Kinetics of methane oxidation over La-Sr-Ce-Fe-O mixed oxide solids

Article abstract of DOI:10.1039/b103426j

A kinetic study of methane combustion over La_0.7Ce_0.3FeO₃, La_0.7Sr_0.3FeO₃ and La_0.7Sr_0.1Ce_0.2FeO₃ mixed oxide solids has been carried out. From kinetic analyses of reaction rate, the combustion can be expressed by the Rideal-Eley mechanism, in which adsorbed oxygen, in dissociative form, is assumed to react with gaseous methane. True activation energies E_true, in the range 63-75 kJ mol_-1, and heats of adsorption of oxygen λ_O2, in the range 53-211 kJ mol^-1, have been determined. The large values of λ_O2, are related to existence of a SrFeO_3±χ perovskite crystal phase, which is able to uptake large amounts of oxygen.

Full text of DOI:10.1039/b103426j

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Kinetics of methane oxidation over La–Sr–Ce–Fe–O mixed oxide
solids
V. C. Belessi, A. K. Ladavos, G. S. Armatas and P. J. Pomonis*
Department of Chemistry, University of Ioannina, Ioannina 45110, Greece.
E-mail: ppomonis=cc.uoi.gr
Received 17th April 2001, Accepted 24th June 2001
First published as an Advance Article on the web 30th July 2001
A kinetic study of methane combustion over La Ce FeO , La Sr FeO and La Sr Ce FeO mixed
0
.7 0.3
3
0.7 0.3
3
0.7 0.1 0.2
3
oxide solids has been carried out. From kinetic analyses of reaction rate, the combustion can be expressed by
the RidealÈEley mechanism, in which adsorbed oxygen, in dissociative form, is assumed to react with gaseous
methane. True activation energies E , in the range 63È75 kJ mol~1, and heats of adsorption of oxygen j
,
true
O2
in the range 53È211 kJ mol~1, have been determined. The large values of j , are related to existence of a
O2
SrFeO3Bx perovskite crystal phase, which is able to uptake large amounts of oxygen.
ovskite oxides proceeds by both suprafacial and intrafacial
reactions.2 In the suprafacial process the reaction rate appears
to be correlated primarily with the electronic conÐgurations of
the surface transition-metal ions or the surface defects. In this
case the reaction takes place between the adsorbed species on
the surface at relatively low temperatures. Conversely, the
intrafacial mechanism takes over at high temperatures and the
reaction rate appears to be correlated primarily with the ther-
modynamic stability of oxygen vacancies adjacent to a
transition-metal ion.2,4,6,13 However, the role of these oxygen
species in complete and selective oxidation and their partici-
pation in combustion over various ceramic perovskite phases
is still an open question. On the other hand, the Mars and
Van Krevelen (MVK) redox model assumes that the supply of
oxygen from the gas phase is irreversible, and occurs only
when a reduced site is made available by the reaction, allow-
ing site oxidation to be a limiting factor in the kinetics.7,10
Arai et al.6 compared the catalytic oxidation of methane
over various La-Mn perovskite-type oxides with Pt/alumina
catalyst. From kinetic analyses of the reaction rate, the oxida-
tion on Pt/alumina can be expressed by the LangmuirÈ
Hinshelwood mechanism, in which the adsorbed oxygen plays
a major role. On the other hand, weakly bonded adsorbed
oxygen dominantly participates in the reaction on perovskite
oxides at low temperatures, and this oxygen desorbs with
increasing temperature. The lattice oxygen becomes reactive
at high temperatures after thermal desorption of adsorbed
oxygen.
Introduction
The catalytic combustion of hydrocarbons at low tem-
peratures is one of the ways to reduce the formation of nitro-
gen oxides compared with conventional combustion in air
atmosphere which takes place at temperatures up to 1300 ¡C.
