Elementary reactions quasi-equilibrium approximation

An important point concerning the set of reactions 5.2 is worth noting. As already mentioned, it is generally assumed in such reactions that the net rate of generation of an intermediate can be set to zero. In another approach, if an equilibrium step is involved, we use the quasi-equilibrium approximation, in which the ratio of the forward to backward rates of a rapid elementary step is set equal to unity. In either case, it must be remembered that the fundamental... 

In this approximation we assume that one elementary step determines the rate while all other steps are sufficiently fast that they can be considered as being in quasi-equilibrium. If we take the surface reaction to AB (step 3, Eq. 134) as the rate-determining step (RDS), we may write the rate equations for steps (1), (2) and (4) as ... 

This kinetic approximation assumes a single vibrational temperature 77 for CO2 molecules and, therefore, is sometimes referred to as quasi equilibrium of vibrational modes. As one can see from (5-20), most of the vibrationally excited molecules can be considered as being in quasi continuum in this case. Vibrational kinetics of polyatomic molecules in quasi continuum was discussed in Chapter 3. The CO2 dissociation rate is limited not by elementary dissociation itself, but via energy transfer from a low to high vibrational excitation level of the molecule in the W-relaxation processes. Such a kinetic situation was referred to in Chapter 3 as the fast reaction limit. The population of highly excited states with vibrational energy E depends in this case on the number of vibrational degrees of freedom 5 and is proportional to the density of the vibrational states p E) a. The... 

When condition (dai/dt)react (dai/dt)rei is not satisfied, the perturbation of equilibrium distribution is substantial. However, in this case realization of the quasi-steady-state condition is possible, provided the overall rate dai/dt is low compared to partial rates (daj/dt)rei and (dai/dt)i.eact Then, the microscopic kinetic equation can be solved by the quasi-steady-state approximation. The approximation implies that the non-equilibrium distribution functions depend on time implicitly via the total concentration of reactants rather than explicitly. This also means that the macroscopic reaction rates are low compared to microscopic reaction and relaxation rates. Since the distribution functions in this approximation depend on the total concentration only, the reaction rates, according to Eq. (8.50) also depend on the total concentration. Hence, we come to macroscopic kinetic equations that involve only the total concentration of reactants and certain combinations of microscopic rate constants that have the meaning of macroscopic constants. Note that these macroscopic equations need not be consistent with the macroscopic kinetic law as, besides elementary reactive processes, they involve unreactive processes. 

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