Hypothetical reaction surfaces

The catalyst activity depends not only on the chemical composition but also on the diffusion properties of the catalyst material and on the size and shape of the catalyst pellets because transport limitations through the gas boundary layer around the pellets and through the porous material reduce the overall reaction rate. The influence of gas film restrictions, which depends on the pellet size and gas velocity, is usually low in sulphuric acid converters. The effective diffusivity in the catalyst depends on the porosity, the pore size distribution, and the tortuosity of the pore system. It may be improved in the design of the carrier by e.g. increasing the porosity or the pore size, but usually such improvements will also lead to a reduction of mechanical strength. The effect of transport restrictions is normally expressed as an effectiveness factor q defined as the ratio between observed reaction rate for a catalyst pellet and the intrinsic reaction rate, i.e. the hypothetical reaction rate if bulk or surface conditions (temperature, pressure, concentrations) prevailed throughout the pellet [11], For particles with the same intrinsic reaction rate and the same pore system, the surface effectiveness factor only depends on an equivalent particle diameter given by... 

Figure 6 Theoretical reaction surface for the cycloaddition reaction of thieno[3,4-c]thiophene (la) (37 in this chapter) with dicyanoethyne (2) (53) to yield 5,6-dicyanobenzo[c]thiophene (2) (54). Energies for the hypothetical intermediates and possible products are reported per mole of atomic sulfur of the chain or ring units. (Reprinted with permission from K. I. Miller, K. F. Moschner and K. T. Potts J. Am. Chem. Soc., 1983, 105,...

A m, the apparent constant, is the product of an intrinsic constant (a constant valid for a hypothetical uncharged surface) and a Boltzmann factor. / is the surface potential, F the Faraday constant, and AZ the change in the charge number of the surface species of the reaction for which the equilibrium constant is defined (in this case AZ = -bl). The intrinsic constant is experimentally accessible by extrapolating experimental data to the surface charge where op = 0 and where l/ = 0. The correction, as given above, assumes the classical diffuse double-layer model (a planar surface and a diffuse layer of counterions). 

Practically any experimental kinetic curve can be reproduced using a model with a few parallel (competitive) or consecutive surface reactions or a more complicated network of chemical reactions (Fig. 4.70) with properly fitted forward and backward rate constants. For example, Hachiya et al. used a model with two parallel reactions when they were unable to reproduce their experimental curves using a model with one reaction. In view of the discussed above results, such models are likely to represent the actual sorption mechanism on time scale of a fraction of one second (with exception of some adsorbates, e.g, Cr that exchange their ligands very slowly). Nevertheless, models based on kinetic equations of chemical reactions were also used to model slow processes. For example, the kinetic model proposed by Araacher et al. [768] for sorption of multivalent cations and anions by soils involves several types of surface sites, which differ in rate constants of forward and backward reaction. These hypothetical reactions are consecutive or concurrent, some reactions are also irreversible. Model parameters were calculated for two and three... 

In Figure 3, the curved line represents the heat generation rate (self-heating rate) as a function of temperature under adiabatic conditions. That is, under adiabatic conditions or no heat transfer, heat will be generated (in this hypothetical reaction) according to the function shown. In the actual chemical process, however, some heat will be removed. The straight line represents the rate of heat removal as a function of temperature. The slope of this heat removal line is U x S where U is the heat transfer coefficient and S is the surface area through which heat can be dissipated. The intercept of the line with the x-axis is the temperature of the coolant, Tq. 

Example 9.2. Rate control by a single-step, bimolecular surface reaction. Consider a hypothetical reaction... 

Example 9.8. Parallel and sequential deactivation in a hypothetical reaction. The principle of mechanistic modeling can be illustrated by the oversimplified example of a single-step isomerization reaction A — P with Langmuir-Hinshelwood kinetics, rate control by the surface reaction, and slow second-order deactivation. 

When designing a catalyst the molecular chemistry that is assumed to occur on the catalyst surface should be included in the process (see Table 2.1). Hypothetical reaction mechanisms have to be set up moreover, the knowledge about the kinetics of the reaction steps might be helpful. 

Knowledge on molecular chemistry on the surface Hypothetical reaction mechanism Kinetics of reaction steps... 

A hypothetical reaction path is proposed involving the elision of a CF fragment after the nC5Fj2 molecule has passed through a transition state on the clean iron surface. 

FIGURE 48.1 Hypothetical energy surface for a cleavage and decarbonylation reactions illustrating the confining effect of a crystalline lattice. Reactions in crystals require low activation energies at points C and P and sufficiently long lifetimes at points B and D in order to increase the probability of efficient decarbonylation. 

