Ind. Eng. Chem. Fundam. 1986, 25, 656-658
656
Classical Catalytic Kinetics: A Placebo or the Real Thing? Michel Boudart Department of Chemical Engineering, Stanford University, Stanford, California 94305
There exist many catalytic reactions that proceed under set conditions on a given catalyst at a turnover rate that does not depend on the crystallographic orientation of the surface. I t is suggested that these so-called structure -insensitive reactions are usually operated under conditions of high surface coverage, 8, so that the structural features prevailing at low 8 are overwhelmed by the effect of lateral interactions at high 8. Under the same conditions, Langmuir-Hinshelwood, or Hougen-Watson, or classical kinetics applies within the same approximation as that applying to structure insensitivity. Thus, structure-insensitive reactions obey classical catalytic kinetics.
Introduction The recognition that the heat of adsorption of chemisorbed molecules on solid surfaces varies with fraction of surface coverage, 8, goes back to early measurements of calorimetric heats and of adsorption equilibria, the latter yielding isosteric heats of adsorption. This led Taylor (1925) to postulate nonuniform surfaces on which certain active centers may be needed for a chosen catalytic reaction. In the interpretation of Taylor and of his Princeton school in the 1930s and 19409, the main cause for a decrease of heat of chemisorption with 8 was the presence on the surface of various active sites, e.g., sites with low coordination numbers endowed with a particularly high adsorption potential. By contrast, at the same time work at Cambridge University in the school of Rideal focused on the study of clean metal surfaces, e.g., tungsten polycrystalline wires, with the conclusion that the main cause for the decrease of heat of chemisorption with 8 was lateral repulsive interactions between adsorbate species (Miller, 1949). These opposed views have now been shown to be mutally compatible as a result of the extensive adsorption work carrier out over the past 25 years on large single crystals of metals (Somorjai, 1981). For example, let us look (Figure 1) at the curves of heat of adsorption of H2 on various forms of tungsten single crystals as a function of coverage, expressed as a number density of hydrogen adatoms (Schmidt, 1974). In this figure, I also show the heat of adsorption of H2on a tungsten polycrystalline wire, as determined in 1935 a t Cambridge. Clearly, the results of Roberts, scattered around the straight line shown, go through the various curves of Schmidt for individual planes. A t low values of 8, structural effects predominate, while at high values of 8, the fall of heats of adsorption is attributed to the effect of lateral repulsive interactions. The effect may be indirect in that lateral repulsion forces adatoms from sites with a high binding energy into sites with a lower binding energy, or the effect may be direct at higher values of 8. At small values of 0, a small attractive interaction between adspecies may take place, leading to ordered overlayers. On the whole, the heat of chemisorption falls with 0, often in an approximately linear manner, at least over a range of 8 values that are neither too small nor too large. Clearly, the complete description of all the phenomena occurring as a monolayer dosed onto a solid surface is very complex. The net result, namely the curve of heat of adsorption vs. 8, is the signature of a heterogeneous surface, more appropriately called a nonuniform surface.
The Nonuniform Surface Many studies have been devoted to chemisorption of monolayers on nonuniform surfaces, consisting of large single crystals of metals (BBnard, 1983), small single crystals of zeolites (Benson et al., 1967), polycrystalline metals (Roberts, 1949), or X-ray amorphous materials (Clark et al., 1962). Surface nonuniformity is expressed both thermodynamically and kinetically. Thus, as 0 increases, to a linear decrease of heat of adsorption, q, with coverage corresponds a linear increase of the activation energy for adsorption, E,, and a linear decrease of the activation energy for desorption. In turn, these relations correspond to a logarithmic adsorption isotherm, to a rate of adsorption that decreases exponentially with increasing 8 (as expressed in an equation of Elovich), and to a rate of desorption increasing exponentially with increasing 0 (as expressed in an equation of Langmuir). The thermodynamic and kinetic expressions of nonuniformity are related through a relation that has been used for a long time in a semiempirical form, under various names (Bransted, Polanyi, Semenov) E , = C - aq (1) where C and (Y are constants. The constants, C and a, have recently been obtained theoretically by Shustorovich for adsorption of diatomic molecules on metal surfaces (Shustorovich, 1984) with C being ‘I4 of the dissociation energy of a molecule A2 and a = 3 / 4 . The best investigated surface that exhibits both thermodynamic and kinetic nonuniformity connected through eq 1 is that of metallic iron used as ammonia synthesis catalyst. The consequences of this nonuniformity and of eq 1 in catalytic kinetics were first formulated by Temkin and Pyzhev (1940). The rate equation is a power law expression where the rate, u, is expressed in terms of concentration of species as
The k’s are rate constants, and a is the parameter of eq 1. This rate expression, or minor modifications thereof, has been widely used to fit kinetic data over broad ranges of temperature and pressure. Yet taking surface nonuniformity into account in catalytic kinetics has remained a singular exception, except among the members of Temkin’s school (Kiperman, 1964). Weller (1956) reflected on surface nonuniformity and on the fact that power rate laws of the type of eq 2 fit kinetic data just as well as, or
0196-4313/86/1025-0656$01.50/00 1986 American Chemical Society
Ind. Eng. Chem. Fundam., Vol. 25, No. 4, 1986
The purpose of the present paper is to bring attention to a recent kinetic development in surface catalysis that provides an independent justification for using classical rate equations, not as a placebo, but as a correct representation of kinetics on a real surface.
