Article pubs.acs.org/JPCC
Kinetics of Catalytic Oxidation of Methane over Palladium Oxide by Wire Microcalorimetry Yuxuan Xin,† Sydnie Lieb,‡ Hai Wang,‡ and Chung K. Law†,* †
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, United States Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, California 90089, United States
‡
ABSTRACT: The kinetics of catalytic oxidation of methane (1−3% in air) over a palladium oxide (PdO) surface was investigated by wire microcalorimetry at atmospheric pressure and over the temperature range from 560 to 800 K. Wire surface structures and compositions were characterized by scanning electron microscopy, X-ray photoelectron spectroscopy, and atom force microscopy. It was found that a porous PdO layer with a constant thickness of 1−2 μm was formed on the Pd wire after it was heat treated in nitrogen followed by air at elevated temperatures. Under the condition of the experiment, the reaction was found to be in the pseudo-first-order regime with respect to the methane concentration. The apparent rate constant of methane oxidation on PdO was determined to be kapp(cm/s) = (3.2 ± 0.8) × 104e−(62.8±1.6)(kJ/mol)/RT for 600 < T < 740 K. Experimental data were analyzed using a gas−surface reaction model proposed previously. Analysis shows that the overall catalytic oxidation rate is governed by equilibrium adsorption/desorption of molecular oxygen, which determines the density of surface palladium sites and dissociative adsorption of methane on these sites. The equilibrium constant of O2 adsorption and desorption was estimated from literature values of desorption energy and molecular parameters of adsorbed oxygen atoms. The rate coefficient of methane dissociative adsorption was estimated to be k16(cm/s) = (7.7 ± 1.6) × 104e−(59.9±1.2)(kJ/mol)/RT, derived from the equilibrium constant of oxygen adsorption over the same temperature range.
I. INTRODUCTION Catalytic combustion of methane over palladium oxide (PdO) catalyst has been studied extensively over the past few decades.1 As an efficient low-temperature reaction process, catalytic combustion serves as a promising alternative to converting energy from natural gas with minimal soot and NOX emission. It is known that the heterogeneous reaction occurs around and above a temperature of 550 K.2−5 Toward higher temperatures, the catalytic activity is impacted by Pd/PdO phase equilibrium. PdO was identified as the stable phase below 1070 K in air under atmospheric pressure.6 Heterogeneous reaction kinetics of methane oxidation over PdO has been examined over supported catalysts2,5,7 and on wires.4 The apparent activation energy was reported to be in the range from 46 to 105 kJ/mol, while reaction orders are close to unity and zero for methane and oxygen, respectively. A Mars−van Krevelen-type mechanism has been widely accepted. Methane interacts with the lattice oxygen on a PdO surface, thus forming adsorbed methyl radicals. Further dissociation of the C−H bonds proceeds rapidly on the catalyst surface, eventually leading to formation and desorption of CO2.8,9 The resulting oxygen vacancy is reoccupied by the oxygen from gas phase or support,10 which completes the catalytic cycle. Initial C−H bond breaking in methane has been proposed as a rate-limiting step in the overall catalytic oxidation process.11−13 Fujimoto et al.14 suggested that methane undergoes physi-adsorption on the surface first and interacts © 2013 American Chemical Society
with neighboring oxygen vacancies, producing surface CH3 and OH species. This mechanism is challenged by the low probability of physi-adsorption to account for the surface reaction rates observed experimentally.2−5 Rather, the initial reaction of methane with the surface probably proceeds through dissociative adsorption on a Pd−O dimer, generating CH3 and OH species bound to the neighboring Pd centers.1,15 Direct observation of dissociative adsorption is difficult to make, because the products react with the neighboring surface oxygen rather rapidly. Theoretically, density functional theory (DFT) has been used to probe the reaction mechanism. Interaction of methane with a single PdO dimer was examined,16,17 and the energy barrier was calculated to be 102.4 kJ/mol. Recently, methane adsorption over a PdO(101) surface was examined. The energy barrier to dissociative adsorption was found to be 64.2 kJ/mol.18 Oxygen adsorption and desorption is another critical process to methane oxidation. The sticking coefficient of O2 was determined over various single- and polycrystalline Pd/PdO surfaces.19−23 Engel19 studied the adsorption of O2 on Pd (111) by a molecular beam technique and identified the temperature and coverage dependency of this process. The sticking coefficient on a bare Pd surface was found to decrease Received: June 12, 2013 Revised: August 30, 2013 Published: August 30, 2013 19499
