Dissociation rate-determined model

We commence by creating a simple model for a heterogeneously catalyzed reaction, which proceeds from a diatomic reactant and necessitates the cleavage of a strong molecular bond. A large number of important reactions belong to this category. One of the most simple such reactions that can be envisioned is the reaction  

Model 1 Dissociative chemisorption as the rate-determining step. 

To analytically determine such volcano curves for the simple model reaction, we need to make some further assumptions (the assumptions are realistic at least for the case of NH3 synthesis)  

Using these assumptions, we avoid the more involved treatment of the detailed adsorption processes. Specific variations in sticking coefficients or steering effects can be calculated theoretically [126,127], but often these lead to relatively small variations compared to the trends induced by varying the energetics. Under these assumptions, the universal BEP-relation allows the analytical calculation of the turnover frequency when dissociation is rate-determining. 

We start by considering the simplest possible surface-catalyzed reaction treated in some detail in Chapter 5  

Fundamental Concepts in Heterogeneous Catalysis, First Edition. Jens K. N0rskov, Felix Studt, Frank Abild-Pedersen and Thomas Bligaard. 

Let us assume that A dissociation is rate limiting. The turnover frequency (TOF) of the reaction is then (see also Eq. 5.35) 

is the temperature-dependent rate constant for the forward reaction in Equation (7.2), which is assumed to foUow an Arrhenius expression 

FIGURE 7.1 Potential energy diagram for the reaction A + 2B 2AB where A adsorbs dissociatively on the surface and B reacts without prior adsorption with adsorbed A. 

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The mechanism of the synthesis reaction remains unclear. Both a molecular mechanism and an atomic mechanism have been proposed. Strong support has been gathered for the atomic mechanism through measurements of adsorbed nitrogen atom concentrations on the surface of model working catalysts where dissociative N2 chemisorption is the rate-determining step (17). The likely mechanism, where (ad) indicates surface-adsorbed species, is as follows ... 

NO, the monomer C is CO, and the products are A2 = N2 and CB = CO2. The adsorption probability of C species (Fc) is the parameter of the model. The slow rate-determining step in this sequence is the dissociation of NO which requires a neighboring site to proceed. Since product formation liberates more vacant sites than those necessary for the dissociation of NO, an autocatalytic production of vacant sites takes place. 

Surface plasmon resonance studies were employed to measure the equilibrium constants and association and dissociation rate constants of bisnaphthalimide derivatives (20, 21) with hairpin DNA immobilized on the metal surface.123 The equilibrium constants were higher and the dynamics slower for compounds 20 and 21 when compared to the equilibrium constants and dynamics of the model monomer (19). The values for ka and kd were determined from the change in the surface plasmon resonance signal when, respectively, the ligand solution was flowed over the... 

Alternative kinetic models were considered for this reaction. Both of them predict rapid reduction of Cu(II) Cu(II) to Cu(I) Cu(I) by H2DTBC and subsequent formation of the Cu(II)(0 -)Cu(II) intermediate in the reaction of the reduced form with 02. The first model assumes that the rate determining formation of the intermediate is followed by a fast, acid assisted dissociation into the oxidized form of the catalyst and H202. In the other model, the rate determining step is the oxidation of H2DTBC by the intermediate. The two models predict... 

Kinetic studies of the stoichiometric carbonylation of [Ir(CO)2l3Me] were conducted to model the rate-determining step of the catalytic cycle [73,85]. The reaction can form both fac,cis and mer,trans isomers of [Ir(CO)2l3 (COMe)] (Scheme 13), the product ratio varying with the solvent and temperature used. An X-ray crystal structure was obtained for the fac,cis isomer. Carbonylation of [Ir(CO)2l3Me] is rather slow and requires temperatures > 80 °C in chlorinated solvents (e.g. PhCl). However, the presence of protic solvents (e.g. methanol) has a dramatic accelerating effect. This is interpreted in terms of the protic solvent aiding iodide dissociation by solvation. 

