0.7
3.9
5.4
7.5
6.7
3.2 × 10-12
12
the calculation of rc performed by Zare et al., the value of
(303 K)
25,26
3.15 eV for EAv(NO2) was selected,
while in our calculation
2.4 × 10-10
15.8 × 10-12
Mg/NO2 2.7
836 K)
2
7,28
the lower and more recent value of 2.36 eV
The values for rc of the Mg(Ca,Sr)/NO2 reactions obtained from
eq 10 are shown in Table 5.
will be taken.
(
Ca/NO2 3.8 2.5 × 10-
10
2.6 × 10-10
8.7 × 10-10
7.2 × 10-10
8.7 × 10-10
(303 K)
Ca/NO2 3.8 4.3 × 10-
10
10
In the next step, the values of the electron jump rate constants
can be calculated at each temperature by means of eq 9 and
can then be compared with the value of the experimental rate
constant at the same temperature. Table 5 only shows the results
at room temperature and at the highest experimental temperature.
From Table 5, it is clear that the Mg/NO2 reaction is far too
slow to proceed according to the electron jump mechanism, and
thus a classical oxygen atom abstraction mechanism is most
likely. This is consistent with the higher ionization energy of
the Mg atom compared to the Ca and Sr atoms. For the Ca/
NO2 reaction at room temperature, the experimentally deter-
mined rate constant seems to be in very good agreement with
the predicted value on the basis of the electron jump mechanism.
However, it should be pointed out that for all measurements at
higher temperature, the electron jump rate constant is lower than
the experimental value; for example, at the highest temperature
of 916 K, the electron jump rate constant is even 50% lower
than the experimentally observed value. This has also been seen
for the Sr/NO2 reaction over the entire temperature range. These
larger experimental values might be explained by taking into
(
916 K)
Sr/NO2 4.3 2.7 × 10-
8.2 × 10-10
6.4 × 10-10
(303 K)
4.8 × 10-10
11.7 × 10-10
7.8 × 10-10
Sr/NO2 4.3
(986 K)
-
17
J Å6
Sr/NO2 reactions, respectively, equal to 6.2 × 10
-1
-17
6
-1
molecule and 7.2 × 10 J Å molecule are obtained, which
are much larger than the corresponding values of the induced
ind
dipole component C .
6
According to the modified electron jump mechanism, the rate
3
3
constant kmej is given by eq 14,
C6 1/3
8RT
πµ
1/2
2
kmej ) π( ) (
Γ (2/3) cm molecule s-1 (14)
3
-1
)
RT
2
2
in which Γ ( /3) is the gamma function of /3 ()1.354), T is the
-23
gas temperature, R is the universal gas constant ()1.38 × 10
-
1
-1
J molecule K ), and µ is the reduced mass of the reacting
species.
