Ind. Eng. Chem. Res. 1989, 28, 376-379
376
CORRESPONDENCE Classical Catalytic Kinetics: What Is the Point of the Matter? Sir: Realibility of kinetic models applied to describe heterogeneous catalytic processes is rather important both from theoretical and practical points of view. An interesting paper by Boudart (1986) brought attention to a significant problem, namely, to the inadequacy of kinetic models with respect to the specific features and mechanism of catalytic reactions. The principal conceptions stated by Boudart can be summarized as follows: 1. As a rule, the kinetics of heterogeneous catalytic reactions may be described either by power law expressions or by equations popularized by Langmuir-Hinshelwood and then by Hougen-Watson. Most of the power law equations applied have been empirically derived or approximate more complicated relations. 2. The surface nonuniformity of solid catalysts does not practically influence the reaction kinetics (“the paradox of chemical kinetics” (Boudart, 1956)). Usually, the kinetics can be described by Langmuir-Hinshelwood or Hougen-Watson equations referred to by Boudart as “classical kinetic equations”. These equations correspond to the concept of processes in ideal adsorbed layers. 3. The power law form of the kinetic expressions should be considered not as an empirical approximation but as the right model when it is applied to take into account surface nonuniformity. Yet, the only case of such an interpretation seems to be the rate expression for ammonia synthesis formulated by Temkin and Pyzhev (1939):
(0
It does not take into account a broad group of equations relating to none of the classes mentioned. Thus, isomerization of n-pentane into isopentane over a platinum-lead-alumina catalyst is described by the equation (Vartanov et al., 1984)
where y is a parameter considering the back-reaction effect (Kiperman and Gadji-Kasumov, 1965). The isoamylene dehydrogenation over a zinc-chromia catalyst is described by the equation (Voikina et al., 1975, 1977)
r=h
ply
(P1+ k’P,)’
(4)
where PI and Pz denote the partial pressures of the reactant and the reaction product, respectively, and 1 = 0.5. The same equation for 1 = 0.5-0.6 characterizes the cyclohexanol dehydrogenation into cyclohexanone on copper-magnesia catalyst (Medvedeva et al., 1976). The rate of selective hydrogenation of dimethylethynyl carbinol on a palladium-lead catalyst follows the equation (Levin et al., 1971) PlY r=k (5) ( P I+ ~ ’ P H ; ’ ~ ) ’ for 2 < 1 < 3. The kinetic equation describing phosgene synthesis over a coal catalyst (Shapatina et al., 1976,1977, 1979) has the form
< a < 1).
Boudart notes that such an approach to consider surface nonuniformity has been applied solely by Kiperman in his monograph (1964). On the other hand, Boudart maintains that eq 1 can be quite successfully replaced by a classical kinetic equation (Boudart, 1956): 6PN2- &PNHS2/PH,3 r = (2) 1 + KPNH,2/PH,3 4. Structure-sensitive reactions can be described by means of power law kinetic equations. Structure-insensitive reactions are supposed to proceed under conditions of high coverage surface. It is almost self-evident that the latter obey the classical kinetics. A reaction may exhibit either structure sensitivity or structure insensitivity depending on the process conditions. 5 . Since classical kinetic equations can reflect the process mechanism and prove to be useful in practice, they should not be regarded as a placebo. Some of the points presented don’t seem to be well grounded, and we should like to discuss them. Kinetic Equations Considering Surface Non uniformity The classification of heterogeneous catalytic reactions proposed by Boudart appears to not be complete enough.
