Reactions of Cr atoms with NO, N2O, CO2, NO 2, and SO2 molecules

Article abstract of DOI:10.1134/S0023158410050010

Experimental results on the interaction of Cr atoms with various oxygen-containing molecules (NO, N₂O, CO₂, NO₂, and SO₂) at high temperatures (>1000 K) are presented. It is demonstrated that activation barrier

Full text of DOI:10.1134/S0023158410050010

ISSN 0023ꢀ1584, Kinetics and Catalysis, 2010, Vol. 51, No. 5, pp. 617–623. © Pleiades Publishing, Ltd., 2010.
Original Russian Text © V.N. Smirnov, U.S. Akhmadov, 2010, published in Kinetika i Kataliz, 2010, Vol. 51, No. 5, pp. 643–649.
Reactions of Cr Atoms with NO, N O, CO , NO ,
2
2
2
and SO Molecules
V. N. Smirnov and U. S. Akhmadov
2
a
b
a
Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow, Russia
b
Chechen State University, Grozny, Chechen Republic, Russia
eꢀmail: vns1951@yandex.ru
Received December 11, 2009
Abstract—Experimental results on the interaction of Cr atoms with various oxygenꢀcontaining molecules
NO, N O, CO , NO , and SO ) at high temperatures (>1000 K) are presented. It is demonstrated that actiꢀ
(
2
2
2
2
vation barrier for spinꢀforbidden reactions is higher, all other things being equal. For the reaction of Cr atoms
with N O, an interpolated temperature dependence of the rate constant, based on the highꢀtemperature meaꢀ
2
surements conducted in the present work and the published lowꢀtemperature data, is proposed.
DOI: 10.1134/S0023158410050010
Interest in the oxidation of metals stems from the
In the present work, we measured the kinetic charꢀ
role they play in natural and technological processes: acteristics of the interaction of Cr with NO, N O,
2
in atmospheric chemistry, homogeneous and heteroꢀ CO , NO , and SO and analyzed them together with
2
2
2
geneous catalysis, production of structures and nanoꢀ the available literature data.
particles of oxides, and thermal processing of waste
[
1–4]. These applications stimulated extensive studies
of the reactions of transition metals with oxidizers by
various experimental methods [5–7].
EXPERIMENTAL
Measurements were taken behind incident shock
waves in a shock tube equipped with means of atomic
absorption measurements [5]. Chromium atoms were
One of such metals is chromium. Previously, in a
short communication [8], we reported, without giving
experimental details and primary data, the rate conꢀ
stants of the interaction of chromium atoms with varꢀ
ious oxidizers at high temperatures, which were meaꢀ
sured behind shock waves by using atomic absorption
spectroscopy. At the time of publication of [8], there
were virtually no other measurements, even at low
monitored using the resonance transition at
λ
=
4
52.4 nm. The compositions of the mixtures and the
temperatures and total densities of the shocked gas are
listed in the table. The source of metal atoms was a fast
temperatures. In recent years, such measurements, Experimental conditions of the oxidation of Cr atoms by varꢀ
ious oxidizers (OX)*
although scarce, have been reported, which makes it
possible to examine the mechanism of these reactions
more thoroughly and obtain reliable values of their
kinetic characteristics. Note that an extension of the
temperature range in which an elementary chemical
reaction is experimentally investigated is highly
important for gaining deeper insights into its mechaꢀ
nism.
6
Total density ×10 ,
Mixture
OX, %
T, K
3
mol/cm
Cr + NO
1.3–5.3
Cr + N O
1
2
5.0
2220–3150
1130–2570
2
0.20
2.5–3.0
Cr + CO2
1.5–3.5
These circumstances prompted us to jointly interꢀ
pret our highꢀtemperature data and the recently pubꢀ
lished results on the reactions of Cr atoms with various
oxidizers, NO [9], N O [9–12], CO [9], and SO
3
4
5
10.0
30.0
50.0
1429–3020
926–2200
940–2080
2
2
2
Cr + NO2
1.4–2.6
Cr + SO2
[
13], at low and medium temperatures. While perꢀ
6
0.01
1130–2700
1080–2920
forming this analysis, we more carefully processed the
primary experimental data than it was done in our preꢀ
vious study [8], in particular, made an allowance for a
finite time resolution of the data acquisition system
7
8
0.20
0.54
1.5–2.7
(
~2–3
μ
s).