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measures the heat release rate of a surface reaction. A metallic wire with catalytic activity forms its essential component. Mechanically, the wire is suspended in a closed chamber by two copper columns, which is connected to a dc electrical power. The wire temperature can be determined by its electric resistance. The temperature-dependent resistance of the palladium material was taken from ref 30. In wire microcalorimetry, a background relationship between electric power input and wire temperature is established with the use of an inert gas, typically nitrogen, at a certain pressure. Heat loss from the wire to the surrounding gas balances with the heat produced by resistive heating. Because of an increased rate of heat loss, the steady-state power input increases with an increase in wire temperature, as shown in Figure 1. For a
from 0.5 to 0.25 over the surface temperature from 300 to 800 K. At certain temperatures the sticking coefficient can decrease notably with an increase in surface coverage. Goschnick et al.20 examined the oxygen adsorption on Pd (110) by low-energy electron diffraction (LEED) and mass spectrometry (MS) with surface temperature ranging from 100 to 600 K. They observed a constant initial sticking coefficient of 0.5 above room temperature. Jones et al.21 reported similar results by X-ray photoelectron spectroscopy (XPS) and molecule beam experiments. Matsuchima et al.22 conducted Auger electron spectroscopy (AES) on O2 adsorption on a polycrystalline palladium surface. They reported an initial sticking coefficient of 0.8 at 463 K. Carstens et al.23 examined methane adsorption of methane with PdO supported on zirconia as a function of temperature and reported an apparently lower binding energy for oxygen atoms on a crystalline surface of PdO than on a metallic Pd surface. Recently, catalytic combustion of methane has attracted renewed attention for high-speed combustion. In hypersonic combustion, the local residence time in an engine can be as short as a few milliseconds, which approaches the time scale of combustion reactions.24 Depending on local thermodynamic conditions, this extremely short residence time can be significantly less than the time needed to initiate gas-phase radical processes during the induction time to flame ignition. Nanocatalysis, an approach by which freely suspended nanoparticles induce catalytic surface reaction and local heat release, was proposed to address this problem.25 The concept shares the chemical considerations of traditional catalysis functionalized on a wall, but it differs in the physical aspects of the problem. Catalyst size is substantially smaller than the mean free path of the gas. Hence, the oxidation reaction rate is limited by gas−surface reaction kinetics without complications from mass and heat transfer. In that context, Shimizu et al.25,26 studied the catalytic combustion of methane in a flow reactor by generating PdO nanoparticles in situ from a soluble precursor. They examined the heterogeneous reaction kinetics of methane oxidation over the surfaces of palladium nanoparticles and demonstrated that it is possible to reduce the ignition delay time by 1−2 orders of magnitude compared to homogeneous ignition. Zhang et al.27,28 measured the heat release rate of methane oxidation over a PdO surface by wire microcalorimetry and extracted kinetic parameters from experimental observations. In these earlier studies, a gas− surface reaction model was proposed 25 and improved subsequently based on experimental observations.26−28 Analysis of the data again shows that in the realm of nanocatalysis, the oxidation rate of methane is largely limited by two principal kinetic processes: adsorption and desorption of O2 and dissociative adsorption of CH4. The present work addresses the ambiguous issues in previous wire microcalorimetry measurements and updates the kinetic and thermodynamic parameters of the reaction model. In particular, it is shown that the wire microcalorimetry experiments are able to produce a fundamental gas−surface reaction rate coefficient when they are properly designed and conducted. The rate constant of dissociative adsorption of CH4 was obtained over the temperature range of 600−740 K.
Figure 1. Principle of wire microcalorimetry. Symbols are experimental data; lines are drawn to guide the eye. Difference in power input p with and without methane is directly proportional to the surface heat release rate.
reactive gas, e.g., a mixture of methane and air, undergoing exothermic catalytic reaction on the wire surface, the wire requires a smaller power input to reach the same temperature. The difference in the specific power input (Δp) measures the specific heat release rate due to exothermic surface reactions. Here methane oxidation over a PdO surface was examined at atmospheric pressure and over the temperature range of 560− 800 K. The Pd wire is 10 cm long and 0.01 cm in diameter (99.99%, Aldrich). Methane (99%, Airgas) and high-purity air (21% O2 + 79% N2, Airgas) were used without further purification. The surface composition and morphology of the catalyst wire was examined by scanning electron microscopy (SEM) before and after wire exposure to reactive mixtures at elevated temperatures and X-ray photoelectron spectroscopy (XPS) after exposure to oxygen. SEM analysis was carried out using a XL300 FEG SEM, and XPS measurement was accomplished with a VG Scientific ESCALAB MKII. Additionally, the wire surface fine structure was probed by a Vecco Multimode V AFM operating in tapping mode. Silicon AFM tips used in this study have a nominal radius of 9 ± 2 nm and a sidewall inclination of 35°.
