Rate adsorption enthalpy

We again assume that the pre-exponential factor and the entropy contributions do not depend on temperature. This assumption is not strictly correct but, as we shall see in Chapter 3, the latter dependence is much weaker than that of the energy in the exponential terms. The normalized activation energy is also shown in Fig. 2.11 as a function of mole fraction. Notice that the activation energy is not just that of the rate-limiting step. It also depends on the adsorption enthalpies of the steps prior to the rate-limiting step and the coverages. 

Fig. 9. Effect of the chain length of hydrocarbons on the adsorption enthalpy and rates of desorption. (A) Hydrocarbon in interaction with zeolite framework. Methyl groups interact with the framework oxygen protons exhibit an additional attractive force. (B) Heat of adsorption as a function of carbon number for zeolites MFI and FAU in the acidic and non-acidic form. (C) Relative desorption rates of a C12, Ci6, and C20 alkane compared to octane at 348 K. Values calculated from the linear extrapolation of the heat of adsorption values shown in (B).

True activation energies are obtained when the reaction order is zero and probably also when the rate coefficient, k, and adsorption coefficient, Ka, have been separated by treatment of rate data by means of eqn. (3). In the case of the first-order rate equation, the apparent activation energy, calculated from k values [eqn. (5)] by means of the Arrhenius equation, is the difference between the true activation energy and the adsorption enthalpy of the reactant A... 

It should be emphasized that the LHHW kinetic rate expressions are derived with assumptions of energetic uniformity and if this is violated then these constraints should be used with caution. In a transient kinetics study Dckker et al. [21] have shown that an occupancy dependent CO adsorption enthalpy on Pt results in very low values of the reaction activation energy, and might even become negative. 

Effect Change in catalytic rate r Change in work function <1) Change in adsorption enthalpies AHj ... 

The key step in the derivation by Reuter et al. of their lattice model is the use of detailed balance to determine the sticking coefficients for each species on each type of site.31 The total adsorption rate at a particular site can be expressed as Tad = SI(p, T), where S is the local sticking coefficient and I(p,T) is the impingement rate of the species of interest from a gas phase with partial pressure p and temperature T. At steady state, the total adsorption and desorption rates must satisfy the detailed balance condition TdesjTad = exp[(Fb—/j,(T, p))/kT, where Fb is the free energy of the adsorbed species and fi(T, p) is the chemical potential of the gas phase species. The adsorption free energy is well approximated by the adsorption enthalpy, which is simply the adsorption energy calculated by a DFT calculation. This approach provides a direct link between the adsorption and desorption rates and the pressure and temperature of the bulk gas phase. 

The observed activation energy contains contributions from the rate-determining step ( 32) and from the adsorption enthalpies of A and B, the latter depending on the fractional occupancies. Obviously, ° will depend on the experimental conditions. Therefore, it is not surprising that a wide range of values have been reported for the same reaction system. 

Unfortunately, in the continuous on-line experiments with transactinoid elements, the application of the above Second Law and related procedures has not been possible because of the very poor statistics of detected decays. Measurements of this type have been done only with long-lived lighter homologs of the transactinoids in batch tests. Packed columns and low flow rates of the carrier gas were employed to achieve narrow peaks. Major contribution came from Bachmann and co-workers. In Refs. [6,9-11] they measured the adsorption enthalpies and entropies on solid... 

In our case study, the two-sink model fitted most experimental data very efficiently. However, it is not supposed to provide a complete physical description of the real adsorption process(es). Increasing the number of regression parameters in any equation improves its adherence to the data. However, the model is supposed to be a better approximation to the more complex reality. This reality may include adsorption sites with a distribution of adsorption enthalpies instead of simply two distinct values, and may also include diffusion processes within the sorbing material. A further development of the two-sink model could take into consideration the transfer of molecules from the faster (more superficial) to the slower (deeper) sink sites. The model in its present form can be used to estimate four unknown parameters, i.e. the adsorption and desorption rate constants for each of the two sinks. 

Table 1 summarises the steady state experiments over the zeolite crystals and pellets. The activation energy for the intrinsic rate constant kmtr was 34.4 kJ/mol. The low value indicates that the adsorption enthalpy is of the same order as the reaction enthalpy, i.e. (ERx ,obs = Ekr + EAds). The diffusion coefficient under steady state conditions was found to be an order of magnitude higher than that calculated from Knudsen diffusion (2x10 cmVs) using an average pore size of 3.8x10 cm measured by BET and a tortuosity factor of 4. The estimated... 

While the relationship between the electronic properties and the reaction enthalpy is important in understanding energetics, the more important thermodynamic feature to focus on is the free energy. Indeed, in Chapter 4 the maximum for the rate of a zeolite-catalyzed reaction is not found for the zeolite with the smallest pore size (maximum adsorption enthalpy) but for medium-sized micropores where adsorbates have a higher entropy, and as a consequence, their concentration is a maximum. The gain in entropy often balances the loss in adsorption enthalpy. 

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