Linear free energy relationships Involving rate constants

There are two major concepts involved in the physico-chemical description of a chemical reaction the energetics, which determines the feasibility of the reaction, and the kinetics which determines its rate. In general these two concepts are independent and the rate of a chemical reaction can be varied according to the mechanism (e.g. catalysis) but within certain assumptions there is a mathematical relationship between the rate constant and the reaction free energy difference. These relationships are either linear (linear free energy relationship, LFE) or quadratic (QFE), the latter being often referred to as the Marcus model — a description which should not hide the important contributions of other workers in this field [1],... 

The [Ruv(N40)(0)]2+ complex is shown to oxidize a variety of organic substrates such as alcohols, alkenes, THF, and saturated hydrocarbons, which follows a second-order kinetics with rate = MRu(V)][substrate] (142). The oxidation reaction is accompanied by a concomitant reduction of [Ruv(N40)(0)]2+ to [RuIII(N40)(0H2)]2+. The mechanism of C—H bond oxidation by this Ru(V) complex has also been investigated. The C—H bond kinetic isotope effects for the oxidation of cyclohexane, tetrahydrofuran, propan-2-ol, and benzyl alcohol are 5.3 0.6, 6.0 0.7, 5.3 0.5, and 5.9 0.5, respectively. A mechanism involving a linear [Ru=0"H"-R] transition state has been suggested for the oxidation of C—H bonds. Since a linear free-energy relationship between log(rate constant) and the ionization potential of alcohols is observed, facilitation by charge transfer from the C—H bond to the Ru=0 moiety is suggested for the oxidation. 

Figure 4. A linear free-energy relationship between the logarithm of rate constant for metal-catalyzed hydrolysis log fcMeOK) of p-nitrophenyl acetate (NPA), dinitrophenyl acetate (DNPA), and trinitrophenyl acetate (TNPA) and the hydrolysis constant (MeH2O MeOH + H+) for the formation of the corresponding hydroxy complex. This relationship provides support for the argument that the MeOH species is involved in a direct nucleophilic attack on the carbonyl carbon of the nitrophenyl acetate esters.

There have been many attempts to develop linear free energy relationships for nucleophilicity so that rate constants of substitution reactions could be predicted quantitatively and so that the effects on reactivity of changing reaction conditions could be ascribed to particular aspects of the intermediates involved. This has not been easy to accomplish, however, because at least seventeen different factors have been suggested as contributors to nucleophilic reactivity. ° ° The following discussion will highlight some of the more prominent methods that have been proposed. Further details are available in reviews. ... 

Recall that Eqs. 8.48 and 8.50 are called BrDnsted linear free energy relationships. If an acid or base is involved in the rate-determining step of a reaction, the rate of that reaction should depend upon the strength of the acid or base. Hence, a Bronsted correlation is often found. Eqs. 8.51 and 8.52 relate the rate constants for an acid- or base-catalyzed reaction, respectively, to the pfC, of the acid or conjugate acid of the base. The sensitivity of an acid-catalyzed reaction to the strength of the acid is a, whereas the sensitivity of a base-catalyzed reaction to the strength of the base is p. The a and p reaction constants indicate the extent of proton transfer in the transition state. In Chapter 9 we explore the use of these two equations in much more detail, and we apply them in Chapters 10 and 11. 

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