Kinetics of Oxygen Exchange and N2O Decomposition Reaction over MeOx/CeO2 (Me = Fe, Co, Ni) Catalysts

MeOx/CeO2 (Me = Fe, Co, Ni) samples were tested in an 18O2 temperature-programmed isotope exchange and N2O decomposition (deN2O). A decrease in the rate of deN2O in the presence of oxygen evidences the competitive adsorption of N2O and O2 on the same sites. A study of isotope oxygen exchange revealed dissociative oxygen adsorption with the subsequent formation of surface oxygen species. The same species, more probably, result from N2O adsorption and the following N2 evolution to the gas phase. We supposed the same mechanism of O2 formation from surface oxygen species in both reactions, including the stages responsible for its mobility. A detailed analysis of the kinetics of isotope exchange has been performed, and the rates of one-atom (RI) and two-atom (RII) types of exchange were evaluated. The rate of the stage characterizing the mobility of surface oxygen was calculated, supposing the same two-step mechanism was relevant for both types of exchange. The effect of oxygen mobility on the kinetics of deN2O was estimated. An analysis of the possible pathways of isotope transfer from MeOx to CeOx showed that direct oxygen exchange on the Me–Ce interface makes a valuable contribution to the rate of this reaction. The principal role of the Me–Ce interface in deN2O was confirmed with independent experiments on FeOx/CeO2 samples with a different iron content.


Introduction
N 2 O is one of the side products of NH 3 oxidation to nitric acid over Pt-Rh gauzes; its emissions into the atmosphere are strictly regulated. It is commonly considered that N 2 O decomposition (deN 2 O) is initiated by the interaction of gas-phase N 2 O with an active site S (oxygen vacancies, in our case), resulting in the gas-phase N 2  (3b) O-S + N 2 O → N 2 + O 2 + S Reaction inhibition in oxygen presence was observed for most bulk oxide systems [1,2], which can be due to the competitive adsorption of N 2 O and oxygen on the same active sites. At 300-600 • C, oxygen desorption was shown to be the rate-controlling step of the reaction [4][5][6]. N 2 O decomposition in the ammonia burner with the catalyst located directly under Pt-Rh gauzes is also industrially applied as an attractive technology for N 2 O abatement. Such a catalyst operates at above 800 • C. Under these conditions, the importance of oxygen mobility for the deN 2 O activity was highlighted for La-Sr-Mn perovskite-type oxides [7] and supported MeO x /Al 2 O 3 (CeO 2 ) (Me = Fe, Co, Ni) [8] and FeO x /(CeO 2 + Al 2 O 3 ) samples [9], while reaction retardation with oxygen was observed as well. The mechanism of oxygen formation through the recombination of two O-S species (step 3a) is unlikely to fit this case because oxygen species are strongly bonded with anion vacancies and cannot diffuse on the catalyst surface. Kondratenko et al. [10][11][12][13] showed that N 2 O decomposition over different Fe-containing oxidic systems used in a wide range of temperatures is better fitted using an intermediate scheme. With this scheme, O 2 and N 2 O adsorb on the same active site S, as in the case of the traditional Langmuir-Hinshelwood mechanism. However, oxygen adsorption proceeds without dissociation, and the molecular form of adsorbed O 2 (O 2 -S) has been formed by a N 2 O reaction with O-S: However, samples with preferentially isolated active Fe sites (Fe-ZSM-5, Fe-silicalite, and BaFeAl 11 O 19 ) have been studied, and non-dissociative O 2 adsorption can be supposed in this case. Data from Boreskov and Muzykantov [14] show that at >~400 • C, oxygen dissociative adsorption proceeds on the surface of bulk α-Fe 2 O 3 and NiO. In CeO 2, oxygen from the gas phase first forms adsorbed superoxide or peroxide species which incorporate into the lattice via the following sequence of reactions [15][16][17]: Isotopic oxygen exchange in gas-solid systems is widely used in heterogeneous catalysis for studying oxygen activation, characterization of its state on the catalyst surface, and elucidation of kinetic peculiarities of oxygen transfer, including bulk oxide oxygen atoms, depending on sample microstructure. The basic theory is based on the classification of exchange types, depending on the number of surface oxygen atoms participating in an exchange with O 2 (zero-atom, single-atom, or two-atom exchange) [6,[18][19][20][21][22]. Regarding the exchange type, one may reveal the most probable mechanisms of oxygen activation on the surface. The unified mechanism was proposed by Muzykantov [14,23,24] for the interpretation of different types of oxygen exchange in oxides. It includes two types of surface oxygen species resulting from oxygen adsorption on the catalyst surface, i.e., O strongly bound with oxygen vacancy (O v ) and O located on the surface (O s ). The last, in turn, can diffuse on the surface and occupy the oxygen vacancy, thus transforming to O v . Such transformation is reversible: strongly bound oxygen can diffuse to the surface as well. O 2 formation proceeds by recombination of O v and O s . According to Muzykantov's theory, it is the mobility of O s that determines the type of exchange. Heteroexchange with the participation of two atoms of oxide surface oxygen is realized at a high diffusion rate of O s , and one oxygen atom participates in the exchange at a low rate of diffusion. Therefore, one can estimate the mobility of surface oxygen from the ratio of different types of exchange. Boreskov and Muzykantov [14] presented the characteristics of surface oxygen mobility of some simple and complex oxides and noted its high value for α-Fe 2 O 3 . We supposed that the same mechanism of oxygen species recombination could realize in the reaction of N 2 O decomposition.
At high temperatures, the bulk oxide oxygen atoms take part in the exchange process. That is why many recent studies focused on the estimation of the rate of bulk oxygen substitution, which may be used for characterizing the mobility of lattice oxygen [7,25,26]. The oxygen exchange behavior at high temperatures in La-Sr-Mn-O samples has been studied with a special emphasis on its relation to catalytic activity in N 2 O decomposition [7]. It was shown that the appearance of the second faster pathway of oxygen transfer in the bulk of the catalyst through oxygen vacancies or disordered-free channels in the perovskite structure resulted in increased catalytic activity. Evaluation of the rates of surface oxygen exchange and the coefficient of lattice oxygen diffusion in three La-Sr-Fe-O catalysts with close element content but different phases and surface compositions revealed the direct correlation between the surface exchange rate constant and the rate of N 2 O decomposition [27]. The results obtained can be useful for developing active catalysts.
In the present study, we investigated the main features of oxygen transfer on the surface and in the bulk of CeO 2 and MeO x /CeO 2 (Me = Fe, Co, Ni) samples using 18 O isotope exchange. It allowed us to reveal the interdependence of these processes and the kinetics of the reaction of N 2 O decomposition.

