Intrinsic surface reaction constants determination

It is interesting to note that the chlorinated ethylenes do not appear to follow this trend of increasing rates with increasing chlorination. (Lowry and Reinhard 1999 Schreier 1996) This may be due in part to the extremely fast rates of these reactions, which increase the relative importance of mass transfer limitations. For very fast reactions, mass transfer of compounds to the catalyst surface, rather than the intrinsic catalytic reaction rate, may determine the rate of disappearance of hydrocarbons and the resulting apparent rate constants. 

In summary, it can be seen for the three-step reaction scheme of this example that the net rate of the overall reaction is controlled by three kinetic parameters, KTSi, that depend only on the properties of the transition states for the elementary steps relative to the reactants (and possibly the products) of the overall reaction. The reaction scheme is represented by six individual rate constants /c, and /c the product of which must give the equilibrium constant for the overall reaction. However, it is not necessary to determine values for five linearly independent rate constants to determine the rate of the overall reaction. We conclude that the maximum number of kinetic parameters needed to determine the net rate of overall reaction is equal to the number of transition states in the reaction scheme (equal to three in the current case) since each kinetic parameter is related to a quasi-equilibrium constant for the formation of each transition state from the reactants and/or products of the overall reaction. To calculate rates of heterogeneous catalytic reactions, an addition kinetic parameter is required for each surface species that is abundant on the catalyst surface. Specifically, the net rate of the overall reaction is determined by the intrinsic kinetic parameters Kf s as well as by the fraction of the surface sites, 0, available for formation of the transition states furthermore, the value of o. is determined by the extent of site blocking by abundant surface species. 

Using the data presented here we have no basis for distinguishing between these alternative reactions. The possible reactions for the interactions of the ions with the goethite surface as well as the corresponding estimate of the intrinsic equilibrium constants determined by the double extrapolation method are summarized in Table I. The intrinsic acidity constants,... 

Data obtained in fixed-bed reactors and in continuous high-velocity coil-t ype reactors (fluid catalyst) indicate that the catalytic cracking of gas oils is approximately a first-order reaction, but that the apparent order approaches two because of the effect of nonhomogeneity of the feed and because of the increasing dilution of reactant with cracked products as conversion increases at constant total pressure (73). The extent of reaction is determined by the intrinsic activity of the catalyst surface, reaction time at the surface, temperature, and susceptibility of the feed to cracking. Superficial contact time in the reactor is of little consequence. The effective time of reaction is the time spent by oil on the active surface of the catalyst. For a given extent of adsorption, the reaction time should be inversely proportional to weight space velocity and should also be a function of the reactant partial pressure. Results of experiments with... 

Samples from the site contained considerable amounts of freshly precipitated iron hydroxides. Their transformation into thermodynamically more stable minerals such as goethite or hematite has a very slow kinetics, thus ferrihydrite was chosen as the major adsorbing surface. The Diffuse Double Layer model (Dzombak and Morel, 1990) was selected to describe surface complexation. The respective intrinsic surface parameters and the reaction constants for the ions competing with uranium(VI) for sorption sites were taken from a database mainly based on Dzombak and Morel, 1990, with the urani-um(Vl) sorption parameters as determined by Dicke and Smith, 1996. The results, based on runs with 1000 varied parameter sets, are summarized in Table 5.2. 

The charge regulation model can be used successfully for interpretating pH poten-tiometric titration data, thus enabling the determination of intrinsic equilibrium constants of surface reactions and the prediction of surface composition under various conditions. The following example demonstrates this. 

Since the particle Reynolds numbers in laboratory PBRs are very low, as stated in Section 2.2.2.2, the range of flow rates to be covered for producing adequate increases in transport coefficients has to be rather wide. It is important to determine the minimum gas flow rate after which the exit conversions Xa or the global rates ( Ra)p remain constant (Figure 2.6). All subsequent kinetic experiments must be conducted at flow rates equal to or above this minimum. When the overall process is surface reaction controlled, that is, if intrinsic kinetics is being observed, neither Xa nor -Ra)p will change with increasing linear velocity of the fluid. 

Gouy-Chapman, Stern, and triple layer). Methods which have been used for determining thermodynamic constants from experimental data for surface hydrolysis reactions are examined critically. One method of linear extrapolation of the logarithm of the activity quotient to zero surface charge is shown to bias the values which are obtained for the intrinsic acidity constants of the diprotic surface groups. The advantages of a simple model based on monoprotic surface groups and a Stern model of the electric double layer are discussed. The model is physically plausible, and mathematically consistent with adsorption and surface potential data. 

Davis et al.70) describes a method for determining intrinsic ionisation and complexa-tion constants of oxide surface sites from potentiometric titration data. Analyzing the local equilibrium reaction and the equilibrium constant of the surface sites they use the approach of Chan et al.71) ... 

The intrinsic constants are thermod3mamic constants written for reactions occurring at a hypothetical isolated site on the surface. Actual activities on the surface cannot be directly determined but Q or apparent stability quotients can be calculated based on measurable bulk concentrations. The intrinsic constants and apparent stability quotients are related by considering the electrostatic correction for an ion in solution near the surface compared to an isolated ion on the surface. In an idealized planar model, is the mean potential at the plane of surface charge created by the ionization of the surface functional groups and the formation of surface complexes and is the mean potential at the plane of adsorbed counter ions at a distance 3 from the surface (17). The electrostatic interaction energies at the surface and at a distance 3 are expressed as exponentials. Therefore ... 

From Eq. (2), the measured diffusivities may be used to determine the mean lifetime of the reactant and product molecules within the individual crystallites under the assumption that the molecular exchange is exclusively controlled by intracrystalline diffusion. These values, being of the order of 30 ms, are found to agree with the real intracrystalline mean lifetime directly determined by NMR tracer desorption studies (208], so that any influence of crystallite surface barriers may be excluded. From an analysis of the time dependence of the intracrystalline concentration of the reactant and product molecules, the intrinsic reaction time constant is found to be on the order of 10 s. This value is much larger than the intracrystalline mean lifetimes determined by PFG NMR, and thus any limiting influence of mass transfer for the considered reaction may be excluded. In agreement with this conclusion, the size of the applied crystallites was found to have no influence on the conversion rates in measurements with a flow reactor (208]. 

We now compare the performance of non-porous catalysts with the selectivity expected for porous catalysts in Type III reactions. Referring to the Type III reaction scheme given above, we note that if ki and ki are the intrinsic rate constants per unit internal surface, then on a plane surface the yield of B for first order kinetics would be determined by the equations ... 

The conventional mass-action quotients without electric potential variable for these equilibria are not constants, often called apparent equilibrium constants, and K, or operational reaction quotients, Q i and Qa2- Intrinsic equilibrium constants for surface-charge formation can be determined by means of an extrapolation at zero eleciric potential [6,45] ... 

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