Bronsted linear free energy relation

Finally, there is an extra-thermodynamic assumption, which one can make about two molecules whose reactivity one wishes to compare. The basic idea is not unfamiliar, since it is inherent in the Bronsted linear free-energy relation. The assumption is that the free-energy difference in the transition states is bracketed by reactants and products. The factor provides a numerical index between zero and unity of the... 

The Bronsted Relation Linear Free Energy Relations... 

The Bronsted relation represents only one very successful example of what have come to be known as linear free energy relations. It is found that there exist linear relations between the free energy of activation of... 

According to these linear free energy relations, and (which are the Bronsted slopes -d[ln Xf/)]/df7 and -d[ln k (U) ldiU shown by the dashed lines in Fig. 4.20) are constants. 

The Bronsted relation was the first example of a linear free energy relation between rates and equilibrium constants, and would now be regarded as a particular example of this class. Such relations are now widely used for correlating the effects of substituents or change of solvent... 

The Hammett and Taft equations are not the only linear free-energy relationships known. We shall encounter others—for example, the Bronsted relations, and the Grunwald-Winstein and Swain-Scott equations later in this book. 

In Ch. 19 Williams describes theoretical simulations of free-energy-relation-ships in proton transfer processes. Both linear and non-linear relations are observed, usually described in terms of Bronsted coefficients or Marcus intrinsic barriers. Derived from empirical data, the phenomenological parameters of themselves do not lead to satisfying explanations at a fundamental molecular level. Theoretical simulations can fill in this gap. 

Just as with the pK and pKb scales for Bronsted acids and bases, other scales have been developed to relate the strength of one Lewis acid (electrophile) to another, or one Lewis base (nucleophile) to another. For example, scales based upon the relative reactivities of various nucleophiles and electrophiles in common organic reactions, such as Sn2 transformations, have been defined. We will cover these scales in Chapter 8 after we examine linear free energy relationships. Further, after examining the scales, we will discuss what factors make for a good nucleophile and electrophile. 

A final linear free energy relationship that we cover is one that is still extensively used in modern research—almost as much as Hammett plots. It is called a Bronsted plot, and it relates acidity or basicity to other kinds of reactions. The reason that this LFER is still actively used is in part because this relationship is essential to an understanding of acid-base catalysis in enzymology. However, the same relationship can be used to study nucleophilicity and leaving group ability. We describe all three uses below, but we leave a more detailed analysis of the use of this relationship in studies of acid-base catalysis to Chapter 9. 

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. 

Corollary 1 is the basis of a number of so-called linear free energy relationships, the Bronsted relation being a typical example. 

The success of this model is notable for a number of reasons. In particular, it is remarkable that the model holds so well for such a wide variety of reactions and reactants. Linear free energy relationships (LFERs) relating rate constants with driving force e.g., Bronsted relationships) are a very useful part of reaction chemistry, but they are essentially always limited to a set of closely related compounds and reactions. LFERs such as AG — aAG° + P have parameters (a,j8) that are defined only by this relationship. In contrast, the values that enter into the cross relation, xh/y xh/x and A yh/y and the parameters for the KSE model (a2 and 2 ), are all independently measured and have independent meaning. There are no adjustable or jittedparameters in this model. 

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