Homogeneous reactions quasi-equilibrium

The postulate of quasi-equilibrium of all steps except a single one that controls the rate is very powerful. It reduces the mathematical complexity of kinetics even of large networks to quite simple rate equations and has become a favorite tool, employed today in a great majority of publications on kinetics of multistep homogeneous reactions, sometimes uncritically. In many cases, a sharp distinction between fast and slow steps cannot be justified. A more general approach that avoids the postulate of a single rate-controlling step and contains the results obtained with it as special cases will be described in Sections 4.3 and 6.3 and widely used in later Chapters. 

This set is of the same algebraic form as eqns 5.16 for conversion of a single reactant to two products in parallel steps. Because quasi-equilibrium of isomerization is maintained, the reactant acts as a "homogeneous source" despite being split into two isomers, and the mathematics of product formation is the same as for the simpler reaction with network 5.15. Results from constant-volume batch plotted as lnx versus t for P, Q, and total A give identical straight lines with slope -k, as in Figure 5.6, where... 

Coupled parallel steps are an important combination not covered in any standard texts, and are therefore examined in more detail. Typical examples are isomerization in concert with conversion of the isomers to different products. If isomerization is very fast compared with conversion, the isomers are at quasi-equilibrium and act as "homogeneous source," producing a kinetic behavior like that of a single reactant. If isomerization is very slow compared with conversion, the reactions of the different isomers are essentially uncoupled. If the rates of isomerization and conversion are comparable, a more complex behavior ensues. Most interesting is the case with isomerization being somewhat faster than conversion. The isomer distribution then approaches a steady state (not necessarily close to equilibrium), and from then on the isomers act as homogeneous source. 

LH rate expressions often rely on the quasi steady state assumption that stipulates that one elementaiy step is rate determining whereas the other steps are at equilibrium. The assumption is debatable in me wide temperature range encountered in the monolith, because the rate determiniim step may be different according to tlie temperature level. It would thus be useful to know whether the rate expressions obtained at moderate temperature are still reliable at the higli temperature and low reactant concentrations observed after light-off has occurred. However, care must be taken of the possible transfer limitations, and of flie possible catalytically induced homogeneous reactions. 

The application of quasi-equilibrium statistics and thermodynamics to plasma-chemical systems requires a clear understanding and distinction between the concepts of complete thermodynamic equilibrium (CTE) and local thermodynamic equilibrium (LTE). CTE is related to uniform plasma, in which chemical equilibrium and all plasma properties are unambiguous functions of temperature. This temperature is supposed to be homogeneous and the same for all degrees of freedom, all components, and all possible reactions. In particular, the following five equilibrium statistical distributions should take place for the same temperature T ... 

In this form, Eq. (6.126) applies for simple homogeneous kinetics. If, as is the case for oxygen incorporation, a reservoir of thickness L is coupled, a uniform concentration profile establishes in the sample under the condition of reaction control as directly confirmed by the space-resolved profiles in Fig. 6.51 (quasi-equilibrium). The deviation 6c then determines the flux into this volume and, hence, the amount... 

The kinetic behavior of the heterogeneous esterification of acetic acid with amyl alcohol over Dowex 50 Wx8-100 resin and propionic acid with n-butanol over Amberlyst 35 was investigated by Lee and Lin (2000/2002) in a fixed bed reactor at temperatures from 323 K to 393 K and molar ratios of feed (amyl alcohol to acetic acid) from 1 to 10 and the molar ratios of feed (n-butanol to propionic acid) from 0.5 to 2. The equilibrium conversions of acid were found to increase with an increase in the reaction temperature. The kinetic data was correlated with the quasi-homogeneous, Langmuir-Hinshelwood, Eley-Rideal and modified Langmuir-Hinshelwood models. 

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