Samples Preparation and Characterization
Ce, Co, Ni, and Fe nitrates of a purity of 99.0% and citric acid (99.8%) were purchased from Vekton, Saint Petersburg, Russia. Ethylene glycol (99.0%) was purchased from Ecros, Saint Petersburg, Russia.
CeO 2 (S BET = 1.4 m 2 /g, pore volume 0.42 cm 3 /g) used as the support was obtained using calcination of Ce(NO 3 ) 3 ·6H 2 O at 900 • C for 36 h. MeO x /CeO 2 samples (Me = Fe, Co, Ni) with Me concentration 6.7 × 10 19 at/m 2 (0.86-0.91 wt%) were prepared using incipient wetness impregnation of CeO 2 with a water solution of a corresponding Me nitrate (0.37 mol/L) with added citric acid (0.41 mol/L) and ethylene glycol (0.26 mol/L). A solution 2.9 times more concentrated (with regard to all components) was taken for preparation of FeO x /CeO 2 with an Fe content of 2.5 wt%. After drying first under an IR lamp at continuous mixing and then-at 150 • C for 6 h, samples were calcined at 900 • C for 4 h. S BET values for FeO x /CeO 2 samples were close to that of CeO 2 (1.3-1.4 m 2 /g). X-ray powder diffraction (XRD) patterns were recorded using a Bruker D8 diffractometer with Cu Kα monochromatic radiation. Each sample was scanned in the range of 2θ from 10 • to 70 • with a step 0.05 • of 2θ. The surface composition of the samples was investigated using X-ray photoelectron spectroscopy (XPS) using spectrometer SPECS (SPECS, Berlin, Germany) with Al Kα irradiation (hν = 1486.6 eV). The positions of the peaks of Au 4f 7/2 (84.0 eV) and Cu 2p 3/2 (932.67 eV) core levels were used for calibration of the binding energy (BE) scale.

Temperature-Programmed Isotopic Exchange (TPIE) of O 2
Before every experiment, the sample loaded into a reactor (quartz tube, i.d. = 3 mm) was kept in 0.5 vol.% 16 O 2 + He flow at 900 • C for 30 min; then, the reactor was cooled down to room temperature in the same flow. At T ≤ 100 • C, this mixture was replaced stepwise by the same one but containing 18 O 2 and Ar (1 vol.%) as an inert tracer, and the reactor was heated up to 900 • C (rate of heating 14.7 • C/min). Gas flow rate and catalyst loading were the same in all experiments and amounted to 5.0 L/h and 0.025 g, respectively. Transient changes in the gas isotopic composition ( 16 where α input is the isotope fraction in the inlet mixture (0.95), C O2 is inlet O 2 concentration (0.15 × 10 −2 mol/mol), U is the flow rate of the reaction mixture (mol/s), and N A is Avogadro number.

Catalytic Activity Measurement
The catalytic activity was measured in a fixed-bed U-shaped reactor (3 mm i.d. quartz tube) loaded with 0.038 g of the sample (particles of 250-500 µm in size) at a flow rate of 18-60 L/h, ambient pressure, and at a temperature range of 600-900 • C. A gas mixture containing 0.15-1.0 vol% N 2 O in He was used. To check out the effect of O 2 , 3 vol.% O 2 was added to the inlet mixture. Outlet mixture composition was analyzed using a gas chromatograph equipped with Porapack T (i.d. = 3mm, l = 3 m, N 2 O analysis) and NaX (i.d. = 3 mm, l = 2 m, N 2 analysis) columns. N 2 O conversion (X N2O ) calculated as: where C N2O and C 0 N2O -outlet and inlet concentrations of N 2 O were considered a measure of sample activity.

Qualitative Analysis of Oxygen Isotope Exchange Process
The changes in α(t) during the TPIE O 2 on CeO 2 and different MeO x /CeO 2 samples depending on T are shown in Figure 1. The 18 O fraction in O 2 first decreases as isotope exchange between gas phase oxygen and catalysts starts. Then it goes across the minimum and returns to the initial value after the complete substitution of exchangeable oxygen in the catalyst. One can see that exchange in CoO x /CeO 2 starts at lower temperatures and thus proceeds much faster than in other samples. The quantity of exchangeable oxygen (N O ) in the CoO x /CeO 2 sample is 6.4 × 10 21 atoms/g (Table 1), which is close to the stoichiometric quantity of O atoms in CeO 2 lattice (~7 × 10 21 atoms/g). A lower quantity of oxygen was exchanged in other samples because temperature-programmed heating stopped at 900 • C, while the exchange started at higher temperatures. Based on the similarity of α(t) curves for all samples, we supposed that all oxygen of CeO 2 participates in the exchange therein.

