Activation energy theory

Alternative Activation Energy Theories of Dynamics in Glass-Forming Liquids... 

XL ALTERNATIVE ACTIVATION ENERGY THEORIES OF DYNAMICS IN GLASS-FORMING LIQUIDS... 

The Langmuir-Hinshelwood picture is essentially that of Fig. XVIII-14. If the process is unimolecular, the species meanders around on the surface until it receives the activation energy to go over to product(s), which then desorb. If the process is bimolecular, two species diffuse around until a reactive encounter occurs. The reaction will be diffusion controlled if it occurs on every encounter (see Ref. 211) the theory of surface diffusional encounters has been treated (see Ref. 212) the subject may also be approached by means of Monte Carlo/molecular dynamics techniques [213]. In the case of activated bimolecular reactions, however, there will in general be many encounters before the reactive one, and the rate law for the surface reaction is generally written by analogy to the mass action law for solutions. That is, for a bimolecular process, the rate is taken to be proportional to the product of the two surface concentrations. It is interesting, however, that essentially the same rate law is obtained if the adsorption is strictly localized and species react only if they happen to adsorb on adjacent sites (note Ref. 214). (The apparent rate law, that is, the rate law in terms of gas pressures, depends on the form of the adsorption isotherm, as discussed in the next section.)... 

To a first approximation, the activation energy can be obtained by subtracting the energies of the reactants and transition structure. The hard-sphere theory gives an intuitive description of reaction mechanisms however, the predicted rate constants are quite poor for many reactions. 

Examining transition state theory, one notes that the assumptions of Maxwell-Boltzmann statistics are not completely correct because some of the molecules reaching the activation energy will react, lose excess vibrational energy, and not be able to go back to reactants. Also, some molecules that have reacted may go back to reactants again. 

Activation energy, i.e., the energy of the transition structure relative to reactants, can be observed experimentally. However, the only way that the geometries of transition structures can be evaluated is from theory. Theory also can give energetics and geometry parameters of short-lived reaction intermediates. 

For tme first-order bond mpture reactions, the activation energy, E, is equal to the energy of the mptured bond, and following the transition-state theory... 

The overall requirement is 1.0—2.0 s for low energy waste compared to typical design standards of 2.0 s for RCRA ha2ardous waste units. The most important, ie, rate limiting steps are droplet evaporation and chemical reaction. The calculated time requirements for these steps are only approximations and subject to error. For example, formation of a skin on the evaporating droplet may inhibit evaporation compared to the theory, whereas secondary atomization may accelerate it. Errors in estimates of the activation energy can significantly alter the chemical reaction rate constant, and the pre-exponential factor from equation 36 is only approximate. Also, interactions with free-radical species may accelerate the rate of chemical reaction over that estimated solely as a result of thermal excitation therefore, measurements of the time requirements are desirable. 

In theory two carbanions, (189) and (190), can be formed by deprotonation of 3,5-dimethylisoxazole with a strong base. On the basis of MINDO/2 calculations for these two carbanions, the heat of formation of (189) is calculated to be about 33 kJ moF smaller than that of (190), and the carbanion (189) is thermodynamically more stable than the carbanion (190). The calculation is supported by the deuterium exchange reaction of 3,5-dimethylisoxazole with sodium methoxide in deuterated methanol. The rate of deuterium exchange of the 5-methyl protons is about 280 times faster than that of the 3-methyl protons (AAF = 13.0 kJ moF at room temperature) and its activation energy is about 121 kJ moF These results indicate that the methyl groups of 3,5-dimethylisoxazole are much less reactive than the methyl group of 2-methylpyridine and 2-methylquinoline, whose activation energies under the same reaction conditions were reported to be 105 and 88 kJ moF respectively (79H(12)1343). 

Approximate calculations of this activation energy have been made in a number of examples using the quanmm theory of molecular binding, by making assumptions concerning the stmcture and paitition functions of the Uansition state molecule. 

An estimate of the enthalpy change which conesponds to the activation energy of the collision theory analysis of 167kJmoP may be made by assuming that the formation of tire dimer from two molecules of the monomer is energetically equivalent to tire dipole-dipole and dispersion interactions of two HI molecules. These exothermic sources of interaction are counterbalanced... 

A more complete analysis of interacting molecules would examine all of the involved MOs in a similar wty. A correlation diagram would be constructed to determine which reactant orbital is transformed into wfiich product orbital. Reactions which permit smooth transformation of the reactant orbitals to product orbitals without intervention of high-energy transition states or intermediates can be identified in this way. If no such transformation is possible, a much higher activation energy is likely since the absence of a smooth transformation implies that bonds must be broken before they can be reformed. This treatment is more complete than the frontier orbital treatment because it focuses attention not only on the reactants but also on the products. We will describe this method of analysis in more detail in Chapter 11. The qualitative approach that has been described here is a useful and simple wty to apply MO theory to reactivity problems, and we will employ it in subsequent chapters to problems in reactivity that are best described in MO terms. I... 

Calculations at several levels of theory (AMI, 6-31G, and MP2/6-31G ) find lower activation energies for the transition state leading to the observed product. The transition-state calculations presumably reflect the same structural features as the frontier orbital approach. The greatest transition-state stabilization should arise from the most favorable orbital interactions. As discussed earlier for Diels-Alder reactions, the-HSAB theory can also be applied to interpretation of the regiochemistry of 1,3-dipolar cycloaddi-... 

Simple collision theory does not provide a detailed interpretation of the energy barrier or a method for the calculation of activation energy. It also fails to lead to interpretations in terms of molecular structure. The notable feature of collision theoiy is that, with very simple means, it provides one basis for defining typical or normal kinetic behavior, thereby directing attention to unusual behavior. 

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