Effectiveness factor plot zero-order

Figure 12.7 Effectiveness factor plots for sphere and slab geometries for first- and zero-order kinetics. The Thiele modulus is given by = RyJfor spherical catalysts or by...

Curve B of Figure 12.3 [adopted from Wheeler (38)] represents the dependence of the effectiveness factor on Thiele modulus for second-order kinetics. Values of r for first-order and zero-order kinetics in straight cylindrical pores are shown as curves A and C, respectively. Each curve is plotted versus its appropriate modulus. 

Plots of effectiveness factors versus corresponding Thiele moduli for zero-, first-, and second-order kinetics based on straight cylindrical pore model. For large hr, values of r are as follows ... 

Figure 12.7 adapted from Satterfield (40) contains a plot of the effectiveness factor for a zero-order reaction versus the Thiele modulus... 

A plot of the effectiveness factor as a function of the Thiele modulus is shown in Figure 12-5. Figure l2-3(a) shows t) as a function of the Thiele modulus < )j for a spherical catalyst pellet for reactions of zero, first, and second order. Figure 12-5(b) corresponds to a first-order reaction occurring in three differently shaped pellets of volume Vp and external surface area Ap, and the Thiele modulus for a first-order reaction, < >], is defined difierently for each shape. When volume change accompanies a reaction (i.e., 0) the corrections shown in Figure 12-6 apply to the effectiveness factor for a first-order reaction. 

The scenarios in series A concern initiation by purposely added initiator RX. Figures 1-8 (A-D) and 10 (A-D) show the diagnostic plots for the ideal case (instantaneous initiation, scenario Al, dotted lines) together with the effect of the various complicating factors, i.e., instantaneous initiation plus zero order chain transfer to monomer (scenario A2a), instantaneous initiation plus first order chain transfer to monomer (scenario A2b), instantaneous initiation plus both... 

The rate constant A is a composite parameter, k = ELk, where E is the effectiveness factor, L the concentration of active sites on the surface of the catalyst, and k the actual rate constant of the transformation of the adsorbed species. The effectiveness factor which can attain values from zero to one is a measure of retardation of the reaction by diffusion of reactants or products into or out ofthe pores of the catalyst. For our purpose it should have a value of one or near to one and with careful experimentation this can be achieved. According to Thiele (14) the effectiveness factor is a function of reaction rate and effective diffusion coefficient. Both these parameters depend on the structure of the reacting compound and therefore the effectiveness factor will tend to change with the nature of the substituents. The effect of structure on reaction rate is more critical than on diffusion coefficient and if the reactivity within the series of investigated compounds will vary over some orders there is always danger of diffusional retardation in the case of the most reactive members of the series. This may cause curvature of the log kva a plot. 

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