Qualitative Analysis of Oxygen Isotope Exchange Process
The changes in α(t) during the TPIE O2 on CeO2 and different M depending on T are shown in Figure 1. The 18 О fraction in О2 first de exchange between gas phase oxygen and catalysts starts. Then it goes ac and returns to the initial value after the complete substitution of excha the catalyst. One can see that exchange in CoOx/CeO2 starts at lower thus proceeds much faster than in other samples. The quantity of exc (NO) in the CoOx/CeO2 sample is 6.4 × 10 21 atoms/g (Table 1), which is c ometric quantity of O atoms in CeO2 lattice (~7 × 10 21 atoms/g). A lower q was exchanged in other samples because temperature-programmed h 900 °C, while the exchange started at higher temperatures. Based on th curves for all samples, we supposed that all oxygen of CeO2 participate therein. At the same time, a principally different distribution of labeled O 2 molecules was observed during TPIE ( Figure 2). So, in CeO 2 , NiO x /CeO 2 , and FeO x /CeO 2 samples, 16 O 2 appears in the gas phase first, and its fraction in O 2 (f 32 ) exceeds that of 16 [21,28] proposed the theory of isotope exchange of oxygen with solid oxides, which is currently widely used for the interpretation of mechanisms of oxygen transfer in solids [29][30][31]. With this theory, there are three kinetically distinct types of exchange depending on the number of oxygen atoms from the solid phase participating in the exchange reaction, zero-atom (R 0 ), single-atom (R I ), and two-atom (R II ). The overall rate of heteroexchange R = 0.5R I + R II . Both qualitative and quantitative interdependence between the type of exchange and distribution of isotope molecules during the exchange was determined within the framework of this theory. The observed character of the curves preferentially evidences the two-atom type of exchange in CeO 2 , NiO x /CeO 2 , and FeO x /CeO 2 samples where two O atoms of the catalysts participate in every act of exchange: 18  1 not complete exchange (see Figure 1). 2 not complete exchange (heating up to 820 • C only, afterward, the constant temperature was kept, see Figure 1). At the same time, a principally different distribution of labeled O2 molecu observed during TPIE ( Figure 2). So, in CeO2, NiOx/CeO2, and FeOx/CeO2 sampl appears in the gas phase first, and its fraction in O2 (f32) exceeds that of 16 О 18 О (f long period of time. In the CoOx/CeO2 sample, on the contrary, 16 О 18 О appear first is higher than f32 for all period of monitoring. Klier and Muzykantov [21,28] propo theory of isotope exchange of oxygen with solid oxides, which is currently wide for the interpretation of mechanisms of oxygen transfer in solids [29][30][31]. With this there are three kinetically distinct types of exchange depending on the number of atoms from the solid phase participating in the exchange reaction, zero-atom (R 0 ), atom (R I ), and two-atom (R II ). The overall rate of heteroexchange R = 0.5R I + R II . Bot itative and quantitative interdependence between the type of exchange and distr of isotope molecules during the exchange was determined within the framework theory. The observed character of the curves preferentially evidences the two-ato of exchange in CeO2, NiOx/CeO2, and FeOx/CeO2 samples where two O atoms of th lysts participate in every act of exchange: 18

Quantitative Estimates of Oxygen Isotope Exchange Rates
Numerical analysis of α g (T), f 32 (T), and f 34 (T) was performed to make quantitative estimates of the rates of isotope exchange with an account of types of exchange using the model of flow reactor including diffusion of oxygen isotopes in the bulk of the catalysts (see Appendix A). It revealed that oxygen substitution in the bulk of all samples is determined by the rate of "gas phase-surface" exchange. Diffusion of isotopes in the bulk proceeds very fast. Their concentration in bulk is close to that in the surface layer, which evidences the high mobility of the lattice oxygen. Estimated values of the rates of single-atom (R I ) and two-atom (R II ) exchange, as well as overall rates of heteroexchange (R) and contributions of two-atom exchange to the overall rate (R II /R), have been presented in Table 1. The accuracy of estimation of the overall rates of heteroexchange is reasonably high, and the calculating error lies within ±5%. The values of the rates of different types of exchange are estimated with lower accuracy (±10%). One can see that R, R I , and R II values change in the following order: CeO 2 ≤ NiO x /CeO 2 < FeO x /CeO 2 < CoO x /CeO 2 . R II values vary within one order of magnitude, and differences are more substantial for R and R I . R II /R values are as high as 0.9 for CeO 2 , NiO x /CeO 2, and FeO x /CeO 2 and are only 0.2 for CoO x /CeO 2 . Therefore, a substantially higher rate of exchange in the CoO x /CeO 2 sample compared with other CeO2-based samples is due to one-atomic exchange in the former of them.

Comparison of the Rates of N 2 O Decomposition and Oxygen Isotope Exchange
Dependences of the rates of N 2 O decomposition (R N2O ) versus reverse temperature over different samples have been presented in Figure 3. Their values at 750 • C and activation energy values (E RN2O ), as determined from the Arrhenius dependence on temperature, are presented in Table 2.

Quantitative Estimates of Oxygen Isotope Exchange Rates
Numerical analysis of αg (T), f32(T), and f34(T) was performed to make quantitative estimates of the rates of isotope exchange with an account of types of exchange using the model of flow reactor including diffusion of oxygen isotopes in the bulk of the catalysts (see Appendix A). It revealed that oxygen substitution in the bulk of all samples is determined by the rate of "gas phase-surface" exchange. Diffusion of isotopes in the bulk proceeds very fast. Their concentration in bulk is close to that in the surface layer, which evidences the high mobility of the lattice oxygen. Estimated values of the rates of single-atom (R I ) and two-atom (R II ) exchange, as well as overall rates of heteroexchange (R) and contributions of two-atom exchange to the overall rate (R II /R), have been presented in Table  1. The accuracy of estimation of the overall rates of heteroexchange is reasonably high, and the calculating error lies within ±5%. The values of the rates of different types of exchange are estimated with lower accuracy (±10%). One can see that R, R I , and R II values change in the following order: CeO2 ≤ NiOx/CeO2 < FeOx/CeO2 < CoOx/CeO2. R II values vary within one order of magnitude, and differences are more substantial for R and R I . R II /R values are as high as 0.9 for CeO2, NiOx/CeO2, and FeOx/CeO2 and are only 0.2 for CoOx/CeO2. Therefore, a substantially higher rate of exchange in the CoOx/CeO2 sample compared with other CeO2-based samples is due to one-atomic exchange in the former of them.

