J . Phys. Chem. 1989, 93, 6136-6141
6136
current through electrode element, A photogenerated current of diode, A limiting anodic current at metal RDE, A reverse saturation current of diode, A peak current of diode/electrode circuit for rotating disk simulations, A anodic peak current of diode/electrode circuit for cyclic voltammetric simulations, A cathodic peak current of diode/electrode circuit for cyclic voltammetric simulations, A peak current at metal electrode for cyclic voltammetric simulations, A , or limiting anodic current at metal RDE, A current through diode/electrode system, A dimensionless current variable I/(I, + IL) concentration of oxidized species at distance x at time t , mol/cm3 concentration of reduced species at distance x at time 1, mol/cm3 concentration of oxidized species in first box at time I , mol/cm3 concentration of reduced species in first box at time I , mol/cm3 time, s voltage relative to the open-circuit voltage, V voltage across diode, V voltage across electrode, V open-circuit voltage, V voltage applied across diode/electrode circuit, V scan rate, V/s distance from electrode surface, cm distance between the average concentration of redox species in the first box and the plane of the electrode, cm total coverage of electroactive material, mol/cm2 dimensionless current ratio; Ip,,,/(IL + I,) =O(O,t)/R(O,t)= exp((nF/RT)(V,(t) - EO’)) expWIRT)(V, - EO’)l kinematic viscosity, cm2/s
Acknowledgment. We thank the Department of Energy, Office of Basic Energy Sciences, and the donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this work. N.S.L. also acknowledges support as a Dreyfus Teacher-Scholar and as an A. P. Sloan Foundation Fellow. We are indebted to Dr. Stephen Feldberg of Brookhaven National Laboratory for a critical reading of the manuscript and for numerous helpful discussions. We also acknowledge helpful suggestions regarding computing methodology from Professor Hans Andersen of Stanford University.
diode quality factor electrode surface area, cm2 bulk concentration of reduced species, mol/cm3 bulk concentration of oxidized species, mol/cm3 diffusion coefficient of reduced species, cm2/s diffusion coefficient of oxidized species, cm2/s initial potential, V final potential, V formal potential of redox species, V potential where I = Ip/4, V potential where I = IP/2, V potential where I = (3/4)Ip, V (EP + E,)/2 for cyclic voltammetry, V, or Eo’ + (2kT/3q) In (DR/Do) for rotating disk voltammetry, V EIl2for a metal electrode, V EIl2for a semiconductor electrode, V E,-- Epl2, V E,(metal) - E,(semiconductor), V E,(metal) - E,(semiconductor), V Eii2(metal) - l?l/2(semiconductor),V E, - E,, V flux of reduced species at electrode surface at time I , mol SKI cni2 flux of oxidized species at electrode surface at time I , mol s-I
( D ~ / D ~ ) ~ / ~ ~ (DO/DR)’’~@
current, A current through diode element, A
angular frequency of rotation, s-I
Activation Energy of the Catalytic Oxidation of Methylbenzenes over Metal Oxides Ragnar Larsson* and Bo Jonsont Group of Catalysis Research, Inorganic Chemistry 1 , Chemical Center, P.O. Box 124, S-221 00 Lund, Sweden (Received: November 21, 1988; In Final Form: February 21, 1989)
A model for the dynamics of catalysis is applied to the oxidation of methylbenzenes (toluene and xylenes). The stepwise change of activation energies found for data from literature is used to determine the frequency of that vibration mode that relates to the reaction coordinate. From this value, about 1040 h 50 cm-I, one can conclude that the distortion of the methyl rocking mode (IR absorption at 1042 f 4 cm-I) is of prime importance for the rate-determining step of the catalytic reaction. The anharmonicity parameter, x, is estimated for two cases from these data; the first one is by neglection of the contribution to the apparent activation energy from the heat of adsorption. This gives x = -2 cm-I. In the other case correction is made for the heat of adsorption, resulting in x = -5 f 1 cm-I.