1 30
0
0
05
1.0
1.5
2.0
25
n x 10-'51cm-2
Figure 1. Heat of chemisorption, q, of H2on tungsten vs. the number density of surface H atoms. The straight line represents the heat of adsorption of H, on polycrystalline tungsten according to Roberts (cf. Miller, 1949). The other curves are adapted from the review of L. D. Schmidt (1974).
sometimes better than, classical rate equations first popularized by Langmuir and Hinshelwood and then by Hougen and Watson (1947). He warned against what I call here the placebo effect of classical catalytic kinetic equations, in that their ability to fit kinetic data may be often accidental and their support of the kinetic mechanisms on which they are founded may be illusory. Weller recommended instead to use empirical power rate laws in place of the classical equations with kinetic and thermodynamic parameters of questionable meaning as they reflect a nonexistent surface uniformity. After Weller's article was submitted to AIChE J.,I was asked to comment on it by the editor of the Journal. This led to a companion paper (Boudart, 1956) published side by side with that of Weller. I acknowledged the existence and importance of surface nonuniformity but noted that, even in the case of ammonia synthesis, a classical rate expression based on the same kinetic mechanism as that of Temkin and Pyzhev led to a rate equation u=
m 2 1
- m-I3I2/[H2l3
1 + K["3I2/[H2l3
657
(3)
very similar to eq 2, with an adsorption equilibrium constant K replacing (Y as an adjustable parameter. Although eq 3 may well be considered as an approximation of the more realistic eq 2, I pointed out that both equations are very similar in their ability to fit kinetic data. If so, the advantage of classical rate equations such as eq 3 might be that, in spite of their approximate nature, they hinted at a kinetic mechanism that might be verifiable or improvable, as contrasted with empirical power rate laws that are solely designed to fit data. Since in most cases little is known about the very complex nature of surface nonuniformity, it is rare indeed to encounter a case where a power rate law such as that of Temkin and Pyzhev can be said to have theoretical meaning. In conclusion, I recommended the use of classical rate equations. That the latter may frequently be little more than a placebo making the practical kineticst feel better because their possible approximate theoretical content remained a possibility. More recently, Weller (1975) reexamined the situation and concluded he had no reason to modify his earlier position.
Structure-Insensitive Reactions During a period of 10 years (Boudart et al., 1966; Boudart, 1977), we encountered a representative number of reactions catalyzed by metals that were called structure insensitive. Their number is still growing (Boudart, 1985). A given structure-insensitive reaction proceeds on a given catalyst at a turnover rate that depends very little on the plane exposed on a large single crystal or on the crystal size of a small (1-10 nm) crystal, varies little with a modifier (sulfur, alloying element), and changes by a few orders of magnitude or less with the nature of the metal. By contrast, a structure-sensitive reaction is one for which everything that has just been said about structure-insensitive reactions is escalated by 1 or more orders of magnitude. The archetype of a structure-sensitive reaction is ammonia synthesis (Boudart and DjBga-Mariadassou, 1984). Another example is hydrogenolysis of alkanes (Engstrom et al., in press; Sinfelt, 1981). Typical structure-insensitive reactions are hydrogenation of alkenes and arenes, dehydrogenation of cycloalkanes, methanation on nickel, and dehydrogenation of secondary alcohols. In 1982, we added another characteristic differentiating structure-insensitive and structure-sensitive reactions (Boudart and Dj6ga-Mariadassou, 1982). The kinetics of structure-insensitive reactions has been described successfully by classical kinetics. By contrast, the rate of typical structure-sensitive reactions (ammonia synthesis, alkane hydrogenolysis) has been frequently expressed in terms of power rate laws. Before commenting further on this kinetic matter, I want to discuss briefly possible reasons for the occurrence of structure-insensitive reactions.
