Rate-controlling steps surface reaction

S, Es values for bimolecular surface rate-controlling step in reaction k specific reaction rate constant... 

Equation 9.19 is typical for Michaelis-Menten kinetics (see Section 8.3, cycle 8.14), which might arise here from quasi-equilibrium adsorption of MCH followed by a rate-controlling, irreversible surface reaction (possibly in more than one step) ... 

In the A sector (lower right), the deposition is controlled by surface-reaction kinetics as the rate-limiting step. In the B sector (upper left), the deposition is controlled by the mass-transport process and the growth rate is related linearly to the partial pressure of the silicon reactant in the carrier gas. Transition from one rate-control regime to the other is not sharp, but involves a transition zone where both are significant. The presence of a maximum in the curves in Area B would indicate the onset of gas-phase precipitation, where the substrate has become starved and the deposition rate decreased. 

Irreversible Unimolecular Reactions. Consider the irreversible catalytic reaction A P of Example 10.1. There are three kinetic steps adsorption of A, the surface reaction, and desorption of P. All three of these steps must occur at exactly the same rate, but the relative magnitudes of the three rate constants, ka, and kd, determine the concentration of surface species. Suppose that ka is much smaller than the other two rate constants. Then the surface sites will be mostly unoccupied so that [S] Sq. Adsorption is the rate-controlling step. As soon as a molecule of A is absorbed it reacts to P, which is then quickly desorbed. If, on the other hand, the reaction step is slow, the entire surface wiU be saturated with A waiting to react, [ASJ Sq, and the surface reaction is rate-controlling. Finally, it may be that k is small. Then the surface will be saturated with P waiting to desorb, [PS] Sq, and desorption is rate-controlling. The corresponding forms for the overall rate are ... 

Bimolecular Reactions. Models of surface-catalyzed reactions involving two gas-phase reactants can be derived using either the equal rates method or the method of rate-controlling steps. The latter technique is algebraically simpler and serves to illustrate general principles. 

In general, the overall reaction process may comprise several individual steps, as shown in Figure 3.24. It could be seen that these steps pertain to (i) mass transfers of reactants and the products between the bulk of the fluid and the external surface of the solids (ii) transport of reactants and the products within the pores of the solid and (iii) chemical reaction between the reactants in the fluid and those in the solid. In order to be able to determine the rate-controlling step and to ascertain whether more than a single step should be consid-... 

All of these steps are rate processes and are temperature dependent. It is important to realize that very large temperature gradients may exist between active sites and the bulk gas phase. Usually, one step is slower than the others, and it is this rate-controlling step. The effectiveness factor is the ratio of the observed rate to that which would be obtained if the whole of the internal surface of the pellet were available to the reagents at the same concentrations as they have at the external surface. Generally, the higher the effectiveness factor, the higher the rate of reaction. 

Special forms of equation 8.5-50 arise depending on the relative importance of mass transfer, pore diffusion, and surface reaction in such cases, one or two of the three may be the rate-controlling step or steps. These cases are explored in problem 8-18. The result given there for problem 8-18(a) is derived in the following example. 

If the surface reaction is the rate-controlling step, any effects of external mass transfer and pore-diffusion are negligible in comparison. The interpretation of this, in terms of the various parameters, is that Ag kA, cAs - cAg, and T) and 17 both approach the value of 1. Thus, the rate law, from equation 8.5-50, is just that for a homogeneous gas-phase... 

For the case where surface reaction is the rate controlling step [124], the rate of adsorption can be expressed as ... 

Fig. 2.3 Rate-limiting steps in mineral dissolution (a) transport-controlled, (b) surface reaction-controlled, and (c) mixed transport and surface reaction control. Concentration (C) versus distance (r) from a crystal surface for three rate-controUing processes, where is the saturation concentration and is the concentration in an infinitely diluted solution. Reprinted from Sparks DL (1988) Kinetics of soil chemical processes. Academic Press New York 210 pp. Copyright 2005 with permission of Elsevier...