Figure 5-2. A hypothetical potential energy surface for the reaction A -I- BC —> AB -I- C.

The rate (or kinetics) and form of a corrosion reaction will be affected by a variety of factors associated with the metal and the metal surface (which can range from a planar outer surface to the surface within pits or fine cracks), and the environment. Thus heterogeneities in a metal (see Section 1.3) may have a marked effect on the kinetics of a reaction without affecting the thermodynamics of the system there is no reason to believe that a perfect single crystal of pure zinc completely free from lattic defects (a hypothetical concept) would not corrode when immersed in hydrochloric acid, but it would probably corrode at a significantly slower rate than polycrystalline pure zinc, although there is no thermodynamic difference between these two forms of zinc. Furthermore, although heavy metal impurities in zinc will affect the rate of reaction they cannot alter the final position of equilibrium. 

Figure 1 Relative positions of the potential energy (E) surfaces of the electronic states involved in a hypothetical chemiluminescent reaction as a function of intemuclear separation (r). P and P represent the ground and lowest electronically excited singlet states of the product of the reaction, respectively. R represents the ground electronic state of the reactant. AH is the enthalpy of the dark reaction while AHa is its enthalpy of activation. AH is the enthalpy of activation of the photoreaction, hv denotes the emission of chemiluminescence.

To see how this process works, we construct a model in which reaction of a hypothetical drainage water with calcite leads to the precipitation of ferric hydroxide [Fe(OH)3, which we use to represent HFO] and the sorption of dissolved species onto this phase. We assume that the precipitate remains suspended in solution with its surface in equilibrium with the changing fluid chemistry, using the surface com-plexation model described in Chapter 10. In our model, we envisage the precipitate eventually settling to the stream bed and hence removing the sorbed metals from the drainage. 

A depiction of a hypothetical potential energy surface for a reacting system as a function of two chosen coordinates (c.g., the lengths of two bonds being broken). Such diagrams are useful in assessing structural effects on transition states for stepwise or concerted pathways. An example of More O Ferrall-Jencks diagrams for j8-elimina-tion reactions is shown below. 

Reaction 5.45 is at least partly hypothetical. Evidence that the Cl does react with the Na component of the alanate to form NaCl was found by means of X-ray diffraction (XRD), but the final form of the Ti catalyst is not clear [68]. Ti is probably metallic in the form of an alloy or intermetallic compound (e.g. with Al) rather than elemental. Another possibility is that the transition metal dopant (e.g. Ti) actually does not act as a classic surface catalyst on NaAlH4, but rather enters the entire Na sublattice as a variable valence species to produce vacancies and lattice distortions, thus aiding the necessary short-range diffusion of Na and Al atoms [69]. Ti, derived from the decomposition of TiCU during ball-milling, seems to also promote the decomposition of LiAlH4 and the release of H2 [70]. In order to understand the role of the catalyst, Sandrock et al. performed detailed desorption kinetics studies (forward reactions, both steps, of the reaction) as a function of temperature and catalyst level [71] (Figure 5.39). 

There can be, however, no doubt that in catalytic processes, purely physical factors play an important role, in addition to the chemical valence forces. This is particularly true for the solid catalysts of heterogeneous reactions for which the properties of surfaces, as the seats of catalytic action are of prime importance. The total surface areas, the fine structure of the surfaces, the transport of reactants to and from surfaces, and the adsorption of the reactants on the surfaces, can all be considered as processes of a predominantly physical nature which contribute to the catalytic overall effect. Any attempt, however, to draw too sharp a line between chemical and physical processes would be futile. This is illustrated clearly by the fact that the adsorption of gases on surfaces can be described either as a mere physical condensation of the gas molecules on top of the solid surface, as well as the result of chemical affinities between adsorbate and adsorbent. Every single case of adsorption may lie closer to either one of the hypothetical extremes of a purely physcial or of a purely chemical adsorption, and it would be misleading to maintain an artificial differentiation between physical and chemical factors. 

Detailed electronic structure studies, including insights gained from ligand field theory (46), can be especially useful in interpreting the reaction profiles and understanding the reactivity and selectivity of these systems. The exploration of two-state reactivity and the value of detailed electronic structure analysis are illustrated by our studies of the H atom abstraction step catalyzed by TauD (23,47), which are presented here for each spin-state surface the hypothetical septet, the quintet, and the triplet. 

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