Adsorption reactant surface concentration

The course of a surface reaction can in principle be followed directly with the use of various surface spectroscopic techniques plus equipment allowing the rapid transfer of the surface from reaction to high-vacuum conditions see Campbell [232]. More often, however, the experimental observables are the changes with time of the concentrations of reactants and products in the gas phase. The rate law in terms of surface concentrations might be called the true rate law and the one analogous to that for a homogeneous system. What is observed, however, is an apparent rate law giving the dependence of the rate on the various gas pressures. The true and the apparent rate laws can be related if one assumes that adsorption equilibrium is rapid compared to the surface reaction. 

However, with an inhomogeneous electrode surface and adsorption energies that are different at different sites, the reaction rate constant and the related parameter will also assume different values for different sites. In this case the idea that the reaction rate might be proportional to surface concentration is no longer correct. It was shown by M. Temkin that when the logarithmic adsorption isotherm (10.15) is obeyed, the reaction rate will be an exponential function of the degree of surface coverage by the reactant ... 

The second most apparent limitation on studies of surface reactivity, at least as they relate to catalysis, is the pressure range in which such studies are conducted. The 10 to 10 Torr pressure region commonly used is imposed by the need to prevent the adsorption of undesired molecules onto the surface and by the techniques employed to determine surface structure and composition, which require relatively long mean free paths for electrons in the vacuum. For reasons that are detailed later, however, this so-called pressure gap may not be as severe a problem as it first appears. There are many reaction systems for which the surface concentration of reactants and intermediates found on catalysts can be duplicated in surface reactivity studies by adjusting the reaction temperature. For such reactions the mechanism can be quite pressure insensitive, and surface reactivity studies will prove very useful for greater understanding of the catalytic process. 

This identity of formulation means that in normal cases correct results for the velocity equation will be obtained by assuming that adsorption equilibrium is established and the adsorbed molecules react at a rate proportional to their surface concentration when they possess the critical energy. Then, for the surface concentration 07 of every reactant the Langmuir adsorption isotherm holds ... 

The adsorption of reactant in the Cd(II)-I system [44], and the influence of electrolyte concentration (1-6 M NaCl04) on the parameters of the Frumkin isotherm system were investigated [45]. The obtained data indicated that the maximum surface concentration of Cdl2 (/kaax = 1 x... 

The rate expressions Rj — Rj(T,ck,6m x) typically contain functional dependencies on reaction conditions (temperature, gas-phase and surface concentrations of reactants and products) as well as on adaptive parameters x (i.e., selected pre-exponential factors k0j, activation energies Ej, inhibition constants K, effective storage capacities i//ec and adsorption capacities T03 1 and Q). Such rate parameters are estimated by multiresponse non-linear regression according to the integral method of kinetic analysis based on classical least-squares principles (Froment and Bischoff, 1979). The objective function to be minimized in the weighted least squares method is... 

The simple model just discussed shows multistability even when the system is clean but requires the involvement of a poison for oscillations. One reason for this is that the latter is needed to provide a second independent surface concentration, so we theij. have a two-variable system. It was mentioned in 12.3.1 that implicit in the rate law used above may be the adsorption of a second reactant which participates in the reaction step. The latter did not provide a second concentration variable there since its adsorption and desorption processes were assumed to be on a very much faster (instantaneous) timescale. 

The basic premise of the original kinetic description of inhibition was that, for a reaction to proceed on a surface, one or more of the reactants (A) must be adsorbed on that surface in reversible equilibrium with the external solution, having an equilibrium adsorption constant of KA, and the adsorbed species must undergo some transformation involving one or more adsorbed intermediates (n) in the rate-limiting step, which leads to product formation. The product must desorb for the reaction cycle to be complete. If other species in the reaction mixture (I) can compete for the same adsorption site, the concentration of the adsorbed reactant (Aad) on the surface will be lower than when only pure reactant A is present. Thus, the rate of conversion will depend on the fraction of the adsorption sites covered by the reactant (0A) rather than the actual concentration of the reactant in solution, and the observed rate coefficient (fcobs) will be different from the true rate coefficient (ktme). In its simplest form the kinetic expression for this phenomenon in a first-order reaction can be described as follows ... 

In the following discussion we will concentrate on the surface reaction, adsorption, and desorption. The complications induced by the transport phenomena will be ignored. In order to develop an expression for the overall rate, the surface concentrations, AL, BL, etc., are related to the concentrations of the reactants in the bulk phase by an "Equilibrium constant". For example ... 

