Surface reaction adsorption equilibrium

Surface reaction at equilibrium, only A not in adsorptive equilibrium. 

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 ... 

Another important characteristic of the surface processes is a ratio g of the adspecies migration rate constant to those of the surface reaction, adsorption, and desorption rates. At small coverages the parameter g controls the surface process conditions r 1 in the kinetic and g l in the diffusion mode. A fast surface mobility of the adspecies and their equilibrium distribution on the surface are the most frequently adopted assumptions. At r < 1 the macroscopic concentrations of adspecies 6 cannot be used for calculating the process rates, and a more detailed description of their distribution is essential. 

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. 

TABLE 7-2 Surface-reaction Controlling (Adsorptive Equilibrium Maintained of All Participants)... 

In the case of coupled heterogeneous catalytic reactions the form of the concentration curves of analytically determined gaseous or liquid components in the course of the reaction strongly depends on the relation between the rates of adsorption-desorption steps and the rates of surface chemical reactions. This is associated with the fact that even in the case of the simplest consecutive or parallel catalytic reaction the elementary steps (adsorption, surface reaction, and desorption) always constitute a system of both consecutive and parallel processes. If the slowest, i.e. ratedetermining steps, are surface reactions of adsorbed compounds, the concentration curves of the compounds in bulk phase will be qualitatively of the same form as the curves typical for noncatalytic consecutive (cf. Fig. 3b) or parallel reactions. However, anomalies in the course of bulk concentration curves may occur if the rate of one or more steps of adsorption-desorption character becomes comparable or even significantly lower then the rates of surface reactions, i.e. when surface and bulk concentration are not in equilibrium. 

As discussed in Chapter 7, this form can provide a good fit of the data if the reaction is not too close to equilibrium. However, most reaction engineers prefer a mechanistically based rate expression. This section describes how to obtain plausible functional forms for based on simple models of the surface reactions and on the observation that aU the rates in Steps 2 through 8 must be equal at steady state. Thus, the rate of transfer across the film resistance equals the rate of diffusion into a pore equals the rate of adsorption equals the rate of reaction equals the rate of desorption, and so on. This rate is the pseudohomo-geneous rate shown in Steps 1 and 9. 

It is important to realize that the assumption of a rate-determining step limits the scope of our description. As with the steady state approximation, it is not possible to describe transients in the quasi-equilibrium model. In addition, the rate-determining step in the mechanism might shift to a different step if the reaction conditions change, e.g. if the partial pressure of a gas changes markedly. For a surface science study of the reaction A -i- B in an ultrahigh vacuum chamber with a single crystal as the catalyst, the partial pressures of A and B may be so small that the rates of adsorption become smaller than the rate of the surface reaction. 

CO oxidation is often quoted as a structure-insensitive reaction, implying that the turnover frequency on a certain metal is the same for every type of site, or for every crystallographic surface plane. Figure 10.7 shows that the rates on Rh(lll) and Rh(llO) are indeed similar on the low-temperature side of the maximum, but that they differ at higher temperatures. This is because on the low-temperature side the surface is mainly covered by CO. Hence the rate at which the reaction produces CO2 becomes determined by the probability that CO desorbs to release sites for the oxygen. As the heats of adsorption of CO on the two surfaces are very similar, the resulting rates for CO oxidation are very similar for the two surfaces. However, at temperatures where the CO adsorption-desorption equilibrium lies more towards the gas phase, the surface reaction between O and CO determines the rate, and here the two rhodium surfaces show a difference (Fig. 10.7). The apparent structure insensitivity of the CO oxidation appears to be a coincidence that is not necessarily caused by equality of sites or ensembles thereof on the different surfaces. 

Depending on the nature of the system, the adsorption process can be either reversible or irreversible. In the first case an adsorption equilibrium exists between the particles adsorbed on the adsorbent s surface and the particles in the electrolyte (or in any other phase contacting with the adsorbent). After removing the substance from the electrolyte, adsorbed particles leave the surface and reenter into the electrolyte. In the case of an irreversible adsorption, the adsorbed particles remain at the surface even if their concentration in the bulk phase drops to zero. In this case the adsorbed particles can be removed from the surface only by means of a chemical reaction... 

If the electrolyte components can react chemically, it often occurs that, in the absence of current flow, they are in chemical equilibrium, while their formation or consumption during the electrode process results in a chemical reaction leading to renewal of equilibrium. Electroactive substances mostly enter the charge transfer reaction when they approach the electrode to a distance roughly equal to that of the outer Helmholtz plane (Section 5.3.1). It is, however, sometimes necessary that they first be adsorbed. Similarly, adsorption of the products of the electrode reaction affects the electrode reaction and often retards it. Sometimes, the electroinactive components of the solution are also adsorbed, leading to a change in the structure of the electrical double layer which makes the approach of the electroactive substances to the electrode easier or more difficult. Electroactive substances can also be formed through surface reactions of the adsorbed substances. Crystallization processes can also play a role in processes connected with the formation of the solid phase, e.g. in the cathodic deposition of metals. 