Comparison of the Rates of N2O Decomposition and Oxygen Isotope Exchange
Dependences of the rates of N2O decomposition (RN2O) versus reverse temperature over different samples have been presented in Figure 3. Their values at 750 °C and activation energy values (ERN2O), as determined from the Arrhenius dependence on temperature, are presented in Table 2.   One can see that activity in N 2 O decomposition changes in the following order: CeO 2 < NiO x /CeO 2 < FeO x /CeO 2 < CoO x /CeO 2 excluding the temperature interval above 750 • C where R N2O value for FeO x /CeO 2 and CoO x /CeO 2 become close. One can suppose that such approaching activity values at the distinct difference between R I and R II can be due to the different phase composition of the CoO x /CeO 2 sample under oxygen-deficient conditions (case of deN 2 O) and in the presence of oxygen. Indeed, the reduction of Co 3 O 4 to CoO took place at above 750 • C during temperature-programmed heating in the inert [8,32,33], while oxygen presence shifted the temperature of the beginning of Co 3 O 4 reduction to substantially higher temperatures [32,33]. At the same time, CeO 2 , NiO, Fe 2 O 3 , and supported Ni(Fe)O x /CeO 2 samples were stable during TPD in He up to 900 • C, at least [8].
R N2O values are substantially lower than R II and R, but R II /R N2O values for all samples are comparable and lie within 10 (±5), while R/R N2O values vary from 5 to 70. Therefore, some correlation between R N2O and R II , but not R, can be supposed. Below, we attempted to derive steady-state rates kinetic equations using known conceptions about the mechanisms of these reactions. Finally, the R II /R N2O ratios were derived through reaction rate constants and initial concentrations of the reagents.

Mechanism and Form of Rate Equation for Oxygen Isotope Exchange in Oxides
A certain set of mechanisms can describe every type of oxygen exchange (with the participation of one or two oxygen atoms) in oxides. Single-atom type of exchange is more often described by the Eley-Rideal mechanism that considers the formation of three atomic surface complexes, including two atoms of molecular oxygen and one oxygen atom of the catalyst [34]. The two-atom mechanism is usually interpreted using the two-step mechanism of Bonhoeffer and Farkas [35]. Reversible dissociation of the O 2 molecule proceeds in the first stage resulting in two equivalent atoms of adsorbed oxygen. In the second stage, the incorporation of adsorbed oxygen to the lattice of oxide proceeds, followed by isotope exchange between adsorbed and lattice oxygens. However, these are the anionic surface defects (oxygen vacancies) that are responsible for the activation of O 2 on the oxide surface. As a rule, their concentration is low, and it is doubtful whether simultaneous interaction of O 2 with two defects, which is necessary for molecule dissociation, is possible. We consider that the two-step mechanism proposed by Muzykantov and Boreskov [14,23,24] and presented in Scheme 1 is the most well-grounded.
approaching activity values at the distinct difference between R I and R II can b different phase composition of the CoOx/CeO2 sample under oxygen-deficien (case of deN2O) and in the presence of oxygen. Indeed, the reduction of Co3O4 t place at above 750 °C during temperature-programmed heating in the ine while oxygen presence shifted the temperature of the beginning of Co3O4 r substantially higher temperatures [32,33]. At the same time, CeO2, NiO, Fe2O ported Ni(Fe)Ox/CeO2 samples were stable during TPD in He up to 900 °C, at RN2O values are substantially lower than R II and R, but R II /RN2O values for are comparable and lie within 10 (±5), while R/RN2O values vary from 5 to 70 some correlation between RN2O and R II , but not R, can be supposed. Below, we to derive steady-state rates kinetic equations using known conceptions about nisms of these reactions. Finally, the R II /RN2O ratios were derived through r constants and initial concentrations of the reagents.

Mechanism and Form of Rate Equation for Oxygen Isotope Exchange in Oxides
A certain set of mechanisms can describe every type of oxygen exchang participation of one or two oxygen atoms) in oxides. Single-atom type of excha often described by the Eley-Rideal mechanism that considers the formati atomic surface complexes, including two atoms of molecular oxygen and atom of the catalyst [34]. The two-atom mechanism is usually interpreted usi step mechanism of Bonhoeffer and Farkas [35]. Reversible dissociation of the O proceeds in the first stage resulting in two equivalent atoms of adsorbed oxy second stage, the incorporation of adsorbed oxygen to the lattice of oxide pr lowed by isotope exchange between adsorbed and lattice oxygens. However, t anionic surface defects (oxygen vacancies) that are responsible for the activati the oxide surface. As a rule, their concentration is low, and it is doubtful whe taneous interaction of O2 with two defects, which is necessary for molecule d is possible. We consider that the two-step mechanism proposed by Muzy Boreskov [14,23,24] and presented in Scheme 1 is the most well-grounded. According to this mechanism, the O2 molecule dissociates on oxygen vac sulting in a strongly bound oxygen atom Ov which is included in the oxide  (Scheme 1, stage 2). This stage is reversible, i.e., strongly bound oxygen can leave this place and come on the surface. As a matter of fact, the second stage characterizes the mobility of O s . This mechanism allows the interpretation of both two-and single-atomic exchanges. Two-atom exchange is realized according to the following pathway: step 1 (r 1 ) → step 2 (r 2 ) → step −2 (r −2 ) → step −1 (r −1 ), while the single-atom mechanism includes only two steps: step 1 (r 1 ) → step −1 (r −1 ). The selectivity of the reaction of isotope exchange by pathway corresponding to the two-atom exchange (S) is determined by the ratio of the rates of step −1 and step 2: Muzykantov et al. derived an equation for the rate of two-atomic exchange for the case of its strong limitation by stage 2 (Scheme 1) using this mechanism [14,23,24]. They supposed as well that the degree of the population of [ ] v by strongly bound oxygen (O v ) is close to 1, while surface coverage by O s → 0. In this case, the order of reaction for O is close to 0.5. In our study, we considered a more general case when the rate-determining step is unknown. No restrictions will be imposed on the concentration of O v as well, and only the degree of surface coverage by O s will be supposed as negligible. In this case, rate equations for stages 1 and 2 (Scheme 1) can be represented as follows: Here, θ V and θ S are the concentrations of O v and O s , respectively, and k i are the reaction rate constants of the ith stage. Under the conditions of adsorption-desorption equilibrium, the rates of direct and reverse reactions are equal: We expressed θ v and θ s solving Equations (8) and (9) simultaneously. Finally, substituting them in Equations (4)-(7), we obtained: The rate of the reaction of two-atomic exchange can be expressed with the following equation: where Detailed derivation of the Equations (10)- (14) is given in Appendix B In the case r 2 >> r −1 (stage 2 is not rate-determining), the following approximate equation is applicable for the description of the two-atomic isotope exchange: According to Equation (15), the rate equation can have an order dependence on oxygen concentration (n) varying from 0.5 to 1, depending on the value of the k 1 C O2 k 2 /k −1 k −2 ratio.
In the case of k 1 C O2 k 2 >> k −1 k −2 (reaction equilibrium is shifted to direct steps and, thus, θ v → 1), the n value will be close to 0.5. In the opposite case (k 1 C O2 k 2 << k −1 k −2 ) n → 1. According to Equation (13), the n value can be even less than 0.5 in the case k 1 C O2 > k −2 (the rate of two-atomic exchange is strictly determined by stage 2).