The latter function needs special attention as it contains the mean surface concentrations c 0 and cR corresponding to the d.c. potential control. In the absence of reactant adsorption, one would have ip —Dq2Cq + Dr2cr, but in the presence of reactant adsorption, this expression should be corrected by a term containing T0 [143]. 

Co-adsorption and mutual interactions between the reactants on the surface form the basis for understanding the microscopic steps of the reaction. Since product formation takes place rather rapidly above room temperature, this information mainly became available from low-temperature studies. As a result, these processes are much more complicated than can be described by a Langmuir-type adsorption model (i.e., simple competition for free adsorption sites) and, moreover, an asymmetric behavior is found which means that pre-adsorbed CO inhibits the adsorption of oxygen, whereas the reverse is not the case. At very low surface concentrations of CO and Oad these will be randomly distributed over the surface as illustrated schematically by Fig. 32a (88). 

If the adsorption of A is the rate determining step in the sequence of adsorption, surface reaction and desorption processes, then equation 3.71 will be the appropriate equation to use for expressing the overall chemical rate. To be of use, however, it is first necessary to express CA, Cv and Cs in terms of the partial pressures of reactants and products. To do this an approximation is made it is assumed that all processes except the adsorption of A are at equilibrium. Thus the processes involving B and P are in a state of pseudo-equilibrium. The surface concentration of B can therefore be expressed in terms of an equilibrium constant KB for the adsorption-desorption equilibrium of B ... 

In contrast, toluene and methanol coadsorbed on Rb-X do not form a bimolecular precursor complex and both reactants seem to be independently adsorbed at the surface. It should be noted, however, that after equilibration of the catalyst with equal partial pressures of both reactants, toluene was the main adsorptive. During toluene methylation, sorbed toluene was again the main surface species, the reaction rate, however, was proportional to the surface concentrations of both chemisorbed species (toluene, formaldehyde). The onset of the reaction was observed at much higher temperatures than in the ring alkylation which is at large ascribed to the indispensable conversion of methanol to a formaldehyde (or formate) species. 

An important aspect of this reaction is the way in which reactants are concentrated near the oxide surface. The free, ionized carboxylate group of MPT - provides a basis for specific adsorption, through complex formation with surface Al centers. Monophenyl terephthalate also experiences favorable electrostatic attraction towards the positive-charged oxide surface. The positive Al oxide surface charge and extent of MPT adsorption both diminish as the pH is decreased (Stone, 1989a). The extent of MPT-adsorption also decreases as the ionic strength is increased, an indication that the surface complex is outer sphere rather than inner sphere (Hayes et al.,... 

At steady state the rates of adsorption r, surface reaction r, and desorption are e qual. To express the rate solely in terms of fluid concentrations, the adsorbed concentrations C, Cg, Q, and C must be eliminated from Eqs. (9-15) to (9-22). In principle, this can be done for any reaction, but the resultant rate equatLOJiTnYoLves-all-the-rate-co-nstantS-/r,-a-nd-the-eq-uilibHum-constants Ki. Normally neither type of constant can be evaluated independently. Both must be determined from measurements of the rate of conversion from fluid reactants to fluid products. However, there are far too many constants, even for simple reactions, to obtain meaningful values from such overall rate data. The problem can be eased, with some confidence from experimental data, by supposing that one step in the overall reaction controls the rate. Then the other two steps occur at near-equilibrium conditions. This greatly simplifies the rate expression and reduces the number of rate and equilibrium constants tr t must be determined from experiment. To illustrate the procedure equations for the rate will be developed, for various controlling steps, for the reaction system... 

For non-porous catalyst pellets the reactants are chemisorbed on their external surface. However, for porous pellets the main surface area is distributed inside the pores of the catalyst pellets and the reactant molecules diffuse through these pores in order to reach the internal surface of these pellets. This process is usually called intraparticle diffusion of reactant molecules. The molecules are then chemisorbed on the internal surface of the catalyst pellets. The diffusion through the pores is usually described by Fickian diffusion models together with effective diffusivities that include porosity and tortuosity. Tortuosity accounts for the complex porous structure of the pellet. A more rigorous formulation for multicomponent systems is through the use of Stefan-Maxwell equations for multicomponent diffusion. Chemisorption is described through the net rate of adsorption (reaction with active sites) and desorption. Equilibrium adsorption isotherms are usually used to relate the gas phase concentrations to the solid surface concentrations. 

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