Criteria for diffusion control

In assessing whether a reactor is influenced by intraparticle mass transfer effects WeiSZ and Prater 24 developed a criterion for isothermal reactions based upon the observation that the effectiveness factor approaches unity when the generalised Thiele modulus is of the order of unity. It has been shown I7) that the effectiveness factor for all catalyst geometries and reaction orders (except zero order) tends to unity when the generalised Thiele modulus falls below a value of one. Since tj is about unity when 0 ll for zero-order reactions, a quite general criterion for diffusion control of simple isothermal reactions not affected by product inhibition is 1. Since the Thiele modulus (see equation 3.19) contains the specific rate constant for chemical reaction, which is often unknown, a more useful criterion is obtained by substituting l v/CAm (for a first-order reaction) for k to give  

PETERSEN 25 points out that this criterion is invalid for more complex chemical reactions whose rate is retarded by products. In such cases the observed kinetic rate expression should be substituted into the material balance equation for the particular geometry of particle concerned. An asymptotic solution to the material balance equation then gives the correct form of the effectiveness factor. The results indicate that the inequality 3.36 is applicable only at high partial pressures of product. For low partial pressures of product (often the condition in an experimental differential 

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 and the rate of reaction can 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 for, under these conditions, the effectiveness factor is sensitive to changes in the partial pressure of product. 

Weisz and Hicks 21) showed that when reaction conditions within the particle are non-isothermal a suitable criterion defining conditions under which a reaction is not controlled by mass and heat transfer effects in the solid is  

Selectivity in Catalytic Reactions Influenced by Mass and Heat Transfer Effects 

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At pH 5.3 the complex exhibited a cathodic peak at -0.282 V and its anodic counterpart at -0.220 V for Ru /Ru" couple as shown in Figure 3B.a. In presence of azide ion (<5 mM), a two fold increase in cathodic peak (Epc = -0.315 V, Ep/2 -Ep = 103 mV) and complete disappearance of the anodic peak at lower scan speeds (<0.1 V s" ) were noticed (Figure 3B.b). In addition, a shift in cathodic peak with the change in scan speed and appearance of low intense anodic peak at -0.256 V at higher scan speed were observed. The peak current had linear square root dependence on scan speed fulfilling the criteria for diffusion controlled process. The electrode behaviour, in higher concentrations also was same as observed in the lower concentrations. 

Various criteria have been developed to indicate whether film- or pellet-diffusion will be controlling. In one, proposed by Helffrich and Plesset(15), the times are compared for a pellet to become half-saturated under the hypothetical conditions of either film-diffusion control, f/( 1/2), or pellet-diffusion control, (1/2). 

By comparing time-resolved and steady-state fluorescence parameters, Ross et alm> have shown that in oxytocin, a lactation and uterine contraction hormone in mammals, the internal disulfide bridge quenches the fluorescence of the single tyrosine by a static mechanism. The quenching complex was attributed to an interaction between one C — tyrosine rotamer and the disulfide bond. Swadesh et al.(()<>> have studied the dithiothreitol quenching of the six tyrosine residues in ribonuclease A. They carefully examined the steady-state criteria that are useful for distinguishing pure static from pure dynamic quenching by consideration of the Smoluchowski equation(70) for the diffusion-controlled bimolecular rate constant k0,... 

We can use the two hypothetical steps of section Clb i.e., that kcJKM be maximized and that KM be greater than [S], to set up criteria for judging the state of evolution of an enzyme whose function is to maximize rate. We recall from Chapter 3 that the maximum value of kcJKM is the rate constant for the diffusion-controlled encounter of the enzyme and substrate, and from Chapter 4 that this is about 108 to 109 s "1 M l. A perfectly evolved enzyme should have a kcJKM in the range of 108 to 109 s"1 and a KM greater than [S]. Using the data for kcJKM listed in Table 4.4 and the substrate concentrations and KM values mentioned in this chapter, it appears that carbonic anhydrase and triosephosphate isomerase are perfectly evolved for the maximization of rate, which agrees with the conclusions of W. J. Albery and J. R. Knowles on triosephosphate isomerase.5... 

D. The chronoamperometric results can also be used to ascertain the number of electrons involved in the formation of benzonitrile from p-chloro-benzonitrile. In order to translate the chronoamperometric data into a meaningful n value, a compound is selected that has a diffusion coefficient very similar to that of p-chlorobenzonitrile and that gives a stable, known product upon electroreduction. Tolunitrile, which satisfies these criteria, is known to be reduced to its radical anion at a diffusion-controlled rate. Since this one-electron process gives a value of 168 pA s1/2- M x cm 2 for it1/2/CA, the corresponding value of 480 pA s1/2 A/ 1 cm-2 for the reduction of p-chlorobenzonitrile to benzonitrile anion radical must represent an overall three-electron process. When we subtract the one electron that is required to reduce benzonitrile to its radical anion from this total, we immediately conclude that two electrons are involved in cleavage of the carbon-chlorine bond in p-chlorobenzonitrile. A scheme that is consistent with these data is described by Equations 21.1 to 21.6. 

Table 7.2 shows the activation ena-gies determined for the various etching systems. In general, the apparent activation ena-gy, as determined from the dependence of etch rate on temperature, is 3-6 kcal/mol or 0.13-0.26eV for diffusion-limited reactions, whereas it is 10-20 kcal/mol or 0.44-0.87 eV for surface-controlled reactions. Using these criteria to evaluate the values of activation energy in Table 7.2, it appears... 

This equation is often used to determine the formal potential of a given redox system with the help of cyclic voltammetry. However, the assumption that mid-peak potential is equal to formal potential holds only for a reversible electrode reaction. The diagnostic criteria and characteristics of cyclic voltammetric responses for solution systems undergoing reversible, quasi-reversible, or irreversible heterogeneous electron-transfer process are discussed, for example in Ref [9c]. An electro-chemically reversible process implies that the anodic to cathodic peak current ratio, lpa/- pc equal to 1 and fipc — pa is 2.218RT/nF, which at 298 K is equal to 57/n mV and is independent of the scan rate. For a diffusion-controlled reduction process, Ip should be proportional to the square root of the scan rate v, according to the Randles-Sevcik equation [10] ... 

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