Kinetic ambiguity equivalence

Any two reaction schemes are considered to be kinet-ically equivalent if they imply the same orders of reaction for all chemical species involved. For example, assume that the rate expression for a particular scheme for a chemical reaction is given by d[P]/df = v = kik3[A][B]/(k2 + ksp]). For a second scheme, the expression is found to be ki k3 [A][B]/(k2 + [B]). Both expressions have the same general form and have the same dependence on reactant concentrations. Thus, the two schemes are kinetically equivalent. See Kinetic Ambiguity... 

MICROTUBULE ASSEMBLY KINETICS KINETIC ELECTROLYTE EFFECT IONIC STRENGTH KINETIC EQUIVALENCE KINETIC AMBIGUITY KINETIC HALDANE RELATIONSHIPS HALDANE RELATIONSHIPS... 

Kinetic ambiguity arises when different mechanisms lead to the same predicted rate equation, i.e. the mechanisms are kinetically equivalent (see Chapters 3 and 4). It is very widespread in reactions catalysed by acids and bases, but strategies have been developed to resolve some of the ambiguities. 

In principle, reactions which are subject to electrophilic catalysis by protons can be catalysed by metal ions also (e.g. Tee and Iyengar, 1988 Suh, 1992). However, metal ions may function in other ways, such as to deliver a hydroxide ion nucleophile to the reaction centre (e.g. Dugas, 1989 Chin, 1991), and it is often difficult to decide between kinetically equivalent mechanisms without resorting to extensive (and intensive) model studies. Use of the Kurz approach may help to resolve such ambiguities, as shown below. 

There is an inherent ambiguity, the principle of kinetic equivalence, in interpreting the pH dependence of chemical reactions. When a rate law shows, for example, that the reaction rate is proportional to the concentration of an acid HA, it means that the net ionic charge of the acid appears in the transition state of the reaction that is, either as the undissociated HA or as the two ions H+ and A-. Similarly, if the reaction rate varies as the concentration of A-, the transition state contains either A or HA and OH-. This may be shown algebraically as follows. 

Some years later, Geneste and coworkers reported the photochemistry of several benzothiophene derivatives [103]. Photolysis of 2-methylbenzothiophene sulfoxide 200 leads to sulfide in modest yield and tars but is accompanied by none of the [2+2] olefin chemistry observed with other related derivatives. The dimer mechanism requires a dependence of the quantum yield on the sulfoxide concentration due to competition between unimolecular deactivation and bimolecular reaction. The quantum yield for deoxygenation of 200 was found to vary from about 0.03 to 0.08 over a concentration range of 2-9 mM. The data gave a linear double reciprocal plot with intercept/slope = 4.3. (For simple bimolecular quenching kinetics, this value is equivalent to fcqT). The fit of the quantum yield data to a double reciprocal plot is consistent with the dimer mechanism but was somewhat balanced by ambiguous results for cyclooctadiene quenching experiments in which no relationship between quantum yield and quencher could be established. 

While the analysis of intermediates and/or products in the preceding examples unambiguously demonstrates the participation of zinc-coordinated nucleophiles in the chemical transformation, it generally is not possible to demonstrate unequivocally that the activation of a coordinated water molecule assumes the same mechanistic significance in metal ion-catalyzed hydrolytic reactions. This happenstance, as pointed out by Breslow et al. 19), is due (a) to the extremely labile nature of most aquo complexes, (b) to the invariance of water concentration in aqueous milieu, and (c) to the mechanistic ambiguity arising from the kinetic equivalance of the two mechanisms, A and B, illustrated below (here p-nitro-phenyl picolinate is used as the hypothetical example). 

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