Introduction The use of activation energy data to describe details of the dynamics of heterogeneous catalysis has for a long time been in disrepute. This situation undoubtedly is caused by the complexity of adsorption equilibria that gives a relation between the true activation energy and the heat of adsorption that may be quite comp1icated.I Recently, however, it has been pointed out by one of usz that for many reactions in heterogeneous catalysis one can observe a
’Present address:
Glass Research Institute, Box 3093, 35003
Vaxjo,
Sweden.
certain stepwise change of activation energies within a series of similar catalysts operating on one and the same substrate. This empirical result has been further demonstrated, e.g., for the hydrocracking of alkanes in zeolite catalysts3 and NzO decompositi01-1.~ ( 1) Boudart, M.; Dj6ga-MariadassouKinetics of Heterogeneous Catalytic Reactions; Princeton University Press: Princeton, NJ, 1984. (2) Larsson, R . Z . Phys. Chem. Leipzig 1987, 268, 721. (3) Larsson, R. Proc. X X . Jahrestreffen Katalytiker DDR; Reinhardsbrunn, 1987;Catal. Today 1988, 3, 387. (4)Larsson, R.Proc. 20th Swedish Catal. Lund,1987; Catal. Today 1989, 4,
0022-3654/89/2093-6 136$01.50/0
235.
0 1989 American Chemical Society
Catalytic Oxidation of Methylbenzenes over Metal Oxides Such a stepwise change, as astonishing as it might seem, is a consequence of a model of catalysis implying selective energy transfer from catalyst to ~ubstrate.~In its extreme form this model is identical with the model of resonance (vibrational or electronic) for c a t a l y ~ i s . ~The - ~ point of interest in this connection is that the catalyst is supposed to supply energy in such a way that it excites that vibrational mode of the reactant (substrate) that will bring it to reaction. This mode of vibration must be the one that will give the molecule the structure described as the “activated state”. Hence it is, in principle, possible to deduce what vibration of the molecule that is operative. In the oxidation of toluene, e.g., it is known from kinetics investigationss that the rate-determining step is a hydrogen abstraction from the methyl group. This means that a planar CsH5-CH2radical will be the proper intermediate. Hence, as argued in a previous paper? the vibration that causes the molecule to attain the activated state is the one that most efficiently takes the molecule to a planar structure, while at the same time it lets one of the methyl group hydrogens be more unlike than the others. As pointed out,9 this vibration could be nothing but the methyl rocking that is related to a strong IR absorption at 1041 cm-l and a weak one at 967 cm-’ in the gas-phase spectrum.I0 The basic idea of the model proposed is that the activation energy of the catalytic reaction is made up of that number of vibrational quanta that has to be used to excite the molecule to reaction. Other vibration modes are of course also excited in the reacting molecule according to Boltzmann’s distribution law, but these vibrations are also excited (still according to Boltzmann’s distribution law) in the nonreacting molecules. As the activation energy is defined from statistical thermodynamics“ as the energy which the reacting molecule has in excess of the mean energy of its nonreacting partners, the present model implies that it is only those quanta of the vibrational mode that activates the molecule to reaction (in the present case the methyl rocking mode) that actually constitute the activation energy. One might object, however, that most data published on activation energies of heterogeneous catalysis are of the type that is denoted E,, the apparent activation energy,’ or perhaps better,12 the experimental activation energy. This entity is usually related to the true activation energy, E , by the relation (1) E a = E - Qads where Qadsis the heat of adsorption of the reactant on the catalyst surface. This is part of the complication alluded to above. Of course, this problem vanishes if the activation energy is measured under zero-order conditions. In the present paper we will first pursue the discussion as if Qadswas zero. Thereafter we will consider what consequences a finite but constant value of Qads might have. Irrespective of the problem just discussed, Le., the influence of Qads on the experimental value of E, another factor related to the theory of absolute rates must be taken into account. In the conventionally used model of transition state theory, the main step is the one of transfer through the top of the barrier. This is described by a frequency of the order of magnitude kBT/h. Even if the present model puts emphasis on the problem of how to come to the top of this barrier, it seems that the same transition step frequency should describe the very happening of the reaction; i.e., the preexponential factor will contain the factor k B T / h . Therefore In k will contain the term In T , resulting in a reformulation of eq 1: E, = E - Qads R T (2)
+
(5)Larsson, R. Catal. Today 1987, 1 , 93. (6) Myers, R. R.Ann. N.Y. Acad. Sci. 1958, 72, 339. (7)Scheve, J.; Scheve, E. Z . Anorg. Allg. Chem. 1964, 333, 143. (8)Gates, B.C.; Katzer, J. R.; Schuit, G. C. B. Chemistry of Catalytic Processes; McGraw-Hill: New York, 1978;p 339. (9)Jonson, B.;Larsson, R.; Rebenstorf, B. J . Catal. 1986, 102, 29. (10)La Lau, C.; Snyder, R. G. Spectrochim. Acta 1971, 27A, 2073. (11) Fowler, R. H.; Guggenheim, E. A. Statisrical Thermodynamics; Cambridge University Press: Cambridge, 1939;pp 491-506. (12)Glasstone, S.;Laidler, K. J.; Eyring, H. The Theory of Rate Processes; McGraw-Hill: New York, 1941.