* The concentration of Cr(CO) was 3.0 ×
10–4% in all experiments.
6
617

6
18
SMIRNOV, AKHMADOV
decomposition of chromium hexacarbonyl: over the with NO has been studied only at room temperature or
temperature range covered, it decomposes within 1
14].
μs
somewhat higher temperatures. In all the metal–NO
systems studied, the interaction occurs by the recomꢀ
[
One particular feature of atomic absorption meaꢀ bination mechanism if the N–O bond is stronger than
surements is that the optical density generally does not the metal–O bond, or by the exchange mechanism in
obey the Beer–Lambert law. The reason is that the the opposite case.
width of the line emitted by the source is comparable
After the publication of our work [8], the interacꢀ
with the absorbing line width, or even exceeds it [15]. tion of Cr atoms with NO has been studied only in [9],
It turned out, however, that, at medium values of at a temperature of 298 K and pressures from 1 to
the optical density, the generally complex relationship 700 Torr. It was revealed that the rate constant nearly
between the concentration of atoms (absorbing layer linearly depends on the pressure, a behavior typical of
thickness) and the optical density
by the modified Beer–Lambert law [16]:
D
can be described recombination reactions. Using a simplified method
for constructing falloff curves, the authors determined
the values of the rate constant in the lowꢀ and highꢀ
pressure limits.
γ
D
= ln( 0
and I0 are the intensities of probing light beam
before and after passing the absorbing layer, is the
absorption coefficient, [A] is the concentration of
atoms (Cr atoms in our case), is the optical path
length, is a dimensionless exponent, ~0.5–1.0.
Based on the calibrations conducted in [5], the value
of was set at 0.73.
Given that the oxidizer molecules are present in a
I
/I)
=
(ε[A]
l
) ,
(1)
where
I
In the present work, the interaction of chromium
atoms was studied at temperatures high enough to
ensure the occurrence of reaction (I).
ε
l
Processing the primary experimental data by forꢀ
mula (3) yielded the temperature dependence of the
rate constant displayed in Fig. 1a, which can be preꢀ
sented by the expression (activation energy in kJ/mol)
γ
γ
14
3
–1 –1
large excess compared to chromium atoms and are not
consumed during the experiment and that the atoms
are formed virtually instantaneously, the reaction rate
can be closely described by the firstꢀorder kinetic
equation:
k1 = 7.1 10 exp(–166.1/RT) cm mol s . (4)
×
The monotonically positive character of the Arrheꢀ
nius dependence at high temperatures, characterized
by a high activation energy, suggests that the interacꢀ
tion between the chromium atoms and nitrogen oxide
–(1/[Cr])
×
(d[Cr]/dt) = kobs = k[OX],
(2) occurs by the exchange mechanism (Eq. (I)).
Figure 1b compares our results with those from [9]
where kobs is the observed firstꢀorder rate;
k, constant
for the bimolecular reaction between the Cr atom and at the same total pressure. This comparison clearly
oxidizer OX and [OX] is the oxidizer concentration. shows that, in the present work and in [9], different
Substituting expression (1) into (2) yields a working processes were studied: exchange reaction and recomꢀ
formula for determining
k
{
:
d
bination, respectively.
–1
According to [20], the observed activation energy is
related to the reaction barrier (which equals the
enthalpy change for this reaction, since it is spinꢀ
allowed) as
k
=
–(γ[OK])
×
[lnln(I0
/I)]/dt}.
