J. Phys. Chem. 1993,97, 216-222
216
Origin of Kinetic Isotope Effects during the Oxidative Coupling of Methane over a Li+/MgO Catalyst Chunlei Shi, Mingting Xu, Michael P. Rosynek, and Jack H. Lunsford' Department of Chemistry, Texas A&M University, College Station, Texas 77843 Received: June 15, 1992; In Final Form: September I , 1992
Kinetic isotope effects (KIEs) during the oxidative coupling of methane over a Li+/MgO catalyst a t 700 OC have been determined using several different experimental methods and by a reaction model that includes both heterogeneous and homogeneous reactions. By maintaining a constant partial pressure of methane of 190 Torr and changing the partial pressure of oxygen, a variation in the H / D KIE, based on differing rates of C H 4 and CD4 conversion, was observed. In addition, a similar variation in KIE was found from the isotopic distribution of H and D in the ethane product when CH4 and CD4 were co-fed into the reactor. The decrease in KIE with increasing methane-to-oxygen reactant ratio is evidence that a unique rate-limiting step does not exist; rather, the rates of methane activation and of oxygen incorporation, as individual steps, are comparable. Other factors, such as the absolute partial pressures of the reagents may become even more important than the methaneto-oxygen ratio under some conditions. When N20 was used as the oxidant instead of 02 and normal catalytic conditions were employed, the observed KIE was unity, even though the N20 was present in excess. In this case, a unique rate-limiting step was operative, viz., the incorporation of oxygen into the lattice. The KIE was also determined separately for the production of methyl radicals, but these experiments were carried out a t much lower reagent partial pressures (40). This result confirms that there is a KIE associated with the activation of methane on the surface but that this is not necessarily a unique rate-limiting step. With N20 as the oxidant, it was possible to vary the methane-to-nitrous oxide ratio over a large range (from 0.29 to 44). At low ratios, the KIE was 1.9 f 0.2. The former appears to be a case where methane activation a t the surface is uniquely rate-limiting. In general, the oxidative coupling of methane over Li+/MgO is not characterized by a unique rate-limiting step; however, rate-limiting cases may be found, particularly with N20 as the oxidant.
Introduction The mechanistic framework for the oxidative coupling of methane to form ethane and ethylene (C2 products) is now generally accepted to be one in which methyl radicals are formed on the surface and then subsequently couple in the gas phase.Iv2 The catalytic cycle involving the surface may be described as follows: CH,
+ 0,-(or 1/202,2-)
-
CH,'
+ OH,-
(1)
It should be noted that reaction 3 is not a single elementary step. It involves several reactions, including the dissociation of 02, electron transfer, ionic mobility, etc., but in the absence of details on these processes they are consolidated into one reaction. For catalysts such as Li+/MgOor Na+/CaO, there is evidence that 0,ions are responsible for the activation of CH4;3-5however, for catalysts such as Na+/La203, Na+/CaO, and Ba2+/La203, it appears that 0 2 s 2 - ions serve as the active form of oxygen.69' Because 0,derived from N20 reacts with CH, at temperatures as low as -135 OC, it was previously suggested that, at the temperatures of the catalytic reaction (620-720 OC), reaction 1 would not be the rate-limiting step in the cycle. Moreover, it was shown that the peroxides, Na202 and Ba02, activate CHI to form C2H6 at 400 OC, although not in a catalytic cycle.* By contrast, kinetic isotope effect (KIE) studies, first carried out by Cant et aL9andmorerecent1yby that groupandothers,l*l3
* To whom correspondence should be addressed. 0022-3654/ 58 /2097-02 16$04.00/0
indicate that a C-H bond is being broken in the rate-limiting step. (Here, the KIE is based either on the rate of disappearance of methane or the rate of formation of methyl radicals.) On the basis of experiments in which D2O or H20 were co-fed with CH4 and 02, and no KIE was observed, it was concluded that the breaking of a C-H bond, rather than an 0-H bond, was responsible for the KIE.9 Thus, it has been concluded by several groups that reaction 1 is rate-limiting, not only with Li+/MgO but also with Sm203, SrCO3(SrO), and N a / M n 0 , / S i 0 2 catalysts.9-13 Since the catalytic oxidation of methane involves a complex set of heterogeneous and homogeneous reactions, of which reactions 1-3 constitute only a small subset, it is important to explore other possibleoriginsof the observed KIEs. For example, Kung14 has considered the catalytic oxidation of hydrocarbons in general and has shown that a KIE may occur when the ratelimiting step is the reoxidation of the catalyst (reaction 