534
J . Phys. Chem. 1986, 90, 534-537
energy is not the result of a vibrational mode with predominantly hydrogen atom character, but is a reflection of the weak coupling of H atoms to the TO3framework modes. The smaller root mean square atomic displacement associated with the zeolite framework gives rise to the lower intensity observed at this frequency. Less clear is the origin of the inelastic feature at 360 cm-'. No vibrational frequencies in this spectral range are generated by the normal mode analysis, which in fact is not reliable at such low energies. The intensity of this peak suggests a large-amplitude vibration. One possibility consistent with this is an oxygen-hydrogen torsional motion, but no more definitive statement may be made in the absence of further data. Heating of the acid Rho samaple to 548 K causes major reversible changes in its inelastic spectrum (see Figure 2). Considerable intensity is lost from the scattering features which are dominant at room temperature. Of greatest interest is the appearance of a new energy loss centered at 260 cm-l, the size of which is characteristic of a large-amplitude hydrogen motion. Some new site apparently is populated at higher temperature; the overall changes in the spectrum suggest a transfer of some significant fraction of the hydrogen atoms to different lattice sites. Removing the noncentrosymmetric distortion of the zeolite structure by heating therefore leads to a change in bonding of proton to the oxide. Quasi-elastic neutron scattering spectra were recorded in order to study diffusion of hydrogen on the zeolite framework. These experiments were suggested by the apparent site-to-site proton transfer observed at elevated temperatures. Diffusion on partially dehydroxylated acid Rho (H/AI = 0.5) has been examined; no water loss from the lattice of this sample would be expected even on prolonged heating. The dehydroxylated zeolite exhibits a room temperature vibrational density of states spectrum nearly identical with that of the acid form, and shows no change on heating to 673 K, except for a uniform decrease in spectral intensity. This is caused by the increase in mean square displacement of the zeolite atoms at elevated temperature.12 Quasi-elastic spectra of the partially dehydroxylated Rho sample have been recorded at 293, 573, and 673 K at momentum-transfer values chosen to preclude overlap with diffraction features. In all cases, a single Gaussian peak centered at zero energy transfer is observed. This peak exhibits an invariant width (100 peV fwhm) equal to that of the instrumental response function. N o energy transfer to or from the scattered neutrons, and hence no indication (12) Ashcroft, N. W.; Mermin, N. D. "Solid State Physics"; Holt, Rhinehart and Winston: New York, 1976; pp 790-795.
of diffusion on Rho,S is found within the resolution of the measurement. In the absence of more concrete information, a rough upper limit to the diffusion rate may be estimated. Assuming proton jump diffusion between uniform sites, a Lorentzian peak of width AE = (2h/7)(1 - (sin Q L / Q L ) ) would be expected,13 where 7 is the time between jumps, L the distance between sites, and Q the magnitude of the momentum transfer. A Lorentzian peak of fwhm 30 MeV could have been detected; at Q = 1.95 A-I, using L = 2.54 A (based upon the distance between nearest neighbor oxygen^*-^), a lower limit to the lifetime r = 5 X lo-" s for hydrogen at a specific site is obtained. This corresponds to a maximum two-dimensional 7-'L2)of 4 X lo4 cm2 s-'. This result diffusion coefficient13 is consistent with previous measurements of hydrogen mobility on zeolites based upon N M R relaxation rates and line ~ i d t h s . ~ ~ , ' ~ These experiments have yielded diffusion coefficients of 3 X lom9 cm2 s-I on H-Y zeolite at 673 K, and 1 X lo-'' cm2 s-I on partially desodiated Na-A, -X, and -Y zeolites at 573 K. No incompatibility between these numbers exists: the difference in magnitude between the published observations and the limit obtained by using neutron scattering arises from the instrumental resolution of the latter. Thus, while the precise nature of the hydrogen atom binding sites on zeolite Rho has not been determined, the information obtained is consistent with the commonly accepted idea of bridging hydroxyl groups. Further, it is clear that some alteration in hydrogen-framework bonding accompanies the thermal treatment. Additional work is necessary to determine whether there is a causal relationship between these effects, or whether their simultaneous occurrence is accidental.