(3)
RESULTS AND DISCUSSION
Interaction of Cr Atoms with NO
E0
is the exponent in the generalized Arrhenius
law and Tm is the mean temperature. The value of is
normally set at 0.5, whereas Tm is defined as Tm
=
Ea
–
nRTm
,
(5)
where
n
Interest in this reaction is motivated by that the NO
molecule is a stable radical and that this process conꢀ
stitutes one of the steps in the transformations of chroꢀ
miumꢀcontaining species during incineration of
metalꢀcontaining waste. The tabulated bond dissociaꢀ
tion energies of the NO and CrO molecules,
n
=
0.5
(
T1T ) (T1 and T2 are the boundaries of the temperaꢀ
2
ture range covered) [21]. In this case, E0.1
1
6
=
Δ
H1(0 K)
55 kJ/mol, whence, given that D0(N–O)
27 kJ/mol [17], D0(Cr–O) = 472 kJ/mol.
This quantity is somewhat higher than the value
=
=
D0(N
7
⎯
O) = 627 kJ/mol [17] and D0(Cr–O) = 457
±
kJ/mol [18], suggest that the reaction
7
2
5
–1) + N(4S0) (I)
presented in the databases [18] and [19], which is
based on the massꢀspectrometric measurements of the
Cr + AlO = CrO + Al equilibrium (see refs. in [18]):
Cr(a S ) + NO(X
3
Πr)
CrO(X
Π
is endothermic by 169.8 kJ/mol. Since the dissociaꢀ
tion energy of the Cr–N bond (D0(Cr–N)
61.5 kJ/mol [19]) is substantially lower than that of
the Cr–O bond, the reaction
=
D0(Cr–O) = 457
D0(Cr–O) = 457
±
7
kJ/mol. A nearly identical value
3
±
9 kJ/mol was obtained in a study of
the interaction of chromium atoms with oxygen molꢀ
ecules in crossed molecular beams [22]. A close value
7
2
CrN(X4 –
) + O( P) (II)
3
Cr(a S ) + NO(X
3
Π
r)
Σ
is even more endothermic and can hardly compete can be derived from our experimental results. Indeed,
with reaction (I).
There is a large body of publications concerning differ from 0.5 because of the contribution from the
the interaction of metal atoms with the NO molecule, internal degrees of freedom and setting = 0, we
but, as far as we know, the interaction of metal atoms obtained D0(Cr–O) = 460.1 kJ/mol, a value close to
taking into account the remark made in [20] that n can
n
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2010

REACTIONS OF CR ATOMS WITH NO, N O, CO , NO , AND SO MOLECULES
619
2
2
2
2
3
−
1
−
1
3
−
1
−
1
log
k
[cm mol s ]
log
15
k [cm mol s ]
16
15
14
13
12
(a)
(a)
1
2
3
1
2
3
14
13
12
1
1
0
1
0
0.1
0.2
0.3
0.4
0.5
0
0.2
0.4
0.6
0.8
1.0
15
14
13
12
11
10
15
(
b)
(
b)
1
2
3
4
5
6
14
13
12
11
10
9
8
1
2
0
1
2
3
1
4
0
1
2
3
4
−
−
1
1
000/
T, K
1000/
T
, K
Fig. 2. (a) Temperature dependence of the rate constant for
the interaction of Cr atoms with N O: ( ) measurements
behind incident shock waves in a 0.0003% Cr(CO) + 0.2%
Fig. 1. (a) Temperature dependence of the rate constant
for the interaction of Cr atoms with NO: ( ) measurements
behind incident shock waves in a 0.0003% Cr(CO) + 5%
1
2
1
6
N O + Ar mixture, (
2
) linear regression, and (
fidence interval; (b) comparison with the published data: (
present work, ( ) [9], ( ) [10], ( ) [11], ( ) [12], and (
dependence obtained by averaging data ( )–( ).
3) 95% conꢀ
6
2
NO + Ar mixture, (
fidence interval; (b) comparison with the published data:
) present work and ( ) [9].
