Surface reaction as the rate determining step

on the other hand, surface reaction determined the overall chemical rate, equation 3.68 (or 3.69 if an Eley-Rideal mechanism operates) would represent the rate. If it is assumed that a pseudo-equilibrium state is reached for each of the adsorption-desorption processes then, by a similar method to that already discussed for reactions where adsorption is rate determining, it can be shown that the rate of chemical reaction is (for a Langmuir-Hinshelwood mechanism)  

This equation also contains a driving force term and an adsorption term. A similar equation may be derived for the case of an Eley-Rideal mechanism and its form is interpreted in Table 3.3. 

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For the situation in Example 9-1, derive the result for t(/B) for reaction-rate control, that is, for the surface reaction as the rate-determining step (rds), and confirm that it is the... 

Equation (24) is, in fact, a Langmuir—Hinshelwood-type equation. Similar models with a single site surface reaction as the rate-determining step were used for other liquid phase esterifications [448,451]. Experimental data for the l-butanol-x>leic acid system were best fitted by eqn. (24) [452] or eqn. (25) [451]... 

It is well accepted that the oxidation of the adsorbed CO at Pt and Pd follows a Langmuir-Hinshelwood mechanism with the reaction between adsorbed CO and surface OH as the rate-determining step as follows (Spendelow et al., 2004) ... 

In this approximation we assume that one elementary step determines the rate while all other steps are sufficiently fast that they can be considered as being in quasi-equilibrium. If we take the surface reaction to AB (step 3, Eq. 134) as the rate-determining step (RDS), we may write the rate equations for steps (1), (2) and (4) as ... 

Here A(g) and B(g) denote reactant and product in the bulk gas at concentrations CA and Cg, respectively kAg and kBg are mass-transfer coefficients, s is an adsorption site, and A s is a surface-reaction intermediate. In this scheme, it is assumed that B is not adsorbed. In focusing on step (3) as the rate-determining step, we assume kAg and kBg are relatively large, and step (2) represents adsorption-desorption equilibrium. 

When, as it is assumed here, the B —> C reaction is the rate-determining step, the dimensionless rate parameter, 2, is the same as in the ECE case. As 2 increases, the wave loses its reversibility while the electron stoichiometry passes from 1 to 2, as in the ECE case. Unlike the latter, there is no trace crossing upon scan reversible. This is related to the fact that now only the reduction of A contributes to the current. C has indeed disappeared by means of its reaction with B before being able to reach back to the electrode surface. The characteristic equations, their dimensionless expression, and their resolution are detailed in Section 6.2.1. The dimensionless peak current, tjj, thus varies with the kinetic parameter, 2, from 0.446, the value characterizing the reversible uptake of one electron, to 2 x 0.496 = 0.992, the value characterizing the irreversible exchange of two electrons (Figure 2.11a). 

Several authors have proposed that CH4 combustion over PdO occurs via a redox mechanism [82-85]. Methane activation through assisted hydrogen extraction is generally regarded as the rate-determining step, although there is not a general consensus on the nature of the adsorption sites. Further, desorption of H2O by decomposition of surface hydroxyls has been reported to play a key role in reaction kinetics at temperatures below 450 °C [67, 86]. 

Results were modelled on the basis of CO adsorption/desorption equilibrium with oxygen adsorption as the rate determining step and an irreversible Langmuir-Hinshelwood surface reaction. It was assumed that adsorption and... 

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. 

A catalytic reaction is in general composed of a series of elementary processes, and the surface atoms are necessarily involved in making intermediates and/or activated complexes, as well as in the adsorption of reactant and product molecules. For this reason, the participation of surface atoms is indispensable in all of the elementary processes accomplishing the catalysis, but the kinetics are mainly influenced by the manner of the participation of surface atoms in the rate-determining steps. Accordingly, in order to make clear the roles of the surface atoms in catalysis, it should be clarified how the surface atoms participate in the rate-determining steps as well as in the other elementary processes. 

Fig. 4 shows a simple phase diagram for a metal (1) covered with a passivating oxide layer (2) contacting the electrolyte (3) with the reactions at the interfaces and the transfer processes across the film. This model is oversimplified. Most passive layers have a multilayer structure, but usually at least one of these partial layers has barrier character for the transfer of cations and anions. Three main reactions have to be distinguished. The corrosion in the passive state involves the transfer of cations from the metal to the oxide, across the oxide and to the electrolyte (reaction 1). It is a matter of a detailed kinetic investigation as to which part of this sequence of reactions is the rate-determining step. The transfer of O2 or OH- from the electrolyte to the film corresponds to film growth or film dissolution if it occurs in the opposite direction (reaction 2). These anions will combine with cations to new oxide at the metal/oxide and the oxide/electrolyte interface. Finally, one has to discuss electron transfer across the layer which is involved especially when cathodic redox processes have to occur to compensate the anodic metal dissolution and film formation (reaction 3). In addition, one has to discuss the formation of complexes of cations at the surface of the passive layer, which may increase their transfer into the electrolyte and thus the corrosion current density (reaction 4). The scheme of Fig. 4 explains the interaction of the partial electrode processes that are linked to each other by the elec-... 

Table 4 contains a collection of diffusion coefficients determined experimentally for a variety of adsorbate systems. It shows that the values may vary considerably, which is of course due to the specific bonding of the adsorbate to the surface under consideration. Surface diffusion plays a vital role in surface chemical reactions because it is one factor that determines the rates of the reactions. Those reactions with diffusion as the rate-determining step are called diffusion-limited reactions. The above-mentioned photoelectron emission microscope is an interesting tool to effectively study diffusion processes under reaction conditions [158], In the world of real catalysts, diffusion may be vital because the porous structure of the catalyst particle may impose stringent conditions on molecular diffusivities, which in turn leads to massive consequences for reaction yields. 

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