Mechanism and Equation Rate for N 2 O Decomposition Reaction
We observed a decrease in N 2 O conversion in the presence of oxygen in the reaction mixture over FeO x /CeO 2 and CoO x /CeO 2 (Table 3) and FeO x /(CeO 2 + Al 2 O 3 ) [9] samples, which can be due to the competitive adsorption of N 2 O and oxygen on the same active sites. Therefore, O 2 formation by step 3 is preferable for CeO 2 -based samples. However, oxygen species localized in anionic vacancies (O v ) are strongly bound with cations, and it is doubtful whether they can diffuse easily on the catalyst surface. We supposed that the recombination of two oxygen atoms proceeds with the same mechanism as at oxygen exchange, i.e., with the interaction of O v with O s . The last, in turn, is capable of diffusing on the surface and can result from O v (lattice oxygen) coming to the surface. The mechanism of N 2 O decomposition accounting for the above reactions is represented in Scheme 2. We consider that oxygen re-adsorption by reverse stage 3N (Scheme 2) because of low oxygen concentration at low N2O conversion values in the done for reaction rate evaluation and fast oxygen washing out from the rea case, the degree of surface coverage with Os under reaction conditions can as negligible, like in the reaction of oxygen isotope exchange. One can see th reverse stages 2N and 3N (Scheme 2) are represented in the scheme of oxy exchange (Scheme 1) as well. Therefore, the rates of these stages can be expres of rate constants of isotope exchange as follows: We consider that oxygen re-adsorption by reverse stage 3N (Scheme 2) is negligible because of low oxygen concentration at low N 2 O conversion values in the experiments done for reaction rate evaluation and fast oxygen washing out from the reactor. In this case, the degree of surface coverage with O s under reaction conditions can be supposed as negligible, like in the reaction of oxygen isotope exchange. One can see that direct and reverse stages 2N and 3N (Scheme 2) are represented in the scheme of oxygen isotope exchange (Scheme 1) as well. Therefore, the rates of these stages can be expressed in terms of rate constants of isotope exchange as follows: Designating the rate constant of the stage of N 2 O adsorption as k 1N , one can obtain the equation for r 1N : Under the steady state: r 1N = r −2N − r 2N = r 3N , so the system of steady-state equations looks as follows: Solving Equations (20) and (21) simultaneously, we found θ V and θ S . Finally, substituting them in the expression for r 1N , we obtained the following kinetic equation for the rate of reaction of N 2 O decomposition (see details in Appendix C): where The following approximate kinetic equation is applicable in the case k 1 N C N2O /k −2 (stage 2N is not rate-determining): One can see that the equations for R N2O , Equation (22) and R II Equation (13), are close by the form. In the general case, the ratio between the rates of these reactions is determined with the following equation: In the case when stages 2 (Scheme 1) and 2N (Scheme 2) are not rate-determining for both reactions, the ratio between rates of these reactions is determined with the following approximate equation: According to literature data, on oxides, the rate is usually proportional to C N2O or has a slightly lower order due to the inhibition of produced oxygen [36]. In line with this, the dependence of the rate on N 2 O concentration (varied from 0.15 vol.% to 1.0 vol.%) was around 0.97 for FeO x /CeO 2 (Appendix D). Such close to 1 order means that the value of 2k 1N C N2O k 2 /k −1 k −2 in Equations (24) and (26) is much less than unity. In this case, the ratio between the rates of reactions of two-atomic exchange and N 2 O decomposition depends on the values of rate constants of the stages of oxygen and N 2 O adsorption and their concentrations.