II. EXPERIMENTAL SECTION Wire microcalorimetry has been described in detail elsewhere.27−30 For a given gas-phase composition, pressure, catalytic material, and surface temperature, microcalorimetry
III. NUMERICAL SIMULATION Gas-phase composition and surface temperature may be assumed to be invariant along the length of the catalyst wire 19500
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2% CH4−air mixture scanning from 500 to 800 K over a 1 h period. Morphologically, the wire surface evolved from a polycrystalline structure to a porous layer 1−2 μm in thickness. XPS analysis in that surface region shows both Pd and PdO crystal structures. Because the reactive mixture is extremely fuel lean, there is a sufficient amount of gas-phase molecular oxygen in constant contact with the surface. The reaction oxidized the surface to form PdO, as expected from thermodynamic considerations.6 Modification of the surface resulting in an increase in the surface area poses a notable challenge in data interpretation. In a previous study,27 the surface area was only estimated on the basis of experimental work reported by Rieo et al.4 Using scanning tunneling microscopy and 18O isotope exchange they observed a fact of 2−3 increase in the surface area upon oxidation of a Pd surface to PdO. In the current work, however, the surface area change was carefully examined. Furthermore, a method was developed that pretreats the surface of as-received wires to achieve reliable and repeatable microcalorimetry results, as discussed in what follows. The wire was first heated in quiescent nitrogen at the surface temperature of 900 K for 1 h, followed by a 2% methane−air mixture at the same temperature for another hour. This pretreatment produces a porous PdO layer 1−2 μm in thickness whose catalytic activities were reproducible over the reactant and temperature ranges of interest. We used a two-step procedure to determine the surface area. As shown in Figure 4, SEM analysis shows that the wire as received (wire a) has a polycrystalline surface that is smooth at the micrometer level, but at a finer scale AFM probing shows ∼100 nm surface islands and ∼10 nm crystal grains and steps. The surface area of the untreated wire was determined by integrating the locally rough surfaces as determined by AFM, which gives a value 1.7 times that of an ideal cylinder. Unfortunately, SEM is not able to determine the surface area of the wire treated in CH4−air mixtures. Figure 4 shows surface pores that were formed during wire treatment in a 2% CH4−air mixture (wire b). The wire pretreated in 6% CH4 in air at 900 K for 1 h has an even greater porosity and surface area (wire c). Surface pores have a feature size around 100 nm, but the depth and distribution of the pores under the surface is difficult to determine. Hence, the surface area has to be measured indirectly using an alternative method. Comparison of the specific heat release rates for 2% CH4 oxidized in air using wires a and b reveals the surface area difference between them. For wire a, microcalorimetric data can be obtained reliably only under 650 K. Above this temperature,
given its large length-to-diameter aspect ratio. To examine buoyancy-induced natural convection in the chamber, fluid simulation was conducted using FLUENT by assuming axisymmetry, as shown in Figure 2. The wire was represented
Figure 2. Schematic of the computational domain. Boundary conditions: T = 300 K, P = 1 atm, and fresh reactant mixture.
by an ideal cylinder. The square domain size is 70 times the wire diameter. An increase in the domain size has a negligible effect on simulation results. The boundary temperature and pressures are T = 300 K and P = 1 atm, respectively. The reactive mixture is quiescent on the boundaries. Additional details may be found in ref 27. The Rayleigh (Ra) and Nusselt number (Nu) were calculated from pure air environment as a function of the wire surface temperatures. The relationship between these two dimensionless numbers was compared to the empirical expression for a natural flow with a reasonable agreement. The gas-phase chemistry is described by USC Mech II.32 For surface chemistry, a previously available model28 was refined here as will be discussed later.