The Journal of Physical Chemistry, Vol. 93, No. 16, 1989 6137 TABLE I: Activation Energies for Oxidation of Methylbenzenes‘ compound catalyst E. RT E. - R T In A ref p-xyleneb p-xylene‘ toluene
tin vanadate molybdenum trioxide
o-chlorotoluene m-chlorotoluene p-chlorotoluene m-xylene p-xylene toluene molybdenum as cerium salt o-xylene V205/Ti02
toluene m-xylene p-xylene o-xylene toluene
W/Mo oxides
49.1 8.2 27.4 16.9 17.4 17.2 17.1 18.05 28.7
1 6‘ 26’ 1 4‘ 27d 27d 20-26‘ 32 12.0 12.0 10.0 9.0
1.3 1.2 1.4
47.8 7.0 26.0
13 13
1.4
15.5 16.0 15.8 15.7 16.7 27.3
14 14 14 14 14 15
14
16
1.3
10.7 10.7 8.7 7.7
17
x % vanadium
on TiOl x = 10 x=2 x = 0.5 x = 0.2 x = 0.1 x=o
18 28.6 24.0 15.6 13.2 20.8 34.4
1.3
27.3 22.7 14.3 11.9 19.5 33.1
21.7 17.1 8.3 5.4 9.9 18.8
‘ R T is calculated from a mean value of the temperature given in the quoted papers. All energies are expressed in terms of kcal mol-’. bTemperature range 650 K < T < 690 K. cTemperature range 590 K < T < 630 K. ‘Literature quotations in ref 15.
Activation Energies of the Toluene and Xylene Oxidations A number of determinations of energies of activation for catalytic oxidation of toluene, or substituted toluenes, have appeared in literature.I3-l7 For example, one of these” treats p-xylene over tin vanadate catalysts, and another onel4 tests a series of toluene derivatives over molybdenum trioxide. All data13-17 are collected in Table I. Also included in Table I are results recently obtained from this laboratoryls on toluene oxidation over vanadium oxides supported on titanium dioxide. One trivial difficulty in determining the activation energies in several of these investigations is the circumstance that more than one product is formed. Especially the “total combustion“ to C O and C 0 2 should not be allowed to interfere. Our previous results are therefore reported here as the activation energy found by following the kinetics of the formation of benzaldehyde only. Therefore the data reported here differ somewhat-and instructively so-from those reported in our previous workla on that system. In that latter paper the kinetics of the disappearance of toluene was followed, Le., the formation of “products”. The same problem arises for the data given by Wachs et a1.I6 which therefore must be taken cum grano salis. Popova and Kabakova in their work,I7 however, clearly distinguish the parameters for oxidation to aromatic products and for total combustion. Therefore these data can be used advantageously. On the other hand the catalysts used by Nag, Fransen, and MarsIs seem to differ very strongly in selectivity. Therefore only one datum from this work has been used, the one with the best qualitative selectivity for benzaldehyde. In order to be. able to get a better view of the coherence between the data they are presented graphically in a histogram in Figure 1. (Figure 1 a represents all data given in Table I. Only those (13)Mathur, B. C.;Viswanath, D. S. J . Catal. 1974, 32, 1. (14)Trimm, D.L.; Irshad, M. J . Catal. 1970, 18, 142. (15)Nag, N . K.;Fransen, T.; Mars, P. J . Catal. 1981, 68, 77. (16)Saleh, R.Y.; Wachs, I . E. Appl. Coral. 1987, 311, 87. (17) Popova, N . I.; Kabakova, B. V. Kiner. Katal. 1965, 6, 499. (18)Jonson, B.;Rebenstorf, B.; Larsson, R.; Anderson, S. L. T. J . Chem. Soc., Faraday Trans. 1 1988, 84, 3547.
