Controlling Rate Factor

The kinetic expression was derived by Akers and White (10) who assumed that the rate-controlling factor in methane formation was the reaction between the adsorbed reactants to form adsorbed products. However, the observed temperature-dependence of the rate was small, which indicates a low activation energy, and diffusion was probably rate-controlling for the catalyst used. 

The premise that nucleation was always the rate controlling factor in kinetic theories was first disputed by Sadler in 1983 [44]. The disagreement arises from a comparison of the morphologies which would be obtained using the free energies from the Lauritzen-Hoffman theory with those observed experimentally. The... 

The retarding influence of the product barrier in many solid—solid interactions is a rate-controlling factor that is not usually apparent in the decompositions of single solids. However, even where diffusion control operates, this is often in addition to, and in conjunction with, geometric factors (i.e. changes in reaction interfacial area with a) and kinetic equations based on contributions from both sources are discussed in Chap. 3, Sect. 3.3. As in the decompositions of single solids, reaction rate coefficients (and the shapes of a—time curves) for solid + solid reactions are sensitive to sizes, shapes and, here, also on the relative dispositions of the components of the reactant mixture. Inevitably as the number of different crystalline components present initially is increased, the number of variables requiring specification to define the reactant completely rises the parameters concerned are mentioned in Table 17. 

Particle size is the rate-controlling factor in the case of cements formed using IP zinc oxide (Smith, 1958 Norman e/a/., 1964). Setting time appears to be proportional to the median particle size (Prosser Wilson, 1982). By contrast, the setting times of cements prepared from TD zinc oxide do not appear to relate to particle size. 

Bradshaw, A.V. (1970) Rate controlling factors in gas - solid reactions of metallurgical interest. Trans. Inst. Min. Metall. 79 C281-294... 

Lede J, Ricart EE, Ferrer M (2001) Solar thermal splitting of zinc oxide A review of some of the rate controlling factors. J Solar Energy Eng 123 91-97... 

Finally, there are two special cases in which the rectilinear law is observed when the rate-controlling factor is the rate of supply of O2 and when the metal oxide is volatile at the temperature of oxidation. The latter case occurs in the high temperature oxidation of molybdenum, since M0O3 is quite volatile, and in this case dw/dt is negative. 

The kinetics of concerted thermal elimination reactions of a series of ethyl (hetero) arylcarboxylate esters (2-thienyl-, 3-thienyl-, 2-furyl, 3-furyl, 4-pyridyl-, 3-pyridyl-, and 2 -pyridylcarbo x y I ate) in the gas phase seem to indicate that there is tittle charge separation in the transition state (83) this is in contrast with the behaviour of the corresponding /-butyl and isopropyl esters for which a semi-concerted transition state (82) was proposed previously.49 Results of a kinetic study of the gas-phase elimination reactions of methylbenzoyl fonnate (84) and 3-hydroxy-3-methylbutan-2-one (85) have been compared with those for pyruvic acid (87) and benzoylformic acid (86).50 The relative rates of reaction [(86)/(87) 46, (87)/(85) = 1.1 x 105 and (86)/(82) = 1 x 106] reveal that the acidity of the hydrogen atom involved in the elimination process, rather than the initial polarization of the C—C bond which undergoes cleavage, is the important rate-controlling factor. 

There are two ways in which a chemical reaction can affect ion exchange rates (Helfferich, 1983). One possibility is that the reaction is slow compared with diffusion. Thus, in the limit, diffusion is fast enough to cause a leveling out of any concentration gradients within the ion exchanger particle. Thus, the reaction is the sole rate-controlling factor, and rate is independent of particle size. 

Diffusion controlled adsorption of proteins at an interface can imply either that the molecules diffuse to the interface and adsorb without further spreading, or that spreading or unfolding is so rapid that diffusion becomes the rate-controlling factor. 

Deuterium substitution of the hydroxyl group in a hindered phenol leads to a decrease in the rate of reaction which suggests that scission of the OH-bond is the rate controlling factor. However, the effects of deuterium substitution on the complex formation and its subsequent reactions are not clearly understood. 

These calculations are uncertain, however. The permeation equation may pass through a regime proportional to pressure rather than root pressure. Additionally, the rate controlling factor may not be permeation, but rather the rate at which tritium atoms skating about on the low pressure surface find other atoms and leave the surface as gaseous molecules. 

The reactivity of the residual char is the rate-controlling factor for brown coal hydrogasification (16). 

In Chapter 6, K. Bunzl examines the kinetics of ion exchanger in heterogeneous systems in order to provide a better understanding of the behavior of natural ion exchangers in the soil (clay minerals, humic substances, sesquioxides). With film diffusion as the rate-controlling factor in these mixtures, several important characteristics become predictable. 

The various experimental studies in these two different fields had stimulated the development of theory, which in turn stimulated new experiments. The further introduction of new technology—lasers for example—expanded the variety of systems which could be studied, ultimately extending to ultra-fast reactions in the picosecond (e.g., photosynthesis) or even the femtosecond regime. Indeed, some of these reactions occur so rapidly that the sluggishness of the solvent (e.g., solvent dielectric relaxation) becomes a rate-controlling or partially rate-controlling factor. 

For all of these reasons, a thorough understanding of the NH3 adsorption-desorption phenomena on the catalyst surface is a prerequisite In fact, typical SCR catalysts can store large amounts of ammonia, whose surface evolution becomes the rate-controlling factor of the reactor dynamics. Also, mathematical modeling appears to be even more useful for the analysis and development of unsteady SCR processes than in the case of steady-state operation. 

Activation polarization is because of a rate-controlling step within the corrosion reaction(s) at either the cathode or anode sites. An example of this can be seen with the H /H2 conversion reaction. The first step of this process, 2H+ + 2e 2H, takes place at a rapid pace. The second part of this reaction, 2H H2, occurs more slowly and can become a rate-controlling factor. 

The oxidation of durene, ultimately to pyromellitic acid, illustrates the connection of the reactivity data with the rate-controlling factors temperature and pressure see Table 2. Note that the relative reactivity of durene is 20 times higher than that observed for the corresponding monocarboxylic acid. 

On heating, many hydrides dissociate reversibly into the metal and Hj gas. The rate of gas evolution is a function of both temperature and /KH2) but will proceed to completion if the volatile product is removed continuously [1], which is experimentally difficult in many systems. The combination of hydrogen atoms at the metal surface to yield Hj may be slow [2] and is comparable with many heterogeneous catalytic reactions. While much is known about the mobility of H within many metallic hydride phases, the gas evolution step is influenced by additional rate controlling factors. Depending on surface conditions, the surface-to-volume ratio and the impurities present, the rate of Hj release may be determined by either the rate at which hydrogen arrives at the solid-gas inteifece (diffusion control), or by the rate of desorption. 

The kinetics of the initial stages of the thermal decompositions of the Group lA metal (Na, K, Rb, Cs) perchlorates between 623 and 773 K were studied by Cordes and Smith [3]. The major reaction products were the corresponding chlorates and oxygen. Because the rates of oxygen evolution below 683 K from all four reactants were almost equal, it was suggested that the rate-controlling factor was a property... 

The discussion in Section 4.6.2 suggests that weathering rates of minerals are proportional to the water flow rate. This is only true if the waters are close to saturation (Box 4.12) with respect to the weathering mineral. If water flow is continuous and sufficiently high, a limit is reached beyond which further flushing is no longer a rate-controlling factor. 

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