Acknowledgment. We thank E. R. Neitzel for construction of a scattering cell, and A. J. Vega and R. Wormsbecher for helpful discussions. I,. M. Johnson typed the manuscript. M.J.W. acknowledges the award of an NBS-NRC Postdoctoral Research Associateship. (13) (a) Chudley, C. T.; Elliott, R. J. Proc. Phys. SOC.1960, 77, 353-361. (b) This equation actually describes translational diffusion by jumps of fixed length in random directions, and thus is not truly appropriate here. Its use is justified by its simplicity, coupled with the lack of explicitly observed quasi-elastic scattering. (14) Mestdagh, M. M.; Stone, W. E. E.; Fripiat, J. J. J. Chem. SOC., Faraday Trans. 1 1976, 72, 154-162. (15) Freude, D.; Oehme, W.; Schmiedel, H.; Staudte, B. J. Catal. 1974, 32, 137-143.
Oxidative Dimerizatlon of Methane over Lanthanum Oxide Chiu-Hsun Lin, Kenneth D. Campbell, Ji-Xiang Wang, and Jack H. Lunsford* Department of Chemistry, Texas A&M University, College Station, Texas 77843 (Received: September 19, 1985)
Under oxygen-limitingconditions La203is a reasonably selectivecatalyst for the conversion of methane to ethane and ethylene (C, compounds). At 725 'C a selectivity to C2 compounds of 47%was achieved at a CHI conversion of 9.4%. Although LazO, is very effective in the generation of gas-phase CH,. radicals, which are believed to be intermediates in the oxidative dimerization, the catalyst also is active for the complete oxidation of CzH6under the reaction conditions. Higher reaction temperatures favor C2H4 which may be formed from CzHs via gas-phase reactions.
Introduction Recent work on lithium-promoted magnesium oxide has demonstrated that this is an effective catalyst for the partial oxidation of methane to ethane and ethylene.'J Methane is activated by (1) Ito, T.; Lunsford, J. H. Nature (London) 1985, 314,
721.
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[Li'O-] centers which are present on the surface, and the resulting CH3. radicals recombine, largely in the gas phase, to yield C2H6. The latter subsequently is dehydrogenated to CzH4. Otsuka et (2) Ito, T.; Wang, J.-X.; Lin, C.-H.; Lunsford, J. H. J . Am. Chem. SOC. 1985, 107, 5062.
0 1986 American Chemical Society
The Journal of Physical Chemistry, Vol. 90, No. 4, 1986 535
Letters 1
2.0
A
TABLE I: Effect of Oxygen on the Generation of Methyl Radicals"
4
re' 2 1.5
-
.. P a
--E
E a
E
P -c -
a
- 2; .-
1.0
p
re1 concn pretreatment of methyl radicals catalyst heated in O2 at 630 OC; 5 X lo-' torr of 1 O2 present with CH4 as reactant same as above, except no O2present as reactant 0.04 catalyst heated in O2at 630 OC, evacuated 2 min 0.03 at 500 "C, no O2present as reactant "Reaction at 500 OC, 0.24 g of Laz03,collection period = 10 min, argon flow = 3.8 mL min-', CHI flow = 1.08 mL min-I, O2= 0.023 mL min-I, total pressure over catalyst 1 torr.
-
a
0.5
-
- 1 K
at -196 "C. The quenched La203 was transferred to a fusedquartz sidearm and the EPR spectrum was recorded. Results and Discussion
0
450
500
0 650
550 600 Temperature ( ' C )
Figure 1. Amounts of CH3. radicals formed over (a) 7 wt % Li/MgO and (b) La2O3; and (c) ratio of amounts over these two catalysts: 0.0551 g of La2O3,0.20 g of 7 wt % Li/MgO, heated at 630 "C in 02. collection period = 30 min, argon flow = 3.8 mL m i d , CH4flow = 1.08 mL min-I, O2= 0.023 mL mi&, total pressure over catalyst 1 torr.
