Critical simplification reaction rates

This latter equation is formally the same as that encountered previously for a first-order reversible reaction and can be easily integrated [cf. Eq. (1-25)]. Simplification of rate equations via the steady-state approximation is often adopted, but evidence for the validity of this approximation should be critically examined in each case where it is used. 

Principle of critical simplification. In accordance with this principle (Yablonsky et al., 2003), the behavior near critical points, for instance ignition or extinction points in catalytic combustion reactions, is governed by the kinetic parameters of only one reaction—adsorption for ignition and desorption for extinction— which is not necessarily the rate-limiting one. 

The main result is that real multiplicity of steady states—the existence of two internal stable steady states and one internal unstable steady state—can be explained using one of the four mechanisms shown in Table 7.3. If the experimentally observed steady-state reaction rate is characterized by two different branches, and multiplicity of steady states is observed, one of these four mechanisms can be used to interpret the data. We prefer to use mechanism B because its steps are characterized by overall reaction orders that are not larger than two. In fact, this mechanism is identical to the mechanism represented by Eq. (7.102), an example of which is the adsorption mechanism for the oxidation of carbon monoxide (Eq. (7.103)). We will return to this mechanism in Chapter 11, in which the problem of critical simplification is discussed. 

Heterogeneous catalysis has to deal not only with the catalyzed reaction itself but, in addition, with the complexities of surface properties (different crystal surfaces, different catalytic sites), possible segregation of adsorbates (so-called island formation), contamination or deterioration of catalytic sites, and adsorption and desorption equilibria and rates. Moreover, mass transfer to and from the reaction site is a factor more often than in homogeneous catalysis. In practice, these complications may affect behavior more profoundly than does the kinetics of the surface reaction itself. A practical and balanced kinetic treatment therefore uses simplifications and approximations much more generously than was done in the preceding chapters. Excellent textbooks on the subject are available [G1-G7], so coverage here can remain restricted to a critical overview and indications showing when and how concepts and methods developed in the earlier chapters can be useful. 

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