6138
The Journal of Physical Chemistry, Vol. 93, No. 16, 1989
ii,LL ,,,
i,
,
Larsson and Jonson
, ,
J 10
20
30
40
50 k c a l i m l
io
20
30
40
50 kcallmol
2
1 I
Figure 1. Histogram of the activation energies ( E , - RT) quoted in Table I . N = number of observations: (a, top) all data; (b, bottom) only data with high accuracy; lines sloping right to left, ref 13; horizontal lines, ref 14; lines sloping left to right, ref 15; solid lines, ref 17; dots, ref 18.
I
I
TABLE 11: Formation of Mean Values of the Data That Can Be Grouped Together from the Histogram of Figure 1‘
E, - RT(exp) 7.0 7.7 8.7 11.9 10.7 10.7 14.3 15.5 16.0 15.8 15.7 16.7 19.5 22.7 26.0 27.3 27.3 33.1 47.8
E, - RT(mean)
n
(E, - RVIn
ReMlon coordlfute
$tetrMdrlc $splitting $=O
7.8
3
2.6
11.1 14.3
4 5
2.78 2.86
Figure 2. Schematic representation of interacting potential curves. The left one corresponds to the reactant, and the other ones corresponds to the primary product and the final product, respectively. The reaction coordinate is the decrease of the angle between the CHH plane and the plane of the phenyl group (cf. Figure 3). / /
15.9 19.5 22.7
6 8
2.65 2.79 2.84
26.9 33.1 47.8
IO 12 18
2.69 2.76 2.62
I
‘Successive formation of the entity E, - RT/n according to eq 7; see Discussion. E, - RT and E, - RT/n expressed in kcal mol-’. data that are reported with an accuracy of three figures are used in Figure 1b and the following quantitative treatments.) One gets the impression that the data seem to gather in certain regions. In Table 11 the values are grouped together following the indications of Figure 1b. The mean values of the data found in these regions are calculated and also presented in Table 11. With this rearranged set of data one can observe that the values seem to order themselves approximately according to
( E , - RT)i+I - ( E , - RT)i = AE (3) where A E is some common increment. Before discussing the data in detail we must check if it is meaningful to lump together the substrates in the way it is done here. The crucial point, for our argument, is obviously if the methyl rocking has about the same frequency for all the compounds. A collation of vibrational datalOvl+zlfor some substituted toluenes indicate that the strong absorption bands for all the substances reported in Table I fall in the very narrow range of 1042 i 4 cm-I. This observation shows that it is admissible to treat these substances together. Discussion
The Model. The problem now arises, which factors determine the need for activation by x quanta in some cases and by y quanta in others. We suggest that a model of catalysis, “the principle of specific energy might illustrate this question. The basic concepts of this model are presented in Figure 2. The (19) Green, J. H. S . Spectrochim. Acta 1970, 26A, 1503. (20) Green, J . H. S. Spectrochim. Acta 1970, 26A, 1523. (21) Mooney, E. F. Spectrochim. Acta 1964, 20, 1343.
a
Figure 3. Sketch of the positioning of the toluene molecule above a metal
oxide surface, determining the reaction coordinate. @ denotes the angle between the CHH plane and that of the aromatic group. potential curve of the reacting molecule (e.g., toluene) is a onedimensional representation along the reaction coordinate. The breaking of the C-H bond occurs at the crossover point where the first potential curve is crossed by the corresponding curve of the planar intermediate rocking vibration. The reaction coordinate is the angle between the phenyl plane and the C H H plane defined by the methyl carbon atom and the two residual hydrogen atoms. When the third hydrogen is splitting off, the rest of the system will be in a very excited state as the geometry of this fragment deviates so strongly from that of the ground state of the product (the planar C,H,CHz radical). To approach the ground state, rehybridization of the binding orbitals ought to take place (= the ”electronic” relaxation in Figure 2), followed by a final vibrational relaxation. The product is then the true intermediate C6H5.CH2. (However, from the viewpoint of the present hypothesis, what happens after the C-H split is of little importance.) In Figure 3 we try to sketch the geometric consequences of the model. The crossover point is obviously related to that degree of rocking that makes possible the acceptance of the hydrogen atom, Le., the close approach to an oxide ion to form M-OH. Thus, if the metal ion-oxide ion distance is such that the “distance of catching” (doH)between the 02-and the H atom is reached at the rocking angle 4, splitting will occur. If such a distance is reached after, e.g., two quanta of vibrational excitation to an angle 4(2), the reaction occurs with an activation energy of two quanta. If instead eight quanta are needed to reach this same distance of catching, the angle will be 4(8) and the activation energy will be 8 quanta. It is obvious that the geometrical conditions are such that many parameters might contribute in determining the angle
The Journal of Physical Chemistry, Vol. 93, No. 16, 1989 6139
Catalytic Oxidation of Methylbenzenes over Metal Oxides
3.0
t 2.8
-
+
kcallmol
I 0 0
0 0
-
0 0
0
I
I
5
10
I 15
1
n
Figure 4. Graphical representation of ( E , - R T ) / n as a function of the quantum number n, cf. eq 7.
