Elementary surface reaction steps transition state

In the subsections that follow we will focus on the factors that maximize the rate constant for elementary surface reaction steps. Again we will stress the need explicitly to include entropic contributions. According to transition-state reaction rate theoryl l, the rate of the elementary conversion step is defined as... 

The latter concept is basic to the specific dependence of the activation energies of elementary reaction steps on different surfaces. There is not always an immediate relation with the coordinative unsaturation of the metal surface atoms. Ge and Neurock noted an exeptionally low barrier for the dissociation of NO adsorbed on the non-reconstructed Pt(lOO) surface. The corresponding transition state is shown in Fig. 3.37. The calculated activation energies for NO dissociation over the (111) and (110) surfaces are 160 and 105... 

It is mosdy accepted that CO oxidation on nohle metals occurs between the CO and O adsorbates (Karadeniz et al., 2013 Karakaya, 2013). The intrinsic kinetics of the CO oxidation over Rh/Al203 is taken here from the recent study of Karakaya et al. (2014) without any modification. This surface reaction mechanism is a subset of the kinetics of the water-gas shift reaction over Rh/Al203 catalysts given hy Karakaya et al. (2014). This direct oxidation of CO involves 10 elementary-hke surface reaction steps among 4 surfaces and 3 gas-phase species. The reaction rates are modeled by a modified Arrhenius expression as given in Eq. (2.6). The nominal values of the preexponential factors are assumed to he IO Na/T (cm /mol s), where is Avogadro s number (the surface site density was estimated to be 1.637 X 10 site/cm derived from a Rh(llO) surface). The nominal value of 10 is the value calculated from transition state theory k T/h) with being Boltzmann s constant and h Plank s constant (Maier et al., 2011). 

The models developed here account for unmeasurable intermediates such as adsorbed ions or free radicals. Microkinetic analysis, pioneered by Dumesic and cowokers"", is an example of this approach. It quantifies catalytic reactions in terms of the kinetics of elementary surface reactions. This is done by estimating the gas-phase rate constants from transition state theory and adjusting these constants for surface reactions. For instance, isobutane cracking over zeolite Y-based FCC catalysts has 21 reversible steps defined by 60 kinetic parameters." The rate constants are estimated from transition state theory... 

In summary, it can be seen for the three-step reaction scheme of this example that the net rate of the overall reaction is controlled by three kinetic parameters, KTSi, that depend only on the properties of the transition states for the elementary steps relative to the reactants (and possibly the products) of the overall reaction. The reaction scheme is represented by six individual rate constants /c, and /c the product of which must give the equilibrium constant for the overall reaction. However, it is not necessary to determine values for five linearly independent rate constants to determine the rate of the overall reaction. We conclude that the maximum number of kinetic parameters needed to determine the net rate of overall reaction is equal to the number of transition states in the reaction scheme (equal to three in the current case) since each kinetic parameter is related to a quasi-equilibrium constant for the formation of each transition state from the reactants and/or products of the overall reaction. To calculate rates of heterogeneous catalytic reactions, an addition kinetic parameter is required for each surface species that is abundant on the catalyst surface. Specifically, the net rate of the overall reaction is determined by the intrinsic kinetic parameters Kf s as well as by the fraction of the surface sites, 0, available for formation of the transition states furthermore, the value of o. is determined by the extent of site blocking by abundant surface species. 

Elementary reactions are individual reaction steps that are caused by collisions of molecules. The collision can occur in a more or less homogeneous reaction medium or at the reaction sites on a catalyst surface. Only three elementary kinetic processes exist mono-, bi-, and trimolecular processes. Of these, trimolecular processes are rarely found, because the chance of three molecules colliding at the same time is very small. Each elementary reaction consists of an activation of the reactants, followed by a transition state and decomposition of the latter into reaction products ... 

Take the excess surface energy of compound K as equal to 1 J/m and the correlation coefficients between enthalpy of the elementary step and the potential barrier height for the transition state of elemen tary reactions 1 and 2 as equal to X = 0,5. 