Towards this end, several catalytic materials have been tested
in a number of laboratories worldwide.1 The combustion at
low temperatures is assured by highly active catalysts, such as
supported noble metals, which so far are used almost exclu-
sively, although more economical and possibly more poison-
resistant substitutes, particularly from the group of transition
metal oxides, have been actively sought for more than three
decades. Among them perovskite oxides appear to be some of
the most promising candidates, owing to the fact that they
guarantee a fair catalytic activity and stability at compara-
tively high temperatures.2h5 The early lanthanide perovskites,
particularly LaBO (B \ Ðrst-row transition metal) have
received the most attention for catalytic combustion of hydro-
carbons. In the majority of studies the identity of the B cation
3
has
a large inÑuence on the catalytic activity. Single
La A BO
or doubly La A B B O
substituted
1~x x 3Bd
1~x x 1~y y 3Bd
perovskites have been also extensively tested6h10 and syn-
ergistic e†ects, showing superior performance in the case of
mixed materials, have been reported in most cases.11,12 In the
vast majority of these studies, catalytic rates were examined at
a single gas composition or only in terms of light-o† tem-
peratures. On the contrary, full kinetic studies of methane
combustion were obtained only in a small number of
cases.6,7,10,13
The reaction rate of methane combustion over
La Sr NiO
13 solids was found to consist of two rate
2
~x 4~j
x
There is no single consistent mechanism that describes ade-
quately the kinetics of oxidation of alkanes, alkenes, aro-
matics, oxygenates etc. over typical VOC oxidation catalysts
such as noble metals or perovskites. The investigation of com-
plete oxidation of C ÈC alkanes over Pt, Pd and Rh catalysts
carried out by Yao14 showed various reaction mechanisms
and the reaction orders for hydrocarbon and oxygen varies for
di†erent molecules and catalysts. Kinetic analyses of reaction
rate data over Pt/alumina are consistent with a LangmuirÈ
Hinshelwood mechanism, in which the chemisorbed oxygen
reacts with adsorbed methane molecules.6,15 In many investi-
gations it has been proposed that the oxidation over per-
components, one suprafacial, employing oxygen from the gas
phase and active at low temperatures, and another intrafacial,
employing oxygen from the perovskite lattice and apparent
mainly at high temperatures. The reaction dependence was
Ðrst order relative to methane while the reaction order for
oxygen decreases from 0.5 to 0.2 as the temperature increases.
Klvana et al.10 examined two kinetic models, for the kinetic
1
4
study of methane combustion over La
Sr
.66 0.34 0.3 0.7 3
O perovskites. A simple Ðrst order
Ni Co
O
0
and La Sr Fe
.4 0.6 0.4Co0.6 3
0
model r \ kP
and
a
two-term model r \ (k
CH4
1
] k P0.5)P , were tested. The Ðrst order model gave a good
2
O2 CH4
Ðt to the experimental data for La
.66Sr0.34Ni0.3Co0.7O3 and
0
3856
Phys. Chem. Chem. Phys., 2001, 3, 3856È3862
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DOI: 10.1039/b103426j

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was also found to be adequate for La Sr Fe Co O .
However, in the case of the latter catalyst the experimental
data was best described by a MVK model.
for the whole series are given in ref. 17. BrieÑy, calculated
0.4 0.6 0.4 0.6 3
amounts of La(NO ) É 6H O (Merck), Fe(NO ) É 9H O
3
3
2
3 3
2
(Merck), Sr(NO ) (Ferak) and CeO (Aldrich) were mixed
3
2
2
Stojanovic et al.7 found that the catalytic activity for
thoroughly in an agate mortar and heated slowly up to 400 ¡C
for complete nitrate decomposition. The mixtures were further
heated at 900 ¡C for 4 h under atmospheric conditions. Then
the mixtures were cooled and ground in an agate mortar and
heated again at 1050 ¡C for a further 4 h. The solids obtained
after grinding were checked for their structural properties.
The speciÐc surface area of the solids, after the Ðnal heating,
methane oxidation over LaCr Ni O increases monotoni-
1
~x x 4
cally with the value of x. The kinetics behaviour correlated
well with an oxidationÈreduction mechanism, similar to that
proposed by the MVK model, for all catalysts, proposing
NiÈOÈNi ensembles as the key surface reagents.
LaMn1~xMgxO3 perovskite catalysts were tested for the
deep oxidation of methane by Saracco et al.16 A RidealÈEley
mechanism Ðtted satisfactorily the experimental kinetics for
and Mg-doped LaMnO . However, as opposed to
was checked by N adsorption at 77 K in a conventional
2
Fisons 1900 Sorptomatic apparatus. The values found were
LaMnO3
low, 1È4 m2 g~1, as expected.
