Activation energy of the elementary step

Two adsorption complexes were found for the interaction of the neutral water and methanol molecules with the methoxy-zeolite lattice, as shown in Fig. 15. The water molecule essentially is a spectator during the formation of DME, although it does stabilize the DME once it is formed. The largest activation energy of the elementary steps is that for methoxy formation (160 kJ/mol). This is similar to the barrier to DME formation via the... 

Equations (12a) through (12c) are of great significance because they allow formulation of quantitative relationships between the activation energies of the elementary steps of the Fischer-Tropsch reaction that have to be satisfied for a high chain-growth selectivity. 

All these expressions eventually provide a definition of the activation energy of the elementary step that varies slightly with temperature. These variations are nearly impossible to detect experimentally, since the range of variations for one reaction is usually quite narrow in order to keep reaction rates measurable. 

Derive the expression for v (= —d[0 j/df), making steady-state and long-chain approximations. How is Ea for the overall reaction related to the activation energies of the elementary reaction steps ... 

Based on the experimental data and some speculations on detailed elementary steps taking place over the catalyst, one can propose the dynamic model. The model discriminates between adsorption of carbon monoxide on catalyst inert sites as well as on oxidized and reduced catalyst active sites. Apart from that, the diffusion of the subsurface species in the catalyst and the reoxidation of reduced catalyst sites by subsurface lattice oxygen species is considered in the model. The model allows us to calculate activation energies of all elementary steps considered, as well as the bulk... 

Relate the size of the activation energy of an elementary step in a complex reaction to the rate of that step. 

Relationship between the activation energies of two elementary steps belonging to the same type. 

The reason why this set of coupled reactions prevails over a direct reaction between H2 and CI2 becomes clear if we consider the activation energies of the reaction steps. Whereas the direct reaction between H2 and CI2 requires an activation energy of over 200 kJ/mol, the activation energies of the two propagation steps are only 25 and 13 kJ/mol, respectively, which favors the chain process over the direct reaction. The difficult step is the initiation it is facilitated by the absorption of a photon. The dynamics of elementary steps of the type H + CI2 -> HCl + Cl have been extensively studied in the past. We will return to these reactions in Chapters 4 and 5. 

The activation energy of the overall reaction equals that of the first step, a,i-Note that fast elementary steps following the one that limits the rate become kine-tically insignificant, whereas fast steps before the rate-determining step do enter the rate equation, as they directly affect the concentration of the intermediate that is converted in the rate-determining step. 

The results here clearly demonstrate some of the important differences between reactions in the vapor phase and those in the aqueous phase. Water solvates the ions that form and thus enhances the heterolytic bond activation processes. This leads to more significant stabilization of the charged transition and product states over the neutral reactant state. The changes that result in the overall energies and the activation barriers of particular elementary steps can also act to alter the reaction selectivity and change the mechanism. 

The activation energies of the respective elementary steps are denoted as g, Agl, 4gc, and dgj the corresponding anodic reaction rates are denoted as u., iJb, Vc, and Ud. Then, we obtain the rate equations shown in Eqns. 9-25a through 9-25d ... 

Since all of the above-mentioned interconversion reactions are reversible, any kinetic analysis is difficult. In particular, this holds for the reaction Sg - Sy since the backward reaction Sy -+ Sg is much faster and, therefore, cannot be neglected even in the early stages of the forward reaction. The observation that the equilibrium is reached by first order kinetics (the half-life is independent of the initial Sg concentration) does not necessarily indicate that the single steps Sg Sy and Sg Sg are first order reactions. In fact, no definite conclusions about the reaction order of these elementary steps are possible at the present time. The reaction order of 1.5 of the Sy decomposition supports this view. Furthermore, the measured overall activation energy of 95 kJ/mol, obtained with the assumption of first order kinetics, must be a function of the true activation energies of the forward and backward reactions. The value found should therefore be interpreted with caution. 

In this case, the apparent activation energy is not equal to the activation energy of the rate-determining step. By definition, the activation energy for elementary step 2 equals... 

This corresponds to the activation energy Ea2 of the elementary step of the product P elimination from intermediate K-, and equals approximately (to an accuracy of RT) the heat of the formation of the transition state of elementary reaction 2 from the standard state of intermediate Ki (Figure 4.2A). Note that here and in other examples of catalytic reaction schemes with the high occupation of the active center with intermediates the value of the apparent activation energy does not follow the statement in Section 1.4.5 on the apparent activation energies of noncatalytic consecutive processes. 

Whenever an activation energy is known for one metal surface, then the activation energies of the same elementary reaction step on other metals can be deduced from the differences in the adsorption energies of C and O on the two metals. This procedure has been used to generate the activation barriers presented in Table 1. 

Because of their great importance in chemical industry, much effort has been devoted to the study of autoxidation and combustion, and a large data base of rate coefficients and activation energies of common elementary reaction steps has been compiled [51,51,60,69-71],... 

TABLE 1. Values for the rate parameters of the elementary steps in our MC model, p stands for pressure, u for prefaotors, Eact for activation energy, and So for the initial sticking coefficient. For the reactions which have zero activation barriers, we have considered the rate constants as effective, temperature-independent parameters. 

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