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Linear mechanisms, complex reaction

Equation (3) is linear with respect to the reaction rate variable, R. In the further analysis of more complex, non-linear, mechanisms and corresponding kinetic models, we will present the polynomial as an equation, which generalizes Equation (3), and term it as the kinetic polynomial. We will demonstrate that the overall reaction rate, in the general non-linear case, cannot generally be presented as a difference between two terms representing the forward and reverse reaction rates. This presentation is valid only at the special conditions that will be described. [Pg.54]

The similar analysis for particular multi-route linear mechanism was done in 1960s by VoTkenstein and GoTdstein (1966) and VoTkenstein (1967). In 1970s, the rigorous "structurized" equation for the rate of multi-route linear mechanism was derived by Yablonskii and Evstigneev (see monograph by Yablonskii et al., 1991). It reflects the structure of detailed mechanism, particularly coupling between different routes (cycles) of complex reaction. Some of these results were rediscovered many years later and not once (e.g. Chen and Chern, 2002 Helfferich, 2001). [Pg.54]

Of course, each of the two reactions may proceed via a multi-step mechanism of the types discussed in Sect. 4, e.g. 0= 0, O + e Y, Y + e Z, etc. where O and Y are unstable intermediates. In order to avoid too complex mathematics, only such linear mechanisms will be admitted, so that for each of the two overall reactions a linear rate law can be adopted. [Pg.300]

For linear mechanisms we have obtained structurized forms of steady-state kinetic equations (Chap. 4). These forms make possible a rapid derivation of steady-state kinetic equations on the basis of a reaction scheme without laborious intermediate calculations. The advantage of these forms is, however, not so much in the simplicity of derivation as in the fact that, on their basis, various physico-chemical conclusions can be drawn, in particular those concerning the relation between the characteristics of detailed mechanisms and the observable kinetic parameters. An interesting and important property of the structurized forms is that they vividly show in what way a complex chemical reaction is assembled from simple ones. Thus, for a single-route linear mechanism, the numerator of a steady-state kinetic equation always corresponds to the kinetic law of the overall reaction as if it were simple and obeyed the law of mass action. This type of numerator is absolutely independent of the number of steps (a thousand, a million) involved in a single-route mechanism. The denominator, however, characterizes the "non-elementary character accounting for the retardation of the complex catalytic reaction by the initial substances and products. [Pg.4]

Due to the fulfilment of this law of conservation, the number of linearly independent intermediates is not three but one fewer, i.e. it amounts to two. To the right of mechanism (1) we gave a column of numerals. Steps of the detailed mechanism must be multiplied by these numerals so that, after the subsequent addition of the equations, a stoichiometric equation for a complex reaction (a brutto equation) is obtained that contains no intermediates. The Japanese physical chemist Horiuti suggested that these numerals should be called "stoichiometric numerals. We believe this term is not too suitable, since it is often confused with stoichiometric coefficients, indicating the number of reactant molecules taking part in the reaction. In our opinion it would be more correct to call them Horiuti numerals. For our simplest mechanism, eqn. (1), these numerals amount to unity. [Pg.186]

Let us write a formula whose application will give us a possibility to simplify essentially the derivation of kinetic equations for complex reactions following a linear mechanism... [Pg.189]

Relationship (11) was first reported by King and Altman [1]. They examined a linear set of quasi-steady-state equations for the intermediates of the complex enzyme reaction following a linear mechanism. For its derivation the authors applied the well-known Kramer rule. [Pg.189]

This equation is independent of the order in which the steps are numbered. Temkin suggested an algorithm on the basis of eqn. (30) to obtain an explicit form of the steady-state kinetic equations. For linear mechanisms in this algorithm it is essential to apply a complex reaction graph. In some cases the derivation of a steady-state equation for non-linear mechanisms on the basis of eqn. (30) is also less difficult. [Pg.197]

Investigations with the graphs of non-linear mechanisms had been stimulated by an actual problem of chemical kinetics to examine a complex dynamic behaviour. This problem was formulated as follows for what mechanisms or, for a given mechanism, in what region of the parameters can a multiplicity of steady-states and self-oscillations of the reaction rates be observed Neither of the above formalisms (of both enzyme kinetics and the steady-state reaction theory) could answer this question. Hence it was necessary to construct a mainly new formalism using bipartite graphs. It was this formalism that was elaborated in the 1970s. [Pg.198]

GENERAL FORM OF STEADY-STATE KINETIC EQUATION FOR COMPLEX CATALYTIC REACTIONS WITH MULTI-ROUTE LINEAR MECHANISMS... [Pg.202]