r=k
PCOPCI~O.~~ ( k ‘Pco + Pcoc12)o.25
(6)
None of these kinetic equations can be related to the classical or to the power law class of relations. Nevertheless, they have been derived by use of rigorous kinetic methods within broad ranges of parameter variation and correspond to certain step schemes supported by isotopic, spectral, and adsorption investigations (Kiperman, 1978a,b, 1982, 1984). A detailed analysis carried out using the method of Koltsov and Kiperman (1978) showed that such kinetic expressions do fit experimental data more adequately than other relations, including classical kinetics. Equations 3-6, although not being of power law form, arise directly from the concept of processes occurring on nonuniform surfaces. As Boudart rightly notes, the power law expressions are in most cases approximations of more real equations. However, they may approximate not only classical catalytic kinetics but more complicated kinetic expressions for processes on nonuniform surfaces, as well. Thus, the power law equation (eq I), being correct for the reaction occurring not far from the equilibrium via one slow step, follows from a more general relation (Temkin, 1979; Temkin et al., 1963). The possibility pointed out by Boudart (1956,1986) to replace eq 1 by classical eq 2 would not be realizable
088S-5SS5/S9/262S-0376~0~.50/0‘0 1989 American Chemical Society
Ind. Eng. Chem. Res., Vol. 28, No. 3, 1989 377 within the whole range of pressures (up to 500 atm; see Kiperman (1964, 1979a,b)) for which eq 1 is valid. Indeed, eq 1characterizes the reaction rate on nonuniform catalyst surfaces for the region of medium surface coverages, where the adsorption equilibrium corresponds to the logarithmic adsorption isotherm and is therefore slightly sensitive to equilibrium pressure variations. This is the reason that eq 1 is reliable in such a broad pressure interval. By contrast, eq 2 corresponds to the reaction rates in the region of medium coverages of uniform surfaces where the Langmuir isotherm is sensitive to the pressure variations and should not fit such a broad interval of pressures. We cannot agree with Boudart’s statement that the ammonia synthesis and some reactions mentioned in Kiperman’s monograph (1964) are the only examples of treating the kinetic data from the point of view of surface nonuniformity. Obviously, such an opinion follows from poor information about a series of works carried out, in particular, by Soviet and Bulgarian investigators after 1964. These papers are in Chemical Abstracts; some of them are published in English as well. By way of example, we should mention the kinetics of a series of processes such as benzene hydrogenation, cyclohexene hydrogenation, toluene hydrogenation, cyclohexane dehydrogenation (Zlotina and Kiperman, 1967; Gudkov et al., 1970; Andreev et al., 1965, 1966a,b; Kiperman et al., 1971; Mamaladze et al., 1977); hydrogenation of benzene and hexene mixtures (Palazov et al., 1971); isoprene hydrogenation (Beisembaeva et al., 1976, 1984); nitrobenzene hydrogenation (Pogorelov et al., 1975; Vigdorovich et al., 1980); liquidphase hydrogenation of organic compounds (Kiperman, 1968, 1978a,b, 1986); configuration isomerization of cis, trans-dimethylcyclohexane mixtures (Petrov and Shopov, 1969); ethylene oxidation with gas-phase promotion (Talaeva et al., 1980); methane and CO oxidation (Andrievskaya et al., 1980); oxidation of alcohols (Slouka and Beranek, 1979); oxidative ammonoxidation of propylene (Sadovskii and Gelbstein, 1973);oxidative dehydrogenation of n-butane (Aliev et al., 1980); oxidative chlorination of ethane (Shcheglova et al., 1975); methanol synthesis (Pomeranzev, 1973); and isotopic exchange of oxides (Avetisov and Goldstein, 1975). We should like to accentuate once more that most of the processes mentioned have been studied by means of a complex of various methods (Kiperman, 1978a,b). The kinetic data fit the expressions corresponding to definite reaction scheme on nonuniform surfaces more adequately than the classical kinetic equations. In addition, nonpower equations (3)-(6) were treated from the point of view of surface nonuniformity observed in such systems. In a number of investigations devoted to catalyst deactivation in the course of the reaction (Kiperman et al., 1982; Avetisov et al., 1984), the authors took into account surface nonuniformity. Snagovsky and Avetisov (1971, 1972) developed an algorithm to derive kinetic equations for multiroute reactions on nonuniform surfaces. Evidently, by contrast to Boudart’s statement, the literature is rich in works describing kinetics of catalytic reactions that fit not the classical equations but rather are in accordance with the conception of surface nonuniformity. We would like to bring further attention to the fact that the forms of the kinetic equations mentioned do not cover the whole variety of effects caused by surface nonuniformity on the kinetics of catalytic reactions.