2) linear regression, and (
3) 95% conꢀ
1)
)
2
3
4
5
6
(1
2
1
5
the value reported in the above handbooks. In a review temperatures [9–12]. The results of our measurements
paper [2], D0(Cr–O) = 464.0 kJ/mol was given.
and a comparison thereof with the published data are
presented in Fig. 2. The linear regression of the temꢀ
perature dependence of the experimental values
obtained in the present work yielded the following
expression for the rate constant of this reaction:
A lower value, D0(Cr–O) = 436.2 8.9 kJ/mol,
±
was determined based on an analysis of highꢀtemperaꢀ
ture massꢀspectrometric data on the composition of
the vapor in the europium–chromium–phosphorus–
oxygen system [24].
1014.0
±
0.3
k3 = 2.0
exp[–(33.5 9.0)/RT)] cm mol s
Considered together, the available measurements
Fig. 2b) demonstrate a nonꢀArrhenius behavior,
which can be described by the expression
k3 = 1.4
1014
– 3690/ ) cm mol s
The reaction of chromium atoms with nitrous The observed activation energy at the middle of the
oxide,
temperature range covered was found to be
d(ln )/d(1/ ) = 25.5 kJ/mol
×
Thus, the obtained characteristics of the interacꢀ
tion of chromium atoms with nitrogen oxide are in
close agreement with the available thermochemical
data for this reaction.
3
–1 –1
×
±
.
(6)
(
×
2
Interaction of Cr Atoms with N O and CO2
exp(155000/ 2
3
–1 –1
×
T
T
.
(7)
7
1 +
Σ
CrO(X5
Cr(a S ) + N O(X
)
Πꢀ1)
E
obs
=
R
k
3
T
.
(8)
3
2
1
+
This value is markedly higher than that predicted by
the quantumꢀchemical calculations performed in [25]
+
N2(X Σ
)
(III)
g
is spinꢀforbidden, but, at the same time, it is exotherꢀ
(
15.5 kJ/mol), but markedly lower than the value
o
mic, ΔH3 (0 K) = –295.2 kJ/mol [17, 18]. This reacꢀ obtained from the quantumꢀchemical calculations
tion was first investigated in our previous study [8]. carried out in [26] (33 kJ/mol). Nevertheless, one can
Later, this reaction was studied at medium and low claim that the experimental data are in satisfactory
KINETICS AND CATALYSIS Vol. 51
No. 5
2010

620
SMIRNOV, AKHMADOV
3
−
1
−
1
CO molecules to form complexes or by the presence
of small admixtures of oxygen in the test mixture,
log
k
[cm mol s ]
2
13
12
11
10
since the rate of the interaction of molecular oxygen
with chromium atoms is fairly high [27]. We favor the
latter possibility, because quantumꢀchemical calculaꢀ
tions [28] and experiments on the interaction of tranꢀ
sition metal atoms with carbon dioxide in cryogenic
matrices suggest that such complexes, having a bondꢀ
ing energy below 100 kJ/mol [28–30], cannot exist at
temperatures above 1000 K. In addition, the rate conꢀ
stant of the formation of such a complex in the lowꢀ
pressure limit estimated from the data presented in
Fig. 3a is approximately 2–3 orders of magnitude
lower than the values typical of atom–triatomic moleꢀ
cule recombination reactions [31], making implausiꢀ
(
a)
1
2
3
4
5
0
0.2
0.4
0.6
b)
0.8
1.0
1.2
1
1
1
1
3
2
1
(
ble the assumption that Cr and CO recombine.
2
1
2
Subtracting the contribution from admixed oxygen
the concentration of which was estimated as 0.002%)
(
gives the following expression for the rate constant of
reaction (IV):
1014.0
±
0.6
k4 = 2.8
×
(9)
0
3
–1 –1
×
exp[–(140.7 23.0)/RT)] cm mol s .