3). This situation arises when the selectivity for the hydrocarbon product is greater with the H-labeled molecule than with the D-labeled molecule. Although this condition is indeed met for the case of methane oxidation, it will be demonstrated below that the predicted KIE is small compared to the one actually observed. As a second possibility, we suggested that the observed KIE could result from homogeneous rea~ti0ns.I~That is, surfacegenerated CH3' radicals might initiate chain-branchinggas-phase reactions that result in the consumption of a considerablefraction of the CH4. In such a case, reaction 1 might not be rate-limiting, but a KIE would be observed. Using a kinetic model described below we have shown that under the conditions of a "normal" catalytic reaction (Le., over Li+/MgO at 700 "C), the extent of the gas-phase conversion of CHI would never exceed 15% of the surface conversion.16 This amount is not adequate to account for the observed KIEs. In this paper, additional results will be described that elucidate 0 1993 American Chemical Society
The Journal of Physical Chemistry, Vol. 97, NO. 1, 1993 217
Kinetic Isotope Effects during Methane Oxidation the relative rates of reactions 1 and 3. It should be noted that there need not be a single rate-limiting step, as is often assumed, but in fact, two or more steps may have comparable rates. Moreover, the rate of a particular step will involve a number of factors, including the temperature and the concentration of reagents. For example, the relative rates of reactions 1 and 3 depend on the partial pressures of CH4 and 02,respectively. By observing the KIE as a function of the methane-to-oxygen ratio, it should, therefore, be possible to determine whether there is a unique rate-limiting step over the range of conditions studied. In addition, based on the KIE observed for methyl radical formation (reaction l), other factors, such as the effect of alternative pathways for the consumption of methane, can be eliminated. Finally, the variation in KIE upon substituting NzO for 0 2 is instructive, as the rate of oxygen incorporation could be very different for the two oxidants.
Experimental Section The Li+/MgO catalyst used in this study was similar to that described previous1y.I The lithium was introduced as Li2CO3 to an aqueous slurry that contained MgO. The resulting material was calcined at 750 OC for 16 h and then sieved to 20-42-mesh particles. The catalyst contained 4.1 wt Q Li. The conventional catalytic experiments were conducted at 1 atm total pressure in a single-pass U-shaped fused-quartz flow reactor, with the catalyst bed located in the outlet section of the reactor. The reactor was mounted vertically and was heated with a crucible furnace. The catalyst (0.5 g) was placed between layers of fusedquartz chips which served to minimize the postcatalytic reactor volume and, hence, the purely homogeneous oxidation reaction. A thermocouple was placed adjacent to the outer wall of the reactor at the level of the catalyst bed. The feed gases, consisting of CH4 (Matheson, UHP), O2 (Matheson, Extra Dry), NzO (Matheson, CP), and He (Airco, CP), were used without further purification. The isotopically labeled gases used in this study were CD4 (99.9 atom 9%D) and CzD6 (99.9 atom 5% D). Both were obtained from MSD Isotopes. Individual gas flow rates were controlled to f0.1 mL/min using Scott mass flow controllers. Prior to each experiment, the catalyst was first pretreated by heating it to the reaction temperature in flowing 0 2 for 0.5 h. The reaction mixture of methane and oxygen, diluted with helium to achieve a total pressure of 1 atm, was then passed over the catalyst. With N20 as the oxidant, no He was used as a diluent. The valving of the reactant gas supply allowed either partial or complete substitution of CH4 by CD4. The effluent gas was analyzed by GC, using a Porapak R (80-100-mesh) column and a thermal conductivity detector. Thesystem wascalibrated usinga standard gas mixture (Matheson) having a composition similar to that of a typical product mixture. Experiments were carried out at relatively low oxygen conversions ( 1 for these very large ratios is surprising, in view of the KIEs obtained in the more conventional catalytic experiments. These differences are even more apparent with N20 as the oxidant. In the conventional reaction with N20, the KIE was nearly unity, indicating that oxygen incorporation is rate-limiting. At a similarly small methane-to-nitrous oxide ratio in the MIESR experiment, with frozen nitrous oxide serving as the matrix, (Table IV expt 1) a KIE of 1.9 was observed, which is in agreement with the theoretical limit at 700 OC.26 In this case, methyl peroxy rather than methyl radicals were mainly detected in the matrix, which indicates that some of the N20 formed 0 2 over the catalyst. The actual