Is There “a Kinetic Paradox”? In the cases when two or more intermediates of comparable surface concentration take part in the reaction, the
kinetic data usually do not fit power law expressions. Equations 3-6 are the very examples of kinetic descriptions considering the adsorption of several species on nonuniform catalytic surfaces. The kinetics of a number of other processes occurring on nonuniform catalyst surfaces obey rate equations reflecting this concept. At the same time, these relations coincide with the classical kinetic equations. Thus, the reaction rate on a nonuniform surface can be described in general form by the equation (Kiperman, 1964, 1979a,b)
IIPj.1 r=k
I
(Ck/Pj)‘
(7)
j
Here, Pj denotes the partial pressures of the reatants, p j is the fugativities of the species adsorbed, 1 = ma, and 0 < CY < 1. This equation is valid for any of the following rate-determining steps: dissociative adsorption into m particles; desorption of m particles of dissociatively adsorbed products; interaction of m adsorbed components. The cases of CY = 1 or 0 correspond formally to processes on surfaces of total or slight coverage, respectively. The value of CY is often about 0.5 for reactions in the region of medium surface coverage. Equations 3-6 follow from eq 7 for m = 1and CY = 0.5. Equation 7 a t CY = 0.5 takes the form of the classical kinetic equations when m = 2. Kinetic equations of this type, reflecting the concept of surface nonuniformity, have been obtained for many processes. In connection with this, a lot of papers can be cited in which the reaction kinetics and process mechanism have been studied, For example, hydrogenation of C,-C9 olefins and their mixtures in the presence of aromatics (Matveeva et al., 1982, 1983), heptene hydrogenation (Fialkova et al., 1980), catalytic transformations of methyl furfural (Yuskovets et al., 1983,1984), 2-propanol dehydrogenation (Gegenava and Kiperman, 1974), n-pentane hydrogenolysis (Davydov et al., 1977, 1978), isobutene dehydrogenation on platinum catalysts (Luu Kam Lok et al., 1986a,b), isooctane dehydrocyclization (Bragin et al., 1980; Krasavin et al., 1982), and CO methanation (Ibraeva et al., 1987). It should be noted that the concept of surface uniformity would bring entirely different relations containing a denominator to the second power. Such equations either poorly describe the experimental data or prove not to be adequate at all for the information concerning kinetics and mechanism of the process. It should be pointed out that Boudart (1972) had a reasonable statement, namely that “...great care must be exercised in the case of rate equations based on the assumption of ideal surfaces.” As is well-known (see, e.g., Kiperman (1964, 1979a,b)), the kinetic laws of the reactions become apparent in the region of medium coverages. In the regions of low and full coverage, the surface nonuniformity is not manifested in relationships simulating the ideal adsorbed layer. Such a situation has been observed for many catalytic reactions carried out on surfaces certain to be nonuniform both at low and high coverage. By way of example, we shall mention the following processes: ethane hydrogenolysis (Gudkov et al., 1982), benzene deuteriogenation (Gudkov, 1979), oxidative dehydrogenation of ethylbenzene (Shakhnovich et al., 1984), isotopic exchange in cyclohexane (Nekrasov et al., 1974), total oxidation of organic compounds (Kiperman, 1979a,b, 1981, 1986), and the water shift reaction (Turchaninov et al., 1987). For this reason, describing the kinetics of processes by use of equations simulating the ideal adsorbed layer should not be considered a kinetic paradox, but rather a realiza-