±
As can be seen, this expression is characterized by a
normal preexponential factor and an activation energy
substantially higher than the endothermicity of the
reaction (69.1 kJ/mol). Such a behavior is likely due to
this reaction being spinꢀforbidden, since an analogous
9
0
1
2
3
1
4
−
1
000/T, K
Fig. 3. (a) Temperature dependence of the rate constant
for the interaction of Cr atoms with CO measured behind
incident shock waves in 0.0003% Cr(CO) + CO + Ar
reaction of iron atoms with CO (spinꢀallowed) has an
2
2
activation energy close to its endothermicity.
6
2
mixtures with various CO concentrations: (
1
) 50, (
) 95% confidence interꢀ
val. (b) Comparison with the published data: ( ) present
work and ( ) upper estimate [9].
2) 30
2
and (3) 10%; (4) regression and (5
1
Interaction of Cr Atoms with NO and SO2
2
2
Unlike CO and N O, the NO and SO molecules
2
2
2
2
form rather stable complexes with transition metal
agreement with the theoretical predictions, although atoms [13, 26, 32]. According to [26, 32], one of the
the accuracy of such predictions remains insufficient. factors responsible for a high reactivity of NO and
2
That the calculations performed in [25] gave a subꢀ SO compared to CO and N O is that their electron
2
2
2
stantially lower value can be tentatively explained by affinities (2.273 0.005 eV for NO [33] and 1.1 eV for
±
2
that the authors used only one potential energy surꢀ SO [17]) are substantially higher than those of N O
2
2
face, without regard for the intersection of the quintet (0.15 eV [34]) and CO (<0 [35]). The NO and SO
2
2
2
and septet terms.
The interaction of chromium atoms with carbon
dioxide is similar to their reaction with nitrous oxide:
molecules have a similar geometric structure, differing
in the strength of the bond between the central atom
and the oxygen atoms and in the electronic structure.
For this reason, it is interesting to examine the reactivꢀ
ity of these molecules with respect to chromium, a
typical representative of the transition metal atoms.
+
g
7
1
Σ
Cr(a S ) + СO (X
3
CrO(X5
)
2
(IV)
) + CO(X1 +).
Π
–
Σ
1
To our knowledge, there are no published data on
the interaction of chromium atoms with nitrogen
Note, however, that, in contrast to (III), this reacꢀ
o
tion is endothermic, with ΔH4 (0 K) = 69.1 kJ/mol dioxide, whereas the data on the reaction with sulfur
[
17, 18].
The results of our measurements are displayed in
Fig. 3. Apart from our data, there is only one upper
dioxide have been obtained only at low temperatures
(
297–534 K) [13].
Quantumꢀchemical calculations within the frameꢀ
estimate of the rate constant of the interaction of chroꢀ work of density functional theory [26] showed that,
mium atoms with carbon dioxide [9]. As can be seen, except for the Ti atom, which forms a complex with
in the lower part of the temperature range used in the the NO molecule by bonding to the N and O atoms
2
present work, the rate constant is virtually temperaꢀ
tureꢀindependent. Such a behavior can be explained
2
N,O
(
η
complex), the rest of the transition metal atoms
2
by either the recombination of chromium atoms with bond to each of the two oxygen atoms (
η
O,O complex).
KINETICS AND CATALYSIS Vol. 51
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REACTIONS OF CR ATOMS WITH NO, N O, CO , NO , AND SO MOLECULES
621
2
2
2
2
The complex then rearranges by passing over a barrier, which is also likely to be endothermic. As far as we
the height of which does not exceed, however, the know, there are no experimental data on the stability of
energy of the starting reactants, a factor that allows the CrNO molecule. As to theoretical treatment, we
these reactions to occur without an appreciable barꢀ managed to find only one work in which the value of
rier. Finally, an oxoꢀnitrosyl complex forms with a D0(Cr–NO) was calculated by quantumꢀchemical
bond strength of ~120 kJ/mol. Note that the stability methods [42]. It turned out that this value depends on
of similar complexes of transition metal atoms with the accepted spin multiplicity, reaching 259 kJ/mol at
nitrous oxide does not exceed 10 kJ/mol.
