Single-step reactions, mechanisms

All the techniques discussed in this chapter are applicable to single-step reaction mechanism. For multiple-step mechanisms, it is necessary to work through this process for each step in the reaction. 

Ligands with cone angles >136° show a single-step reaction mechanism ... 

Short of determining an entire reaction coordinate, there are a number of structures and their energies that are important to defining a reaction mechanism. For the simplest single-step reaction, there would be five such structures ... 

We derived the relation between the equilibrium constant and the rate constant for a single-step reaction. However, suppose that a reaction has a complex mechanism in which the elementary reactions have rate constants ku k2, and the reverse elementary reactions have rate constants kf, k2, . .Then, by an argument similar to that for the single-step reaction, the overall equilibrium constant is related to the rate constants as follows ... 

Figure 6.2 Effect of preincubation time with inhibitor on the steady state velocity of an enzymatic reaction for a very slow binding inhibitor. (A) Preincubation time dependence of velocity in the presence of a slow binding inhibitor that conforms to the single-step binding mechanism of scheme B of Figure 6.3. (B) Preincubation time dependence of velocity in the presence of a slow binding inhibitor that conforms to the two-step binding mechanism of scheme C of Figure 6.3. Note that in panel B both the initial velocity (y-intercept values) and steady state velocity are affected by the presence of inhibitor in a concentration-dependent fashion.

This chapter provides an introduction to several types of homogeneous (single-phase) reaction mechanisms and the rate laws which result from them. The concept of a reaction mechanism as a sequence of elementary processes involving both analytically detectable species (normal reactants and products) and transient reactive intermediates is introduced in Section 6.1.2. In constructing the rate laws, we use the fact that the elementary steps which make up the mechanism have individual rate laws predicted by the simple theories discussed in Chapter 6. The resulting rate law for an overall reaction often differs significantly from the type discussed in Chapters 3 and 4. 

Boreskov assumed the power law dependence for reaction rate, which is mathematically incorrect. Thus, strictly speaking, he did not prove Equations (13) and (14). Authors performed the analysis of the model corresponding to the single-route reaction mechanism with the rate-limiting step and proved these relations rigorously (see Lazman and Yablonskii, 1988 Lazman and Yablonskii, 1991). Mathematically, expression (12) is the first term of infinite power series by powers kinetic parameters of rate-limiting step. 

For the analysis of nonlinear cycles the new concept of kinetic polynomial was developed (Lazman and Yablonskii, 1991 Yablonskii et al., 1982). It was proven that the stationary state of the single-route reaction mechanism of catalytic reaction can be described by a single polynomial equation for the reaction rate. The roots of the kinetic polynomial are the values of the reaction rate in the steady state. For a system with limiting step the kinetic polynomial can be approximately solved and the reaction rate found in the form of a series in powers of the limiting-step constant (Lazman and Yablonskii, 1988). 

Single-step reactions of this type, with different or identical reactants, are found mostly in textbooks. The mathematics of the HI reaction fits this formalism although the reaction actually proceeds by a different, two-step mechanism (see Section 4.2). 

The typical textbook example of autocatalysis is that of a hypothetical single-step reaction with stoichiometry A — P, but mechanism... 

At least three genereil pathways need to be considered for the ringopening reactions of cyclopropanes with electrophiles, each of which could proceed with either inversion or retention. The most straightforward mechanism would involve a direct, single-step reaction leading to a carbonium ion, a reaction which could truly be considered an Se2 process. 

Cellulase was found to be effective in the synthesis of artificial cellulose in a single-step reaction by polycondensation of /J-D-cellobiosyl fluoride (Scheme 13).123 The polymerization is a repetition of the transglycosylation reaction, which became predominant over the hydrolysis reaction when the enzymatic polycondensation was carried out in a mixed solvent of acetonitrile/acetate buffer (5 1, pH 5). This synthesis is therefore kinetically controlled as well as equilibrium controlled. The fi configuration of the Cl fluorine atom is necessary to form a reactive intermediate leading to a / (1—4) product via a double displacement mechanism .124 Thus, this method provided the first successful in vitro synthesis of cellulose, the most abundant biomacromolecules on the earth, the synthesis of which had been unsolved for one-half a century.123... 

In the case of a single-step reaction such as the reduction of Fe to Fe " (in the absence of diffusion control), no assumptions are required about a rate-determining step in the usual sense (although microscopically, for such redox reactions in solution, consideration can be given to solvent reorganization in the formation of the transition state associated with electron transfer). Correspondingly, no intermediate (except the transition state itself ) need be considered in the reaction mechanism scheme. 

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