Mobility of Surface Oxygen and Rate Determining Steps of Two Atomic Isotope Exchange and N 2 O Decomposition Reaction
According to the proposed mechanisms of isotope exchange and N 2 O decomposition, the mobility of surface oxygen is characterized by the rate of the same stage designated as stage 2 (Scheme 1) and 2N (Scheme 2). One can estimate the rate of this stage in the reaction of isotope exchange directly from experimental data. So, at known ratios of R I and R II (Table 1) to the overall rate of oxygen adsorption-desorption, one can estimate the selectivity of exchange running by different pathways. The rate of oxygen adsorption-desorption is equal to the sum of R I and R II : Therefore, the selectivity of the reaction of isotope exchange with the pathway corresponding to the two-atomic exchange (S) will be determined in the following way: At a known r −1 and S, one can calculate the rate of stage 2 (Scheme 1) using Equation (3): Calculated values of S and the rates of different stages of isotope exchange in the samples have been presented in Table 4. The value of S for CoO x /CeO 2 is low, and the estimation of r 2 = r −2 , in this case, is quite precise. The higher the selectivity, the less precise the estimate.  The values of θ V and θ S in the reaction of N 2 O decomposition can differ from those in isotope exchange, thus resulting in the change of the ratio between rates of these stages. So, the r −2 /r −1 ratio in the reaction of isotope exchange is determined with the values corresponding rate constants and θ S value: The ratio r −2N /r 3N that determines the rate-determining stage in the reaction of N 2 O decomposition is the same: The formation of weakly bound oxygen O s proceeds with both stage 2N and stage of oxygen adsorption 3N (Scheme 2). Gas phase oxygen concentration under the conditions of N 2 O decomposition (<0.01% on average by the length of the catalyst layer) is much less than during isotope exchange experiments (0.5%). Accordingly, we consider that the θ S value in the reaction conditions cannot be higher than at isotope exchange. In this case r −2 >> r −1 for CeO 2 , NiO x /CeO 2 , and FeO x /CeO 2 samples. Therefore r −2N >> r 3N as well. In this case, stages 2 (Scheme 1) and 2N (Scheme 2) are not rate-determining in the reaction of oxygen isotope exchange and in N 2 O decomposition. The ratio between the rates of these reactions is thus determined with Equation (26) and depends mainly on the ratio of rate constants of the stages of oxygen and N 2 O adsorption and their concentrations.
In the case of CoO x /CeO 2 , r −2 < r −1 , i.e., stage 2 is rate-determining in the reaction of isotope exchange. However, it is not so obvious for the reaction of N 2 O decomposition because r −2N /r 3N can be higher than r −2 /r −1 . Finally, the ratio between rates of these reactions will be determined with Equation (25).

Role of MeO x -CeO 2 Interface in the Reactions of Isotope Exchange and N 2 O Decomposition
Estimates of the rates of different stages made above were based on the assumption of equivalence of all active sites participating in the reactions. It is true only for CeO 2 . Supporting of MeOx produces other sites which can be responsible for efficient O 2 adsorption as well. First of all, these are oxygen vacancies located on the surface of crystalline Fe 2 O 3 , NiO, and Co 3 O 4 particles (Figure 4) detected in the samples or their smaller clusters and on the Me-Ce interface. The relative surface concentration of MeO x is reasonably low (Me/Ce = 0.13 ± 0.1) ( Table 5), but their contribution to the rate of exchange can be prominent. We estimated the values of R I and R II on MeOx normalized to their concentra (Me,Ce) and R II (Me,Ce), respectively) using Me/Ce values on the surface as measured w and supposing overall concentration of active sites as 1.67 × 10 5 mole/m 2 . Then S and rates of reactions of stages 1 and 2 (Scheme 1) for isotope exchange on differe ((r1 = r−1) (Me,Ce) and (r2 = r−2)(Me,Ce)) were calculated as well using Equations (27)-(29) 5). Table 5. Me/Ce (Me = Ni, Fe, Co) atomic ratios in the surface layers (XPS) of different MeO samples, normalized rates of isotope exchange on MeOx and CeO2 (R I (Me,Ce) and R II (Me,Ce)) a of reactions of stages 1 and 2 (Scheme 1) of isotope exchange on different sites ((r1 = r−1) (Me,Ce = r−2) (Me,Ce)). Me concentration-0.86-0.91 wt.%.

Sample
Me/Ce R I (Me,Ce), s −1 R II (Me,Ce), s −1 (r1 = r−1) ( It is logical to suppose that exchange between surface and bulk oxygen on oxid ceeds with the participation of strongly bound oxygen OV. Scheme 3 describes  Table 5. Me/Ce (Me = Ni, Fe, Co) atomic ratios in the surface layers (XPS) of different MeO x /CeO 2 samples, normalized rates of isotope exchange on MeOx and CeO 2 (R I (Me,Ce) and R II (Me,Ce) ) and rates of reactions of stages 1 and 2 (Scheme 1) of isotope exchange on different sites ((r 1 = r −1 ) (Me,Ce) and (r 2 = r −2 ) (Me,Ce) ). Me concentration-0.86-0.91 wt.%.

