Controlling step external transport

The observed rate will depend on the molecular weight of the inert gas if it is influenced by the first step. External transport can also influence or control the rate of sorption/desorption if the sorbent consists of agglomerates of zeolite crystals such as pellets or layers. The rate of sorption or desorption will then depend on the size or shape of the agglomerates if it is influenced by the transport in the macropores between the crystals. 

In general, the overall reaction process may comprise several individual steps, as shown in Figure 3.24. It could be seen that these steps pertain to (i) mass transfers of reactants and the products between the bulk of the fluid and the external surface of the solids (ii) transport of reactants and the products within the pores of the solid and (iii) chemical reaction between the reactants in the fluid and those in the solid. In order to be able to determine the rate-controlling step and to ascertain whether more than a single step should be consid-... 

Zogorski et al. [125] indicate that external transport is the rate-limiting step in systems having poor mixing, dilute concentration of adsorbate, small particle sizes of adsorbent, and a high affinity of adsorbate for adsorbent. Some experiments conducted at low concentrations have shown that film diffusion solely controls the adsorption kinetics of low molecular weight substances [81,85]. 

Applying to the electrolysis cell a constant current step is technically the easiest method of operation. The electrode to be investigated may be inert and at equilibrium with a redox reaction + e Red. An external anodic current will oxidize the Red components immediately after its onset and their concentrations will decrease at the interface, while that of the Ox" components will increase in parallel. For pare diffusion control of the transport. 

We compare the intrinsic rate of adsorption of nitrogen with an experimentally observed rate of adsorption of nitrogen at 6 bar and 25°C (Crittenden et al. 1995). Appropriate substitution of numerical values into equation (4.1) gives the maximum intrinsic rate of adsorption as 2 x 10 kg m s" . On the other hand, the experimentally observed rate is approximately 4 x 10 kg s (c. 0.33 mol s" at 6 bar, 25°C onto a surface of 250 m g ). Thus the intrinsic rate of adsorption is some 10 times faster than the observed rate of adsorption. It is generally acknowledged throughout the literature on physical adsorption processes that the dominant rate-controlling step is not the actual physical attachment of adsorbate to adsorbent (normally referred to as very rapid) but rather intraparticle transport of gas within the porous structure of the adsorbent to its available surface. Interparticle transport from bulk fluid to the external surface of the porous adsorbent may also have an effect on the overall rate of adsorption under some circumstances. 

Mass transport is much more likely to be rate-controlling in the heterogeneous catalysis of solution reactions than in that of gas reactions. The reason lies in the magnitudes of the respective diffusion coefficients [48] for molecules in normal gases at 1 bar and 300 K these are 10 5 to 10 4 m2s while, for typical solutes in aqueous solution, they are 10 10 to 10 9 m2 s. The rate-determining step in many solution catalyses has indeed been found to be external diffusion of reactant(s) to the outer surface of the catalyst and/or diffusion of product(s) away from it [3, 6]. Another possibility is internal diffusion within the pores of the catalytic solid, a step that often determines the rates of catalysed gas reactions [49-51]. It is clearly an essential part of a kinetic investigation to ascertain whether any of these steps control the rate of the overall catalytic process. Five main diagnostic criteria have been employed for this purpose ... 

When the discussion turns to removal of some component from a fluid stream by a high surface area porous solid, such as silica gel, which is found in many consumer products (often in a small packet and sometimes in the product itself), then the term "adsorption" becomes more global and hence ambiguous. The reason for this ironically is that mass transfer may be convoluted with adsorption. In other words the component to be adsorbed must move from the bulk gas phase to the near vicinity of the adsorbent particle, and this is termed external mass transfer. From the near external surface region, the component must now be transported through the pore space of the particles. This is called internal mass transfer because it is within the particle. Finally, from the fluid phase within the pores, the component must be adsorbed by the surface in order to be removed from the gas. Any of these processes, external, internal, or adsorption, can, in principle, be the slowest step and therefore the process that controls the observed rate. Most often it is not the adsorption that is slow in fact, this step usually comes to equilibrium quickly (after all just think of how fast frost forms on a beer mug taken from the freezer on a humid summer afternoon). More typically it is the internal mass transport process that is rate limiting. This, however, is lumped with the true adsorption process and the overall rate is called "adsorption." We will avoid this problem and focus on adsorption alone as if it were the rate-controlling process so that we may understand this fundamentally. 

If the rates of the chemical steps 3-5 are comparable or higher than the transport processes 1, 2 and 6, 7, significant concentration profiles of and A2 inside the catalyst particle or in the surrounding layer will occur. If the intrinsic rates are very high as compared to the diffusion process in the pores, the reaction will take place only near the external surface, and the observed transformation rate will be controlled by the external mass transfer. The same situation is observed for non-porous pellets or so-called egg-shell catalysts, where the active phase is placed in a layer near the outer pellet surface. If the intrinsic reaction rate is comparable with the diffusion rate within the pores, a pronounced concentration profile of the reactant within the pellet will develop. 

Steps 4 and S are the reverse processes of steps 2 and 1, respectively. The kinetics of ion exchange are governed by either a diffusion or mass action mechanism, depending on which is the slowest step. In general, the diffusion of ions in the external solution is teimed film diffusion control. This is a useful concept but hydrodynamically it is ill defined. The diffusion or transport of ions within the exchanger phase is commonly term particle diffusion control. Chemical reaction at the exchanger sites can be rate controlling in certain cases. 

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