Why Structure-Insensitive Reactions Exist Various reasons to explain the existence of structureinsensitive reactions have been put forward (Boudart, 1985). The original one (Boudart, 1977) is that the ratedetermining step requires only one, or perhaps two, adjacent surface atoms. By contrast, a structure-sensitive reaction would need surface clusters, multiplets, or ensembles of more than two atoms. Other possibilities to explain structure insensitivity are surface reconstruction (Hanson and Boudart, 1978), extractive chemisorption (Kung et al., 1976),and formation of a catalytic metal alkyl overlayer (Madon et al., 1978; Thomson and Webb, 1976; Zaera et al., 1986). The above four possibilities may all explain in part specific examples of structure-insensitive reactions. As a conjecture, I want to suggest another factor that explains structure insensitivity in a general way. Consider for instance the oxidation of carbon monoxide palladium as reviewed elsewhere (Boudart and DjBga-Mariadassou, 1984). At low pressures, for a range of reactant ratios and at about 400 K, the turnover rate is rigorously structure insensitive, which means invariant, as shown by work on small crystals (1-8 nm) and large single crystals exposing different planes. The turnover rate, ut, is expressed by a classical rate law that goes back to Langmuir U t = ~[O,I/K[COl (4) where Iz is a rate constant for dissociative chemisorption of O2 on a surface almost completely covered with CO reversibly adsorbed, as expressed by its equilibrium constant K. The familiar reason why the denominator of eq
658
Ind. Eng. Chem. Fundam., Vol. 25, No. 4 , 1986
4 is K[CO] and not 1 + K[CO] is that the surface is assumed to be completely covered with CO. Now, at high surface coverage, as shown in Figure 1, structural nonuniformities are overwhelmed by surface interactions. It is proposed that this is the main reason for the structure inuariance of the rate. It must be noted that the rate is inversely proportional to [CO] and not to [CO]1’2. This suggests that the O2 requires only one atom and not two atoms for its chemisorption in a precursor state prior to dissociation. Thus, the original explanation of structure insensitivity (Boudart, 1977) is preserved: i.e., only one atom (or perhaps a couple) is needed for the critical step. But besides, it is noted that the steady-state surface is almost completely saturated. Finally, it must be noted that surface reconstruction, extractive chemisorption, or the presence of a carbonaceous overlayer has been ruled out experimentally for the reaction just discussed under the conditions specified above. Examination of the other structure-insensitive reactions listed elsewhere (Boudart and DjBga-Mariadassou, 1982; Boudart and Dj6ga-Mariadassou, 1984) shows that they all are run under conditions of a completely covered surface. This does not necessarily lead to trivial, i.e., zeroorder, rate equations as shown by eq 4 for the oxidation of carbon monoxide on palladium or the elegant example of cohydrogenation of various aromatic molecules on nickel, in which case the whole surface is partitioned between various adsorbed species characterized by adsorption equilibrium constants that are entirely self-consistent in the framework of classical kinetics (Boudart and DjBgaMariadassou, 1984). The latter example is a fine illustration of the self-consistent application of chemical kinetics that was mentioned in my early assessment of the subject (Boudart, 1956). From the conjecture that a necessary but not sufficient condition for a reaction to be structure insensitive is that it take place on a surface a t high coverage, it follows that a reaction could be structure sensitive, say at low pressure and high temperature, but become structure insensitive at low temperature and high pressure. This was observed for the H2-D2 equilibration reaction, under the former conditions by Christmann and Ertl(1976) and under the latter conditions by Poltorak and Boronin (1965). It also follows from the above conjecture that a reaction requiring a sizable surface ensemble or multiplet must be structure sensitive since it cannot take place in a quasisaturated layer due to the low probability of finding the necessary ensembles in such a layer. A t any rate, irrespective of the reason or reasons explaining structure insensitivity, it is almost self-evident that a reaction run under conditions of structure insensitivity can be described kinetically in a rigorous manner by classical kinetics. Indeed, if the reaction takes place at the same turnover rate on the main surface structures available, the nonuniformity of the surface inherent in these structures does not manifest itself kinetically.
