Reactant concentration, effect distribution constant

The catalytic effect for reactions involving an ionic reactant usually shows a strong dependence on the total amphiphile concentration. The maximal effective rate constant is attained at concentrations just over the CMC. Romsted284 showed that this occurs due to the competition between the ion binding of the reactive ions (OH- in the example above) and the counterions of the amphiphile. Recently, Diekman and Frahm285 286 showed that it is possible to rationalize the kinetic data by describing the ion distribution through a solution of the Poisson-Boltzman equation. (See Fig. 5.1). 

Thus, the reaction order in the reactant itself is useful to evaluate. If the reactant is likely to be adsorbed significantly, then the reaction order must be interpreted, as in other types of heterogeneous reactions, with due attention to the type of adsorption isotherm and the extent of coverage. Since the kinetics of electrode reactions depend in a primary way on the potential (see Section 4), the reaction order must be specified and evaluated with respect to a constant electrode potential. Usually a supporting (electrochemically inactive) electrolyte is used so that effects of ion distribution and potential in the double layer remain approximately constant as other quantities are varied in the experimental analysis, viz., pH, reactant concentration. 

Spielman and Levenspiel (1965) appear to have been the earliest to propose a Monte Carlo technique, which comes under the purview of this section, for the simulation of a population balance model. They simulated the model due to Curl on the effect of drop mixing on chemical reaction conversion in a liquid-liquid dispersion that is discussed in Section 3.3.6. The drops, all of identical size and distributed with respect to reactant concentration, coalesce in pairs and instantly redisperse into the original pairs (after mixing of their contents) within the domain of a perfectly stirred continuous reactor. Feed droplets enter the reactor at a constant rate and concentration density, while the resident drops wash out at the same constant rate. Reaction occurs in individual droplets in accord with nth-order kinetics. 

Because of the small size of micelles, the use of the mean concentrations of the reactants in the micellar phase would not fit in all cases. The effect of the intermicellar distribution of the reactant molecules on the reaction rate was considered by Moroi [12] for three types of distributions (Poisson, binomial and Gauss) and the equations for the resulting effective rate constants were derived. If the multistep equilibrium (1-3) can be prolonged infinitely with equilibrium constants =kiJjk, the reactants... 

The following, well-acceptable assumptions are applied in the presented models of automobile exhaust gas converters Ideal gas behavior and constant pressure are considered (system open to ambient atmosphere, very low pressure drop). Relatively low concentration of key reactants enables to approximate diffusion processes by the Fick s law and to assume negligible change in the number of moles caused by the reactions. Axial dispersion and heat conduction effects in the flowing gas can be neglected due to short residence times ( 0.1 s). The description of heat and mass transfer between bulk of flowing gas and catalytic washcoat is approximated by distributed transfer coefficients, calculated from suitable correlations (cf. Section III.C). All physical properties of gas (cp, p, p, X, Z>k) and solid phase heat capacity are evaluated in dependence on temperature. Effective heat conductivity, density and heat capacity are used for the entire solid phase, which consists of catalytic washcoat layer and monolith substrate (wall). 

In conclusion of Section 6.3 we wish to stress that the elastic attraction of similar defects (reactants) leads to their dynamic aggregation which, in turn, reduces considerably the reaction rate. This effect is mostly pronounced for the intermediate times (dependent on the initial defect concentration and spatial distribution), when the effective radius of the interaction re = - JTX exceeds greatly the diffusion length = y/Dt. In this case the reaction kinetics is governed by the elastic interaction of both similar and dissimilar particles. A comparative study shows that for equal elastic constants A the elastic attraction of similar particles has greater impact on the kinetics than interaction of dissimilar particles. 

Several interesting features of the above simple relationships are noteworthy. If an inert liquid phase is introduced into an all-gas-phase differential reactor, keeping the inlet gas-phase composition constant, the reaction rate would, in general, be distributed between gas and liquid phases thus reducing the overall effective concentration of the reactant. In the limiting case, if the feed liquid is saturated with the reactant, the reaction rate will be unaffected by the introduction of liquid, ln an integral reactor, the overall reaction rate (as a space time yield) would increase if the feed liquid is saturated with the reactant. The conversion is always decreased by the introduction of liquid because of the contribution of the term QL(rG/Bi5L) in the denominator of Eq. (4-19). 

Exercise 9.9.4. Show that the distribution function of residence times for laminar flow in a tubular reactor has the form 2z /Zp, where tp is the time of passage of any fluid annulus and the minimum time of passage. Diffusion and entrance effects may be neglected. Hence show that the fractional conversion to be expected in a second order reaction with velocity constant k is 2B[1 + j lnu5/(5 + 1)] where B = akt n and a is the initial concentration of both reactants. (C.U.)... 

In reality, a typical catalyst pellet will be a porous solid that may be quite complicated or even irregular in shape with a large number of catalytic reaction sites distributed throughout. However, to simplify the problem for present purposes, the catalyst pellet will be approximated as being spherical in shape. Furthermore, we will assume that the catalyst pellet is uniform in constitution. Thus we assume that it can be characterized by an effective reaction-rate constant kef that has the same value at every point inside the pellet. In addition, we assume that the transport of reactant within the pellet can be modeled as pure diffusion with a spatially uniform effective diffusivity To Author simplify the problem, we assume that the transport of product out of the pellet is decoupled from the transport of reactant into the pellet. Finally, the concentration of reactant in the bulk-phase fluid (usually... 

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