2
9
It needs to be pointed out that eq 14 is only valid when the
following condition is fulfilled:
account long-range forces between the reacting species. These
forces are mainly attractive dispersion forces which are active
at distances larger than the electron jump distance. The long-
range interaction is being controlled by the C6/R potential,
which contains two components: a dispersion coefficient C6
2
C6
6
6
>
RT
(15)
disp
r
c
ind 30
and a dipole-induced component C6
:
in which the value of rc is calculated by means of the classic
electron jump mechanism (eq 10). When eq 15 is applied to
the Ca/NO2 and the Sr/NO2 reactions, this condition is fulfilled
at each temperature. The values of the rate constant kmej are
calculated by means of eq 14 over the entire temperature range,
but only the values at room temperature and at the highest
temperature are shown in Table 5. For the Ca/NO2 reaction at
303 and 916 K, the value of kmej is, respectively, equal to 7.2
disp
ind
C ) C6 + C6
(11)
(12)
6
ind
The dipole-induced component C6 is given by eq 12,
RCa(Sr)
2
ind
C6 ) (µNO2)
2
(4πꢀ0)
-
10
3
-1 -1
-10
3
-1
×
10
cm molecule
s
and 8.7 × 10
cm molecule
-
1
in which µNO represents the permanent dipole moment of NO2
s . One notices that kmej at 303 K is much higher than the
experimental value, while kmej at 916 K is in perfect agreement
with the experimental value. However, if one checks the rate
constants over the entire temperature range, the general trend
for the Ca/NO2 reaction is that, except for a few values at 390,
2
-
30
(
)1.336 × 10
Cm), RCa(Sr) is the polarizability of the metal
-
30
3
atom, respectively, Ca ()22.8 × 10
m ) and Sr ()27.6 ×
-
-
30
12
3
1
1
0
0
m ), and ꢀ0 is the permittivity in a vacuum ()8.854 ×
2 -1 -1
C J m ). When these numbers are inserted into eq
ind
4
47, 509, and 700 K, all the other rate constants lie in the range
1
2, one obtains values of C6 for the Ca/NO2 and the Sr/NO2
-
10
-10
3
-1 -1
-
19
6
from 6.6 × 10 to 11 × 10 cm molecule s . This is in
reaction partners, respectively, equal to 3.6 × 10
J Å
-10
-
1
-19
6
-1
fairly good agreement with the values between 7.2 × 10 and
-10 3 -1 -1
molecule and 4.4 × 10
J Å molecule .
disp
6
0
8
.7 × 10
cm molecule
s
calculated on the basis of the
The dispersion coefficient C
can be calculated on the
basis of the London-expression,3
modified electron jump model (see Table 5).
In the case of the Sr/NO2 reaction at 303 and 986 K kmej is
-
10
3
-1 -1
(
IECa(Sr)IENO2)
respectively equal to 6.4 × 10
cm molecule
s
and 7.8
disp
3
2
-10
3
-1 -1
C6 ) RCa(Sr)RNO2
(13)
× 10
cm molecule s . For the Sr/NO2 reaction one can
(IECa(Sr) + IENO2)
notice that the rate constants predicted by the modified electron
jump mechanism over the entire temperature range also ap-
proach the experimental values much more than the values on
the basis of the classical electron jump mechanism, but
apparently this modified electron jump mechanism still slightly
underestimates k1Sr.
in which RNO is the polarizability of NO2 ()3.0 × 10 m3),31
-30
2
IECa(Sr) and IENO are the ionization energies of Ca, Sr, and NO2,
2
-
1 32
respectively, equal to 589.5, 548.1, and 942.1 kJ mol . When
disp
C6 is calculated from eq 13 values for the Ca/NO2 and the

Reactions of Mg(1S), Ca(1S), and Sr(1S) with NO2
J. Phys. Chem. A, Vol. 103, No. 51, 1999 11327
It needs to be pointed out here that the electron jump or
modified electron jump mechanisms imply the absence of an
energy barrier,15 which is in agreement with the very low
Arrhenius activation energies of 2.9 ( 1.2 and 0.9 ( 0.3 kJ
mol for, respectively, the Ca/NO2 and the Sr/NO2 reactions.
These small barriers are thought to be due to the closed-shell
configuration of the alkaline earth metal atoms with two paired
electrons on the outermost orbital.
(13) Herm, R. R.; Lin, S. M.; Mims, C. A. J. Phys. Chem. 1973, 77,
931.
2
(14) Parrish, D. D.; Herm, R. R. J. Chem. Phys. 1971, 54, 2518.
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-
1
Phys. Chem. 1990, 94, 1193.
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6, 3569.
8
(
(
18) Brouwers, H. Ph.D. thesis, Faculty of Science, K.U. Leuven, 1984.
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Acknowledgment. We thank the Fund for Joint Basic
Research (FKFO), Brussels, Belgium, for a research grant. C.V.
is a Research Director of the National Fund for Scientific
Research (Belgium). J.H. and J.R. are grateful to the Institute
for Science and Technology (IWT) for granting her a doctoral
fellowship.
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(
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2