Models Based on a Rate-Controlling Step

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  

Surface reaction is rate-controlling,. 01 = kRSo (zero order in A) 

These results can be confirmed by taking the appropriate limits on the rate 

Reversible Unimolecular Reactions. The intrinsic reaction steps in heterogeneously catalyzed reactions are usually reversible. The various limiting cases can be found by taking limits before redefining the constants, e.g., take limits on Equation (10.11), not Equation (10.12). However, a more direct route is to assume that the fast steps achieve equilibrium before deriving the counterpart to Equation (10.11). 

Surface reaction is rate-controlling, 31 = kRSo (zero order in A) Adsorption is rate-controlling, 31 = kjSo (zero order in A) 

Example 10.3 Suppose that adsorption is much slower than surface reaction or desorption for the heterogeneously catalyzed reaction A P. 

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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. 

A transient control volume model of the S-I and HyS cycle is presented. An important conclusion based on the results of this model is that the rate-limiting step of the entire S-I cycle is the HI decomposition section. In the HyS cycle, the rate-limiting step is the H2S04 decomposition. A generalised methodology for coupling these thermochemical cycle models to a nuclear reactor model is overviewed. The models were coupled to a THERMIX-DIREKT thermal model of a PBMR-268 and a point kinetics model. Key assumptions in the PBMR-268 model include flattening of the core and parallelisation of the flow channels. 

Maxwell et al. [ 11 ] proposed a radical entry model for the initiator-derived radicals on the basis of the following scheme and assumptions. The major assumptions made in this model are as follows An aqueous-phase free radical will irreversibly enter a polymer particle only when it adds a critical number z of monomer units. The entrance rate is so rapid that the z-mer radicals can survive the termination reaction with any other free radicals in the aqueous phase, and so the generation of z-mer radicals from (z-l)-mer radicals by the propagation reaction is the rate-controlling step for radical entry. Therefore, based on the generation rate of z-mer radicals from (z-l)-mer radicals by propagation reaction in the aqueous phase, they considered that the radical entry rate per polymer particle, p p=pJNp) is given by... 

Sorption Kinetics. The adsorption and desorption data were analyzed in terms of a model based on the following main assumptions. Micropore diffusion within the sieve crystals is the rate-controlling process. Diffusion may be described by Fick s law for spherical particle geometry with a constant micropore diffusivity. The helium present in the system is inert and plays no direct role in the sorption or diffusion process. Sorption occurs under isothermal conditions. Sorption equilibrium is maintained at the crystal surface, which is subjected to a step change in gas composition. These assumptions lead to the following relation for the amount of ethane adsorbed or desorbed by a single particle as a function of time (Crank, 4). 

Zmcevic and Rusic (1988) used commercial nickel on a silica-alumina catalyst (code Rl-10, manufactured by BASF) containing 21% Ni. They proposed a mechanism based on the dual site adsorption model followed by a bimolecular surface reaction which is the rate-controlling step for the formation of cyclohexane from benzene. The rate equation obtained has the form ... 

In a kinetic investigation it-is not known a priori which is the rate-controlling step and therefore the form of the rate equation or the model. Also unknown, of course, are the values of the rate coefficient k and of the adsorption coefficients Kyf, Kk, As,..., or, in other words, of the parameters of the model. A kinetic investigation, therefore, consists mainly of two parts model discrimination and parameter estimation. This can ultimately only be based on experimental results. 

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