The reaction is carried out in close-loop reactor connected to a mass spectrometer for 1S02, 180160 and 1602 analyses as a function of time [38], The gases should be in equilibrium with the metallic surface (fast adsorption/desorption steps 1 and f ) If the bulk diffusion is slow (step 6) and the direct exchange (step 5) does occur at a negligible rate, coefficients of surface diffusion Ds can be calculated from the simple relationship between the number of exchanged atoms Ne and given by the model of circular sources developed by Kramer and Andre [41] ... 

Gomez-Sainero et al. (11) reported X-ray photoelectron spectroscopy results on their Pd/C catalysts prepared by an incipient wetness method. XPS showed that Pd° (metallic) and Pdn+ (electron-deficient) species are present on the catalyst surface and the properties depend on the reduction temperature and nature of the palladium precursor. With this understanding of the dual sites nature of Pd, it is believed that organic species S and A are chemisorbed on to Pdn+ (SI) and H2 is chemisorbed dissociatively on to Pd°(S2) in a noncompetitive manner. In the catalytic cycle, quasi-equilibrium ( ) was assumed for adsorption of reactants, SM and hydrogen in liquid phase and the product A (12). Applying Horiuti s concept of rate determining step (13,14), the surface reaction between the adsorbed SM on site SI and adsorbed hydrogen on S2 is the key step in the rate equation. 

Category I. Adsorption equilibrium is maintained at all times, and the overall rate of reaction is governed by the rate of chemical reaction on the surface. The expressions developed for 0 in Section 6.2 can be used in this case. 

Category II. The rate of chemical reaction on the surface is so rapid that adsorption equilibrium is not achieved, but a steady-state condition is reached in which the amount of adsorbed material remains constant at some value less than the equilibrium value. This value is presumed to be that corresponding to equilibrium for the surface reaction at the appropriate fractional coverages of the other species involved in the surface reaction. The rate of adsorption or desorption of one species is presumed to be much slower than that of any other species. This step is then the rate limiting step in the overall reaction. 

In the general case the value of K appearing in the driving force term is the product of the equilibrium constant for the surface reaction Kr and the product of the adsorption equilibrium constants for the reactants divided by the product of the adsorption equilibrium constants for the reaction products. 

Kinetic Term The designation kinetic term is something of a misnomer in that it contains both rate constants and adsorption equilibrium constants. For thfe cases where surface reaction controls the overall conversion rate it is the product of the surface reaction rate constant for the forward reaction and the adsorption equilibrium constants for the reactant surface species participating in the reaction. When adsorption or desorption of a reactant or product species is the rate limiting step, it will involve other factors. 

Hougen- Watson Models for Cases where Adsorption and Desorption Processes are the Rate Limiting Steps. When surface reaction processes are very rapid, the overall conversion rate may be limited by the rate at which adsorption of reactants or desorption of products takes place. Usually only one of the many species in a reaction mixture will not be in adsorptive equilibrium. This generalization will be taken as a basis for developing the expressions for overall conversion rates that apply when adsorption or desorption processes are rate limiting. In this treatment we will assume that chemical reaction equilibrium exists between various adsorbed species on the catalyst surface, even though reaction equilibrium will not prevail in the fluid phase. 

As stated earlier, the retardation term owing to the product adsorption or the constant K in the Langmuir-type equation, v = k/(l + /<[P]) (Equation 13.4), where P is the condensable product), is related to its adsorption equilibrium driven by the concentration term in solutions. Under boiling conditions, the reaction products are desorbed not only to the solution bulk but also into the bubble formed at the catalyst surface. Because the molecular translational entropy is far larger in the gas phase than in the liquid phase, the... 

At the beginning stage of dehydrogenation, the substrate organic hydride is adsorbed onto the catalyst surface from the liquid phase directly and easily. Catalytic reaction processes will succeed it, until the surface sites are filled with the adsorbed reactant and products. Once product desorption starts to form and grow a bubble, product readsorption becomes unfavorable due to the increment of translational entropy of the product molecule in the bubble, if compared with that in the solution, shifting the adsorption equilibrium for the product and suppressing its effect of rate retardation. 

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. 

As a typical case take the reaction, A+B M+N, in which A is the only participant not in adsorptive equilibrium, and surface chemical reaction is not in equilibrium. Various equations are... 

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