The crystal structure of the prepared materials was deter-
mined by XRD analysis using a SIEMENS Di†ract 500
3
LaMnO , the catalytic combustion over LaMn Mg
O
3
0.8
0.2 3
seemed to involve two di†erent types of adsorbed oxygen
species, depending on the operating temperature.
system employing CuKa, radiation (j \ 1.5418 A
the corresponding XRD patterns are included in refs. 17 and
18. 57Fe Mossbauer spectra were obtained for the three
Ž ). Details of
Although the above studies give a good account of kinetics
for deep oxidation of methane over noble metals and ceramic
catalysts, various questions remain. Namely, in some of the
cases mentioned above6,7,10,13,16 apparent activation energies
were calculated while in fewer cases true activation energies
were also found.6,10,13,14 Is there perhaps any internal consis-
tency between those results? Another interesting question is
what is the meaning of apparent reaction orders found for
methane and oxygen6,7,13 and how are they related to the
more formal LangmuirÈHinshelwood or RidealÈEley kinetic
models? Are perhaps those apparent reaction orders, rep-
resenting kinetic parameters, somehow related to the strength
of adsorption of the reacting species, i.e. to thermodynamic
parameters? And if so what can this relationship be?
Ž
samples at 300 and 20 K, using a closed loop refrigerator
system. The spectrometer was calibrated with a-Fe and isomer
shift values are given relative to this. The experimental data
were Ðtted by a least-squared computer minimization routine
using a sum of spectral components characterizing di†erent
iron phases.19
Table 1 shows the catalysts used together with some of their
structural characteristics as determined and published pre-
viously.12,17,18
CH combustion kinetics
4
The kinetics experiments were carried out in a bench scale
tubular plug Ñow reactor (PFR), at 1 atm total pressure, con-
nected to a gas chromatograph (GC) for analyses. Catalysts
were activated at 500 ¡C for 1 h in 60 ml min~1 helium Ñow.
After cooling to 400 ¡C, a mixture of CH /O /He, at a total
The aim of this paper is a detailed kinetic study of the
methane combustion over the mixed oxide perovskites
La Ce FeO , La Sr FeO and La Sr Ce FeO .
0
.7 0.3
3
0.7 0.3
3
0.7 0.1 0.2
3
Such solids are members of a more extensive series with
general formulae La Sr Ce FeO studied recently by the
4
2
1
~x~y
x
y
3
Ñow rate of 115 ml min~1, was passed through the catalyst
bed containing 0.25 g of the catalyst. Variation of the partial
pressures of oxygen and methane, using suitable controls and
Ñow meters, was possible to calculate the dependence of the
present group; the relevant results have been published pre-
viously elsewhere.17,18
reaction rate on the partial pressures P
partial pressure values are listed in Table 2. The catalysts were
and P . The used
Experimental
CH4
O2
active from H \ 440 ¡C and the conversions of CH were
Methods of catalysts preparation and characterization
4
checked at intervals of 20 ¡C up to 620 ¡C. Analyses of the
The tested catalysts La Sr FeO , La Ce FeO and
reactants and products were carried out by sampling 1 ml of
the gases to a Shimadzu 15 A GC equipped with a TCD, with
He as carrier gas and connected to a Chromatopak C-R6A
integrator system. The column used for analysis was a 60/80
Carboxen 1000 (15@ ] 1/8A, s.s. supplied by Supelco). The
0
.7 0.3
3
0.7 0.3
3
La Sr Ce FeO can be considered as members of the
.7 0.1 0.2
three sub-groups of the series La
0
3
Sr Ce FeO with the
~x~y
nominal formulae La Sr FeO , La Ce FeO
1
x
1~y
y
3
and
Sr Ce FeO . Details about the preparation method
1
~x
x
3
y
3
La1~x~y
x
y
3
Table 1 Catalysts used, crystal phases as found by XRD and percentage of iron-containing crystal phases as found by Mossbauer spectroscopy
Ž
at 20 K
Crystal phases (%) as found by
Mossbauer spectroscopy at 20 K
Catalyst
Crystal phases as found by XRD
Ž
La0.7Ce0.3FeO
LaFeO /Fe O /CeO /La(OH) a
LaFeO
Fe O
64
36
39
28
33
55
33
12
3
3
2
3
2
3
3
3
2
3
La0.7Sr0.3FeO
LaFeO /SrFeO
/SrFeLaO a/La(OH) a/SrFe
12O19a
LaFeO
Fe O
3
3
3~x
3~x
4
3
2
3
SrFeO
3
Bx
La0.7Sr0.1Ce0.2FeO
LaFeO /SrFeO
/Fe O /CeO /La(OH) a/SrFe
12O19a
LaFeO
3
Fe O
3
3
2
3
2
3
2
3
SrFeO
3
Bx
a Trace amounts.