Conclusion: The Validity of Classical Catalytic Kinetics The common observation that classical catalytic kinetics describes adequately data obtained on nonuniform surfaces has been called a paradox (Boudart, 1956). One resolution of the paradox may be that classical catalytic kinetics is only approximaate. Thus, J. M. Smith (1982) concludes the following in a review entitled “Thirty-Five Years of Applied Catalytic Kinetics”. “Most practitioners of applied kinetics now properly describe the adjustable quantities in the final rate equa-
tions as parameters rather than as true rates and equilibrium constants. This pronouncement does not differ significantly from the one given in the conclusion of Weller’s 1975 paper, and that, in turn, does not differ greatly from the evaluation he offered much earlier (Weller, 19561.’’ Another resolution of the paradox is proposed in this paper. For structure-insensitive reactions, classical catalytic kinetics applies rigorously, and this may be considered as an experimental fact, no matter what the explanation or explanations of structure insensitivity may be. Thus, for structure-insensitive reactions, the use of classical catalytic kinetics is not only useful as I suggested earlier (Boudart, 1956), but it also is correct. The applied kineticist who uses systematically classical catalytic kinetics (Froment and Hosten, 1981) in the modeling of rate data is not using a placebo: not only is it always a useful approximation, even in the case of structure-sensitive reactions that perceive the nonuniformity of surfaces, but it can also be t h e real thing in the case of structure-insensitive reactions that do not sense this nonuniformity. Thus, Hougen and Watson (1947) were wise in systematizing the use of classical catalytic kinetics: the corresponding equations can be not only approximately right, but they are correct for structure-insensitive reactions. In all cases, their use by the process engineer provides physical intuition, improvable rate equations, and mechanistic insights unattainable through empirical power rate laws.
Acknowledgment This work has been made possible through a long series of continuing NSF Grants, currently NSF-CBT-8219066.
Literature Cited BBnard, J. Adsorption on Metal Surfaces : Elsevier Scientific Publishing: Amsterdam, 1983. Benson, J. E.; Ushiba, K.; Boudart, M. J. Catal. 1967, 9, 91. Boudart, M. AIChE J. 1956, 2 , 62. Boudart, M. Proc. Int. Congr. Catal., 5th, 1976, 1977, 7 , 1. Boudart, M.; Aldag, A. W.; Benson, J. W.; Dougharty, N. A,; Harkins, C. G. J . Catal. 1966, 6 , 92. Boudart, M.; DjBga-Mariadassou. G. Cinetique des Rgactions en Catalyse HBtBroghe; Masson Pubiishers: Paris, 1982; p 208. Boudart, M.; DjBga-Mariadassou, G. Kinetics of Heterogeneous Catalytic Reactions ; Princeton University Press: Princeton, NJ, 1984. Boudart, M. J . Mol. Catal. 1985, 30,27. Christmann, K.; Ertl, G. Surf. Sci. 1976, 6 0 , 365. Clark, A,; Holm, V. C.; Blackburn, D. M. 3 . Catal. 1962, 7 , 244. Engstrom, J. R.; Goodman, D. W.; Weinberg, J. Am. Chem. Soc., in press. Froment, G. F.; Hosten, L. In Catalysis: Science and Technology;Anderson, J. R., Boudart, M., Eds.; Springer-Verlag: Heidelberg, 1981; Voi. 2, p 97. Hanson, F. V.;Boudart, M. J. Cafal. 1978, 53,56. Hougen, D. A,; Watson, K . M. Chemical Process Principles; Wiiey: New York, 1947; Part 111. Kiperman, S. L. Introduction to the Kinetics of Heterogeneous Catalytic Reactions ; Moscow, 1964. Kung, H. H.; Pellet, R. J.; Burwell, R. L., Jr. J . Am. Chem. SOC.1976, 9 8 , 5603. Madon, R. J.; O’Connell, J. P.; Boudart. M. AIChE J . 1978. 2 4 , 104. Miller, A. R. The Adsorption of Gases on Solids; Cambridge University Press: Cambridge, MA, 1949; p 19. Poltorak, 0. M.: Boronin, V. S. Zh. Fir. Khim. 1965, 3 9 , 2471 Schmidt. L. D. Catal. Rev.-Sci. €no. 1974. 9 . 115. Shustorovich, E. J. Am. Chem. Socy 1984, 106. 6479. Sinfelt, J. H. I n Catalysis: Science and Technology; Anderson, J. R., Boudart, M., Eds.; Springer-Verlag: Heidelberg, 1981; Vol. 1, P 270. Smith, J. M. Ind. Eng. Chem. Fundam. 1982, 2 1 , 327. Somorjai, G. A. Chemistry in Two Dimensions: Surfaces; Cornell University Press: Ithaca, NY, 1981. Taylor, H. S. Proc. R. SOC.London, A 1925, 108, 105. Temkin, V . I.; Pyzhev, V. Acta Physicochim. URSS 1940, 12, 217. Thomson, S. J.; Webb, G. J. Chem. Soc., Chem. Commun. 1976, 526. Weiler, S. AIChE J. 1956, 2 , 59. Weller, S . Adv. Chem. Ser. 1975, No. 148, 156. Zaera, F . ; Gellman, A. J.; Somorjai, G. A. Acc. Chem. Res. 1986. 79, 24.
Recezued for review June 12, 1986 Accepted J u l y 29, 1986
