Activation energy thermodynamic limitations

It may come as a surprise to some that two commensurate surfaces withstand finite shear forces even if they are separated by a fluid.31 But one has to keep in mind that breaking translational invariance automatically induces a potential of mean force T. From the symmetry breaking, commensurate walls can be pinned even by an ideal gas embedded between them.32 The reason is that T scales linearly with the area of contact. In the thermodynamic limit, the energy barrier for the slider to move by one lattice constant becomes infinitely high so that the motion cannot be thermally activated, and hence, static friction becomes finite. No such argument applies when the surfaces do not share a common period. 

Reactions of carbocations with free CN- occur preferentially at carbon, and not nitrogen as predicted by the principle of hard and soft acids and bases.69 Isocyano compounds (N-attack) are only formed with highly reactive carbocations where the reaction with cyanide occurs without an activation barrier because the diffusion limit has been reached. A study with the nitrite nucleophile led to a similar observation.70 This led to a conclusion that the ambident reactivity of nitrite in terms of charge control versus orbital control needs revision. In particular, it is proposed that SNl-type reactions of carbocations with nitrite only give kinetically controlled products when these reactions proceed without activation energy (i.e. are diffusion controlled). Activation controlled combinations are reversible and result in the thermodynamically more stable product. The kinetics of the reactions of benzhydrylium ions with alkoxides dissolved in the corresponding alcohols were determined.71 The order of nucleophilicities (OH- MeO- < EtO- < n-PrCT < / -PrO ) shows that alkoxides differ in reactivity only moderately, but are considerably more nucleophilic than hydroxide. 

No activation (energy) barrier separates the donor and the acceptor from the ET products (and vice versa). The electron transfer in Scheme 18 is not a kinetic process, but is dependent on the thermodynamics, whereby electron redistribution is concurrent with complex formation. Accordingly, the rate-limiting activation barrier is simply given by the sum of the energy gain from complex formation and the driving force for electron transfer, i.e. ... 

Much more can be said about the magnitude of pre-exponcntial factors and activation energies of elementary processes based on statistical thermodynamics applied to collision and reaction-rate theory [2, 61], but in view of the remark above one should be cautious in their application and limit it to well-defined model reactions and catalyst surfaces. 

Changing activation energies are, however, not always indicative for the presence of limitations. The approach of thermodynamic equilibrium in the case of exothermal reactions can cause this phenomenon, as for hydrogenation reactions [44]. Also, changes in rate determining steps and catalyst deactivation might be causes. The same holds for reaction orders. Table 3 gives the various observations that can be made when mass transfer affects the isothermal kinetic behavior of catalyst particles. 

In a closed system and at a fixed temperature, the thermodynamic equilibrium constant of any reaction has a fixed value. A catalyst has an impact on the reaction rate by lowering the activation energy, reducing the required time to achieve the thermodynamic equilibrium and it can have an impact on the reaction channel by favoring one of several possible transition states, but a catalyst does not influence the thermodynamic equilibrium itself. That means the maximal achievable yield cannot be higher than that predicted by thermodynamics. An important consequence of this limitation is that for a comparison of different catalysts the experimental conditions must not allow that the thermodynamic equilibrium is reached. Typical reaction conditions for this case would be low reactant flow (setup then resembling a closed system) and/or a temperature allowing a very fast reaction. If the experimental conditions allow the reaction to approach the thermodynamic equilibrium, a comparison of different catalysts is usually impossible. For any kinetic studies the... 

An important detail is that an individual rate-limiting step may be endothermic whereas the overall reaction is exothermic as in this case. This is illustrated in Fig. 7.3. The chemisorption of N2 is exothermic and its dissociation is endothermic (1A). However, the overall reaction of N2 + H2 to NH3 is exothermic (1B). The overall activation energy and kinetics are dictated by the slow step. The reaction heat liberated (A H25°C) = — 11 kcal/mole is the thermodynamic value associated with the overall reaction. 

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