IV. RESULTS AND DISCUSSION The surface of the catalyst wire undergoes chemical and morphological changes when it was exposed to oxygen or mixtures of methane and oxygen. Figure 3 shows SEM images of the cross sections of a Pd wire before and after it was employed in a wire microcalorimetry experiment, which used a
Figure 3. Scanning electron microscopy images of the wire cross sections before (left) and after (middle) exposing the wire in a 2% CH4−air mixture, scanning from 500 to 800 K, at 1 atm for ∼1 h. XPS spectrum of the wire (right). 19501
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Figure 4. Atomic force microscopy of untreated Pd wire surface (upper left) and scanning electron microscopy images of (a) untreated Pd wire surface and (b and c) wire surfaces treated in 2% CH4− and 6% CH4−air, respectively, at 900 K and 1 atm for approximately 1 h.
surface is expected to cause greater diffusional resistance to reaction. Yet, over the 600−670 K temperature range the ratio of specific heat release rates of wire c to wire b is a constant (cf. the inset of Figure 5). Had the reaction been limited by mass transport or heat transport, one would expect the heat release rate to decrease as the temperature is increased, as is the case for observations made above 670 K. The above analyses allow us to define the surface area by combining the AFM measurement with the result of reactive area measurements, leading to a surface area enhancement of 3.5 for wire b compared to an ideal cylinder. The apparent reaction rate may now be defined as
drastic surface morphological change accompanies the catalytic reaction and the surface sublayer undergoes oxidation in addition to surface reactions leading to methane oxidation. As shown in Figure 5, in the temperature range of 600−670 K the ratio of wire b to wire a is around 2 for the specific heat release rates measured. This difference can only be attributed to an increase in the surface area. Within the same temperature range, the reaction is expected to be kinetically limited. Evidence supporting this fact comes from experiments with 2% CH4 oxidized over the surface of wire c at 900 K for 1 h. Such a
ωapp =
Δp = kapp[CH4]n 3.5ΔHr(T )
where ΔHr(T) is the enthalpy of combustion of methane (lower heating value). Hence, measurement of the apparent reaction rate allows us to determine the apparent rate constant kapp and the overall reaction order n with respect to the concentration of CH4. Figure 6 shows the variations of the specific heat release rate and the apparent reaction rate ωapp as a function of temperature for 1%, 2%, and 3% CH4 oxidized over the surface of wire b in air. Within the range of temperature and CH4 concentrations tested, the catalyst surface retained its composition and surface morphology after reaction, and the results shown in the figure are highly reproducible. The overall reaction order n with respect to the CH4 concentration may be obtained from the slope in a plot of log ωapp versus log[CH4]. Figure 7 shows the n values as a function of wire surface temperature. We found n = 1.03 ± 0.03, independent of temperature over its range tested. Since O2 concentration in the unreacted mixture is substantially
Figure 5. Specific heat release rates measured for oxidation of 2% CH4 in air over several wire surfaces. Wire surface area is assumed to be that of a perfect cylinder. Symbols are experimental data; lines are drawn to guide the eye. Measurements over the untreated Pd wire are unstable above 650 K. (Inset) Ratios of specific heat release rates. 19502
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Figure 6. Heat release (top) and surface reaction (bottom) rates determined for oxidation of CH4 in air over PdO surface. Symbols are experimental data; lines are drawn to guide the eye.
Figure 8. Apparent specific reaction rate versus methane concentration. Symbols are experimental data; lines are fits to data assuming the reaction order n = 1 with respect to methane concentration.
Figure 7. Reaction order n determined for CH4 oxidation in air over a PdO surface. Symbols are experimental data determined at each temperature; line represents the average of the data over the temperature range shown.
higher than that of CH4, the heterogeneous reaction occurs as a pseudo-first-order reaction. The apparent rate constant kapp may be obtained as the intercept by fitting the measured reaction rate as log ωapp = log kapp + log[CH4], as shown in Figure 8. The resulting rate constant value is plotted as an Arrhenius plot as seen in Figure 9. The rate constant may be expressed as kapp(cm/s) = (3.2 ± 0.8) × 104e−(62.8 ± 1.6)(kJ/mol)/ RT for 600 < T < 740 K Figure 9. Arrhenius plot for the global oxidation reaction of CH4 in air over a PdO surface. Symbols are experimental data; line represents a simple Arrhenius fit to data.