Table 2 Partial pressures of methane (P ) and of oxygen (P ) used for the determination of kinetics of methane oxidation
CH4
O2
P
/atm
CH4
/atm
O2
0.017
0.07
0.026
0.07
0.035
0.07
0.043
0.07
0.052
0.07
0.035
0.035
0.035
0.052
0.035
0.070
0.035
0.087
0.035
0.104
P
H/¡C
For each pair of pressures (P , P ) the conversion was examined at H \ 440, 460, 480, 500, 540, 580 and 620 ¡C
CH4 O2
Phys. Chem. Chem. Phys., 2001, 3, 3856È3862
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system was heated externally via a tubular furnace, regulated
by a SUR BERLIN controller, within ^1 ¡C, via a thermo-
couple in contact with the catalyst bed. The carrier gas Ñow
was kept at 30 ml min~1 and the only detected products were
CO and H O. In each experiment the integral reaction rates
2
2
were calculated as the amount (lmol) reacted per unit time
and unit mass.
Results
The obtained experimental data were treated using various
models, such as adsorption of oxygen in dissociative or non-
dissociative form, adsorption or no adsorption of methane on
the surface, adsorption of oxygen and methane at distinct
sites, and reaction rates made up of one suprafacial mecha-
nism using oxygen from the gas phase plus a second intrafa-
cial mechanism at higher temperatures using oxygen from the
solid. We also treated the data phenomenologically as shown
below. In all cases describing formal kinetics, treatment took
place using a suitable computer program,20 written in
FORTRAN, based on the well-known “SimplexÏ method.21,22
The criterion used to choose the best cases was the least sum
of square errors (SSE) of the simulation curves with the
experimental data. At the end we found that the best Ðtting
was achieved using RidealÈEley kinetics. Apart from this case,
the mis-Ðtting example of the well-known LangmuirÈ
Hinshelwood kinetics is shown, as well as the phenomenologi-
cal kinetics. The purpose of this was to correlate, eventually,
the phenomenological reaction orders of methane and oxygen
with the thermodynamic parameters of adsorption, as will be
discussed in the last part of the paper.
Fig. 1 Graphical representation of eqn. (2) for the calculation of
phenomenological reaction orders n and m. Points: experimental;
lines: best Ðttings using Ðrst order equations. Solid symbols: 440 ¡C,
open symbols: 500 ¡C. Squares: La Ce FeO , circles:
Phenomenological dependence of oxidation rate on the partial
pressures of O and CH
0.7 0.3
FeO .
3
FeO and triangles: La
La0.7Sr0.3 0.7Sr0.1Ce0.2
3
3
2
4
In a Ðrst approach the reaction kinetics of methane oxidation
over the three catalysts, La Ce FeO , La Sr FeO and
The catalysts showed nearly Ðrst order kinetics with respect to
methane with m around 0.7È0.8 in most cases. On the other
hand, the exponents, n, for oxygen were much smaller and
that for solid LaÈSrÈFeÈO was around 0.10È0.15 in most
cases. For the LaÈCeÈFeÈO material the values were some-
what larger, in the range 0.3È0.4. Finally, for the LaÈSrÈCeÈ
FeÈO system there was a variation of n values from 0.02 up to
0
.7 0.3
3
0.7 0.3
3
La Sr Ce FeO , were examined by changing the partial
0
.7 0.1 0.2
3
pressures of oxygen and methane. The results were expressed
by the empirical rate equation
R \ k@(P )m(P )n
CH4 O2
(1)
where R is the oxidation rate of methane and m and n are the
apparent reaction orders for methane and oxygen, respec-
tively. Phenomenological rate equations similar to eqn. (1)
have been used in the past by various groups.6,7,13 Then,
taking logarithms, eqn. (1) obtains the form
0.3 (Table 3). The apparent reaction orders m and n are shown
in Fig. 2 as a function of reaction temperature.
Rideal–Eley mechanism
Here, in a second approach, the reaction rate is expressed by
the RidealÈEley mechanism where adsorbed oxygen, in disso-
ciative form, is assumed to react with gaseous methane:
ln R \ ln k@ ] m ln P ] n ln P
(2)
CH4
O2
The graphical representation of ln R \ f (ln P ) at T , P
\
CH4
O2
constant and/or ln R \ f (ln P ) at T , P \ constant,
k(K P )1@2P
O2
CH4
R \ 1 O2 O2
] (K
CH4
(3)
should give straight lines with slopes m and n respectively.