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tion of the predictions of the theory of processes on nonuniform surfaces. The real state of affairs can be summarized as follows. The kinetics of reactions on nonuniform surfaces at medium coverage can be formally described by use of expressions which stimulate classical kinetics. Yet, with interpretation from the point of view of the ideal surface layer, the reaction mechanisms that follow from these models do not correspond to independent experimental data. The kinetics of reactions occurring at low or high surface coverage is insensitive to surface nonuniformity. Again, this phenomenon is not a paradox, since it is explained by the fact that reactions occur, respectively, on the few sites of maximal activity available or on some vacant sites of minimal activity. Structure-Sensitive a n d Structure-Insensitive Reactions As stated above, structure-sensitive reactions (such as ammonia synthesis, hydrogenolysis of hydrocarbons and others) are certainly not described by use of power law equations. About structure-insensitive reactions, Boudart suggests that they should occur at high coverage of surface and can be rigorously described by classical kinetics. However, as evident from the results listed above, structure-insensitive reactions neither proceed obligatorily a t high surface coverages nor are bound to classical kinetic descriptions. It is sufficient for us to point out the hydrogenation reactions (Kiperman, 1968, 1978a,b, 1979a,b, 1981, 1982, 1983a,b, 1986; Kiperman et al., 1971), as well as of the reactions of dehydrogenation, CO methanation on Ni, isotopic exchange, and other reactions cited above (see also Boudart (1985)). Boudart’s statement (1986) that structure-sensitive reactions are hardly probable at high surface coverage, due to the “ensemble effect”, seems not well grounded. Indeed, the probability that a fraction of the layer adsorbed comes in touch with ensembles of the necessary configuration may even increase at total coverage of the surface compared to low coverage, especially when the process is accompanied by gas-phase exchange or surface migration. The results listed indicate that reactions regarded to be structure sensitive under certain conditions (Boudart, 1985, 1986) can take place at high surface coverage. This shows once again that there is no direct correspondence between the region of surface coverage and the structure sensitivity of the reactions occurring. Conclusions In view of our discussion, we come back now to the question stated by Boudart in his paper (1986). As is known, exact and reliable kinetic descriptions of the catalytic reactions are of primary importance for the process simulation and reactor design. For this reason, it is desirable to use kinetic models fitting adequately the experimental data and supported by reasonable reaction mechanisms. Equations following classical kinetics as well as equations not corresponding to this approach (Kiperman, 1978a,b, 1984) can be successfully applied for the simulation of different catalytic processes. Any rigorous nonempirical kinetic description is useful for process design and therfore, as Boudart holds, is not a placebo only. However, such an important feature of the kinetic models should not depend on whether they correspond or not to our classical kinetics. In connection with this, we bring our attention to the following question: what is to be treated as classical catalytic kinetics? The fact that a given kinetic equation follows from Langmuir-Hinshelwood-Hougen-Watson