Sample
Me/Ce R I (Me,Ce), s −1 R II (Me,Ce), s −1 (r 1 = r −1 ) (Me,Ce) , s −1 (r 2 = r −2 ) (Me,Ce) , s −1 We estimated the values of R I and R II on MeO x normalized to their concentration (R I (Me,Ce) and R II (Me,Ce) , respectively) using Me/Ce values on the surface as measured with XPS and supposing overall concentration of active sites as 1.67 × 10 5 mole/m 2 . Then S values and rates of reactions of stages 1 and 2 (Scheme 1) for isotope exchange on different sites ((r 1 = r −1 ) (Me,Ce) and (r 2 = r −2 )( Me,Ce) ) were calculated as well using Equations (27)-(29) ( Table 5).
It is logical to suppose that exchange between surface and bulk oxygen on oxides proceeds with the participation of strongly bound oxygen O V . Scheme 3 describes isotope transfer between gas phase O 2 and ceria bulk (O bulk(Ce) ) for this case.
CoOx/CeO2 0.14 190 23 210 (±7) 2 It is logical to suppose that exchange between surface and bulk oxygen o ceeds with the participation of strongly bound oxygen OV. Scheme 3 desc transfer between gas phase O2 and ceria bulk (Obulk(Ce)) for this case. To keep the general rate of heteroexchange and selectivity to the two-atom exchange observed in the experiments, the rate of stage 3 (Scheme 3) should be at least equal to the sum of the rates of stages 1 and 2, i.e., r surfbulk(Ce) ≥ r 1(Ce) + r 2(Ce) . An additional pathway of isotope transfer between O 2 and ceria bulk appears in MeO x /CeO 2 samples with the participation of MeO x particles (Scheme 4).  This scheme includes two pathways of isotope transfer from the MeOx part Obulk(Се). Spillover of weakly bound oxygen from the MeOx surface to the CeO2 surfa lowed by transfer to CeO2 bulk through Ov(Ce) (stage 3a, Scheme 4) provides for th pathway. By the second pathway (stage 4a), the exchange proceeds first-be strongly bound oxygen of MeOx (OV(Me)) and that in MeOx bulk (Obulk(Me)), and then tween Obulk(Me) and oxygen in CeO2 bulk, Obulk(Се). The overall rate of isotope trans stages 3a and 4a cannot be less than r1(Mе) + r2(Mе).
Numerical analysis of isotope experiments showed that isotope diffusion to th of CeO2 (Os(Cе) ↔ Obulk(Ce)) is not the rate-determining step of the isotope exchange re This agrees with the results of earlier studies performed on ceria [37], where high bility of the oxygen in the lattice than the rate of exchange with the gas phase ha shown. In contrast with CeO2, the rate of isotope exchange of the surface and th oxygen in Fe, Co, Ni, or mixed La-Fe-O oxides is much lower than the rate of exc with gas phase O2 [37][38][39]. So, in the LaFeO3 sample representing a mixture of pero α-Fe2O3, and La2O3, the rate constant of heteroexchange at 800 °C was 8 s −1 , while th of oxygen diffusion in bulk was three orders of magnitude lower (6 × 10 −3 s −1 ). In vice versa, these values were 1.2 s −1 and >0.1 s −1 , respectively [39]. Solsona et al. perf 18 O2 TPIE experiments and showed that the addition of ceria into the NiO cataly creases the diffusion of oxygen in the bulk of the samples [40]. Hence, we suppos the rate of stage 4a in all MeOx/CeO2 samples is negligible compared with the rate o gen exchange on the surface of the MeOx particle.
We tried to estimate whether the rate of stage 3a (Scheme 4) can provide an in This scheme includes two pathways of isotope transfer from the MeO x particle to O bulk(Ce) . Spillover of weakly bound oxygen from the MeO x surface to the CeO 2 surface followed by transfer to CeO 2 bulk through O v(Ce) (stage 3a, Scheme 4) provides for the first pathway. By the second pathway (stage 4a), the exchange proceeds first-between strongly bound oxygen of MeO x (O V(Me) ) and that in MeO x bulk (O bulk(Me) ) , and then-between O bulk(Me) and oxygen in CeO 2 bulk, Ob ulk(Ce) . The overall rate of isotope transfer by stages 3a and 4a cannot be less than r 1(Me) + r 2(Me) .
Numerical analysis of isotope experiments showed that isotope diffusion to the bulk of CeO 2 (O s(Ce) ↔ O bulk(Ce) ) is not the rate-determining step of the isotope exchange reaction. This agrees with the results of earlier studies performed on ceria [37], where higher mobility of the oxygen in the lattice than the rate of exchange with the gas phase has been shown. In contrast with CeO 2 , the rate of isotope exchange of the surface and the bulk oxygen in Fe, Co, Ni, or mixed La-Fe-O oxides is much lower than the rate of exchange with gas phase O 2 [37][38][39]. So, in the LaFeO 3 sample representing a mixture of perovskite, α-Fe 2 O 3, and La 2 O 3, the rate constant of heteroexchange at 800 • C was 8 s −1 , while the rate of oxygen diffusion in bulk was three orders of magnitude lower (6 × 10 −3 s −1 ). In CeO 2 , vice versa, these values were 1.2 s −1 and >0.1 s −1 , respectively [39]. Solsona et al. performed 18 O 2 TPIE experiments and showed that the addition of ceria into the NiO catalysts increases the diffusion of oxygen in the bulk of the samples [40]. Hence, we suppose that the rate of stage 4a in all MeO x /CeO 2 samples is negligible compared with the rate of oxygen exchange on the surface of the MeO x particle.
We tried to estimate whether the rate of stage 3a (Scheme 4) can provide an increase in the rate of heteroexchange in MeO x /CeO 2 compared with CeO 2 . At the known Me/Ce value (Table 5), the rate of transfer of isotope label by stage 3a (Scheme 4) will be not higher than r 2(Ce) /0.11 = 42 (±20) mole/(mole(Me) × s) for any of MeO x /CeO 2 samples. For the case of FeO x /CeO 2 and CoO x /CeO 2, this value is less than r 1(Me) + r 2(Me) ( Table 5). Therefore, one can conclude that the increase of the rate of isotope exchange in FeO x /CeO 2 and CoO x /CeO 2 samples compared with that in CeO 2 is due to sites on the Me-CeO 2 interface characterized by increased concentration of oxygen vacancies promoting oxygen exchange [41][42][43].
For the case of FeO x /CeO 2, this is confirmed with 18 O 2 TPIE experiments on the samples with different Fe content. One can see (Figure 5a) that the increase of Fe content in the sample from 0.86 wt% to 2.5 wt% resulted in a high-temperature shift in the isotope fraction curve, thus evidencing a decrease in the rate of exchange. Non-proportional growth of the Fe/Ce surface ratio (as measured with XPS) from 0.13 to 0.19 only with Fe content in the sample can be due to the enlargement of Fe 2 O 3 particles decreasing the concentration of sites on the Fe-Ce interface. It is interesting that FeO x /CeO 2 sample with higher Fe content was also less active in deN 2 O (Figure 5b). Therefore, reaction on the Me-CeO 2 interface contributes more substantially to the overall reaction rate than that on Fe sites. The results of TG-DTA-MS experiments performed in an oxygen-containi [33] showed that cobalt in CoOx-CeO2 catalysts are present in the form of C particles and a CoOx-CeO2 system formed on the cobalt oxide-ceria interface crease of N2O conversion under oxygen-deficient conditions at T > 800 °C resu the reduction of Co3O4 to CoO in the particles weakly interacting with CeO2. Th therefore, concluded that the activity of these catalysts originates from the inte cobalt oxide with CeO2. A strong dispersion effect of the cobalt spinel active pha over ceria on the turnover rate of deN2O was observed due to the progressive ation of the Co3O4 nanocrystallites into compact domains with the increasing co ing [44]. Model supposing the cylindrical shape of Co3O4 domains permitted no the deN2O reaction rate with respect to the cobalt content and the length of the C interface periphery. The authors proposed a two-step mechanism operating at face, where the redox properties of the cobalt component were responsible for ciation of N2O molecules and formation of oxygen intermediates, whereas the The results of TG-DTA-MS experiments performed in an oxygen-containing stream [33] showed that cobalt in CoOx-CeO 2 catalysts are present in the form of Co 3 O 4 /CoO particles and a CoO x -CeO 2 system formed on the cobalt oxide-ceria interface. The decrease of N 2 O conversion under oxygen-deficient conditions at T > 800 • C resulted from the reduction of Co 3 O 4 to CoO in the particles weakly interacting with CeO 2 . The authors, therefore, concluded that the activity of these catalysts originates from the interaction of cobalt oxide with CeO 2 . A strong dispersion effect of the cobalt spinel active phase spread over ceria on the turnover rate of deN 2 O was observed due to the progressive agglomeration of the Co 3 O 4 nanocrystallites into compact domains with the increasing cobalt loading [44]. Model supposing the cylindrical shape of Co 3 O 4 domains permitted normalizing the deN 2 O reaction rate with respect to the cobalt content and the length of the Co 3 O 4 /CeO 2 interface periphery. The authors proposed a two-step mechanism operating at the interface, where the redox properties of the cobalt component were responsible for the dissociation of N 2 O molecules and formation of oxygen intermediates, whereas the ceria periphery was responsible for the enhanced diffusion and recombination of oxygen adspecies, closing the catalytic cycle.
For the NiO x /CeO 2 sample, we did not observe the effect of the Ni-ceria interface on the rate of oxygen transfer. Indeed, a minimal red shift of the CeO 2 absorption edge was observed in the UV-vis DR spectra of the NiO x /CeO 2 sample compared to that in the CeO 2 (Eg value of 3.35 eV and 3.27 eV, respectively). For the CoO x /CeO 2 and FeO x /CeO 2 samples, Eg values were substantially lower (3.18-3.22 eV) [8]. It indicates that either (1) Fe/Co ions substitute Ce into the CeO 2 lattice, or (2) the isolated Me ions form a mixed Me-Ce oxide and strongly interact with CeO 2 leading to the electronic structure changes [45]. The additional absorption band at~20,000-23,500 cm −1 in the spectra of Co(Fe)O x /CeO 2 samples [8] is due to O 2 adsorption on the structural defect; more obviously, clusters of oxygen vacancies arose on Fe(Co)-CeO 2 interface.