-
aL3 have demonstrated that certain of the lanthanide oxides also are capable of promoting the oxidation of CH4with exceptional selectivities, but at low conversions. With Sm2O3, for example, they were able to achieve 93% selectivity to Cz compounds at a CH, conversion of 5%. The reactions were run at low oxygento-methane ratios. In this Letter we compare La203 with Li-promoted MgO as catalysts for the partial oxidation of methane. Lanthanum oxide was chosen from the rare-earth oxides because it is reasonably active and selective but does not contain unpaired 4f electrons, which would interfere with the detection of paramagnetic oxygen ions by EPR. Both the nature and the active surface site and the role of surface-generated gas-phase radicals were of particular interest. Experimental Section
The catalyst was prepared by hydrolyzing Aldrich (Gold Label, 99.99%) La203 in deionized water, followed by drying., The resulting material was essentially a hydroxide with some carbonate impurities. Catalysts of 20-40 mesh were used in all tests. The CH4 (>99.97%), O2 (>99.6%), and C2H6(>99%) were obtained from Matheson; He (99.995%) was obtained from Airco. All gases were used as received. The catalytic experiments were carried out in a fixed-bed flow reactor at 1 atm. The La(OH)3 was partially decomposed at 450 O C under flowing O2and the resulting material was heated to 725 OC for 16 h in the reactant gas mixture (CH4,02,and He). The surface area of the resulting material was 3.9 m2/g, based on krypton adsorption. All products except H C H O were analyzed by gas chromatography.5 Methyl radicals were detected by EPR using a matrix isolation system in tandem with a flow reactor. The system has been described in detail Argon, methane, and oxygen were present in the ratio 165:47:1 a t a total pressure of about 1 torr. Relative concentrations of the radicals were determined from the peak-to-peak intensities of the EPR spectra. The EPR spectra of La203were recorded after the sample had been quenched from 650 O C by dropping it into liquid O2or N2 (3) Otsuka, K.; Jinno, K.; Morikawa, A. Chem. Lett. 1985, 499. (4) Magnuson, D. T.; Rosynek, M. P.J. Catal. 1977, 46, 402. (5) Liu, H.-F.; Liu, R.-S.; Liew, K. Y.;Johnson, R. E.; Lunsford, J. H. J . Am. Chem. SOC.1984, 106, 4117. ( 6 ) Driscoll, D.J.; Martir, W.; Wang, J.-X.; Lunsford, J. H. J. Am. Chem. Soc. 1985,107, 58. (7) Martir, W.; Lunsford, .I. H.J . Phys. Chem. 1980, 84,3079.
One of the most striking features of La203 is its ability to generate gas-phase methyl radicals. As depicted in Figure 1 the number of radicals generated over La203was some 4 times greater at 500-600 OC than over 7 wt % Li/MgO. Since the same type of center is believed to be responsible for the activation of methane it is expected that the formation of methyl radicals and the overall conversion would parallel one another. Qualitatively, this is indeed the case as the overall activity of La203 was about 8 times that of Li/MgO when compared at 625 OC and at similar partial pressure of CHI and Oz (322 and 9 torr, respectively). The nature of the active center for the generation of CH3-is not nearly so apparent on L a 2 0 3as it was with the previously studied Li/MgO catalyst.2 In the latter case the EPR spectrum of the [Li+O-] center, with g, = 2.054 and gll = 2.004, was clearly evident upon quenching; however, quenching the La203 catalyst from 650 "C in 170 torr of O2 to -196 OC in liquid oxygen gave rise to an EPR spectrum with g,,= 2.047 and g, = 1.994. This spectrum is characteristic of the 02-ion.* There was no evidence in the spectrum for 0- ions, although their presence in limited amounts may have been masked by the broad spectrum of the superoxide ion. The species decreased over several hours at 100 OC under vacuum, and it did not react with CH4 at temperatures up to 100 "C. There is evidence that 02-ions also were present at 650 OC in the presence of 02:the spectrum of 0, was observed after quenching the catalyst, which was in air at 650 "C, by immersion in liquid nitrogen at -196 OC. Earlier studies of the reactions of simple alkanes with 02-on MgO demonstrated that this form of oxygen was unreactive with CH, at temperatures up to 200 0C,9 but this does not rule out the possibility that Oz- may react with CHI on La203 a t temperatures >600 O C . As an alternative, on La203a transient 0species may indeed be formed via 0, and, in the presence of CH,, may give rise to the CH3. radicals. Kazansky and co-workersIo,il have suggested that the following sequence of reactions may occur: 02(gas) e 02(ads)
+e
- -
02-
+
+e
20-
+Ze
202-
(1)
The 0- ion is stabilized on surfaces having a limiting number of available electrons which would drive the reaction to oxide ions.I2 Additional matrix isolation experiments demonstrated that the active center, whether 0-,02-, or some other site, was transient. As shown by the data in Table I, O2 must be present in the reactant stream if substantial concentrations of CH3. are formed, even though the catalyst had been pretreated in 02.This behavior also is in contrast to the Li/MgO case where residual activity remained for a period of minutes even though no oxidant was present in the gas phase. The difference is that with Li/MgO the active [Li+O-] species was actually part of the lattice, whereas, (8) Wang, K. M.; Lunsford, J. H. J . Phys. Chem. 1971, 75, 1165. (9) Iwamoto, M.; Lunsford, J. H. J . Phys. Chem. 1980, 84,3079. (10) Shvets, V. A,; Vorotyntsev, V. M.; Kazansky, V. B. Kinet. Katal. 1969, 10, 356. (11) Kazansky, V. B. Kinet. Katal. 1977, 18, 43. (12) Rao, G. V. S.; Ramdas, S.; Mehrotra, P. N.;Rao, C. N. R. J . Solid Srare Chem. 1970, 2, 377.
