Diffusion effects involving reaction rates

For reactions in which (i) and (ii) are controlling, the effect of temperature is generally very small and is present only insofar as the kinetic motion of the reactant molecules is influenced by temperature. Similarly, when (i) and (ii) are the controlling steps, particle size exerts a strong effect on reaction rate. Generally, the mass transfer and diffusion are factors of a secondary nature and steps (iii) and (iv) involving activated adsorption and/or the surface reaction are considered as key rate-controlling factors. 

In industrial PET synthesis, two or three phases are involved in every reaction step and mass transport within and between the phases plays a dominant role. The solubility of TPA in the complex mixture within the esterification reactor is critical. Esterification and melt-phase polycondensation take place in the liquid phase and volatile by-products have to be transferred to the gas phase. The effective removal of the volatile by-products from the reaction zone is essential to ensure high reaction rates and low concentrations of undesirable side products. This process includes diffusion of molecules through the bulk phase, as well as mass transfer through the liquid/gas interface. In solid-state polycondensation (SSP), the volatile by-products diffuse through the solid and traverse the solid/gas interface. The situation is further complicated by the co-existence of amorphous and crystalline phases within the solid particles. 

Because this reaction must involve two steps, diffusion of selenate into the interlayer spaces of the green rust followed by electron transfer from Fe(ll) green rust, Johnson and Bullen (2003) interpreted this result using a two-step model similar to that discussed above. The diffusion step presumably has very little isotopic fractionation associated with it. Step 2 might be expected to involve a kinetic isotope effect similar to that observed in the HCl reduction experiments. As is discussed above, if the diffusion step is partially rate-limiting, the isotopic fractionation for the overall process should be less than the kinetic isotope effect occurring at the reduction step. This appears to be the case, as the ese(vi)-se(iv) value of 7.4%o is somewhat smaller than that observed for reduction by strong HCl (12%o). 

The usual experimental criterion for diffusion control involves an evaluation of the rate of reaction as a function of particle size. At a sufficiently small particle size, the measured rate of reaction will become independent of particle size. The reaction rate can then be safely assumed to be independent of intraparticle mass transfer effects. At the other extreme, if the observed rate is inversely proportional to particle size, the reaction is strongly influenced by intraparticle diffusion. For a reaction whose rate is inhibited by the presence of products, there is an attendant danger of misinterpreting experimental results obtained for different particle sizes when a differential reactor is used, because, under these conditions, the effectiveness factor is sensitive to changes in the partial pressure of product. 

That steps involving atomic or molecular motion can be rate determining, even in fluids, is well known through diffusion limited reaction rates and the solvent cage effect. In solids, motion more subtle than translational diffusion can be influential, and cases of rotational diffusion control are familiar [7],... 

For a system with no kinetic or adsorption complications, the forward transition time x decreases while xr increases until finally x = xr in the limit, at steady state. (Because the convergence rate is slow, equality of x and xr is not commonly achieved experimentally before the onset of natural convection and nonplanar diffusion effects.) Quantitative treatments for single component systems, multicomponent systems, stepwise reactions, and systems involving chemical kinetics have been derived. The technique has not been used extensively. 

Our last example does not involve the rate of a chemical reaction, but instead, the effect of temperature on diffusion rates [25]. One of the motivations for using microelectrodes as in the previous example is to allow fast experiments without appreciable iR drop. When used in the opposite extreme of very small scan rates, microdisk electrodes produce steady-state voltammograms that have the same sigmoidal shape as dc polarograms and RDE voltammograms (cf. Chap. 12). 

In the previous section the effects of poisons on reaction rates were related to the active component surface, while the influence of mass transfer was disregarded. It has long been recognized, of course, that the overall rate and selectivity of chemical reactions in porous systems involves the coupling of chemical reactions with convective and diffusive mass transfer processes. Beginning with the pioneering work of Thiele (67), an entire discipline has evolved in which model systems are used to... 

The plug-flow model indicates that the fluid velocity profile is plug shaped, that is, is uniform at all radial positions, fact which normally involves turbulent flow conditions, such that the fluid constituents are well-mixed [99], Additionally, it is considered that the fixed-bed adsorption reactor is packed randomly with adsorbent particles that are fresh or have just been regenerated [103], Moreover, in this adsorption separation process, a rate process and a thermodynamic equilibrium take place, where individual parts of the system react so fast that for practical purposes local equilibrium can be assumed [99], Clearly, the adsorption process is supposed to be very fast relative to the convection and diffusion effects consequently, local equilibrium will exist close to the adsorbent beads [2,103], Further assumptions are that no chemical reactions takes place in the column and that only mass transfer by convection is important. 

If powders are used for the sample material, the packing of the particles will have an effect on the rate of reactions involving gases. Tighter packing inhibits free diffusion of gaseous species in and out of the reaction zones. Hence, the decomposition... 

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