Conclusions
Oxygen transfer on the surface and in the bulk of CeO 2 and MeO x /CeO 2 (Me = Fe, Co, Ni) catalysts was studied using 18 O isotope exchange. The relationship between this process and the kinetics of the reaction of N 2 O decomposition was elucidated.
Supporting of MeO x onto CeO 2 increased the rate of isotope exchange by 20% (Ni), threefold (Fe), and more than ten times (Co). Both single-atom and two-atom exchanges proceed simultaneously in all samples: two-atom exchange predominates in CeO 2 , NiO x /CeO 2, and FeO x /CeO 2 , while the one-atom exchange prevails in CoO x /CeO 2 . One can interpret both types of exchange using a two-step mechanism [14,18,19], considering two forms of surface oxygen. With this mechanism, weakly bound oxygen (O s ) can diffuse on the surface and can transform into a strongly bound form (O v ) after interaction with anionic vacancy. The contribution of every type of exchange to the overall rate of heteroexchange depends on the ratio of the rate of recombination of O s and O v and the rate of their interconversion. The last, in turn, characterizes the mobility of the surface oxygen. We obtained estimates of the surface oxygen mobility in CeO2-based samples using such a model. It turned out that CeO 2 promotion using FeO x and NiO x increases the mobility of surface oxygen, while it doesn't change in the case of CoO x . It is shown that the mobility of surface oxygen can determine the rate of the reaction of N 2 O decomposition on CoO x /CeO 2 . On other samples, it is determined by the rate of N 2 O adsorption.
Detailed analysis of the kinetics of isotope exchange accounting for the surface concentration of MeO x made it possible to estimate their contribution to the rates of different types of exchange and quantify the rates of oxygen transfer from MeOx to the bulk of CeO 2 by different pathways. Oxygen transfer from MeOx to the bulk of CeO 2 realized on the Me-Ce interface is shown to be important in FeOx/CeO 2 and CoOx/CeO 2 and makes a prominent contribution to the overall rate of exchange in these samples. Direct dependence of the rate of isotope exchange in FeO x /CeO 2 samples with different Fe content on the length of the FeO x -CeO 2 interface was shown. The analogous effect was observed for the rate of deN 2 O reaction, which points to the principal role of the interface in both reactions.

Conflicts of Interest:
The authors declare no conflict of interest.
One can express θ S from Equation (A20): and substitute it for Equation (A19): Designating B = k 1 N C N2O /k −2 one can obtain the following quadratic equation: Its solving results in: One can express θ V and (1 − θ V ) from Equation (A25): (1 − θ V ) = 1 1 + B + B + 2Bk 2 /k −1 (A27) Substitution of Equation (A27) to the equation of the rate for stage 1 results in: In the case k 1 N C N2O << k −2 , i.e., stage of N 2 O adsorption is rate-determining, then Equation (A28) can be reduced to:

Appendix D. Determination of the Order of deN 2 O Reaction Rate on FeO x /CeO 2
We used the standard procedure of linearization for logarithmic dependence of the reaction rate on the logarithm of concentration ( Figure A1) to determine the order of reaction for N 2 O. Data of the rates were obtained at two concentrations of N 2 O (0.15% and 1.0%) and three temperatures (600 • C, 650 • C, and 700 • C). The calculated order of the reaction (n) in this temperature interval was close to 1: n = 0.94 (700 • C), n = 1.00 (650 • C), n = 0.91 (600 • C). We did not reveal any dependence of n on the temperature and consider that observed dispersion is due to an error in reaction rate value measuring. The average value of n in this temperature interval is 0.97.