Rate constants consecutive reactions

ILLUSTRATION 5.6 DETERMINATION OF REACTION RATE CONSTANTS FOR COMPETITIVE CONSECUTIVE SECOND-ORDER REACTIONS... 

Passing over to the computation of the rate constants of specific reactions, we again emphasize that the J(R) expansion from (37) in a power series of R is not necessary. It only enables one to obtain analyzable relations through application of different models of a solid. In the general case the problem of the calculation of low-temperature chemical reaction rate constants requires consecutive solution of two problems search of convenient PESs and averaging of the imaginary part of the action along the optimal path from relation (49). 

Figure 2.9. Consecutive irreversible reactions. Rate constants for the three elementary reactions are the same (k = 2 = 3 = 0.1 day" ) and [B]o = ICJo = [D]o = 0.

Using a concatenation of such transition probabilities for consecutive surfaces the TIS expression for the reaction rate constant can be rewritten as... 

Estimation of Activation Energies of Consecutive Steps. The activation energies for the two distinct processes visible in Figs. 69 and 70 were extracted to obtain quantitative kinetic data on the thermal decomposition of Kapton. For this purpose, reaction rate constants are calculated for the imide signal... 

Figure 4.17. Determination of the reaction rate constant for the oxidation of crotonic acid by potassium permanganate, (a) Manifold used (cf. Figs. 4.15c and 4.16). b, c) Absorbancetime response curves actually recorded. The values of the dispersion coefficient Da were obtained by dispersion experiments. All curves in each set of experiments were recorded consecutively from the same starting point (5 ), with an increasing delay time (td - 7, 8, 9, and 10 s, a-d and a -d ) with the stopped-flow period /s = 20 s (additionally, in each series a single run without stop is included), b) KMn04 (C° = 8.54 x lO"" M) in phosphate buffer in absence of crotonic acid, (c) KMn04 (Cli = 8.54 x lO"" M) in phosphate buffer, crotonic acid (C j = 2.10 x lO"" M) in phosphate buffer, stream B. (From Ref 838 by permission of the American Chemical Society).

Wang and Wu [70] analyzed the extraction equilibrium of the effects of catalyst, solvent, NaOH/organic substrate ratio, and temperature on the consecutive reaction between 2,2,2-trifluoroethanol with hexachlorocyclotriphosphazene in the presence of aqueous NaOH. Wu and Meng [69] reported the reaction between phenol with hexachlorocyclotriphosphazene. They first obtained the intrinsic reaction-rate constant and overall mass transfer coefficient simultaneously, and reported that the mass transfer resistance of QX from the organic to aqueous phase is larger than that of QY from the aqueous to organic phase. The intrinsic reaction-rate constant and overall mass transfer coefficients were obtained in three ways. 

The first reaction leads to the desired product whereas di-ethylene (DEG) and higher order glycols are formed in consecutive reactions as undesired by-products. The reaction rate constants of the consecutive reactions are higher than that of the main reaction. Hence, an appropriate process has to be devised in order to achieve satisfactory conversion and selectivity. 

ILLUSTRATION 5.7 Determination of Reaction Rate Constants for Competitive-Consecutive Second-Order Reactions... 

The values of the real systems, obtained from experiments at pressures up to 50 bar, may be extrapolated to still higher pressures since E = f(P) and log A = f(F) are continuous functions. The supply of oxygen in the oxidation experiments at 50 bar pressure is sufficient to ensure attainment of the asymptotic limits at least in the first reaction step (LTO). Evaluation of the second reaction step of the oxidation (fuel deposition) is more difficult because an increase of the heating rate provokes the occurrence of additional peaks, which will be flattened as a consequence of a rise of the pressure. For the consecutive and parallel oxidation and pyrolysis reactions in this step, overall values of E and log A have been found, which only give steady functions for the vacuum residue. The data of the last reaction step (fuel combustion) may be evaluated very easily. They also give steady functions for E = f(P) and log A = f(P). All substances tested behave similarly to activated carbon (charcoal). Only the coke residue of -hexylpyrene reacts completely differently and demonstrates different curves in the plots of the reaction rate constant and the half life time versus the pressure. In this reaction step the curves did not reach the asymptote even at pressures of 50 bar, but they may be extrapolated to higher pressures. 