Good straight lines with correlation coefficients approaching
unity were obtained in all cases. Typical results are shown in
Fig. 1.
P
)1@2
O2 O2
where k is the rate constant, K is the adsorption equilibrium
O2
constant of oxygen and P \ P ¡(P ¡/P ¡ [ 2x), P
\
O2
O2 O2
CH4
CH4
The calculated values of m and n corresponding to the
phenomenological reaction orders, are summarized in Table 3.
P
¡(1 [ x) were P ¡, P ¡ are the initial partial pressures
O2 CH4
of oxygen and methane, respectively, and x is the methane
CH4
Table 3 Phenomenological reaction orders m for methane and n for oxygen calculated from the straight lines of Fig. 1 (according to eqn. (2))
La0.7Ce0.3FeO
m
La0.7Sr0.3FeO
m
La0.7Sr0.1Ce0.2FeO
m
3
3
3
H/¡C
n
n
n
440
460
480
500
540
580
620
0.79 ^ 0.02
0.69 ^ 0.03
0.74 ^ 0.05
0.74 ^ 0.02
0.80 ^ 0.03
0.81 ^ 0.02
0.82 ^ 0.01
0.41 ^ 0.02
0.29 ^ 0.03
0.27 ^ 0.02
0.28 ^ 0.02
0.34 ^ 0.04
0.37 ^ 0.02
0.46 ^ 0.06
0.72 ^ 0.05
0.67 ^ 0.04
0.77 ^ 0.04
0.68 ^ 0.09
0.80 ^ 0.03
0.81 ^ 0.02
0.82 ^ 0.02
0.14 ^ 0.01
0.28 ^ 0.05
0.16 ^ 0.06
0.09 ^ 0.05
0.10 ^ 0.03
0.10 ^ 0.03
0.11 ^ 0.02
0.73 ^ 0.05
0.64 ^ 0.03
0.77 ^ 0.05
0.70 ^ 0.03
0.75 ^ 0.02
0.78 ^ 0.06
0.80 ^ 0.02
0.08 ^ 0.00
0.31 ^ 0.03
0.18 ^ 0.05
0.02 ^ 0.09
0.04 ^ 0.09
0.10 ^ 0.09
0.15 ^ 0.08
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in which the surface reaction between adsorbed methane and
adsorbed oxygen is the rate-determining step:
kK
P
P
(K P )1@2
R \ [1 ] K CH4 CH4 O2 O2
(4)
] (K
P
)1@2]2
CH4 CH4
O2 O2
where k, K , K , P and P
have their customary
O2
CH4
O2
CH4
values are calculated as pre-
meaning and the P and P
O2
CH4
viously.
Plots of the simulated reaction rate curves, according to
eqn. (4), for the three examined catalysts, again using a suit-
able optimizing computer program,20 are shown in Fig. 4 as a
function of the partial pressure of methane and of oxygen. The
corresponding k, K and K
puter program so as to achieve the best Ðt in each case.
were adjusted by the com-
O2
CH4
Discussion
Fig. 2 Variation of apparent reaction orders n and m as a function
of temperature for the three tested catalysts. Upper solid symbols:
orders for methane-m; Lower open symbols: orders for oxygen-n.
From Figs. 3 and 4 it is clear that the experimental results
follow the RidealÈEley kinetic model (Fig. 3). On the contrary,
the LangmuirÈHinshelwood model overshoots gravely the
experimental data, especially at high temperatures and high
conversions. Therefore we shall restrict our attention to the
results obtained from the RidealÈEley treatment (eqn. (3), Fig.
Squares: La Ce FeO , circles:
La0.7Sr0.3FeO
and triangles:
0
.7 0.3
3
3
La0.7Sr0.1Ce0.2
FeO .
3
conversion according to the reaction CH ] 2O ] CO
4
2
2
]
2H O. Similar kinetics have been used in the past by
2
3).
various researchers.3,6,16
The corresponding reaction rate constant k and the adsorp-
tion equilibrium constant of oxygen K calculated from the
Ðtting of the experimental data with the computer simulation
of eqn. (3) show a temperature dependence according to the
well-known relationships
The experimental results for the three examined catalysts
are shown as points in Fig. 3. In the same Ðgure, the best
Ðtting curves, according to the RidealÈEley mechanism, (eqn.
O2
(
3)), are shown as solid lines calculated using a suitable com-
puter program.20 The corresponding k and K constants
O2
were adjusted by an optimization subroutine of the software
k \ ko exp([E /RT ) (Arrhenius)
(5)
(6)
a
and they will be discussed below.