of deformation at the breaking stage. Such parameters are the M-0 distance ( a ) , the distance between the phenyl group to the plane of the surface (4,and the angle (a)that the phenyl group forms with the M-0-M-0 surface plane. This angle might be zero, but will probably have some definite value at step sites. The interaction between catalyst surface and the reactant may very well be of the kind depicted by Mori, Miyamoto, and Murakami in their recent paper.22 These authors suggest bonding to the aromatic ring from a surface OH group and to the CH3 unit from a V=O group. This means that, at surface step positions, the toluene molecule forms a distinct angle to the surface. Relation to Anharmonicity. We have now to consider the unequal spacing of the energy levels of Figure 2. According to the laws of molecular s p e c t r o s ~ o p ythe ~ ~vibrational energy of a molecule measured relative to its zero level energy is
Go(n,O,O) = nu0
+ xn2
(4)
where Gostands for the vibrational energy of the molecule in excess of the zero energy, x is the anharmonicity constant (with negative sign), and wo is the vibration frequency of the zero state. We have arbitrarily put the quantum numbers others than those of interest equal to zero to simplify the notation. These latter states are considered to be in thermal equilibrium during the reaction (cf. above). The frequency of the IR absorption most commonly observed (the n = 0 to n = 1 transition) is with these notations v(1-0) = wo
+x
(5)
From the model presented in Figure 2, making E the sum of all the quantum steps, it follows that
E = Go(n,O,O)
(6)
and, thus from eq 4
E = nu0
+ xn2
(7) It should be noted that E = E, - R T in the present approach, when we assume Qads= 0. Under all circumstances it is E that equals Go(n,O,O). To simplify the presentation we keep the assumption E = E, - R T for a while. From eq 7 it follows that ( E , - R T ) / n should be a linear function of n with the slope equal to x and the limit of ( E , - R T ) / n for n = 0 equal to the intrinsic vibration frequency wo. The value for n = 1 corresponds to the actual vibration frequency, observed in IR spectra. The formation of the quantity ( E , - R T ) / n is reported in Table I1 where we have used the mean values of E , - R T for the groups of similar values. A priori, we do not know the proper values of n. We have tried to find a sequence of n, however, that will give as constant a value of ( E , - R T ) / n as possible. Thus our first choice is that E, - RT = 26.9 kcal mol-' corresponds to n = 10 in eq 3, E, - RT = 11.1 kcal mol-' to n = 4, and E, - R T = 7.8 kcal mol-' to n = 3. This gives an approximate value of the ratio = 2.7 kcal mol-' and the other n (22) Mori, K.; Miyamoto, A,; Murakami, Y . J . Chem. SOC.,Faraday Trans. I 1987,83, 3303. (23) Herzberg, G.Infrared and Raman Spectra of Polyatomic Molecules; Van Nostrand: Princeton, NJ, 1945.
" I 5
I
10
I
15
Figure 5. Graphical representation of EJn quantum number n.
