Rate-determining step heterogeneous reactions

Vijh (6) has suggested more recently that if one assumes the adsorbed species formed in this reaction to be a covalent one, the available data can be interpreted in terms of the Sabatier-Balandin views on heterogeneous catalysis. According to his interpretation, he has indicated a volcanic relationship between the catalytic activity (defind as the temperature at which the reaction first becomes appreciable) against the heat of formation per equivalent of the oxide catalyst, AHe. Based on this volcanic relationship, he has concluded that the rate-determining step (r.d.s.) of the reaction on the oxide catalysts such as CiO, NiO and CoO probably involves rupture of a M-0 bond. On the other hand, r.d.s. on oxides such as MgO,CaO and Ce02 would involve the formation of a M-0 bond. 

In general, the rate (A ) of heterogeneous catalysis in a gas-catalyst (and liquid-catalyst) reaction may be expressed as the product of the rate coefficient A o and a function of pressure (or concentration), p, i.e. k = kof(p) where p is the partial pressure of the reactant, ko depends on the reaction conditions and may involve reaction steps prior to the first rate-determining step of the reaction. A convenient method for determining A o is to use the Arrhenius equation ... 

In this equation, aua represents the product of the coefficient of electron transfer (a) by the number of electrons (na) involved in the rate-determining step, n the total number of electrons involved in the electrochemical reaction, k the heterogeneous electrochemical rate constant at the zero potential, D the coefficient of diffusion of the electroactive species, and c the concentration of the same in the bulk of the solution. The initial potential is E/ and G represents a numerical constant. This equation predicts a linear variation of the logarithm of the current. In/, on the applied potential, E, which can easily be compared with experimental current-potential curves in linear potential scan and cyclic voltammetries. This type of dependence between current and potential does not apply to electron transfer processes with coupled chemical reactions [186]. In several cases, however, linear In/ vs. E plots can be approached in the rising portion of voltammetric curves for the solid-state electron transfer processes involving species immobilized on the electrode surface [131, 187-191], reductive/oxidative dissolution of metallic deposits [79], and reductive/oxidative dissolution of insulating compounds [147,148]. Thus, linear potential scan voltammograms for surface-confined electroactive species verify [79]... 

Thus, the analysis of the rate-determining step, as analyzed for heterogeneous processes in Section 3.1.2, is equally applied in adsorption and ion exchange. The only difference is that the diffusion processes in the fluid film and in the particle are followed by physical adsoiption or ion exchange and not by a reaction step as in catalysis. 

The Rate-Determining Step. Determination of the step that decides the overall rate in a series of consecutive or parallel reactions in heterogeneous catalysis is the most significant part of mechanism determination. It is best to deal with the ideas here in a general way they will be exemplified in three reactions later on in the section. 

In heterogeneous systems, the rate expressions have to be developed on the basis of (a) a relation between the rate and concentrations of the adsorbed species involved in the rate-determining step and (b) a relation between the latter and the directly observable concentrations or partial pressures in the gas phase. In consequence, to obtain adequate kinetic rate expressions it is necessary to have a knowledge of the reaction mechanism, and an accurate means of relating gas phase and surface concentrations through appropriate adsorption isotherms. The nature and types of adsorption isotherm appropriate to chemisorption processes have been discussed in detail elsewhere [16,17] and will not be discussed further except to note that, in spite of its severe theoretical limitations, the Langmuir isotherm is almost invariably used for kinetic interpretations of surface hydrogenation reactions. The appropriate equations are... 

The El mechanism has, as the rate-determining step in solution, the ionisation of the reactant forming a carbonium ion which then decomposes rapidly. For heterogeneous catalytic reactions, the important features are the occurrence of the reaction in two steps and the presence on the solid surface of carbonium ions or species resembling them closely. Again, the kinetic characterisation by way of an unimolecular process is of little value. Even the relative rates of the two steps may be reversed on solid catalysts. A cooperation of an acidic and a basic site is also assumed, the reaction being initiated by the action of the acidic site on the group X. 

In summary, catalytic C-H transformations in small unfunctionalized alkanes is a technically very important family of reactions and processes leading to small olefins or to aromatic compounds. The prototypical catalysts are chromia on alumina or vanadium oxides on basic oxide supports and platinum on alumina. Reaction conditions are harsh with a typical minimum temperature of 673 K at atmospheric pressure and often the presence of excess steam. A consistent view of the reaction pathway in the literature is the assumption that the first C-H abstraction should be the most difficult reaction step. It is noted that other than intuitive plausibility there is little direct evidence in heterogeneous reactions that this assumption is correct. From the fact that many of these reactions are highly selective toward aromatic compounds or olefins it must be concluded that later events in the sequence of elementary steps are possibly more likely candidates for the rate-determining step that controls the overall selectivity. A detailed description of the individual reactions of C2-C4 alkanes can be found in a comprehensive review [59]. 

No precise information about the olefin polymerisation mechanism has been obtained from kinetic measurements in systems with heterogeneous catalysts analysis of kinetic data has not yet afforded consistent indications either concerning monomer adsorption on the catalyst surface or concerning the existence of two steps, i.e. monomer coordination and insertion of the coordinated monomer, in the polymerisation [scheme (2) in chapter 2], Note that, under suitable conditions, each step can be, in principle, the polymerisation rate determining step [241]. Furthermore, no % complexes have been directly identified in the polymerisation process. Indirect indications, however, may favour particular steps [242]. Actually, no general olefin polymerisation mechanism that may be operating in the presence of Ziegler-Natta catalysts exists, but rather the reaction pathway depends on the type of catalyst, the kind of monomer and the polymerisation conditions. 

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