Kinetics consecutive reactions

Consecutive reactions Kinetic analysis of measured rate data must be concerned with a single rate process, and the rate equations used are based on the assumption that a-time data are calculated to refer to only that one chemical change. Reactions proceeding through a sequence of consecutive steps may require individual stoichiometric confirmation, and, certainly, kinetic analyses must consider each single step individually. 

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. 

A kinetic scheme that is fully consistent with experimental observations may yet be ambiguous in the sense that it may not be unique. An example was discussed earlier (Section 3.1, Consecutive Reactions), when it was shown that ki and 2 in Scheme IX may be interchanged without altering some of the rate equations this is the slow-fast ambiguity. Additional examples of kinetically indistinguishable kinetic schemes have been discussed.The following subsection treats one aspect of this problem. 

The procedure for solving the relations between concentrations has been used in kinetic studies of complex catalytic reactions by many authors, among the first of them being Jungers and his co-workers 17-20), Weiss 21, 22), and others [see, e.g. 23-25a). In many papers this approach has been combined with the solution of time dependencies, at least for some of the single reactions. Also solved were some complicated cases [e.g. six-step consecutive reaction 26,26a) 3 and some improvements of this time-elimination procedure were set forth 27). The elimination of time is... 

Saddle point. 170 Salt effects. 206-214 Scavenging (see Reactions, trapping) Second-order kinetics. 18-22, 24 in one component, 18-19 in two components (mixed), 19-22 Selectivity. 112 Sensitivity analysis. 118 Sensitivity factor, 239-240 Sequential reactions (see Consecutive reactions)... 

It should be noted that the kinetics were first-order over at least three half-lives (with the exception of the dicyclopropylcarbonium ion), but the reaction products were not well defined in some cases— probably due to relatively fast consecutive reactions of the unsatmated oxocarbonium ions formed. In the case of the oxocarbonium ions formed from the allyl cations a novel quantitative eyclization to give cyclopentenone derivatives was observed (Hogeveen and Gaasbeek, 1970) ... 

Consecutive Reactions. The prototypical reaction is A B C, although reactions like Equation (6.2) can be treated in the same fashion. It may be that the first reaction is independent of the second. This is the normal case when the first reaction is irreversible and homogeneous (so that component B does not occupy an active site). A kinetic study can then measure the starting and final concentrations of component A (or of A and A2 as per Equation (6.2)), and these data can be used to fit the rate expression. The kinetics of the second reaction can be measured independently by reacting pure B. Thus, it may be possible to perform completely separate kinetic studies of the reactions in a consecutive sequence. The data are fit using two separate versions of Equation (7.8), one for each reaction. The data will be the experimental values of for one sum-of-squares and b ut for another. 

In searching to formulate a mechanism of CuInSc2 phase formation by one-step electrodeposition from acid (pH 1-3) aqueous solutions containing millimolar concentrations of selenous acid and indium and copper sulfates, Kois et al. [178] considered a number of consecutive reactions involving the formation of Se, CuSe, and Cu2Se phases as a pre-requisite for the formation of CIS (Table 3.2). Thermodynamic and kinetic analyses on this basis were used to calculate a potential-pH diagram (Fig. 3.10) for the aqueous Cu+In-i-Se system and construct a distribution diagram of the final products in terms of deposition potential and composition ratio of Se(lV)/Cu(ll) in solution. 

Recently [63], we studied the behavior of two-enzyme system catalyzing two consecutive reactions in a macroheterogeneous medium (modified Lewis cell). The system consisted of lipase-catalyzed hydrolysis of trilinolein and subsequent lipoxygenation of liberated fatty acids (Fig. 3). Our approach compared the kinetic behavior of coupled enzymes in the Lewis cell with the sequential study of separated phenomena presented before ... 

In the synthesis of polypeptides with biological activity on a crosslinked polymer support as pioneered by Merrifield (1 2) a strict control of the amino acid sequence requires that each of the consecutive reactions should go virtually to completion. Thus, for the preparation of a polypeptide with 60 amino acid residues, even an average conversion of 99% would contaminate the product with an unacceptable amount of "defect chains". Yet, it has been observed (13) that with a large excess of an amino acid reagent —Tn the solution reacting with a polymer-bound polypeptide, the reaction kinetics deviate significantly from the expected exponential approach to quantitative conversion, indicating that the reactive sites on the polymer are not equally reactive. 