I
20
I 25
as a function of the
values are chosen to fall in suite with these numbers. In Figure 4, the relation between ( E , - R T ) / n and n is illustrated. The straight line is drawn from a least-squares regression analysis. No weighting of the various points has been done. One obtains an x value that is -0.0052 kcal mol-' corresponding to -2 cm-I. The value of the intercept is 2.77 kcal mol-' corresponding to 969 cm-I. From eq 5 the wavenumber of the I R absorption band should be 969 - 2 = 967 cm-I. This should be compared with the rocking mode absorption of the free molecules, 1042 f 4 cm-I. We have found no data for the anharmonicity of toluene molecular vibrations in literature. The value of x found here, however, seems to be of the right order of magnitude. Comparing bending mode vibrations quoted by H e r ~ b e r gone ~ ~finds -2.9 cm-' for H C N (ao= 712 cm-I); -2.3 cm-' for N 2 0 (wo = 588 cm-'); and -10.6 cm-' for H 2 0 (wo = 1210 cm-'). On the Finite Value of Qads. We now return to the interpretation of eq 1. It is indeed most probable that Qadsis not zero but has a finite value. The question is, under which circumstances is this value a constant one. If it was not, we would not expect to find even such a rough separation into groups of energy levels of E, as we actually do find in, e.g., Figure 1. It seems that the adsorption of toluene on metal oxides would be an ideal case for investigation as there must be more or less the same physical interaction between a chemically intact molecule and the oxide surface, independent of the nature of the oxide. This is also indicated by the data collected in Table I11 from literature s o ~ r c e s . ~One ~ , ~can ~ note that the variation of the data are only a few kilocalories per mole around a mean value that is of the order of 15 kcal mol-'. One observes from Table 111 that the heat of adsorption increases in the order toluene < p-xylene < m-xylene < o-xylene. This sequence is not equally pronounced for the (estimated) values of the chlorotoluenes. We have used the mean values obtained in Table 111 as representative of any oxide, especially of those oxides that are reported in Table I. In Table IV we have used these mean values to by application calculate the corrected activation energy, E = E, of eq 2 for the different catalysts. It is observed, especially for the data of Trimm et al.14 of the substituted toluenes, that the quantity E,,,, = E , - R T + Qads shows a smaller spread than E, - R T . Finally the ratio E,Jn is formed, where n has the same meaning as before. In chosing the proper values of n, three criteria are operating. The new value should correspond to the old one plus an addition that corresponds to the added heat of adsorption divided by the increment of energies (about 3 kcal mol-') from, e.g., Figure 1. This value of the increment also allows us to observe if there should be a number absent in the sequence of numbers as, e.g., between 13 and 15. Finally the doubling of the data of E,,, = 31.1 kcal mol-' to the one of E,, = 62.7 kcal mol-' should correspond to an approximate doubling of the number n (Le., from 11 to 24). The n set is thus not chosen at random. (24) OBrien, M. J.; Grob, R. L. J . Chromathogr. 1978, 155, 129. (25) Ciambelli, P.; Cresitelli, S.; de Simone, V.; Russo, G.Anal. Chim.
1973,63,701.
6140
The Journal of Physical Chemistry, Vol. 93, No. 16, 1989
TABLE 111: Heats of Adsorption (kcal mol-') (Q,& = -AH&) for the Compounds of Interest in This Paper Toluene v205 v204
Sn02 ZnO AI203
11.7 18.8 12.6 13.3 12.2"
24 24 24 24 25
13.7
+Xylene v2°5 v2°4
Sn02 ZnO
18.7 20.4 11.7 13.5
24 24 24 24
16.1
24 24 24 24
15.4
Larsson and Jonson TABLE I V Activation Energies for Oxidation of Methylbenzenes with Corrections for the Heat of Adsorption Given in Table 111' compound p-xylene p-xylene toluene o-chlorotoluene m-chlorotoluene p-chlorotoluene m-xylene p-xylene toluene toluene
m-Xylene v205 v204
Sn02 ZnO
14.9 19.3 12.2 15.3
p-Xylene v205 v2°4
Sn02 ZnO v205 v204
Sn02 ZnO
15.6 16.8 11.5 15.5
24 24 24 24
toluene m-xylene p-xylene o-xylene 'E,,,
14.9
o- Dichlorobenzene 16.3 24 14.9 24 13.7 24 14.8 24
v2°4
Sn02 ZnO
15.3 15.1 12.9 15.1
E.