K
\ K o exp(j /RT ) (vanÏt Ho† )
O2
O2
O2
Langmuir–Hinshelwood mechanism
The relative mechanism is based on the dissociative chemi-
sorption of oxygen molecules at some active sites over the
catalyst surface. This dissociative chemisorption is regulated
In a third approach the kinetics for the system under study
were simulated using a LangmuirÈHinshelwood-type equation
Fig. 3 Graphical representation of eqn. (3). Points: experimental; lines: best computer Ðttings according to the RidealÈEley mechanism, eqn. (3),
for the optimum k and K values. (=) 440; (K) 460; (…) 480; (L) 500; (>) 540; (|) 580 and (@) 620 ¡C.
O2
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Fig. 4 Graphical representation of eqn. (4). Points: experimental; lines: best computer Ðttings according to the LangmuirÈHinshelwood mecha-
nism, eqn. (4), for the optimum k, K and K
values. (=) 440; (K) 460; (…) 480; (L) 500; (>) 540; (|) 580 and (@) 620 ¡C. The arrows show
O2
CH4
the line corresponding to the experimental points.
by a vanÏt Ho† type equilibrium expression (eqn. (6)). In this
ing lines the true activation energies E and the enthalpy j
true
O2
relation j corresponds to the heat of dissociative adsorption
of the dissociative adsorption of oxygen were calculated and
are cited in Table 4 together with similar data from catalytic
tests from other groups referring to the same reaction over
perovskite-type catalysts.
O2
of oxygen. This chemisorptive step is then followed by reac-
tion of gaseous methane with one of the derived oxygen
atoms, which initiates the combustion process with a reaction
rate governed by the kinetic constant k (eqn. (5)).
It is now worthwhile comparing the experimental values of
the present work with other relevant values from the liter-
The constants k and K in their logarithmic form, ln k and
O2
ln K , have been plotted vs. 1000/T in Fig. 5 for the three
ature. This can be done in Table 4 which contains true (E
)
O2
true
catalysts. Good straight lines could be drawn, especially for
and apparent (E ) activation energies, as calculated by di†er-
app
the Arrhenius plots ln k \ f (1000/T ) (left-hand part in Fig. 5).
ent authors using various kinetic models, as well as the heats
For the vanÏt Ho† plots ln K \ f (1000/T ) (right-hand part
of adsorption of oxygen j found in some of these cases.
O2
O2
in Fig. 5) some scattering of the experimental points is appar-
In Table 4 we observe that the data for E
calculated on
app
ent, especially for the Sr-containing catalysts, LaÈSrÈFeÈO
and LaÈSrÈCeÈFeÈO. Such phenomena might be related to
the complex dependence of k on the reaction temperature.
But, in any case, the slopes can give us a fair estimation of the
substituted perovskites are in most cases in the range 80È90
kJ mol~1. The E
values, when comparison is possible, are
of the same order of magnitude, but usually smaller by 5È20
true
kJ mol~1. Finally, the j values appear to fall in two cate-
O2
corresponding j values. From the slopes of the correspond-
gories: one of large j values around 200È300 kJ mol~1 and
O2
O2
another of low j values in the range 50È120 kJ mol~1.
One point to be discussed here is the positive values found
O2
for j (Table 4). Similar positive values have been observed
O2
by other authors.16 Those values mean that the dissociative
adsorption of oxygen on the catalyst surface is an activated
process, which can be described by the following steps
Step 1: O2(g) ] O2(phys. ads) (Physical adsorption)
Step 2: O2(ads) ] 2O(chem. ads)
(Dissociative chemical adsorption)
Of the two steps, usually the chemical one needs activation.
So the j values probably correspond to such a slow and rate
O2
determining process.
Fig. 5 Logarithmic plots of Arrhenius, eqn. (5), and vanÏt Ho†, eqn.
(
6), expressions. Squares: La Ce FeO , circles: La
0.7Sr0.3FeO
One important relevant question is how these values, E
,
0
.7 0.3
3
3
app
and triangles: La
.7Sr0.1Ce0.2
FeO .