Suppose that we attempt to devise a model so that log L = 15, an acceptable value, for Example 4. Let mobile atoms be the adsorbed species. The value of 19 for Step 2 must be decreased by four units. According to Table II, the gas must lose 36.8 e.u. (that is, 4 x 9.2 e.u.) more than is postulated for Step 2. But S for Nj at 690 K and 0.16 atm [Eq. (79)] is only 56.6 e.u. A loss of only 19.8 e.u. (that is, 56.6 e.u. — 36.8 e.u.) upon adsorption seems impossible, since the rotational loss alone (which must be included since the model calls for dissociation into atoms) is 12.9 e.u. The difficulty with Example 4 is that an activation energy of 52 kcal mole is extremely large. We cannot choose a possible rate-determining step from the data. 

In this model, A2 molecules are first adsorbed on the surface non-dissociatively. The A2 molecular precursor might dissociate if there is a free active site adjacent to it, and if it is capable of climbing the dissociation energy barrier due to thermal excitation, or the precursor could be thermally activated to desorb as A2 into the gas phase again. It is still assumed that the dissociation (now from the precursor state and not from the gas phase) is the rate-determining step. If the reaction proceeds to a steady-state, but the over-all gas phase reactants and products are kept out of equilibrium, the precursor state will be in equilibrium with the gas phase reactant, but not with the dissociated state. This model will have a turnover frequency given by ... 

In the other cases discussed above, the optimal catalyst is relatively close to the narrow region of dissociative chemisorption energies from —2 to — leV. It does, however, appear that the models developed so far could also have a problem describing why some high temperature and very exothermic reactions (with corresponding small approaches to equilibrium) also lie within the narrow window of chemisorption energies. To remove these discrepancies we shall relax the assumption of one rate-determining step, but retain an analytic model, by use of a least upper bound approach. 

Recently, Happel et al. [154] using data from Kadlec et al. [167,217] conclude that a model based on the dissociative adsorption of oxygen, which is rate-determining, fits the experimental results best, viz. 

In electrode kinetics, interface reactions have been extensively modeled by electrochemists [K.J. Vetter (1967)]. Adsorption, chemisorption, dissociation, electron transfer, and tunneling may all be rate determining steps. At crystal/crystal interfaces, one expects the kinetic parameters of these steps to depend on the energy levels of the electrons (Fig. 7-4) and the particular conformation of the interface, and thus on the crystal s relative orientation. It follows then that a polycrystalline, that is, a (structurally) inhomogeneous thin film, cannot be characterized by a single rate law. 

With this electric potential Poisson equation (A

el = net charge density) to eventually obtain the concentration of electrons at the film surface (A ). It further follows that Ne(A ) varies with the film layer thickness as A -2. If we now assume that the (catalyzed) rate of dissociation of the adsorbed X2 molecules is proportional to the surface concentration of electrons, and that this dissociation process is rate determining, a cubic rate law for the film growth can be expected (A — At 2 At - t in). In fact, during the oxidation of Ni at temperatures between 250 and 400 °C, an approximately cubic rate law has been experimentally observed. We emphasize, however, that the observed cubic oxidation rate does not prove the validity of the proposed reaction mechanism. Different models and assumptions concerning the atomic reaction mechanism may lead to the same or similar dependences of the growth rate on thickness. 

The reason for this structure sensitivity is not known. Martin340 has concluded that the rate-determining step is the adsorption of ethane on an ensemble of 15 adjacent Ni atoms free of H2. On the other hand, Goodman338 suggests a model in which ethane is adsorbed at interstitial sites involving 6 Ni atoms in the (100) surface or 4 Ni atoms in the (111) surface. He proposes that the difference in activity between these two surfaces may be due either to electronic differences or to the fact that the spacing between the sites in the (100) surface is such as to encourage the dissociation of the C-C bond in ethane. The latter model, while attractive for ethane, would not readily... 

Despite its tetranuclear structure in the solid state, the dicopper(II) complex was found to dissociate in solution into dinuclear units at the concentration levels used for catecholase activity studies. Similarly to the copper(II) complex with the ligand [22]py4pz, the present complex also catalyzes the oxidation of the model substrate DTBCH2 in methanol. However, several unexpected observations have been made in the present case. First, the rate-determining step in the catalytic reaction was found to change with the substrate-to-complex ratio. Thus, at low substrate-to-... 

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