the lowest multiplicity (S = 2). Comparing the meaꢀ
sured rate constant of the Cr + NO recombination
with that calculated using the RRKM theory at various
values of D0(Cr–NO), the authors of [42] concluded
The results of the calculations performed in [13,
3
2] show that the interaction of transition metal atoms
2
O,O
with SO also occurs through an
η
complex, but its
2
that CrNO is formed in a highꢀspin state (
and that the dissociation energy of the Cr–NO bond is
40 kJ/mol. Using this estimates and the tabulated
S = 6 or 8)
further transformations were not considered.
To our knowledge, measurements of the rate conꢀ
1
stants of the interaction of NO with transition metal
2
thermochemical data from [17, 18], we concluded that
reaction (VII) is essentially endothermic (by 45–
atoms have been conducted only for the iron [36, 37],
copper [38], and titanium [39] atoms. In all cases, the
rate constant of the reaction was weakly dependent on
the temperature and independent of the pressure, a
behavior indicative of the reaction occurring by the
exchange mechanism.
The interaction of sulfur dioxide with transition
metal atoms was studied Cr [13], Ni [40], and V, Fe,
Co [32]. All these reactions, except for the reaction
with vanadium atoms, are endothermic and, thereꢀ
fore, proceed by the association mechanism. The
1
65 kJ/mol), and, therefore, it should be characterꢀ
ized by a high activation energy and, correspondingly,
a low rate.
The temperature dependence of the rate constant
for reaction (V), displayed in Fig. 4, can be presented
by the following Arrhenius expression (activation
energy in kJ/mol):
1014
±
0.3
k5 = 6.3
×
(10)
3
–1 –1
×
exp[–(18.3 4.0)/RT], cm mol s .
±
interaction of V atoms with SO occurs by the As can be seen, the rate constant k5 has a normal preꢀ
2
exchange mechanism [32].
exponential factor and an activation energy substanꢀ
The primary experimental data on the interaction tially lower than the enthalpy change for reactions (VI)
of Cr with NO were processed on the assumption that and (VII). Thus, most likely, reaction (V) is the preꢀ
2
the consumption of atoms obeys the firstꢀorder kinetic dominant pathway of the interaction of chromium
equation in Cr concentration (since the oxidizer is atoms with nitrogen dioxide.
present in a large excess). Based on the data from [41],
we concluded that nitrogen dioxide does not decomꢀ of Cr with SO were also processed using the firstꢀ
pose to an appreciable extent at temperatures used in order kinetic equation in Cr concentration.
The primarily experimental data on the interaction
2
[
8] and the present work, except for the highest temꢀ
Judging from the data reported in [43], sulfur dioxꢀ
ide shows no appreciable decomposition within the
temperature range covered in our experiments, except
for the highest temperature.
perature. In this case, the oscillogram was processed
within a time interval shorter than the characteristic
time NO decomposition at this temperature, ~11
μ
s.
As in the case of interaction of other transition
metals with NO , no pressure dependence of the rate
2
The reaction of chromium atoms with SO is
2
2
endothermic and, as discussed above, occurs only by
the association mechanism at low temperatures [13].
The exchange reaction
constant for the interaction of Cr with NO was
2
observed; therefore, it makes sense to assume that the
main pathway of this interaction is the exchange reacꢀ
tion
7
1
Cr(a S ) + SO (X A )
3
2
1
(VIII)
CrO(X5
Π
–1
) + SO(X4 –)
Σ
7
2
Cr(a S ) + NO (X A )
3
2
1
CrO(X5
Π
) + NO(X2
r),
Π
(V) is endothermic, with ΔH8°(0 K) = 88.6 kJ/mol, and,
–
1
therefore, it cannot proceed at a noticeable rate at low
°
which is exothermic: ΔH5 (0 K) = –156.8 kJ/mol temperatures.