E
and j , are eventually interrelated, especially in the case
0
3
true
O2
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Table 4 Apparent and true activation energies (kJ mol~1) and heats of adsorption of oxygen (kJ mol~1) found using various kinetics for
methane combustion
Kinetics employed
1st order
RidealÈEley
Two term model,
k(K
P
)1@2P
R \ kP
R \
O2 O2
CH4
R
\ kP
P
0.5 ] k P
1 CH4
CH4
1 ] (K
P
)1@2
total
CH4 O2
O2 O2
E
/
E
/
j
/
E
/
j
/
E /
app
true
O2
true
O2
1
Catalyst
kJ mol~1
kJ mol~1
kJ mol~1
kJ mol~1
kJ mol~1
kJ mol~1
Ref.
6
La Sr MnO
84.2
65.7
85.0
59.0
291.4
274.7
104.7
166.2
0
.6 0.4
3
3
La Sr MnO
0
.8 0.2
La
La
Sr
NiO
NiO
4~na
È
È
47.4
61.4
È
È
110.8
52.5
13
10
16
1
.25 0.75
Sr
b
1
.25 0.75
4~c
La
.66 0.34 0.3 0.7O3
Sr
Ni Co
92
105
92
84
È
È
92
100
0
La Sr Fe Co
O
0
.4 0.6 0.4 0.6 3
LaMnO
149.0
202.2
121.8
98.4
246.6
18.8
LaMn0. 83 Mg0.2O
HTc
LTd
3
La Ce FeO
90.2
88.9
83.9
75.5 ^ 1.8
63.2 ^ 4.9
66.1 ^ 6.5
52.6 ^ 5.5
211.1 ^ 41.8
122.3 ^ 39.6
This work and 12
0.7 0.3
3
La Sr FeO
0.7 0.3
La Sr
3
.7 0.1Ce0.2FeO3
0
a Nitrate preparation route. b Citrate preparation route. c High reaction temperature. d Low reaction temperature.
of not so clear-cut cases where the RidealÈEley kinetic, eqn.
Of more interest is the second case where, from the slopes
(
3), can not be reduced to a Ðrst order relation R \ kP
?
n \ 0.5 [ a (Fig. 1 and Table 3), we can estimate the relation-
CH4
Furthermore, it can be easily appreciated that empirical
ship between E
(13)
and j using the logarithmic form of eqn.
true
O2
kinetic equations like eqn. (1) used previously and their
graphical treatment (Fig. 1, eqn. (2)) are a rough approx-
imation of formal kinetic curves expressing RidealÈEley
kinetics (Fig. 2). Then what is the meaning of n and m in such
cases? Clearly these values depend on how fast the reaction
rate R approaches a steady value as the pressure P increases.
In other words these phenomenological parameters m and n
are related to the strength of oxygen adsorption. How? What
ln k@ \ ln k ] n ln K
O2
from which we can easily see that
(14)
E
\ E ] nj
(15)
app
true
O2
Similar relationships have been proposed some time ago by
the Novorsibirsk group23 for quite di†erent systems using a
totally di†erent approach.
is their inÑuence on E ? The following treatment is an
app
attempt to trace answers to such questions.
To test this hypothesis we have plotted the ln k@ values cor-
Eqn. (3) can be re-expressed in the form
responding to the intercepts ln R at P \ 0 of the straight
O2
lines in Fig. 1, vs. 1000/T in Fig. 6.
R \ k(K P )1@2P b/(K P )a
O2 O2 CH4 O2 O2
(7)
(8)
We can see that fairly good Arrhenius-type straight lines are
obtained and visual comparison with the relevant slopes in
Fig. 5 is interesting, showing both similarities and di†erences.
where
1
] (K
P
)1@2 \ (K P )a
O2 O2
O2 O2
The calculated slopes from Fig. 6 should correspond to E
app
In the above relationship a is real number whose value is
deÐned by the equation a \ ln(1 ] K 1@2 P 1@2)/ln(K P )
and should be compared to the corresponding E
values
app
found via eqn. (15) using the E
and j values determined
O2
O2
O2 O2
true
O2
and for variations of P of less than one order of magnitude, as
in the present case, can be considered to be approximately
constant.
previously via a totally di†erent way, i.e. the simulation in Fig.
3.
The extent to which the above can be veriÐed is shown in
Table 5 in which a comparison between the relevant results is
Then eqn. (7) can be written in the form
R \ k(K P )0.5~aP
b
(9)
O2 O2
CH4
and after taking logarithms
ln R \ ln k ] (0.5 [ a)ln K ] (0.5 [ a)ln P ] b ln P
O2
O2
CH4
10)
(
Eqn. (10) is similar to eqn. (2) with
m \ b
(11)
(12)
(13)
n \ 0.5 [ a
k@ \ kK 0.5~a \ kK
n
O2
O2
Therefore from the plots given in Fig. 1 the b and a values can
be found in each case. As expected m B b B 1 and indeed m is
found in the range 0.7È0.8 (Table 3). The discrepancies from
the ideal value m \ b \ 1 are due to experimental and/or sys-
tematic errors in the treatment of the data.