kinetics should not be grounds to call the equation classical. Such descriptions often prove to be formal, e.g., equations containing a denominator to the fifth power (Veirosta et al., 1972). It should be pointed out that the concept of possible deviations from the behavior of ideal adsorbed layers has been in fact developed by Langmuir simultaneously with his adsorption theory. Therefore, it is unreasonable to treat as classical only those kinetic equations which correspond to the concept of processes in ideal adsorbed layers. It seems more reasonable to consider as classical those kinetic descriptions which reflect a proved mechanism and have borne the test of time. An obvious case of this is eq 1, having survived near half a century. Kinetic descriptions of this type are few for the present. One of the main problems in the chemical kinetics of heterogeneous catalysis is to enlarge the number of such kinetic models. Literature Cited Aliev, V. S.; Gadji-Kasumov, S. V.; Rizaev, R. G. In Kinetika-3. 3rd Conference on Kinetics of Heterosenously Catalytic Reactions; Slinko, M. G., Ed.; Kalinin: New York, 1980; Vol. 1, p 9. Andreev, A. A.; Shopov, D. M.; Kiperman, S. L. Kinet. Katal. 1965, 6,869. Andreev, A.; Shopov, D.; Kiperman, S. L. Kinet. Katal. 1966a,7,120, 1092. Andreev, A.; Shopov, D.; Kiperman, S. L. C. R. Acad. Buls. Sci. 1966b,19, 1051. Andrievskaya, G. H.; Avetisov, A. A.; Gelbstein, A. I. kinetika 3. In 3rd Conference on Kinetics of Heterosenous Catalytic Reactions; Slinko, M. G., Ed.; Kalinin: New York, 1980; Vol. 1, p 3. Avetisov, A. K.; Goldstein, N. D. Kinetika-2. In 2nd Conference on Kinetics of Catalytic Reactions; Slinko, M. G., Ed.; Novosibirsk: New York, 1975; Vol. 2, p 20. Avetisov, A. K.; Posorelov, V. V.; Visdorovich, F. L. K i n ~ tKatal. . 1983,24,472. Avetisov, A. K.; Posorelov, V. V.; Visdorovich, F. L. Collection of Papers of International Symposium. In Theoretical Problems on Kinetics of Catalytic Reactions; Kiperman, S . L., Ed.; Chernosolovka: New York, 1984; p 34. Beisembaeva, Z. T.; Gudkov, B. S.; Kharson, M. S.; Popov, N. 1.; Kiperman, S. L. Kinetika-2. In 2nd Conference on Kinetics of Catalytic Reactions; Slinko, M. G., Ed.; Novosibirsk: New York, 1975;Vol. 2, p 104. Beisembaeva. Z. T.: PODOV. N. I.:,KiDerman. S. L. I z L ~Acad. . Nauk . SSSR, Ser; Khim. 1976,’37. Beisembaeva, Z.T.; Gudkov, B. S.; Kiperman, S. L. Izu. Acad. Nauk SSSR, Ser. Khim. 1984,525. Boudart, M. AIChE J . 1956,2,62. Boudart, M.AIChE J . 1972,18,405. Boudart, M. J . Mol. Catal. 1985,30, 27. Boudart, M. Ind. Ens. Chem. Fundam. 1986,25,656. Brasin, 0.V.; Krasavin, S. A.; Liberman, A. 1.; Kharson, M. S.; Kiperman, S. L. Izu. Acad. Nauk SSSR, Ser. Khim. 1980, 1946. Davydov, E. M.; Kharson, M. S.; Kiperman, S. L. Itu. Acad. Nauk SSSR, Ser. Khim. 1977,2687. Davydov, E. M.; Kharson, M. S.; Gudkov, B. S.; Koltsov, N. I.; Kiperman, S. L. Kinet. Katal. 1978,19, 650, 955. Fialkova, I. M.; Shvedova, G. N.; Nekrasov, N. V.; Hofman, M. V.; Kiperman, S. L. Kinetika-3. In 3rd Conference on Kinetics of Heterosenous Catalytic Reactions; Slinko, M. G., Ed.; Kalinin: New York, 1980; Vol. 2, p 478. Gesenava, T. P.; Kiperman, S. L. Bull. Acad. Sci. Georgian SSR 1974,74, 613. Gudkov, B. S. Kinet. Katal. 1979,20,668. Gudkov, B. S.; Guczi, L.; Tetenyi, P. J . Catal. 1982,74, 207. Gudkov, B. S.; Zlotina, N. E.; Makhlis, L. A.; Kiperman, S. L. Izu. Acad. Nauk SSSR, Ser. Khim. 1970,2525. Ibraeva, Z. A.; Nekrasov, N. V.; Gudkov, B. S.; Yakerson, V. I.; Golosman, E. Z.; Beisembaeva, Z. T.; Kiperman, S. L. Kinet. Katal. 1987,28, 386. Kiperman, S. L. Nauka. In Introduction to the Kinetics of Heteros. Catalytic Reactions; Wiley: Mowcow, 1964. Kiperman, S. L. Commun. D e p . Chem. Buls. Acad. Sci. 1965,1110; 1968,1, 73.