amount of O2generated may be small, however, since even a methane-to-oxygen ratio of 44:l gives rise to methyl peroxy radicals during the formation of the matrix (see above). The value of 1.9 for the KIE is believed to be related to the large N20 pressure, not to the small amount of 02 in the system. In the MIESR experiment with 02, the effect of changing the methane-to-oxidant ratio was not evident; however, with N2O the effect was more pronounced. When the methane-to-nitrous oxide ratio was changed from 0.29 to 44, the KIE decreased from 1.9 to 1.2. With the larger ratio, only methyl radicals were detected in the matrix. Actually, the value of 1.2 is not significantly different from unity. This change in KIE indicates a clear change in rate-limiting step from C-H bond breaking to oxygen replacement in the catalyst. Moreover, the results of CH3'~roductionrate with respect to N20 partial pressure, which are shown in Figure 4, fit nicely with the KIE results; i.e., at high NzO pressures, the rate is limited by CH4 activation, while at low N20 pressures, it is limited by oxygen incorporation. Kinetic Heterogeneous-Homogeneous Model for Metbane Oxidation. A coupled heterogeneous-homogeneous kinetic model for methane oxidation over Li+/MgO at 700 OC was developed to interpret the KIE results of Figures 2 and 3. Certain aspects of the model, particularly with respect to the limiting C2 yield and the effects of the homogeneouscomponent on CH4 conversion and CZselectivity, have been reported elsewhere.16 The salient features of the model and the results with respect to the KIE will be given here. The model includes in its heterogeneous cycle reactions 1-3 above. Reaction 1 is the major source of CH3' or CD3' radicals in the gas phse, and these radicals initiate chainbranching reactions. The 156 reactions used to describe the homogeneous part of the mechanism are given in Table V. Zanthoff and Baernsz3have recently published a model that is similar to the one that was adopted here. Rate constants were obtained from the National Institute of Science and Technology (NIST) data base.24 The ACUCHEM computer programz5was used to determine the concentrations of all relevant species as a
reaction
+ + +
log(&
+
(153) CO H02 =CO2 OH (1 54) CO 02 C02 0 (155) C02 H CO OH (156) CO2 + 0 = CO 0 2
+ +
14.18 12.40 14.18 13.23
+
n 0.00 0.00
0.00 0.00
Ea/R 11900 24000 13300 26500
function of time, from which rates of conversions and selectivities could be calculated. The KIEs for all C-H and 0-H bondbreaking reactions (both heterogeneous and homogeneous) were taken to be 1.8 and 2.1, respectively. These values were obtained from eq 2-12 of ref 26. One unique feature of this model was the manner in which the reaction
H,O,
-
20H' + M
H,O
+ 1/ 2 0 ,
+M
(4) was treated. We have previously shown that the introduction of quartz rings into an open volume (no catalyst) decreased the conversion of CH4 by almost 1 order or magnitude, even though the residence time was con~tant.~'This phenomenon was taken as evidence that the reaction
H,O,
-
(5)
competed favorably with reaction 4 and, in doing so, removed OH' radicals from the system. It is known that the heterogeneous decomposition of H202, even on a quartz surface, is a facile reaction at elevated temperatures.28 By assuming a rateconstant of k = 3.6 X 10, s-I for reaction 5 , the effects of adding the quartz rings could be adequately accounted for. Increasing this rate constant by several orders of magnitude did not substantially decrease the calculated CH, conversion. Thus, in the catalytic system, reaction 5 was included with the indicated rate constant. In the heterogeneous cycle reaction 3 was replaced by k6
0,F? 20,-
(6)
k+
for computational purposes. The rate constants for these heterogeneous reactions are not known a priori; therefore, they were determined by comparison with the results reported in Table I. In the model, the rate constants were varied so as to optimize the agreement with the methane conversions, CZ selectivities, and KIEs at two methane-to-oxygen ratios. The rate constant for reaction 2 was made very large (k2 = 1.0 X 10-5 cm3/ molecule/s for OH- reacting), and the rate constants k l , k6, and k-6 were varied such that (i) the calculated and observed CH4 conversions agreed at a CH4/O2 ratio of 2, and (ii) the calculated variation in KIE with methane-to-oxygen ratio agreed with the experimental results reasonably well. Using values for kl,k6,and k4 of 5.22 X 10-16 cm3/molecule/ s, 1.40 s-l, and 1.02 X lO-I3 cm3/molecule/s, respectively, the dotted curve (approaching the open circle) in Figure 2 was obtained. Again for computational purposes, the heterogeneous reactions were treated as homogeneous reactions with respect to units. These are the same values used in our previous communication.16 Upon making ks = 2.04 s-1 and k-6 = 1.5 X 