Let us consider a complex catalytic reaction following a multi-route linear mechanism, all steps of which are reversible. [Pg.234]

A non-steady-state kinetic model for a complex catalytic reaction with a linear mechanism is described as... [Pg.251]

The zero-order kinetics is characterized by a linear concentration profile, which is however unrealistic at very large reaction times, since it produces a negative reactant concentration this result confirms that a zero-order reaction derives from a complex reaction mechanism that cannot be active at very low reactant concentrations. On increasing the reaction order, the reaction is faster at the highest concentration values... [Pg.16]

The linear deerease in reaction rate with increasing solvent polarity has been considered as evidenee in support of the proposed reaction mechanism, involving a less dipolar cyclic activated complex [cf. discussion of this reaction in Section 5.3.2). [Pg.449]

The reaction mechanism, including the possible incorporation of the triphenylborane, has not yet been understood in detail very well. This complex reaction may compete with the branching process. We think that the donor-acceptor interaction between BPhj and the MeCbSi- groups of the oligomers induces first a carbosilane formation, which is then followed by a conversion into MeClSi< groups. Therefore the modified polymer has more linear structural units resulting in lower branching... [Pg.294]

We now Ulustrate what has been said so far with an example of a complex multiroute reaction (the isomerization of butenes over C0-M0/AI2O3 (22)) with a linear mechanism ... [Pg.14]

In this chapter, we outline the principles of classification, coding and decoding, and estimating the complexity of reaction mechanisms, as well as develop some approaches to identification of the topological structure of linear mechanisms. [Pg.58]

In formulating hypotheses for the mechanism of a given complex reaction, and in using different procedures for the selection of one out of many hypotheses (discrimination of hypotheses), the question arises as to the hierarchy of the hypotheses. The intuitive principle of simplicity cannot play the role of a tool for the selection of hypotheses in the case of multiroute reactions because the number of vertices and cycles and the ways of linking cycles in the kinetic graph are already variables. Proceeding from linear mechanisms, we examine here possible approaches to the construction of a quantitative scale for mechanistic complexity or to the selection of a complexity index". [Pg.76]

The second complexity level of chemical reaction mechanisms is the complexity level of the kinetic model corresponding to a given mechanism (or KG). Starting from the fact that ultimately the mechanism complexity will manifest itself in kinetics, it seems natural to look for a complexity index that reflects the graph complexity demonstrated in the kinetic model. Two kinds of kinetic models may be used for this purpose (a) fractional-rational equations of the rate of routes in stationary or quasistationary processes having linear mechanisms (b) systems of differential... [Pg.77]

We have proposed the complexity index, K, based on the fractional rational form of the rate laws for reaction routes. This index is deHned as the total number of weights (rate constants) for the elementary steps included in the numerator and denominator of the kinetic laws for all routes of a multiroute reaction. In calculating K it is convenient to use the Vorkenstein-Gordstein algorithm which is applicable to the derivation of the rate laws for the routes of all catdytic and noncatal3d ic reactions having linear mechanisms. [Pg.78]

With chemical relaxation methods, the equilibrium of a reaction mixture is rapidly perturbed by some external factor such as pressure, temperature, or electric-field strength. Rate information can then be obtained by following the approach to a new equilibrium by measuring the relaxation time. The perturbation is small and thus the final equilibrium state is close to the initial equilibrium state. Because of this, all rate expressions are reduced to first-order equations regardless of reaction order or molecularity. Therefore, the rate equations are linearized, simplifying determination of complex reaction mechanisms (Bernasconi, 1986 Sparks, 1989),... [Pg.62]


See other pages where Linear mechanisms, complex reaction is mentioned: [Pg.102]    [Pg.153]    [Pg.707]    [Pg.18]    [Pg.237]    [Pg.50]    [Pg.51]    [Pg.191]    [Pg.192]    [Pg.424]    [Pg.338]    [Pg.164]    [Pg.182]    [Pg.185]    [Pg.191]    [Pg.193]    [Pg.197]    [Pg.198]    [Pg.214]    [Pg.153]    [Pg.419]    [Pg.659]    [Pg.106]    [Pg.38]    [Pg.267]    [Pg.814]    [Pg.14]    [Pg.45]    [Pg.217]   
See also in sourсe #XX -- [ Pg.170 , Pg.171 , Pg.172 , Pg.173 , Pg.174 , Pg.175 , Pg.176 , Pg.177 , Pg.178 ]




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Complex reactions/mechanisms

General form of steady-state kinetic equation for complex catalytic reactions with multi-route linear mechanisms

Linear complexes

Linear reaction

Linear reactions mechanism

Mechanism complexes

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