Ind. E n g . Chem. Res. 1989,28, 379-380 Kiperman, S. L. Usp. Khim. 1978a, 47, 3. Kiperman, S. L. Znt. Chem. Ens. 197813, 18, 59. Kiperman, S. L. Foundations of Chem. Kinetics in Heteros. Catalysis, Moscow, 1979. Kiperman, S. L. Kinetics & Catalysis. In Kinetic Problems in Heteros. Oxidation Catalysis; VINITI: Mowcow, 1979b; Vol. 6. Kiperman, S. L. Problems of Kinetics and Catalysis: Nauka: Moscow, 1981; Vol. 18, p 14. Kiperman, S. L. Kinet. Katal. 1982, 23, 1429. Kiperman, S. L. Commun. Dep. Chem. Buls. Acad. Sci. 1983a, 16, 22. Kiperman, S. L. VZZ Souiet-Japan Seminar on Catalysis, Novosibirsk, 1983b, p 203, Kiuerman. S. L. I Soviet-Indian Seminar on Catalvsis. Novosibirsk. i984, p‘217. Kiperman, S. L. in Catalysis Hydrosenation. Studies in Surface Science and Catalysis; Cerveny, L., Ed.; Elsevier: Amsterdam, 1986; Vol. 27, p 1. Kiperman, S. L.; Gadji-Kasumov, S. V. Izu. Acad. Nauk SSSR, Ser. Khim. 1965, 1110. Kiperman, S. L.; Gaidaj, N. A.; Nekrasov, N. V.; Kostyukovsky, M. M. Chem. Ens. Commun. 1982,18, 39. Kiperman, S.; Shopov, D.; Andreev, A.; Zlotina, N.; Gudkov, B. S. Commun. Dep. Chem. Buls. Acad. Sci. 1971,4, 237. Koltsov, N. I.; Kiperman, S. L. J. Res. Inst. Catal., Hokkaido Uniu. 1978, 26, 85. Krasavin, S. A,; Kharson, M. S.; Kostyukovsky, M. M.; Brasin, 0. V.; Kiperman, S. L. Izu. Acad. Nauk SSSR, Ser. Khim. 1982, 1231. Levin, D. Z.; Besprozvany, M. A.; Melamed, F. A.; Kiperman, S. L. Kinet. Katal. 1971, 12, 1455. Luu Kam Lok, T.; Gaidaj, N. A.; Gudkov, B. S.; Kiperman, S. L.; Kosan, S. B. Kinet. Katal. 1986,27, 1365. Luu Kam Lok, T.; Gaidaj, N. A.; Gudkov, B. S.; Kostyukovsky, M. M.; Kiperman, S. L.; Podkletnova, N. M.; Kosan, S. B.; Bursian, N. R. Kinet. Katal. 1986,27, 1371. Mamaladze, L. M.; Nekrasov, N. V.; Gudkov, B. S.; Kiperman, S. L. Acta Chim. Acad. Sci. Hung. 1977, 92, 73. Matveeva, T. M.; Nekrasov, N. V.; Kostyukovsky, M. M.; Navalikhina, M. D.; Krichko, A. A,; Kiperman, S. L. Izu. Acad. Nauk SSSR, Ser. Khim. 1982, 243; Proc. Intern. Symp. Heteros. Catalysis, Part 1, Varna, 1983, p 207. Medvedeva, 0. N.; Badrian, A. S.; Kiperman, S. L. Kinet. Katal. 1976, 17, 1530. Nekrasov, N. V.; Gudkov, B. S.; Kiperman, S. L. Zzu. Acad. Nauk SSSR, Ser. Khim. 1974, 1262, 2458. Palazov, A.; Andreev, A.; Shopov, D. Kinet. Katal. 1971, 12, 969. Petrov, L.; Shopov, D. C. R. Acad. Buls. Sci. 1969,2,289; Commun. Dep. Chem. Bulg. Acad. Sci. 1969,2, 313, 903. Posorelov, V. V.; Visdorovich, F. L.; Gelbstein, A. I. Kinetika-2. In 2nd Conference on Kinetics of Heteros. Catal. Reactions; Novosibirsk: New York, 1975, Vol. 2, p 88. ~I
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Pomeranzev, V. M. In Processes with Participation of Molecular Hydrogen; Kiperman, S. L., Ed.; Novosibirsk: New York, 1973; p 35. Sadovskii, A. S.; Gelbstein, A. I. Partial Oxidation of Hydrocarbons. Methodical a. Mathematic Problems of Kinetics; Novosibirsk: New York, 1973; p 8. Shakhnovich, G. V.; Belomestnych, I. P.; Nekrasov, N. V.; Kostyukovsky, M. M.; Kiperman, S. L. Appl. Catal. 1984,12, 83. Shapatina, E. N.; Kuchaev, V. L.; Pencovoi, B. L.; Temkin, M. I. Kinet. Katal. 1976, 17,644; 1977, 18, 968; 1979,20, 1183. Shcheslova, G. G.; Feofanova, N. M.; Sharapova, E. D.; Bakshi, Yu. M.; Gelbstein, A. I. Kinetika-2. In 2nd Conference on Kinetics of Catal. Reacts; Slinko, M. G., Ed.; Novosibirsk New York, 1975; Vol. 1, p 85. Slouka, P.; Beranek, L. Collect. Czech. Chem. Commun. 1979, 44, 1591. Snagovsky, Yu. S.; Avetisov, A. K. Dokl. Acad. Nauk SSSR 1971, 196, 878. Snagovsky, Yu. S.; Avetisov, A. K. Kinet. Katal. 1972, 13, 1070. Talaeva, I. G.; Vasilevich, L. A.; Avetisov, A. K.; Chesnokov, B. B.; Gelbstein, A. I. Kinetika-3. In 3rd Conference on Kinetics of Heteros. Catal. React.; Slinko, M. G.; Ed.; Kalinin: New York, 1980; Vol. 2, p 441. Temkin, M. I. Adu. Catal. 