17, 18]. The reaction involving the abstraction of the
nitrogen atom,
[
The measured temperature dependence of the rate
constant for reaction (VIII) is displayed in Fig. 5. As is
seen, it exhibits a wellꢀpronounced nonꢀArrhenius
behavior: at low temperatures, the rate constant is virtuꢀ
ally temperatureꢀindependent and even shows a negaꢀ
tive slope. At higher temperatures, the activation energy
becomes positive. The rate constant of the interaction
can be presented as the sum of two components, lowꢀ
7
2
Cr(a S ) + NO (X A )
3
2
1
−
3
CrN(X4 –
Σ
) + O2(X Σ ),
(VI)
g
°
is endothermic: ΔH6 (0 K) = 72.3 kJ/mol [17–19].
Another possible reaction is
7
2
3
Cr(a S ) + NO (X A )
2
CrNO(X) + O( P ), (VII) and highꢀtemperature ones (solid line in Fig. 5):
J
3
1
KINETICS AND CATALYSIS Vol. 51
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2010

622
SMIRNOV, AKHMADOV
3
−
[cm mol s ]
1
−
1
3
−
1
−
1
log
k
log
16
k
[cm mol s ]
16
15
14
(a)
(a)
1
2
3
1
2
3
15
1
4
3
1
1
3
5
12
0
0.2
0.4
0.6
0.8
1.0
0
0.2
0.4
0.6
0.8
1.0
1
16
(
b)
(b)
1
2
15
14
13
14
1
2
3
4
5
1
3
2
1
12
0
0
1
2
3
4
5
000/
6
1
2
3
4
−
−
1
1
1
T, K
1000/T, K
Fig. 4. (a) Temperature dependence of the rate constant for
the interaction of Cr atoms with NO : ( ) measurements
behind incident shock waves in a 0.0003% Cr(CO) +
1
2
Fig. 5. (a) Temperature dependence of the rate constant
for the interaction of Cr atoms with SO measured behind
6
0
.01% NO + Ar mixture, (
2
) linear regression, and (
3)
2
2
95% confidence interval; (b) comparison with the pubꢀ
incident shock waves in 0.0003% Cr(CO) + SO + Ar
6
2
lished data on the interaction of various transition metal
mixtures with various SO concentrations: (
1
) 0.2 and (
) regression. (b) Comparison with the published
) present work and ( ) [13].
2)
2
atoms with NO : (
1
) Cr, present work, (
2) Fe [36], (3) Fe
0.54%; (
data: (
3
2
[37], (4) Cu [38], and ( ) Ti [39].
5
1
2
1
5
dizer, for example, SO . The nature of this component
3
can be greatly elucidated by performing experiments
at various pressures of the bathꢀgas. If this component
k
= 1.6 × 10 exp(–95.4/RT)
Σ
(11)
12
3
–1 –1
+
6.5 10 (1000/T), cm mol s .
×
Clearly, the highꢀtemperature component, with proved to be strongly dependent on the pressure (total
positive activation energy,
density), it would signify that it characterizes recombiꢀ
nation.
15
3
–1 –1
k8 = 1.6 × 10 exp(–95.4/RT), cm mol s , (12)
Thus, in the present work, the rate constants of the
is associated with the exchange reaction.
interaction of Cr atoms with NO, N O, CO , NO ,
2 2 2
and SO molecules at high temperatures were meaꢀ
2
As can be seen, the preexponential factor is subꢀ
stantially higher than the collision frequency factor,
whereas the activation energy somewhat exceeds the
endothermic effect of the reaction.
Such a behavior can be interpreted within the
framework of the transition state theory on the
assumption that the statistical weight (partition funcꢀ
tion) of the transition state increases at high temperaꢀ
ture (~2000 K) faster than the product of the partition
functions of the starting reactants [44].
sured, which proved to be in close agreement with the
available lowꢀtemperature data. A qualitative interpreꢀ
tation of the results was made, and approximations of
the temperature dependences of the rate constants for
some of the studied reactions over a wide temperature
range were proposed.
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