The reaction pathway for the gas-phase methylation of m-cresol, as inferred from catalytic data here reported, can be summarized as shown in Scheme 1. Methanol and m-cresol react through two parallel reactions, yielding either 3-MA or DMPs. The relative contribution of the two reactions is a function of the physico-chemical features of the catalysts, and of the reaction temperature as well, C-methylation being kinetically favored at high temperature. Consecutive reactions occur on 3-MA, which acts as a methylating agent yielding DMPs, DMAs and polyalkylates (with co-production of m-cresol in all cases) by reaction with m-cresol, 3-MA and DMPs, respectively. Consecutive reactions may also occur on DMPs to yield polyalkylates. 

Kinetics Analysis of Consecutive Reactions Using Nelder-Mead Simplex Optimization... 

Since the discovery of alkylation, the elucidation of its mechanism has attracted great interest. The early findings are associated with Schmerling (17-19), who successfully applied a carbenium ion mechanism with a set of consecutive and simultaneous reaction steps to describe the observed reaction kinetics. Later, most of the mechanistic information about sulfuric acid-catalyzed processes was provided by Albright. Much less information is available about hydrofluoric acid as catalyst. In the following, a consolidated view of the alkylation mechanism is presented. Similarities and dissimilarities between zeolites as representatives of solid acid alkylation catalysts and HF and H2S04 as liquid catalysts are highlighted. Experimental results are compared with quantum-chemical calculations of the individual reaction steps in various media. 

Figure 4.10 Secondary ion intensities of ethylidyne, =CCH3, on platinum(l 11) during reaction with D2 at 383 K. Curves a-d are the measured SIMS intensities of CH + fragments at 15-18 amu, respectively. Curves e-h represent a kinetic simulation for a consecutive reaction via two intermediates (adapted from Creighton et al. [30]).

Some reactions of the type H+hydride - hydride radical+H2 have been studied, mainly at lower temperatures, with H atoms generated by an external source. There might be appreciable errors in extrapolation of these rate coefficients to temperatures where thermal decomposition takes place. In many cases only a lower or upper limit of the rate of consecutive reactions can be given, especially if the decomposition takes place at temperatures appreciably above 1000 °K. We will not discuss reaction mechanisms in detail which lead to untested rate phenomena nor those which are based upon product analysis without a well-defined time history. It is true, however, that no decomposition of a hydride consisting of more than two atoms has a mechanism which is fully understood and which can be completely described in terms of the kinetics of the elementary reactions. 

Most of our knowledge about the kinetics of the homogeneous decomposition has come from shock-tube experiments. These have been performed in several laboratories under a variety of experimental conditions. However, their results are contradictory in some respects especially with regard to activation energy and on the question of the importance of chain reactions. In some cases the experimental conditions are such that consecutive reactions have to be taken into account or at least cannot be safely excluded. Until recently, one reason for the difficulty of reconciling the results of different investigators was that, if they were interpreted in terms of the unimolecular reaction48... 

The fluorescence is generated inside the sample by photons that are already temporally dispersed. After excitation, the fluorescence is scattered backward and forward and diffuses finally to the sample surface. Kinetically, the diffusion process has to be considered as a consecutive reaction step that creates a maximum in the temporal fluorescence intensity profile. 

In an aprotic solution, the mechanism of oxidation of diaryl disulfides was shown to be more complex than a direct cleavage of the S—S linkage [116,117,123], The occurrence of two consecutive reactions being of second kinetic order if potential-determined and of first order if current-determined, was established for the two-electron transfer steps. Dimerization of the cation radicals occurs on the ArS fragment, whose contribution to the HOMO is more important, and produces an intermediate disulfonium dication. The subsequent cleavage of the latter results in two ArS+ cations and a molecule of a disulfide (the same as a starting disulfide in the case of symmetrical compounds). This mechanism, EC2C1E (E = electrochemical, C = Chemical), has... 

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