536
The Journal of Physical Chemistry, Vol. 90, No. 4, 1986
Letters
TABLE 11: Effect of Catalyst and CH, to O2 Ratio on the Partial Oxidation of CHJ
reactant/torr
catalyst
conversion/%
product/%
yield/%'
He
CH4
0 2
CH4
0 2
COzb
C2H6
C2H4
C2
c2
Li/MgO
43 1
320
8.9
2.94
44.2
10.8
66.3
23
89.2
2.62
La203
438 597 613 686
313 155 132 57
8.4 8.3 15 17
3.57 5.68 9.44 19.7
88 88 91 93.3
29 42.7 53.4 76.3
42.6 31.2 23.2 10.2
28.2 26.1 23.4 13.5
71 57.3 46.6 23.7
2.53 3.26 4.40 4.67
"The reaction used 1.0 g of Laz03,0.42 mL s-I, 725 OC; 1.0 g of 7 wt % Li/MgO, 0.83 mL s-', 725 OC. b N o CO was detected at this temperature. 'Yield is defined as the product of conversion and selectivity. TABLE I11 Reactivity of C,H, and CH, over La2Ol0 run column 1
2
3
56.8 0 17.4
0.1 6 17.9
54.7 6.32 18.1
C2H6
8.62 0 46 0.76 0.58
10.4 0.4 0.44 0.46 0.19
9.45 0.65 50 2.17 1.61
CH4
19.7
reactant/torr CH4 C2H6
02
I*
2c
3.59
5.86 0.65
product/torr
CO2
co
CH4 C2H4
0 50 0.318 0.235
0 1.85 1.375
conversion/% C2H6
97
79
7.6 2.82 89.5
36
selectivity/% C2H4
10.2 13.5
CH, Cl(C0 + CO,)
76.3
C2H6
I
64
1.0 g of La2O3,0.42 mL s-l, 725 OC. bColumn 1 was obtained by assuming the CH4 reacted in the CH4 C2H6 mixture of run 3 had the same selectivity pattern as that of run 1. cCoIumn 2 is the difference between the total products of run 3 and the values of column 1.
