Reversible reaction effectiveness factor

The effectiveness factors of reaction I and II decrease continuously with the increase of temperature. Reaction II is exothermic (A//= - 41.15/c//mo/) and reversible, therefore the temperature has conflicting effects on its intrinsic rate of reaction. Increasing the... 

The evolution of the various effectiveness factors is shown in Fig. 11.9.1.A-7. The effectiveness factor of reaction II shows a discontinuity at a reactor length of 3.4 m because the direction of reaction II changes from positive to negative on the catalyst surface, while there is no such tendency yet inside the catalyst particle. The rj2 value switches back from negative to positive values only at a reactor length of 9 m, meaning that the overall effect of the reaction inside the catalyst pellet reverses from the formation of CO2 and H2 out of CO and H2O to the formation of CO and H2O out of CO2 and H2. 

From the colorless state it can be switched with light of short wavelength (A = 380 nm) via an electrocycHc ring opening and cis/trans rotation of one half of the molecule into a state with violet/purple color. The reverse reaction is effected by visible light (A = 580 nm). Since the system is metastable, one of the two reaction directions is matched by a rival thermal reaction, the thermoreversion. This progresses, however, in the case of benzospiropyran, at room temperature by a factor of 10 slower than the light-induced reaction. 

Figure 8-8 shows the analogous situation for a chemical reaction. The solid curve shows the activation energy barrier which must be surmounted for reaction to take place. When a catalyst is added, a new reaction path is provided with a different activation energy barrier, as suggested by the dashed curve. This new reaction path corresponds to a new reaction mechanism that permits the reaction to occur via a different activated complex. Hence, more particles can get over the new, lower energy barrier and the rate of the reaction is increased. Note that the activation energy for the reverse reaction is lowered exactly the same amount as for the forward reaction. This accounts for the experimental fact that a catalyst for a reaction has an equal effect on the reverse reaction that is, both reactions are speeded up by the same factor. If a catalyst doubles the rate in one direction, it also doubles the rate in the reverse direction. 

Oxidation kinetics over platinum proceeds at a negative first order at high concentrations of CO, and reverts to a first-order dependency at very low concentrations. As the CO concentration falls towards the center of a porous catalyst, the rate of reaction increases in a reciprocal fashion, so that the effectiveness factor may be greater than one. This effectiveness factor has been discussed by Roberts and Satterfield (106), and in a paper to be published by Wei and Becker. A reversal of the conventional wisdom is sometimes warranted. When the reaction kinetics has a negative order, and when the catalyst poisons are deposited in a thin layer near the surface, the optimum distribution of active catalytic material is away from the surface to form an egg yolk catalyst. 

Some deactivation processes are reversible. Deactivation by physical adsorption occurs whenever there is a gas-phase impurity that is below its critical point. It can be reversed by eliminating the impurity from the feed stream. This form of deactivation is better modeled using a site-competition model that includes the impurities—e.g., any of Equations (10.18)-(10.21)— rather than using the effectiveness factor. Water may be included in the reaction mixture so that the water-gas shift reaction will minimize the formation of coke. Off-line decoking can be... 

Little more need be said here about the simple ion-exchange reactions such as that between sodium hexametaphosphate and calcium ions (Scheme 10.7). It is useful, however, to consider in more detail those reactions involving chelation (Scheme 10.8). This is a reversible reaction, the equilibrium being dependent on the process pH and the concentrations of the reacting species (Equation 10.2). While chelated complexes are less stable at higher temperatures, this effect can be ignored in practice. The factors involved have been discussed in some considerable detail by Engbers and Dierkes [20,23]. 

Effectiveness Factors for Reversible Reactions. The vast majority of the literature dealing with catalyst effectiveness factors pre-... 

Determine the effectiveness factor for the ion exchange resin at 85 °C, assuming that the reaction is reversible even though the authors presumed the reaction to be irreversible in reporting their data. They note that at 100 °C the equilibrium for the reaction corresponds to a conversion greater than 94%. If the equilibrium constant for the reaction is expressed as the ratio of the t-butanol concentration to the isobutylene concentration and corrected for the temperature change in going from 100 °C to 85 °C, a value of 16.6 may be considered appropriate for use. 

The activity calculated from (7) comprises both film and pore diffusion resistance, but also the positive effect of increased temperature of the catalyst particle due to the exothermic reaction. From the observed reaction rates and mass- and heat transfer coefficients, it is found that the effect of external transport restrictions on the reaction rate is less than 5% in both laboratory and industrial plants. Thus, Table 2 shows that smaller catalyst particles are more active due to less diffusion restriction in the porous particle. For the dilute S02 gas, this effect can be analyzed by an approximate model assuming 1st order reversible and isothermal reaction. In this case, the surface effectiveness factor is calculated from... 

It is important to recognize that one of the factors which may affect the yield of these transformations is that the reaction is reversible (in theory). Seebach and Enders have developed an excellent synthesis for B-hydroxynitrosamines that is effectively the reverse of the transformation discussed here (7 ). The first step of this transformation, shown in equation 5, involves the re-... 

