Energy from unimolecular reactions

The system of coupled differential equations that result from a compound reaction mechanism consists of several different (reversible) elementary steps. The kinetics are described by a system of coupled differential equations rather than a single rate law. This system can sometimes be decoupled by assuming that the concentrations of the intennediate species are small and quasi-stationary. The Lindemann mechanism of thermal unimolecular reactions [18,19] affords an instructive example for the application of such approximations. This mechanism is based on the idea that a molecule A has to pick up sufficient energy... 

For analysing equilibrium solvent effects on reaction rates it is connnon to use the thennodynamic fomuilation of TST and to relate observed solvent-mduced changes in the rate coefficient to variations in Gibbs free-energy differences between solvated reactant and transition states with respect to some reference state. Starting from the simple one-dimensional expression for the TST rate coefficient of a unimolecular reaction a— r... 

From stochastic molecnlar dynamics calcnlations on the same system, in the viscosity regime covered by the experiment, it appears that intra- and intennolecnlar energy flow occur on comparable time scales, which leads to the conclnsion that cyclohexane isomerization in liquid CS2 is an activated process [99]. Classical molecnlar dynamics calcnlations [104] also reprodnce the observed non-monotonic viscosity dependence of ic. Furthennore, they also yield a solvent contribntion to the free energy of activation for tlie isomerization reaction which in liquid CS, increases by abont 0.4 kJ moC when the solvent density is increased from 1.3 to 1.5 g cm T Tims the molecnlar dynamics calcnlations support the conclnsion that the high-pressure limit of this unimolecular reaction is not attained in liquid solntion at ambient pressure. It has to be remembered, though, that the analysis of the measnred isomerization rates depends critically on the estimated valne of... 

Detailed analyses of the above experiments suggest that the apparent steps in k E) may not arise from quantized transition state energy levels [110.111]. Transition state models used to interpret the ketene and acetaldehyde dissociation experiments are not consistent with the results of high-level ab initio calculations [110.111]. The steps observed for NO2 dissociation may originate from the opening of electronically excited dissociation chaimels [107.108]. It is also of interest that RRKM-like steps in k E) are not found from detailed quantum dynamical calculations of unimolecular dissociation [91.101.102.112]. More studies are needed of unimolecular reactions near tln-eshold to detennine whether tiiere are actual quantized transition states and steps in k E) and, if not, what is the origin of the apparent steps in the above measurements of k E). 

While all rates of these unimolecular reactions can be fit quantitatively by LH expressions. Equation 11, the heats of adsorption determined from the temperature dependence of the adsorption equillb-rium constant. Equation 14, do not agree with the measured reaction activation energy except for NH3 where = 16 2 kcal/mole. NO... 

Gas-phase SN2 nucleophilic substitution reactions are particularly interesting because they have attributes of both bimolecular and unimolecular reactions.1 As discovered from experimental studies by Brauman and coworkers2 and electronic structure theory calculations,3 potential energy surfaces for gas-phase SN2 reactions of the type,... 

The rate coefficient kun reflects the unimolecular reaction initiated by exciting reactant molecules to an energy between E and E + 8E. As already noted, there is a minimum excitation energy E0 required to proceed with reaction, usually called the activation energy, E0 and all energies from Eo to oo will be assumed to lead to reaction. Thus, the over-all kuni is found by integrating Equation 14.13 to yield... 

The thermal isomerization of cyclopropane to propylene is perhaps the most important single example of a unimolecular reaction. This system has been studied by numerous workers. Following the work of Trautz and Winkler (1922), who showed that the reaction was first order and had an energy of activation of about 63,900 cal mole measured in the temperature range 550-650° C, Chambers and Kistiakowsky (1934) studied the reaction in greater detail and with higher precision from 469-519° C. They confirmed that it was first order and, for the reaction at its high-pressure limit, obtained the Arrhenius equation... 

It is convenient initially to classify elementary reactions either as energy-transfer-limited or chemical reaction-rate-limited processes. In the former class, the observed rate corresponds to the rate of energy transfer to or from a species either by intermolecular collisions or by radiation, or intramolecular-ly due to energy transfer between different degrees of freedom of a species. All thermally activated unimolecular reactions become energy-transfer-limited at high temperatures and low pressures, because the reactant can receive the necessary activation energy only by intennolecular collisions. 

In this part of the chapter, we will briefly outline the main types of CL reactions which can be functionally classified by the nature of the excitation process that leads to the formation of the electronically excited state of the light-emitting species. Direct chemiluminescence is the term employed for a reaction in which the excited product is formed directly from the unimolecular reaction of a high-energy intermediate that has been formed in prior reaction steps. The simplest example of this type of CL is the unimolecular decomposition of 1,2-dioxetanes, which are isolated HEI. Thermal decomposition of 1,2-dioxetanes leads mainly to the formation of triplet-excited carbonyl compounds. Although singlet-excited carbonyl compounds are produced in much lower yields, their fluorescence emission constitutes the direct chemiluminescence emission observed in these transformations under normal conditions in aerated solutions ... 

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