+
with La203 the active species may be a sorbed form of oxygen, e.g. 02-. Since the formation of C2 compounds depends on [CH3.I2,one might expect that the selectivity for C2H6 and C2H4 over La203 would be greater than that found over Li/MgO. Such was not the case, as demonstrated by the data of Table I1 which shows that at comparable levels of conversion the C2 selectivities were greater for Li/MgO than for La203. Here the reaction over Li/MgO was not even oxygen limited. In order to achieve high activity and selectivity it also is necessary to remove the C2 products from the catalyst zone before they react further. Results of experiments to determine the extent of C2H6 oxidation are summarized in Table 111. In run no. 1 CH4 was the only hydrocarbon, in run no. 2 C2H6 was the only hydrocarbon (except for a CH4 impurity), and in run no. 3 both CH4 and C& were present. The calculated values under column 1 are the partial pressures of products obtained from methane, assuming the product distribution of run no. 1. In column 2, the numbers are the difference between the total products of run no. 3 and the values of column 1; i.e. the values are those expected from the oxidation of C2H6. Clearly, whether one considers only run 2 or the results given in column 2 , the complete oxidation of C2H6 was extensive and accounts for the low selectivity to C2 compounds at moderate conversion levels. If one operates at conditions of low 02:CH4 ratios, where secondary reactions are minimized, the selectivity is greatly improved as shown in Table 11, but at comparable conversion levels the C2 selectivity over La203 is considerably less than that found over Li/MgO. Over 4 g of the latter catalyst, a C 2 selectivity of 89% was achieved at a conversion of 3.7%. These values are comparable to the selectivities and activities which were observed over Sm203.3 It should be noted that the activity of the La203 catalysts decreased about 20% over 9 h and remained essentially constant
01
I
5
500
I
I
lo
700
600
Temperature ("c)
Figure 2. Methane conversion and selectivity variations as a function of
reaction temperature: 0 , CH4 conversion; m, C, selectivity; 7 , C2H4 selectivity, A, CzH6selectivity. A reactant mixture of 56 torr of CH4 and 17 torr of O2was fed over 1.0 g of La20, at a flow rate of 0.42 mL s-1.
for the next 22 h. The decrease in activity was accompanied by a decrease in C 0 2 formation, but the C2H6and C2H4 activity remained constant. The effect of temperature on selectivities, as depicted in Figure 2, provides interesting information on the radical reactions. Under oxygen-limiting conditions the CH4conversion remained constant as the temperature was increased. Moreover, the C1 selectivity (C, = C O C 0 2 ) decreased and the C2H4selectivity increased, while the C2Hs selectivity increased only slightly. In the previous study it was suggested that C O and C 0 2 were formed both by surface reactions
+
CH3.
+ 0'-
-
CO, C02
(2)
and by gas-phase reactions'12 (3)
The equilibrium concentration of CH3O2*,which leads to C O and C02, is favored by lower temperatures.l3lg Thus, with increasing temperatures, under oxygen-limiting conditions, it is not surprising (13) Khachatryan, L. A.; Niazyan, 0. M.; Mantashyan, A. A,; Vedeneev,
V. I.; Teitel'boim, M. A. Int. J . Chem. Kine?. 1982, 14, 1231. (14) (15) 1259. (16) (17) (18)
Parkes, D. A. Int. J . Chem. Kine?. 1977, 9, 451. Selby, K.; Waddington, D. J. J . Chem. Soc., Perkin Trans. 1979, 9,
Batt, L.; Robinson, G. N. In?. J . Chem. Kine?. 1979, 1 1 , 1045. Luckett, G . A.; Mile, B. Combust. Flame 1970, 15, 3 3 . Vardanyan, I. A.; Sachyan, G. A.; Nalbandyan, A. B. Combust. Flame 1971, 17, 315. (19) Bell, K. M.; Tipper, C . F. H. Proc. Roy. SOC.London, Ser. A 1956, 238, 256.
J . Phys. Chem. 1986, 90, 537-538 that the C1selectivity decreased. It perhaps is fortuitous that the decrease is linear with respect to temperature. The related increase in CzH4 selectivity may be the result of the reactions
--
2CH3.
C2H6
E, = 0 kcal/mol
CH3. + C2Hs
CH4 + C2H5.
+ O2
C2H4 H02.
C2H5.
+
(4)
E, = 10 kcal/mol ( 5 )
E , = 5 kcal/mol
(6)
in addition to reaction 3 . As the temperature increases no additional CH,. radicals are available from CH, since the conversion of CH, was constant. We assume, therefore, that CH3. is derived from the reverse of reaction 3. The C2H, via reaction 4 may further react to form CzH4 by two activated processes (reactions 5 and 6).2't25 Thus, the selectivity to CZH4 increases with in(20) Knox, J. H.; Wells, J. W. Trans. Faraday SOC.1963,59,2786,2801.