molybdenum trioxide
molybdenum as cerium salt x% vanadium on TiOl x = IO x=2 x = 0.5 x = 0.2 x = 0.1 x=o
W/Mo oxides
= E, - RT
E,,,
n
E,Jn
49.1 8.2 27.4 16.9 17.4 17.2 17.1 18.05 28.7
62.7 24 21.9 8 39.7 15 31.0 1 1 31.0 1 1 31.1 11 31.1 11 31.6 1 1 41.0 15
2.61 2.74 2.65 2.82 2.82 2.83 2.83 2.87 2.73
28.6 24.0 15.6 13.2 20.8 34.4 12.0 12.0 10.0 9.0
41.0 36.4 28.0 25.6 33.2 46.8 24.4 26.1 23.6 23.8
2.73 2.80 2.80 2.84 2.77 2.75 2.71 2.90 2.95 2.98
15 13 10 9 12 17 9 9 8 8
+ Qadr. All energy data in kcal mol-'
TABLE V: Results of Least-Squares Analyses for the Data of Table IV, Applying a Variation of *I kcal mol-' on Q,& from the Values in Table 111
uo,cm-I ~(1-0), cm-I x , cm-'
m- Dic hlorobenzene v205
catalyst tin vanadate
24 24 24 24
corr coeff
+1
Qads - 1 kcal mol-'
(Table 111)
kcal mol-'
989 985 -4 -0.875
1041 1036 -5 -0.931
1093 1086 -7 -0.952
Qadr
Qads
p- Dichlorobenzene v205 v2°4
Sn02 ZnO v205 v2°4
SnOz ZnO v205 v2°4
Sn02 ZnO v205 v204
Sn02
ZnO
17.1 17.2 13.9 14.8
24 24 24 24
o-Chlorotoluene b b b b
17.5 17.7 12.7 14.2
m-Chlorotoluene 15.1 b 17.2 b 12.6 b 15.2 b p-Chlorotoluene b b b b
16.4 17.0 12.7 15.2
15.5
15.0
15.3
Mean value of data in ref 25. bEstimated value equal to the mean of the values for xylene and dichlorobenzene.
The result is represented graphically in Figure 5 . From a least-squares analysis we get the intercept as 2.98 kcal mol-' corresponding to 1041 cm-I. The anharmonicity parameter x = -5.3 cm-' and ~ ( 1 - 0 )= 1036 cm-' in good agreement with the value 1042 & 4 cm-l of the free molecules. The correlation coefficient is -0.93 1, actually a considerable improvement from the one representing the points of Figure 4, viz., -0.25. The question now remains, if it is correct to use one and the same value of Qadsfor different oxides (but the same adsorbate) as we have done in building up the data of Table IV. However, two factors might favor our choice; the first is the relative constancy for most of the data that we have used. The second is the circumstance that the basis for adsorption must be mainly dis-
'OI
Ea I kJ mol" I 10
1 20
I
30
Figure 6. Compensation effect plot from previous results,'* cf. Table I.
persion forces; there is not formed any specific chemical bond in the situation depicted in Figure 3. In order to show the influence of a systematic error in the choice of Qads,however, we have performed the same operation as in Figure 5 for some other values of QadS (but keeping the n values unchanged). A variation of Qad, with f l kcal mol-l gives the results reported in Table V. The Compensation Effect. In Table I we have included the preexponential terms for the catalytic oxidation of toluene over V/Ti02 previously studied by us.'' This makes it possible to test the relation between In A and the activation energy, often described as the compensation effect.26 In Figure 6, a plot of In A against E is recorded. One can observe that the points are linked by two parallel lines into two groups. These groups of data are exactly the same, with low and high vanadium coverage, respectively, as we found other arguments for in our previous paper.'* Such a sequence of "lines of compensation" are not unusual, something that has strongly been pointed out by Bond.27 The line covering most of the points was drawn from a least-squares regression analysis. The other line has been fitted to the other two points (26) Cremer, E.: Schwab, G. M. Z.Phys. Chem. 1929, A144, 243. (27) Bond, G. C. Z . Phys. Chem. N.F. 1985, 144, 21.
The Journal of Physical Chemisfry, Vol. 93, No. 16, 1989 6141
Catalytic Oxidation of Methylbenzenes over Metal Oxides using the same slope. The slope, 6, makes it possible to calculate the isocatalytic temperature, 8.
0 = l/bR
(8)
As b is found experimentally to be 0.597 (kcal/mol)-’/(f7%) we arrive at e = 837 60 K (9)
*
It may now be interesting to compare this value with the one that can be predicted from formula 10 deduced by one of us previo ~ s l ybased , ~ ~ on the analogy to a classical, coupled and damped oscillator system.