Fig. 6 Plots of the intercepts ln k@ or ln R at P \ 0, from Fig. 1, vs.
O2
1000/T . For details see text. (=) La Ce FeO , (…)
0
.7 0.3
3
La0.7Sr0.3
FeO and (>) La
0.7Sr0.1Ce0.2
FeO .
3
3
Phys. Chem. Chem. Phys., 2001, 3, 3856È3862
3861

View Article Online
Table 5 Comparison of data for the interrelation of E , E , n and j
app true
O2
E
/kJ mol~1
app
Method of estimation
La0.7Ce0.3FeO
La0.7Sr0.3FeO
La0.7Sr0.1Ce0.2FeO
3
3
3
Slopes of ln R \ f (1000/T ) from ref. 12
90.2
93.6a
88.9
92.7b
83.9
82.0c
Eqn. (15) using n values found from Fig. 1, eqn. (2)
and the j and E
values found from Fig. 5, eqn. (5)
O2
true
Plots in Fig. 6
92.3
65.3
68.4
a E (kJ mol~1) \ E ] nj : 93.9 \ 75.5 ] (0.35 ] 52.6). b 94.15 \ 63.2 ] (0.14 ] 221.1). c 82.0 \ 66.1 ] (0.13 ] 122.3).
app true O2
shown. This table contains the E values found by three dif-
A simulation of the kinetic results using a suitable computer
program20 enables the direct estimation of kinetic and equi-
librium constants as well as the determination of true activa-
app
ferent ways for the three tested catalysts: First E
as found
app
from the slopes of the Arrhenius-type lines in ref. 12. Second
the E values as found from eqn. (15) after substituting the
tion energies E and the heats of adsorption of oxygen j
.
app
true
O2
relevant values of E , the mean value of the reaction rate
The exponent n used in the empirical rate equation R \
true
order n and j calculated previously in this work. Third the
k@(P )n(P )m can be related to the extent of contribution of
O2
O2
CH4
E
values calculated from the Arrhenius-type plots in Fig. 6.
the heat of adsorption j to the apparent activation energy
app
O2
The agreement between these values is excellent for the LaÈ
CeÈFeÈO catalysts for the three cases. In the other two cases
catalysts LaÈSrÈFeÈO and LaÈSrÈCeÈFeÈO) the plots in Fig.
give lower values as compared to the other two methods of
according to the relationship E \ E ] nj . This is
applied more precisely in cases where the K
the same order of magnitude as unity, while some discrep-
app
true
O2
P
term is of
O2 O2
(
6
ancies develop as soon as K P becomes larger and larger.
O2 O2
calculation. These discrepancies can be traced to the less satis-
factory matching of the lines in Fig. 1 with the actual RidealÈ
Eley curves in Fig. 3.
Large values of K and j for the above solids were
O2
O2
related to the existence of a SrFeO
phase, which is able to uptake large amounts of oxygen as
perovskite crystal
3Bx
In other words when the reaction rate R, as described by
the RidealÈEley scheme, increases in a smooth way as a func-
established by TPD/O experiments in previous work.18
2
tion of P , as observed in the case of LaÈCeÈFeÈO (Fig. 3),
O2
then the matching between the three cases is perfect. On the
References
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between the calculated values of E , because the exponential
eqn. (9) expresses the situation in a less satisfactory way. In
those cases the values of E
should be nearer to the actual value.
Therefore eqn. (9) is more applicable and useful in cases
where KP values in the denominator of the RidealÈEley
relationship are of the same order of magnitude as unity. In
other words, when KP is relatively small but not too small.
When KP is getting larger and larger, eventually the model
ceases to express the kinetics.
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RidealÈEley relationship and to the fast approach of steady
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table that LaÈSrÈFeÈO contains 33% of SrFeO while LaÈ
O2
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2
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9
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20
21
22
The relevant computer program is available on request from
ppomonis=cc.uoi.gr
Conclusions
The following conclusions can be drawn from this work.
The kinetics of the deep oxidation of CH on oxidic solids
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mixed oxidic and perovskitic components, follow the Rideal-
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3
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3862
Phys. Chem. Chem. Phys., 2001, 3, 3856È3862