Comparing this with the maximum rate in the absence of reversibility found in 6.2.3, we see that reversibility reduces Rmax by a factor (1 + R 1 )2. Perhaps the most significant effect of reversibility on the reaction curve concerns the extent of conversion at which R falls to zero after the maximum. This no longer occurs at complete conversion of A but at... 

The discussion of Kapral s kinetic theory analysis of chemical reaction has been considered in some detail because it provides an alternative and intrinsically more satisfactory route by which to describe molecular scale reactions in solution than using phenomenological Brownian motion equations. Detailed though this analysis is, there are still many other factors which should be incorporated. Some of the more notable are to consider the case of a reversible reaction, geminate pair recombination [286], inter-reactant pair potential [454], soft forces between solvent molecules and with the reactants, and the effect of hydrodynamic repulsion [456b, 544]. Kapral and co-workers have considered some of the points and these are discussed very briefly below [37, 285, 286, 454, 538]. 

The catalyst intraparticle reaction-diffusion process of parallel, equilibrium-restrained reactions for the methanation system was studied. The non-isothermal one-dimensional and two-dimensional reaction-diffusion models for the key components have been established, and solved using an orthogonal collocation method. The simulation values of the effectiveness factors for methanation reaction Ch4 and shift reaction Co2 are fairly in agreement with the experimental values. Ch4 is large, while Co2 is very small. The shift reaction takes place as direct and reverse reaction inside the catalyst pellet because of the interaction of methanation and shift reaction. For parallel, equilibrium-restrained reactions, effectiveness factors are not able to predict the catalyst internal-surface utilization accurately. Therefore, the intraparticle distributions of the temperature, the concentrations of species and so on should be taken into account. 

The effectiveness factor fen, of the methanation reaction is large, while the effectiveness factor < co2 of the WGSR is very small and nearly equal to zero. The interaction between the methanation reaction and the WGSR leads to the existence of the direct and reverse WGSR in catalyst pellet, which is called equilibrium-restrained WGSR. 

Solution The elementary reaction steps of adsorption, reaction, and desorption are now reversible. From this point on, we will set ai = a, pi = P, and so on, since the intrinsic kinetics are desired. The relationships between ai, as, and a are addressed using an effectiveness factor in Section 10.4. The various reaction steps are... 

Many reactions, however, do not run to completion. They will reach a point where they stop, but in this chapter you will learn that when they are in this state they are not really stopped at all. These reactions, where the products can readily reform the reactants, are known as reversible reactions. The way these reactions proceed is analogous to the systems in equilibrium that were discussed in Chapters 8 and 10 (vapor equilibrium and solutions). In the next three chapters, you will study the equilibrium of chemical reactions and learn more about the factors associated with it. The focus of this chapter is to introduce the equilibrium constant, which provides data about the relationships between reactants and products in a system at equilibrium, and Le Chatelier s Principle, which allows you to predict the effects of different stressors on reaction equilibria. 

In reality however, situations also exist where a more complex form of the rate expression has to be applied. Among the numerous possible types of kinetic expressions two important cases will be discussed here in more detail, namely rate laws for reversible reactions and rate laws of the Langmuir-Hinshelwood type. Basically, the purpose of this is to point out additional effects concerning the dependence of the effectiveness factor upon the operating conditions which result from a more complex form of the rate expression. Moreover, without going too much into the details, it is intended at least to demonstrate to what extent the mathematical effort required for an analytical solution of the governing mass and enthalpy conservation equations is increased, and how much a clear presentation of the results is hindered whenever complex kinetic expressions are necessary. 

From this expression it can be seen that the modulus rcv transforms to the standard Thiele modulus (eq 27) when the equilibrium constant approaches infinity. Additionally, it is obvious that the effectiveness factor decreases when, at a given value of the forward rate constant k+, the reverse reaction becomes increasingly important (Fig. 18). This holds for all types of reversible reactions [31, 91]. Therefore, the effectiveness factor of a truly reversible reaction might be considerably overestimated if the reaction is treated as irreversible. 

This problem arises even at low conversion, because although the product concentration may then be negligible at the external pellet surface, in general this is not the case inside the pellet, unless diffusion effects upon the effective reaction rate are absent. Therefore, a difference normally exists between the effectiveness factor of irreversible and reversible reactions which becomes increasingly important as the equilibrium constant A cq of the reaction is shifted to smaller values. 

Figure 18. Effectiveness factor rj of a first-order reversible reaction versus the Weisz modulus ip (related to the forward rate constant k+). Influence of intraparticle diffusion on the effective reaction rate (isothermal reaction in a sphere, equal diffusivitics i,e = Die, equilibrium constant as a parameter).

In Fig. 19, calculated curves of the effectiveness factor versus the Weisz modulus are shown for different values of Kpis [91]. For comparison, this diagram also contains the curves corresponding to the results which apply to simple, irreversible power rate laws of zeroth, first and second order. From this figure it is obvious that a strong adsorption of at least one of the products leads to a similar decrease of the effectiveness factor as it is observed in the case of a reversible reaction. 

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