In mechanistic studies, this form of equation appears whenever the rate-controlling step of a reaction is viewed to involve the association of reactant with some quantity that is present in limited but fixed amounts for example, the association of reactant with enzyme to form a complex, or the association of gaseous reactant with an active site on the catalyst surface. 

While in homogeneous systems the reaction is occurring throughout the entire volume of the reaction vessel and the partial pressures (concentrations) of the species participating in the rate-controlling step are often directly observable, the same is not true for heterogeneous systems. Here, reaction is confined to a monomolecular layer at the surface, around 10 "6 of the total volume of the reaction system, and the concentrations of... 

The ammoxidation of isobutene has not received much attention. The only contribution in this field is by Onsan and Trimm [2.44] for a rather unusual catalyst, a mixture of the oxides of Sn, V and P (ratio 1/9/3) supported on silica. At 520 C, a maximum selectivity to methacrylonitrile + methacrolein of 80% was reached with a Sn—V—P oxide catalyst (ratio 1/9/3), an isobutene/ammonia/oxygen ratio of 1/1.2/2.5 and a contact time of 120 g sec l ]. The kinetics are very similar to those for the pro-pene ammoxidation. Again, the data are initially analysed by means of (parallel) power rate equations, for which the parameters were calculated, while a more detailed analysis proves that a Langmuir—Hinshelwood model with surface reaction as the rate-controlling step provides the best fit with regard to the two main products. At 520° C, the equation which applies for the production of methacrolein plus methacrylonitrile is... 

Test of the Uptake Model Based on the Assumption That Diffusion within the Particle is Rate Controlling. As discussed earlier, the plots of molybdenum and tellurium oxide vapor uptake data vs. diameters and diameters squared of the clay loam particles gave inconclusive evidence as to whether the rate-controlling step was a slow rate of reaction at the surfaces of the particles or a slow rate of diffusion of the condensed vapor into the particles. 

Although surface and interface reactions play a major role in Stage I, any of several processes may be the slowest or rate controlling step in Stages II or III. Surface and interface methods may not be very helpful when surface and interface reactions are not controlling the corrosion rate. 

The rate-controlling step in reductive dissolution of oxides is surface chemical reaction control. The dissolution process involves a series of ligand-substitution and electron-transfer reactions. Two general mechanisms for electron transfer between metal ion complexes and organic compounds have been proposed (Stone, 1986) inner-sphere and outer-sphere. Both mechanisms involve the formation of a precursor complex, electron transfer with the complex, and subsequent breakdown of the successor complex (Stone, 1986). In the inner-sphere mechanism, the reductant... 

Some part of the catalyst surface remains unused as a result of the reaction system and the rate-controlling step. 

The various steps in the removal of a gas from air by a porous adsorbent may be confined broadly to the following processes (a) mass transfer or diffusion of the gas to the gross surface (b) diffusion of the gas into or along the surface of the pores of granular adsorbent (c) adsorption on the interior surface of the granules (d) chemical reaction between the adsorbed gas and adsorbent (e) desorption of the product and (/) transfer of the products from the surface to the gas phase. Whether surface reaction or diffusion (mass transfer) to the surface becomes the rate-controlling step will become evident in the analysis of the experimental data with respect to the rate constant. 

This dependence of k, the rate constant, on flow rate indicates that the surface chemical reaction takes place more rapidly than the diffusion of carbon monoxide molecules to the solid. The latter process is therefore the rate-controlling step and the effect on the rate constant will be given by kD = k/Ln, where kD is proportional to the diffusion constant... 

Either the rate of diffusion to the surface or the speed of the surface reaction governs the rate of removal of the gas from the air stream, depending on which is the slower process. If k is dependent on flow rate, then diffusion is the rate-governing step. From Table XII it is evident that k is proportional to L. Therefore, one can assume that mass transfer is the rate-controlling step and the surface reaction is much faster than the diffusion process. 

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