Steps, elementary competing

To compete with the empirical models (Temkin and improved expressions) for the best fit to experimental data cannot be the prime objective of the microkinetic approaches. Rather, they are means of checking whether our knowledge and understanding of the elementary steps correspond to the reality of catalysts under industrial synthesis conditions. 

The evaluation of absolute rate coefficients of elementary reactions (hereafter referred to only as rate coefficients) is one of the most important steps in the kinetic analysis. Comparison of such values with our general chemical knowledge of radical reactions serves first as a check on the kinetic analysis and second, if shown to be reliable, they may be used in the kinetic analysis of other systems. It is often possible and useful to evaluate the rate coefficients directly in oxidation reactions as well as in much more simplified systems where many of the competing steps have been eliminated. 

Studies show that the measured composition of the product mixture at constant temperature depended on the water density (Fig. 7.7). This was taken as an indication that these products could be formed by competing ionic and free-radical reaction pathways. Usually in gas-phase kinetics the product composition changes with temperature because of the different activation energies and, to a minor extent with pressure, mainly because of the concentration effect on bimolecular elementary reaction steps. In water, the drastic dependence on pressure is likely a consequence of the competition between reactions with different polarity. Free radical reaction rates (involving large free radicals beyond the RRKM high-pressure limit, see, for example, [25]) should decrease with pressure as a result... 

We have now seen that specific steric factors can control catalytic selectivity by guiding specific reactants to specific products. Most heterogeneous catalysts, with the exception of zeolites, can be expected to be intrinsically less selective, since they typically do not contain a three-dimensional architecture that can help to guide the formation of specific products. Therefore, they are optimum for those applications where thermodynamics prescribes the formation of one particular product over the others. The careful choice of transition metals and promoters, however, can appreciably alter chemical reactivity and bias specific reactions, thus altering the relative rates of competing elementary reaction steps. 

The above arguments illustrate the importance of edge and kink sites in catalysis. As a consequence, reconstruction phenomena that change also the edge and kink site distribution can have a large effect not only on the overall rate of a catalytic reaction but also on its selectivity. The latter occurs when competing elementary reaction steps have... 

There are many factors that determine the rate of a reaction sequence that lead to a particular product. Within the same catalytic system, reaction sequences leading to different products may compete. The two key parameters, which are important to the selectivity of a catalytic reaction, are the difference of the rate constants of elementary reaction steps controlled by electronic, geometric or steric parameters and the overlayer composition of the reactive catalytic surface or occupancy of complex or cavity. This affects the relative probability for product molecule formation from the recombination or dissociation of reaction intermediates generated during the catalytic cycle. The relative stability of the fragment molecules determines their concentration and, hence the probability that they are present at high enough concentration to result in a finite quantity for recombination. Site occupancy controls also the probability of surface vacancies necessary for dissociation. The last, for instance, is an important parameter that discriminates between associative... 

Firstly, we should define the types of complexity which need to be considered when dealing with homogeneous chemical reactions coupled to electron transfer. The most common one is that the conversion of primary intermediates into final product is, in fact, a sequence of several, maybe four or five, elementary steps. In addition to defining the reaction pathway, it is necessary to decide which step is the rate determining one and also to consider the possibility that two steps have approximately the same rate, or that the r.d.s. changes, say with concentration of electroactive species. It is, however, also common in organic electrochemistry to find that the electrode reaction leads to a mixture of products and this is a clear indication of a branch mechanism where two competing reactions have comparable rates branch mechanisms can even lead to the same product. A further uncertainty arises as to the source of electrons does the second... 

The whole catalytic cycle of this system, including the mononuclear Mo, Mo, and Mo species as well as the detrimental binuclear p-oxido species and relevant transition states for OAT, have also been viewed from a theoretical perspective [89]. This system hence represents a rare example in which only the heterogenized version is competent to perform the biomimetic catalysis while the homogeneous system is not and, furthermore, for which detailed information concerning the elementary reaction steps is available, being fully congruent with the biological prototype. 

A lesson to learn from this analysis is that the concept of the rate-determining step is rather subtle. Thus, in the diffusion-controlled limit, the condition for the encounter rate to be rate determining is not that it is the slowest step, but that the reaction rate of the encounter pair is much greater than the rate at which the pair breaks up. In the activation-controlled limit, the condition for the rate of energy accumulation to be rate determining is likewise a competition between the rate of reaction of the pair and the rate at which it breaks up, and all three rate constants contribute to the overall rate. The best way to analyze competing rates is to do as we have done here to set up the overall rate law and then to analyze how it simplifies as we allow particular elementary processes to dominate others. 

---