Composite activation energy

The apparent activation energy is then less than the actual one for the surface reaction per se by the heat of adsorption. Most of the algebraic forms cited are complicated by having a composite denominator, itself temperature dependent, which must be allowed for in obtaining k from the experimental data. However, Eq. XVIII-47 would apply directly to the low-pressure limiting form of Eq. XVIII-38. Another limiting form of interest results if one product dominates the adsorption so that the rate law becomes... 

The classical experiment tracks the off-gas composition as a function of temperature at fixed residence time and oxidant level. Treating feed disappearance as first order, the pre-exponential factor and activation energy, E, in the Arrhenius expression (eq. 35) can be obtained. These studies tend to confirm large activation energies typical of the bond mpture mechanism assumed earlier. However, an accelerating effect of the oxidant is also evident in some results, so that the thermal mpture mechanism probably overestimates the time requirement by as much as several orders of magnitude (39). Measurements at several levels of oxidant concentration are useful for determining how important it is to maintain spatial uniformity of oxidant concentration in the incinerator. 

This reaction is catalyzed by iron, and extensive research, including surface science experiments, has led to an understanding of many of the details (72). The adsorption of H2 on iron is fast, and the adsorption of N2 is slow and characterized by a substantial activation energy. N2 and H2 are both dis so datively adsorbed. Adsorption of N2 leads to reconstmction of the iron surface and formation of stmctures called iron nitrides that have depths of several atomic layers with compositions of approximately Fe N. There is a bulk compound Fe N, but it is thermodynamically unstable when the surface stmcture is stable. Adsorbed species such as the intermediates NH and NH2 have been identified spectroscopically. 

The value of the activation energy approaches 50000 near the stoichiometric composition. This diffusion process therefore approximates to the selfdiffusion of metals at stoichiometty where the vacancy concentration on the carbon sub-lattice is small. 

The composite results of benzo-fusion on the rates and activation energies of ethoxylation and of piperidination are summarized in round numbers in Scheme VI to give a broad perspective. 

Each of the steps in this new reaction mechanism is governed by the same prindples that govern a simple reaction. Each reaction has an activation energy. The overall reaction has a potential energy diagram that is merely a composite of the simple energy curves of the succeeding steps. 

Reaction rates almost always increase with temperature the rare ones that do not have a negative activation energy will be dealt with later. The expression of the temperature dependence is always given for the rate constant, rather than the rate. For now, only elementary reactions will be considered, with composite reactions and other more complicated situations deferred to Section 7.5. Two forms are commonly used to express the rate constant as a function of temperature. The first is the familiar Arrhenius equation,... 

The expression for Eq. (8-14) can be interpreted in terms of the activation energy for a composite rate constant as explained in Chapter 7. In those terms Ea is... 

It is worth noting that Io is, in general, strongly dependent both on temperature and on gaseous composition. It increases with temperature with an activation energy which is typically 35-45 kcal/mol for Pt and 20-25 kcal/mole for Ag films deposited on stabilized zirconia.1,5 7 43... 

A catalyst speeds up a reaction by providing an alternative pathway—a different reaction mechanism—between reactants and products. This new pathway has a lower activation energy than the original pathway (Fig. 13.34). At the same temperature, a greater fraction of reactant molecules can cross the lower barrier of the catalyzed path and turn into products than when no catalyst is present. Although the reaction takes place more quickly, a catalyst has no effect on the equilibrium composition. Both forward and reverse reactions are accelerated on the catalyzed path, leaving the equilibrium constant unchanged. 

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