where R is the universal gas constant. The value of the apparent activation energy is consistent with those reported in previous studies.2−5 Though it is measurable, the amount of heat release below 600 K is too small to obtain an accurate rate constant. Above 740 K, the rate constant appears to fall off as the temperature increases, which is indicative of the mass transport limitation. The surface reaction model used here is largely derived from that in refs 26 and 28, as shown in Table 1. The model is established based on experiments conducted on the surfaces of nanoparticles and wires, for which the support effect cannot be taken into account. Consequently, the model is not applicable to supported catalysts. As in previous studies, critical reactions were identified by a sensitivity analysis. The overall oxidation rate was found to be sensitive to the reversible O2 adsorption and desorption O2 + 8Pd(S) ⇄ 2O4 (S)
and methane dissociative adsorption k16
CH4 + O4 (S) + Pd(S) → CH3(S) + OH 4(S) k 2f
O2 + 8Pd(S) ⇄ 2O4 (S) k 2b
(R16)
The sensitivity coefficients of these reactions are more than an order of magnitude greater than those of other reactions over the entire range of temperature and methane concentration considered. We focus on deriving the rate parameters of R2f, R2b, and R16. In the current model, the rate coefficient of O2 adsorption is described in the form of sticking coefficient γ
(R2) 19503
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γ0(T ) = e−T /540
Table 1. Surface Reaction Model of Methane Oxidation over PdO above 450 K
The surface coverage dependency is attributable to the fact that each O atom occupies four surface Pd sites.1 Hence adsorption of each O2 requires at least four adjacent sites that are available. The number of these adjacent sites decreases exponentially as the surface coverage increases. The function F(θ) was computed here by a Monte Carlo simulation in which O atoms are randomly distributed over a surface. The number density of four empty adjacent sites is counted and normalized by that of a bare Pd surface. The results are shown in Figure 10. The correlation may be described quantitatively as
rate parametersb no.
reactiona
A
β
E
1f 1b 2f 2b 3f
H2 + 2Pd(S) → 2H(S) 2H(S) → H2 + 2Pd(S) O2 + 8Pd(S) → 2O4(S) 2O4(S) → O2 + 8Pd(S) H(S) + O4(S) → OH4(S) + Pd(S) OH4(S) + Pd(S) → H(S) + O4(S) H(S) + OH4(S) → H2O4(S) + Pd(S) H2O4(S)+Pd(S)→ H(S)+OH4(S) 2OH4(S) → H2O4(S) + O4(S) H2O4(S) + O4(S) → 2OH4(S) H + Pd(S) → H(S) H(S) → H + Pd(S) O + Pd(S) → O4(S) O4(S) → O + Pd(S) OH+Pd(S)→OH4(S) OH4(S)→OH+Pd(S) H2O + Pd(S) → H2O4(S) H2O4(S) → H2O + Pd(S) CO(S) + O4(S) → CO2 + 5Pd(S) C(S) + O4(S) → CO(S) + 4Pd(S) CO + Pd(S) → CO(S) CO(S) → CO + Pd(S) CH3(S) + 3Pd(S) → C(S) + 3H(S) CH3(S) + 3O4(S) → C(S) + 3OH4(S) CH4 + 2Pd(S) → CH3(S) + H(S) CH4 + Pd(S) + O4(S) → CH3(S) + OH4(S)
1.0c 5.33 × 1016 e−T/540−8.8θdc 3.01 × 1026 2.91 × 1018
−0.5 0.992 0.0 −0.5 1.264
0 87.4 0 230.0−120θd 94.6−60θd
2.29 × 1019
1.156
120.3−30θd
6.56 × 1015
1.403
31.8
2.11 × 1018
1.134
83.8 + 30θd
3.89 × 1017
1.244
14.5 + 60θd
1.40 × 1019
1.1
40.7 + 60θd
1.0c 1.32 1.0c 1.64 1.0c 1.60 1.0c 1.62 1.00
× 1010 × 1019
0 1.1 0 1.1 0 1.1 0 1.1 1.115
0 261.7 0 369.7−60θd 0 227.5−30θd 0 43.8 59.8
1.01 × 1019
1.115
62.8
1.0c 1.65 × 1011 1.07 × 1019
0 1.1 1
0 134.0 85.1
1.07 × 1019
1
25.1
5
4.00 × 10
0
196.0
7.70 × 104
0
59.9
3b 4f 4b 5f 5b 6f 6b 7f 7b 8f 8b 9f 9b 10 11 12f 12b 13 14 15 16
× 1010 × 1010 × 1010
F(θ ) = e−8.8θ
Figure 10. Surface coverage dependency of O2 on a Pd/PdO surface. Symbols are results of Monte Carlo simulation; line is a fit to data.