0 = N h c R ’ ( v Z - w Z ) w - ’ ( f ~ /-2 arctan [0.5vw(v2- w*)-’])-’ (10) Here w means the wavenumber of the catalyst vibrator and v means the wave number of the reactant vibrator. This relation is based on an integration over all possible damping coefficients (representing all possible modes of energy dissipation from the excited molecule). Hence it also takes into account all possible forms of heterogeneity of the catalyst surface that will make the conditions for each reacting molecule always to differ a little. For the case of “perfect resonance” between the catalyst vibrator and the reactant vibrator, i.e., if w = u , the isocatalytic temperature is given28 by 8 = Nhcv/2R = 0.715~ (11) Hence following our present model, v = 1040 cm-I, which will give us 8 = 744 K. This is almost within the limits of error of the experimental investigation. It should also be remembered that the case of “perfect resonance” will give a minimum value for 8. Any other value of the catalyst vibrator will give a (somewhat) larger value of This means that 744 K is the lowest possible value to be expected. Actually, in the previous paperz8the complete function of 8 ( w ) , i.e., eq 10, was calculated for two choices of v, viz., v = 1040 and 1120 cm-I. The latter value was chosen from indications of a volcano curve maximum at 560 cm-’ for the rate of the oxidation of toluene over a series of metal oxides when plotted against the M - 0 stretching frequencies of these metal oxide catalyst^.^ The idea is then that the second harmonic of this frequency (560cm-I) should resonate with the proper rocking frequency of the toluene molecule in its adsorbed state. It is not unreasonable that the rocking frequency is somewhat increased when the methyl group is at a van der Waal’s distance to the adsorbing surface. The curve obtained from eq 10 and v = 1120 cm-’ was found to give 8 = 870 K from a value of w = 985 cm-I, thought to correspond to the Mc=O stretching vibrations29of Moo3. This value was in very good agreement with 0 = 868 K that can be (28) Larsson, R. Chem. Scr. 1987, 27, 371. (29) Trifiro, F.; Centola, P.; Pasquon, I. J . Catal. 1968, 10, 86.
extracted from the most relevant data of Mars et al.15 by use, however, of somewhat more of their data than we have done in the present paper. The same curve (from v = 1 120 cm-’) gives 840 K for w = 1020 cm-’ (corresponding to w ~ = ~This ~ ) is. in very good agreement with the experimental value given by relation 9. It thus seems that the interpretation of the catalytic oxidation of toluene as a case of vibrational resonance can be strengthened by the observations on the compensation effect. It must be recalled that even if E # E,, the relation 10 is shown to holdz8 as long as Qads is constant for all the systems that adhere to one and the same slope of a “compensation effect” line.
Concluding Remarks We conclude that the similarity between the active vibration frequency obtained in the two ways, Le., from the activation energy increment and from the compensation effect formula, indicates that the model proposed is realistic. One should not expect the so determined vibration frequencies to be exactly identical with those of the free molecule. As pointed out above, the proper species to compare with is a molecule slightly perturbed by the adsorption forces. However, it is well-known from coordination chemistry30 that the bonding of the molecule to a metal ion does usually not result in a dramatic change in the frequencies of the coordinated molecule compared to those of its free state. In this specific case one can quite quote the results of Davidson and Riley3’ on solid (CO)3CrC6H5.CH3. These authors report the rocking mode of toluene at 1048 cm-’ from IR spectra and at 1070 cm-’ from Raman spectra. As said above one whould expect a slight increase also from the mere presence of a surface, making the bending of the methyl group somewhat more difficult. This effect probably adds to the electronic effect found by Davidson and Riley.31 Anyway, the increase thus expected is not larger than the error limits reported in Table V. Furthermore, one must keep in mind that one of our working assumptions to reach a simple mathematical treatment is that the heat of adsorption is constant from one catalyst system to another. This in turn implies only rather weak physical adsorption, caused by dispersion forces, chargetransfer interaction, or ion-dipole interaction. The relative proportion of these effects is not very important for the argument presented. All such adsorption forces may very well operate for the aromatic compounds studied in this paper. As is commonly believed,8that the rate-determining step is the splitting of a C-H methyl bond; it is, however, important to note that no other chemical bonds break before the rate-determining step. Hence the present case, the study of an “almost” unperturbed molecule whose vibration modes are known from analogy to the free one, might be considered as a favorable test study for the model proposed. (30) Nakamoto, K. Infrared Spectra of Inorganic and Coordination Compounds; Wiley: New York, 1963. (31) Davidson, G.; Riley, E. M. Spectrochim. Acta 1971, 27A, 1649.