Computational catalysis can make substantial contributions to these issues because it allows for a comparison of the rates of elementary reaction steps proposed for various mechanistic reaction paths. By use of computations, it is also possible to relate surface structure with the relative stabilities of various reaction intermediates and transition states. 

It is insti uctive to compare the values of pre-exponential factors for elementary step rate constants of simple surface reactions to those anticipated by transition state theory. Recall from Chapter 2 that the pre-exponential factor A is on the order ofkTjh= 10 s when the entropy change to form the transition state is negligible. Some pre-exponential factors for simple unimolecular desorption reactions are presented in Table 5.2.2. For the most part, the entries in the table are within a few orders of magnitude of 10 s . The very high values of the preexponential factor are likely attributed to large increases in the entropy upon formation of the transition state. Bimolecular surface reactions can be treated in the same way. However, one must explicitly account for the total number of surface... 

Reuter, Frenkel, and Scheffler have recently used DFT-based calculations to predict the CO turnover frequency on RuO2(110) as a function of 02 pressure, CO pressure, and temperature.31 This was an ambitious undertaking, and as we will see below, remarkably successful. Much of this work was motivated by the earlier success of ab initio thermodynamics, a topic that is reviewed more fully below in section 3.1. The goal of Reuter et al. s work was to derive a lattice model for adsorption, dissociation, surface diffusion, surface reaction, and desorption on defect-free Ru02(l 10) in which the rates of each elementary step were calculated from DFT via transition state theory (TST). As mentioned above, experimental evidence strongly indicates that surface defects do not play a dominant role in this system, so neglecting them entirely is a reasonable approach. The DFT calculations were performed using a GGA full-potential... 

In terms of transition-state theory, the rate of the surface reaction can be related to that of decomposition of an activated surface complex. The rate of production of this activated complex is rapid enough to assume that it is in equilibrium with the reactants responsible for its formation. In homogencoiM systems it is usually easy to identify the nature of the elementary steps leading to... 

It is assumed that the composite catalytic reaction involves several elementary steps, e.g., adsorption, surface reaction, and desorption, which may individually be treated according to TTST, i.e., each step is assumed to possess its own transition state. For example, for the adsorption of A, the forward step is represented by, A + S [X ] - A S. The free energy changes of activation associated with each step may, of course, be substantially different providing justification of the common assumption of the rate determining step (rds). The rate of the forward elementary step i is proportional to the universal frequency, V = kgT jh [2], a transmission coefficient, K, varying between 0 and 1 [3], and the concentration of the transition-state complex (TSC)... 

The concept of chemisorption is a key to the understanding of catalytic reactions. Catalytic events consist of elementary reactions on the catalyst surface in which chemical bonds are formed between surface atoms and an adsorbing molecule. These interactions cause rupture of chemical bonds within the adsorbing molecule and formation of new bonds between the fragments. We will discuss explanations of the selective behavior of metals mainly with respect to three important types of reactions the conversion of synthesis gas, hydrocarbon conversion and selective (metal-catalyzed) oxidation. When particularly relevant, reference to other reactions will be made. We wish to relate proposed reaction intermediates and their chemical change to the electronic properties of the surface site where the surface reaction occurs. One then is interested in the strength of adsorbate-metal chemical bonds before and after chemical change of the reaction intermediate. These values affect the thermodynamics of the elementary steps and hence enable an estimate of the equilibria that exist between different surface species. It is the primary information a chemist requires to rationalize chemical reaction rates. In order to estimate rates, one needs information on transition states. Advanced quantum-chemical calculations can provide such information. 

It appears that a significant amount of energy is required for CH activation, the primary elementary step of the hydrocarbon conversion reaction. If one chemisorbs methane at low temperature on a transition metal surface, it desorbs before reaction can occur. Aliphatic hydrocarbons can dissociate from a preadsorbed state, if they contain enough carbon atoms in their chain to induce a high heat of adsorption whereby CH dissociation can take place at a rate large compared to the desorption rate. So far this has only been found for surfaces containing highly active metal atoms, such as the reconstructed Ir (110) surface or stepped surfaces l. As we will see, both electronic and steric effects may play a role. 

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