Competitive parallel reactions (Fig. 8a) and competitive consecutive reactions (Fig. 8b) are common in chemistry. Here R1 and R2 are two different reagents, S is the substrate, and ki and k2 are reaction rate constants. 

Process improvement obtained with periodic operation has been shown to depend on the reaction rate constants. In the case of consecutive competing chemical reactions (e.g., /ci, /c2, k ), no yield or selectively improvement occurs if fci /c2 or 2- With parallel reactions, a 20% increase over the steady-state operation has been observed (Dorawala and Douglas, 1971). 

The obtained value for AE is likely for this consecutive reaction because Bosscher [ ] found the approximate same value for AE in a chemically, very similar reaction in sulfonation of chlorobep-rene. Assuming at the interface Da — 10 m /s, it follows from eqn. (17) that kj (25 C) s 1.7 10 m /kmol s. Reaction rate constant for the first reaction (eqn. (2)) has been shown to be... 

For the consecutive reactions 2A B and 2B C, concentrations were measured as functions of residence time in a CSTR. In all experiments, C o = 1 lb moPfF. Volumetric flow rate was constant. The data are tabulated in the first three columns. Check the proposed rate equations,... 

Consecutive reactions involving one first-order reaction and one second-order reaction, or two second-order reactions, are very difficult problems. Chien has obtained closed-form integral solutions for many of the possible kinetic schemes, but the results are too complex for straightforward application of the equations. Chien recommends that the kineticist follow the concentration of the initial reactant A, and from this information rate constant k, can be estimated. Then families of curves plotted for the various kinetic schemes, making use of an abscissa scale that is a function of c kit, are compared with concentration-time data for an intermediate or product, seeking a match that will identify the kinetic scheme and possibly lead to additional rate constant estimates. 

Applications have been made to consecutive reactions,with several methods being developed to extract the rate constants. Consider Scheme XIV. 

The example of consecutive, irreversible heterogeneous catalytic reaction of the type A —> B — C has been solved in a more general way by Thomas et al. (16). The authors considered scheme (III) with the listed values of the rate constants of surface reactions along with the constants of adsorption and desorption of the reactant A and of the product C. 

Fig. 5. Dependences of relative concentrations Cj on time variable r (arbitrary units) for consecutive catalytic reactions according to scheme (III) for various values of rate constants of the adsorption k,(ub and desorption fcduB of the intermediate B. Left-hand column (fcdesB/fcs = 0.1) desorption of B is slower than its surface transformation. Middle column (fcde.B/fcs = 1) equal rates of desorption of B and of its surface transformation. Right-hand column (fcdesB/fcj = 10) desorption of B is faster than its surface transformation. From G. Thomas, R. Montarnal, and P. Boutry, C.R. Acad. Sri., Ser. C 269, 283 (1969).

In contrast to consecutive reactions, with parallel competitive reactions it is possible to measure not only the initial rate of isolated reactions, but also the initial rate of reactions in a coupled system. This makes it possible to obtain not only the form of the rate equations and the values of the adsorption coefficients, but also the values of the rate constants in two independent ways. For this reason, the study of mutual influencing of the reactions of this type is centered on the analysis of initial rate data of the single and coupled reactions, rather than on the confrontation of data on single reactions with intergal curves, as is usual with consecutive reactions. 

Competition reactions ad eosdem, 106 ad eundem, 105 (See also Reactions, trapping) Competitive inhibitor, 92 Complexation equilibria, 145-148 Composite rate constants, 161-164 Concentration-jump method, 52-55 Concurrent reactions, 58-64 Consecutive reactions, 70, 130 Continuous-flow method, 254—255 Control factor, 85 Crossover experiment, 112... 

In a consecutive step, a first-order process, the hydroxycyclohexadienyl radicals decompose to give the sulfinic acids as is given in reaction 30. The rate constants /c, and k2 are also given in Table 1. In this case kt was calculated from the build-up of the hydroxycyclohexadienyl radicals. 

Radioactive decay provides splendid examples of first-order sequences of this type. The naturally occurring sequence beginning with and ending with ° Pb has 14 consecutive reactions that generate a or /I particles as by-products. The half-lives in Table 2.1—and the corresponding first-order rate constants, see Equation (1.27)—differ by 21 orders of magnitude. 

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