Second-order reactions diagram

Figure 1-5 Determination of the order of hypothetical reactions with respect to species A. (a) The initial reaction rate method is used. The initial rate versus the initial concentration of A is plotted on a log-log diagram. The slope 2 is the order of the reaction with respect to A. The intercept is related to k. (b) The concentration evolution method is used. Because the exponential function (dashed curve) does not fit the data (points) well, the order is not 1. The solution for the second-order reaction equation (solid curve) fits the data well. Hence, the order of the reaction is 2.

Construct a time-temperature-transformation diagram for a thermoset that follows a second order reaction kinetic model described by... 

Figure 4-18 Schematic diagram of trickle-flow operations for a second-order reaction.

Figure 8.23 Schematic diagram of a trickle-bed system for a second-order reaction.[After Y-T. Shah, Gas-Liquid-Solid Reactor Design, with permission of McGraw-Hill Book Co., New York, NY, (1979).]...

This approximate solution is valid to within 10 percent of the numerical solution. Obviously when Cgi, > C, then y = y and the enhancement factor equals that for pseudo-first-order. When this is not the case f is now obtained from an implicit equation. Van Krevelen and Hoftijzer solved Eq. 6.3.e-l and plotted F versus y in the diagram of Fig. 6.3.C-2, given in Sec. 6.3.c connecting the results for pseudo-first-order and instantaneous second-order reactions. 

Figure 3.7 Da-e regime diagram for a second-order reaction occurring in an isothermal fixed bed. Iso-5 lines given by Equation 3.85.

Figure 8.11 Damkohler-Graetz diagram for nonlinear kinetics. A second-order reaction occurs in the washcoat, but the remaining conditions are identical to previous representations.

Figure 8.12 Damkohkr-dUfiision ratio diagram for nonlinear kinetics (second order reaction). Same conditions from previous representa tions apply.

Fig. 6 Second-order reaction in CSTR/Separator/Recycle a) Control structure relying on selfregulation b) bifurcation diagram showing multiple steady-states...

The above expressions are inserted into the appropriate balance equations, for example, for tanks-in-series, segregated tanks-in-series, and maximum-mixed tanks-in-series models. The models are solved numerically [3], and the results are illustrated in the diagrams presented in Figure 4.29, which displays the differences between the above models for second-order reactions. The figure shows that the differences between the models are the most prominent in moderate Damkohler numbers (Figure 4.29). For very rapid and very slow reactions, it does not matter in practice which tanks-in-series model is used. For the extreme cases, it is natural to use the simplest one, that is, the ordinary tanks-in-series model. 

FIGURE 1. Diagram to show the effect of the increase in the initial concentration value of amine on the rate of substitution expressed as a second-order rate coefficient. Indicative [RNFLlo values and kjbs values are from reactions between 2,4-dinitrofluorobenzene and n-butylamine in toluene259... 

Let us now turn to some aspects of the kinetic theory and follow the transition process from an arbitrary unstable state with a given tj0. We ask for the path which is taken by the system and the rate to reach equilibrium, in other words, the approach to tieq. Possible reaction paths for a second-order phase transition are schematically illustrated in Fig. 12-6. It shows a Gibbs energy vs. tj diagram with T as the curve... 

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. 

Bilous and Amundson [1] were the first to describe the phenomenon of parametric sensitivity in cooled tubular reactors. This parametric sensitivity was used by Barkelew [2] to develop design criteria for cooled tubular reactors in which first order, second order and product- inhibited reactions take place. He presented diagrams from which for a certain tube diameter dt the required combination of CAO and Tc can be derived to avoid runaway or vice versa. Later van Welsenaere and Froment [3] did the same for first order reactions, but they also used the inflexion points in the reactor temperature T versus relative conversion XA trajectories, which describe the course of the reaction in the tubular reactor. With these trajectories they derived a less conservative criterion. Morbidelli and Varma [4] recently devised a method for single order reactions based on the isoclines in a temperature conversion plot as proposed by Oroskar and Stern [5]. 

Along with the orbital diagram for it electron transfer (Figure 2), equation 1 implies an outer-sphere redox (second-order) mechanism. The reduction potential (E°) is calculated from the recently tabulated free-radical reduction potentials for a variety of half-reactions (16) Table I presents reduction potentials of interest. Thus, the oxidation of I by 02 is thermodynamically unfavorable by an abiotic, thermal, one-electron transfer process. Chloride, bromide, and bisulfide one-electron oxidations with 02 are also thermodynamically unfavorable with E° values of -2.57, -2.08, and -1.24 V, respectively. 

Accordingly, the effect of coupling is much more important if the two unperturbed levels have the same energy. This is exactly the situation in the energy surface diagram for non-adiabatic reactions (Fig. 6.1) where the two energy surfaces cross. The effect of perturbation is then first-order, as given by Eq. (6.54), while it is of second-order when A > V (Eq. 6.55). 

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