10-13 cm3/molecule/s, the dashed curve was obtained. By increasing the methane partial pressure from 190 Torr (as was used in the calculationsdescribed above) to 585 Torr, at a methane-to-oxygen ratio of 10, the KIE decreased from 1.2 to 1 1. This demonstrates that the KIE is a function of the total reagent pressure, as well as the methane-to-oxygen ratio. If k6 and k-6 are made much smaller (e.g., k6 = 0.53 s-I and k-6 = 1.0 X lo-" cm3/molecule/ s), the KIE does not change with respect to the methane-tooxygen ratio. That is, the reaction becomes strictly rate-limited by reaction 3, and a KIE of 1-03was calculated. One of the most significant results of the model is its ability to reproduce, in a functional sense, kinetic data obtained by Roos I
222
The Journal of Physical Chemistry, Vol. 97, No. 1, 1993
et They found that the CH4 conversion rate followed a first-order dependence with respect to 0 2 and a complex dependence with respect to CHI. The latter was approximately first-order at lower pressures and zero-order at higher pressures. The transition occurred at a CH4 partial pressure of ca. 150 Torr. This functional relationship is consistent with the comparable rates of reactions 1 and 3 (or 6 ) . For example, when ks and k-6 were made much smaller, as described above, the reaction became zero-order with respect to CH4 over most of the pressure range. The transition from first-order to nearly zero-order at about 150 Torr no longer occurred. Although the homogeneous reactions have very little direct effect on the KIE, they significantly influence the C2 selectivity. In so doing, they alter the concentration of O2that is available for incorporation into the lattice. In this respect, the recent discussion by Kung14 concerning the origin of KIEs should be considered. Kung has recently pointed out that a KIE > 1 is possible even though a reaction may be rate-limited by a reoxidation step. This will occur if the selectivitywith the D-form of the hydrocarbon is less than that with the H-form, a criteria which is met in the present study (Table I). The magnitude of the KIE will depend on the stoichiometry of the nonselective reactions and the selectivity difference. Qualitatively, the origin of the effect results from the fact that the amount of oxygen is limited, and more of it is required to react with D-labeled molecules than with H-labeled molecules. Hence, more CHI reacts than does CD4. But when the calculation was carried out using the data in Table I for a methane-to-oxygen ratio of 4, it was found that the KIE due to this phenomenon was only 1.06. Thus, in the case of the oxidative coupling reaction, other factors must be responsible for the observed KIEs.
Conclusions The variation in KIE with respect to methane-to-oxygen ratio is evidence that, under most conditions, the rate of formation of CH3*radicals at the surface, as a separate reaction, is comparable to the rate of incorporation of oxygen into the lattice, Le., the regeneration of the active center. (Of course, in a catalytic cycle the net rate of all reaction steps must be equivalent.) Therefore, there is no unique rate-limiting step. The relative rates of the methane activation step and the oxygen incorporation step, however, may depend on a number of factors, such as the total pressure of the reagents. The effect of temperature has not been specifically addressed, although this variable also should be important. With N20 as the oxidant, the presence of distinct rate-limiting steps is more evident. At pressures used in conventional catalytic reactions, e.g., 190 Torr of CH4, oxygen incorporation into the lattice is rate-limiting, even though there is a large excess of N;O. By contrast, at much lower pressures, e.g., 0.4 Torr of CH4, but again with a large excess of NzO, the rate-limiting step is the formation of CH3' radicals at the surface. This shift in the
Shi et al. rate-limiting step is evidence that the total pressureof the reagents can be a factor in modifying the relative rates of the individual steps in the catalytic cycle. A model of the coupled heterogeneous-homogeneous network of reactions involved in the oxidation of CH4 confirms that the observed KIEs are not a result of homogeneous reactions, but rather they appear to result from competitive reaction rates as noted above. The KIEs also do not result from oxygen-limited reactions having different COXselectivities for CH4 and CD4.
Acknowledgment. The authors acknowledge financial support of this research by the National Science Foundation under Grant No. CHE-9005808. The authors are also grateful to Professors Cant and Kung for making their manuscripts available prior to publication. References and Notes (1) Ito, T.; Wang, J.-X.; Lin, C.-H.; Lunsford, J . H. J . Am. Chem. SOC. 1985, 107, 5062.
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