537
creasing temperature of reaction under these conditions. An alternate explanation of the data in Figure 2 is that CH3. reacts with the surface to form carbene radicals at higher temperatures and these then combine to yield C2H4. N o evidence for CHI: radicals has been found by matrix isolation, but experiments are underway to detect this species. In summary, La203 is effective in the activation of CH4to form CH3. radicals. These radicals combine in the gas phase to form C&. Further oxidation of C2compounds, however, limits the overall C2 selectivity, except at very low conversions.
Acknowledgment. This work was supported by the National Science Foundation under Grant No. CHE-8405191. (21) (22) (23) (24) (25)
Taylor, J. E.; Kulich, D. M. Inr. J . Chem. Kinet. 1973, 5 , 455. Kulich, D. M.; Taylor, J. E. Inr. J . Chem. Kinet. 1975, 7, 895. Plumb, I. C.; Ryan, K. R. Int. J . Chem. Kinet. 1981, 13, 1011. Slagle, I. R.; Feng, Q.; Gutman, D. J . Phys. Chem. 1984,88,3648. Patel, M.; Hoare, D. E. Trans. Faraday SOC.1969, 65, 1325.
Explicit Consideration of the Excluded Volume in the Formula for Diffusion-Controlled Dissociation Rate Constants' R. D. Astumian* and Z. A. Schelly* Department of Chemistry, The University of Texas at Arlington, Arlington, Texas 76019-0065 (Received: September 23, 1985)
It is shown that the excluded volume in the particle pair AB must be considered explicitly for the correct calculation of the diffusion-controlled dissociation rate constants kd. The formula currently used significantly underestimates kd, especially in case of disparate sizes of A and B.
Introduction In dilute solution, the rate constant k, of a diffusion-controlled ionic association reaction k
A+B+AB kd
can be calculated by the use of the Smoluchowski3-Debye, equation 4rNnaZ n k, = 1000 exp(Z) - 1
-
- -
with the boundary conditions of nBJ 0 for r m and nBr = constant = l/AVk for r a. The last condition simply states that the concentration of species B in the particle pair AB (symbolized by B' in distinction from free B in the bulk solution) is constant, i.e. one B' per the volume AVk of the available spherical shell on the surface of the central particle A (Figure 1). Discussion If one introduces the approximation of using the volume of the sphere with radius r = a instead of the volume of the spherical shell (i.e. AVk i= 4 r a 3 / 3 ) in eq 3 , one obtains6
kb =
320 a 2 [1 - exp(-Z)]
(4)
where No is the Avogadro number, the "reaction distance" a = r, rBis the sum of the radii of A and B, zieOis the ionic charge, c the dielectric constant of the solvent, k the Boltzmann constant, T the absolute temperature, and D = DA + DB is the diffusion coefficient of the relative transport of B toward A. E i g e ~using ~ , ~ a similar approach, derived the expression for the diffusion-controlled dissociation rate constant kd as 4rZ~Zeeo~ D kd = EkTAVk 1 - exp(-z) (3)
which is the formula consistently usedG8 for kd. One reason that might have contributed to the acceptance of the approximation leading to eq 4 is that the ratio k , / k b turns out to be identical with an expression derived through an entirely different route by Fuoss9 for the equilibrium constant of ion association in the BjerrumlO sense. Nevertheless, the approximation is physically unreasonable and leads to large error especially in the case of disparate particle sizes. Since the particles A and B cannot penetrate each other, the
(1) Abstracted in part from R.D.A.'s dissertation, University of Texas at Arlington, 1983. (2) Present address: Laboratory of Biochemistry, National Heart, Lung, and Blood Institute, NIH, Bethesda, MD 20205. (3) M. v. Smoluchowski, Phys. Z., 17, 557, 585 (1916). (4) P. Debye, Trans. Electrochem. SOC.,82, 265 (1942). (5) M. Eigen, Z. Phys. Chem. (Frankfurr am Main), 1, 176 (1954).
(6) M. Eigen, Z. Eekrrochem., 64, 115 (1960). (7) G. G. Hammes, "Principles of Chemical Kinetics", Academic Press, New York, 1978. (8) C. DeLisi, Q. Rev. Biophys., 13, 2 (1980). (9) R. M. Fuoss, J . Am. Chem. SOC.,80, 5059 (1958). (10) N. Bjerrum, Dan. Mar. Fys. Medd., VII, No. 9 (1926).
+
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0 1986 American Chemical Society