1979, 28, 173. Temkin, M. I.; Pyzhev, V. M. Zh. Fiz. Khim. 1939, 13, 851. Temkin, M. I.; Morozov, N. M.; Shapatina, E. N. Kinet. Katal. 1963, 4, 260, 555. Vartanov, I. A.; Kharson, M. S.; Kostyukovsky, M. M.; Kipovich, V. G.; Kiperman, S. L. Kinet. Katal. 1984, 25, 142. Veirosta, J.; Klenha, V.; Beranek, L. Collect. Czech. Chem. Commun. 1972,32, 1097. Vigdorovich, F. L.; Kapkov, Yu. K.; Pogorelov, V. V.; Gorelik, A. G.; Babkova, P. B.; Gelbstein, A. I. Kinetika-3. In 3rd Conference on Kinetics of Heteros. Catal. Reactions; Slinko, M. G., Ed.; Kalinin: New York, 1980; Vol. 1, p 68. Voikina, N. V.; Avetisov, A. K.; Bosdanova, 0. K.; Kiperman, S. L. Kinet. Katal. 1975, 16, 1524; 1977, 18, 518. Yuskovets, Zh. G.; Nekrasov, N. V.; Kharson, M. S.; Kostyukovsky, M. M.; Shimanskaya, M. V.; Kiperman, S. L. Kinet. Katal. 1983, 24, 1524; 1984, 25, 1361. Zlotina, N. E.; Kiperman, S. L. Kinet. Katal. 1967, 8, 393, 1335. Savelii
L. K i p e r m a n *
N . D. Zelinsky Institute of Organic Chemistry USSR Academy of Science Leninsky Prospect 47, Moscow, USSR Krasimira
E. K u m b i l i e v a , L u c h e z a r A. P e t r o v Institute of Kinetics a n d Catalysis Bulgarian Academy of Science Sofia 1040, Bulgaria
Response to “Classical Catalytic Kinetics: What Is the Point of the Matter?” Sir: The fact that surface nonuniformity has been ignored for almost 50 years in catalytic kinetics by physical chemists, chemical engineers, and, more recently, surface scientists, is puzzling. I have tried to explain this attitude by first noting that rate expressions obtained from uniform or nonuniform surface kinetics are frequently similar (Boudart, 1956,1972), by then pointing out that they may be i d e n t i c a l in the case of structure-insensitive reactions run under conditions of high surface coverage 8 (Boudart, 1985,1986),and finally by trying to explain why acceptable estimates of rates of catalytic reactions run under conditions of high 8 can be made from rate parameters determined at low 8 (Boudart, 1988). I wish to elaborate here on this last point. It follows from the theory of nonuniform surface kinetics initiated and developed by the Soviet schools of Temkin and Kiperman, as presented in my textbook (Boudart, 1968) and also in more detail in our recent monograph (Boudart and Dj6ga-Mariadassou, 1984). In this theory, the thermodynamic nonuniformity of the surface is described by a 0888-5885/89/2628-0379$01.50/0
distribution function. One of them, and the simplest, is such that the standard Gibbs free energy of adsorption divided by RT and taken with the minus sign, t, falls linearly with converage 8 except a t values of 8 near zero or unity, with values to a t 8 = 0 and tl a t 8 = 1. The breadth of nonuniformity is to - tl = f. A typical value of f is 10. It corresponds to 15 kcal mol-’ at 750 K. Next, the theory relates t to the standard free energy for adsorption by a Brernsted relation between rate constant k and equilibrium constant K , such that k = constant X K“. Empirically, a common value of a is This value will be taken in what follows. Next, it is assumed that the reaction can be described in two steps, an adsorption step and a desorption step with the same value of a. This assumption is not as limiting as it seems since a multistep reaction can frequently be represented as a two-step reaction with simplifications related to the existence of a rate-determining step and a most abundant reactive surface intermediate (Boudart, 1972). Finally, the rate is integrated between t = to where 0 is assumed to be 0 and 0 1989 American Chemical Society
