Reaction rate constant pseudo homogeneous

In the case of 0-pipettes, the collection efficiency also decreases markedly with increasing separation. The situation becomes more complicated when the transferred ion participates in a homogeneous chemical reaction. For the pseudo-first-order reaction a semiquantita-tive description is given by the family of dimensionless working curves calculated for two disks (Fig. 6) [23]. Clearly, at any separation distance the collection efficiency approaches zero when the dimensionless rate constant (a = 2kr /D, where k is the first-order rate constant of the homogeneous ionic reaction) becomes 1. 

The units on the rate constants reported by DeMaria et al. indicate that they are based on pseudo homogeneous rate expressions (i.e., the product of a catalyst bulk density and a reaction rate per unit mass of catalyst). It may be assumed that these relations pertain to the intrinsic reaction kinetics in the absence of any heat or mass transfer limitations. 

Many of the reactions discussed in the preceding pages are in fact bimolecular processes, which would normally follow second-order kinetics. However, as aheady discussed, under the regime of LFP they behave as pseudo-first-order reactions. The corresponding rate constants and lifetimes are independent of the initial concentration of transient, and therefore knowledge of extinction coefficients and quantum yields is not needed. Further, it is not important to have a homogenous transient concentration. 

Then k, which is the pseudo-rate constant of the homogeneous reaction, is calculated from the relationship... 

For some of the less complex ec processes, cyclic voltammetry (i-E) waves have been used to show, qualitatively, the effects of the follow-up reaction (reaction 2). The model first developed for this scheme consider only pseudo first-order conditions where the heterogeneous process was either reversible (6,7) or irreversible (7,8). Accordingly, when the homogeneous rate constant was very large, the i-E scan appeared similar to a conventional polargraphic wave without any peaks. The complications of Nicholson and Shain (7) provide cyclic i-E data that can be compared directly to experimental results. While these data can be used to fit the case represented by equations 1 and 2 (n - 1), more complex schemes... 

The B coefficient corresponds to the logarithm of the rate constant at Tis, i-e. to the reaction proceeding on the pseudo-homogeneous surface. It is likely, that Tis and B constants may be useful characteristics of heterogeneous surface active sites reactivity towards a test gas reactant. For example, as it follows from Table 5, Tis value increases with enhancement of the chemisorption activation energy for interaction of organosilicon compounds with the free surface of pyrogenic parent and mixed oxides. 

The effectiveness factor is defined as the ratio of the rate of reaction with diffusional resistances over the rate of reaction at bulk conditions. It follows that the effectiveness factor is not constant along the reactor length and therefore has to be calculated at each axial point along the reactor length. In the case of a two dimensional model, the effectiveness factor radial variations should also be calculated. It is important to realize that if the catalyst pellet effectiveness factor is different from unity, then the packed bed reactor model must be described by a heterogeneous model, and pseudo-homogeneous models cannot be used except in a few very special cases as discussed earlier. 

The simple isothermal pseudo-homogeneous model The use of a very simple model to investigate the implications of this nonmonotonic kinetics will give the opportunity to study its effect away from the combined effect of other phenomena which will interfere if a more sophisticated model is used. Xu and Froment s (1989a) rate equations were used in a one dimensional isothermal model for the catalyst tube, with a constant effectiveness factor, taken from Soliman et al. s (1988) work, to bring the actual reaction rates down to reasonable values. 

Remember that the rate equation must be consistent with the measure of the extent of reaction employed if conversion is used, (—r) must be expressed in terms of x if concentration is used, (—r) is in terms of C. If Fis mass flow rate, (—r) and C must be in mass units, and so on. Also, equation (4-45) is often used as a pseudo-homogeneous model for two-phase PER catalytic reactors. In such cases the rate constant contained in (—r) is usually expressed in terms per volume or weight of catalyst. In the former case, V would refer to catalyst volume and a value for bed porosity would be required to obtain reactor volume. In the latter case, catalyst weight would be... 

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