Collision theory active intermediates

The reaction is first order in molecular oxygen and first order in methanol therefore, we say both the reaction and the rate law are elementary. This forn of the rate law can be derived from Collision Theory as shown in the Profes- sion Reference Shelf 3A on the CD-ROM. There are many reactions where the stoichiometric coefficients in the reaction are identical to the reaction orders but the reactions are not elementary owing to such things as pathways involving active intermediates and series reactions. For these reactions that are not elementary but whose stoichiometric coefficients are identical to the reaction orders in the rate law. we say the reaction follows on elememary rate /aw. For example, the oxidation reaction of nitric oxide discussed earlier. 

A more general, and for the moment, less detailed description of the progress of chemical reactions, was developed in the transition state theory of kinetics. This approach considers tire reacting molecules at the point of collision to form a complex intermediate molecule before the final products are formed. This molecular species is assumed to be in thermodynamic equilibrium with the reactant species. An equilibrium constant can therefore be described for the activation process, and this, in turn, can be related to a Gibbs energy of activation ... 

Transition-state theory is based on the assumption of chemical equilibrium between the reactants and an activated complex, which will only be true in the limit of high pressure. At high pressure there are many collisions available to equilibrate the populations of reactants and the reactive intermediate species, namely, the activated complex. When this assumption is true, CTST uses rigorous statistical thermodynamic expressions derived in Chapter 8 to calculate the rate expression. This theory thus has the correct limiting high-pressure behavior. However, it cannot account for the complex pressure dependence of unimolecular and bimolecular (chemical activation) reactions discussed in Sections 10.4 and 10.5. 

The first mechanism implies k19 = k5AK11A 11A the second leads to ki9 = k2iKlm- . Independent evidence suggests the existence of both intermediate species in the nitric oxide-oxygen system, and both mechanisms involve entirely reasonable collision complexes. In both, the equilibrium step is rapid, and the overall kinetics are third order. Theoretical calculations based on the activated complex theory were made by assuming a true termolecular reaction the predicted rates agree well with experiment.161 The experimental rate constants are summarized in Tables 4-3 and 4-4. 

The results of the present calculations that the zero-point vibrational energy of the reactants can pass smoothly into that of the intermediate complexes is entirely consistent with the basic postulate of Eyring s theory that activated complexes are created from the reactants in equilibrium states. It is easy to show that the vibrationally adiabatic model, coupled with the assumption that collision cross sections are the same for all vibrational levels, leads to the conclusion that there is a Boltzmann distribution between the vibrational levels in the activated state. Thus, consider the situation represented by the energy diagram shown in Fig. 6 two levels are shown for the initial and activated states— the ground level and the nth vibrationally excited... 

With decrease in pressure, the chance that an activated molecule will lose its energy decreases more rapidly than the chance of the energy becoming so distributed as to allow a reaction to occur. Consequently, at low pressures the rates of unimolecular reactions cannot remain independent of the pressure. The activated molecule tends to become a Van t Hoff intermediate, and the rate to depend on the collision frequency. This corollary of Lindemann s theory has been... 

Figure 11. Kinetic energy release distribution for metastable loss of CH4 from nascent Co(C3Hg)+ collision complexes. The "unrestricted" phase space theory curve assumes the entrance channel contains only an orbiting transition state, the exit channel has only an orbiting transition state (no reverse activation barrier), and there are no intermediate tight transition states that affect the dynamics. The "restricted" phase space theory calculation includes a tight transition state for insertion into a C-H bond located 0.08 eV below the asymptotic energy of the reactants.

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