Desorption of O2 from a PdO surface may be determined from the adsorption rate constant and the equilibrium constant of the reversible reaction k 2f
O2 + 8Pd(S) ⇄ 2O4 (S)
a
k 2b
Pd site occupancy of O(S), OH(S), and H2O(S) is set to 4. Surface site density is 1.95 × 10−9 mol/cm2. bRate constant is written in the form k = ATβe−E/RT. Units of A are given in terms of mol, cm, and s. E is in kJ/mol. cSticking coefficient. dθ is the total occupied site fraction, i.e., θ = 1 − θPd.
The enthalpy of reaction was taken to be 230 kJ/mol.33 The heat capacity cp and entropy s of surface oxygen may be derived from34 cp
kT k 2f = γ 2πmO2
R
3N − 6
=
s = R
where mO2 is the molecular mass of O2 and k is the Boltzmann constant. On the basis of previous studies,19−23 the sticking coefficient on a bare Pd surface is close to 0.5 at room temperature, which decreases with an increase in surface temperature and coverage. The current model considers the influences of both the surface temperature and the coverage on the sticking coefficient as the product of two functions
∑ i=1 3N − 6
∑ i=1
⎛ hνi ⎞ (hν / kT ) (hν / kT ) ⎜ ⎟e i [e i − 1]−2 ⎝ kT ⎠ ⎡⎛ hνi ⎞ (hν / kT ) ⎤ − 1]−1 − ln(1 − e−(hνi / kT ))⎥ ⎢⎜ ⎟[e i ⎣⎝ kT ⎠ ⎦
where N is the number of atoms in a species, h is Planck’s constant, and νi’s are the vibrational frequencies taken from refs 35 and 36. Figure 11 shows the equilibrium constant computed in this work. A comparison with the earlier work of Deutschmann et al.37 shows reasonably good agreement between the two studies. The discrepancy is the result of a somewhat larger enthalpy of adsorption used in ref 37 and to a lesser extent updated vibrational frequency values used in the present work. Calculation of the equilibrium constant just discussed ignores the impact from surface coverage and thus is valid for a bare Pd surface only. With an increase in coverage, adsorbed oxygen
γ = γ0(T )F(θ )
where γ0(T) is the sticking coefficient on a bare Pd surface and F(θ) accounts for the dependency on coverage. From a molecule beam experiment of O2 adsorption on Pd (111) surface,19 γ0(T) may be given as 19504
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agreement the DFT energy barrier of 64.2 kJ/mol for CH4 dissociative adsorption of over a PdO (101) surface.18 The above rate expression, along with the reaction model of Table 1, gives heat release rates closely matching the experimental observation for all three CH4 concentrations, as seen in Figure 13. Analysis of the computational results
Figure 11. Equilibrium constant of O2 adsorption on a bare Pd surface. Solid line, this work; dashed line, ref 37
becomes less stable, leading to a significantly reduced enthalpy of adsorption. In the gas−surface reaction model proposed by Wolf et al.38 the enthalpy of oxygen adsorption on a Pd/PdO surface is linearly proportional to surface oxygen coverage. In addition, the adsorption enthalpy of O2 on a fully covered surface was chosen to be 110 kJ/mol. The same value was used in the current work. As in a previous study,26 the variation of the enthalpy of O2 adsorption was assumed to be a linear function with respect to coverage using the value just mentioned as the limit for a fully covered surface and 230 kJ/mol for a bare surface. The rate expression for reaction R16 was determined from the experimental heat release rates observed for 2% CH4 in air to be
Figure 13. Heat release rates measured (symbols) and predicted (lines) for oxidation of 1−3% CH4 in air.
suggests that under the experimental conditions tested the reaction is largely kinetically controlled without complications from buoyancy-induced natural convection or gas-phase species concentration gradients near the surface of the catalyst wire. Under this condition, the overall rate of methane oxidation over a PdO surface is governed by dissociative adsorption of methane, as expected, with the reaction rate given by
k16(cm/s) = (7.7 ± 1.6) × 104e−(59.9 ± 1.2)(kJ/mol)/ RT for 600 < T < 740 K
−
The results are plotted in Figure 12. The above rate expression is subject to uncertainties in the equilibrium constant, the rate constant of O2 adsorption, and to an extent the surface area discussed earlier. We note that the activation energy is in close
d[CH4] = k16[CH4]θ O4 (S)θPd(S) dt
Neglecting surface species other than O4(S), this expression can be simplified to −
d[CH4] = k16[CH4]θ O4 (S)(1 − θ O4 (S)) dt
With or without reaction R16, the θO4(S) value changes by
