Brpnsted relations

If p is the number of equivalent acidic protons in BH+, and q the number of equivalent basic sites in its conjugate base B, then a more precise form for the Brpnsted relation is... 

The Hammett equation is not the only LFER." ° Some, like the Hammett equation, correlate structural changes in reactants, but the Grunwald-Winstein relationship (see p. 452) correlates changes in solvent and the Brpnsted relation (see p. 337) relates acidity to catalysis. The Taft equation is a structure-reactivity equation that correlates only field effects. ... 

If two reactions differ in maximum work by a certain amount 8wm (= -SAG ), it follows from the Brpnsted relation [when taking into account the Arrhenius equation and the known relation between the equilibrium constant and the Gibbs standard free energy of reaction, A m = exp(-AGm/J r)] that their activation energies will differ by a fraction of this work, with the opposite sign ... 

Alexander N. Frumkin pointed out in 1932 that an electrochemical reaction occnrring at different potentials can be regarded as an ideal set of chemical reactions of the same type, and suggested that the Brpnsted relation be nsed to explain the potential dependence of electrochemical reaction rates. On the basis of Eqs. (14.6) and (14.11), the relation for the activation energy becomes... 

Other examples of linear free energy relationships include the Brpnsted relation, the Grunwald-Winstein relationship, and the Taft equation. See Rho Value... 

Physical organic chemistry has been built around LFER, which is still a matter of active research from experiment to theoretical simulation [53,54]. We ourselves have also addressed these problems under the perspective of the ISM [10,36a,42]. Here we will only deal with the interpretation of the Brpnsted relations, the postulate of Hammond and the Reactivity-Selectivity Principle (RSP). 

This is referred to as the Brpnsted relation. The proportionality constant and the constant a are characteristic of a given family of reactions. 

When applied to reactions catalyzed by acids or bases, the Brpnsted relation has a slightly different connotation. Examples of these are the base-catalyzed halogenation of ketones and esters and the acid-catalyzed dehydration of acetaldehyde hydrate. For an acid-catalyzed reaction, we... 

Equation 4.40, which is the Brpnsted relation for acid-catalyzed reactions, states that the rate constant of a reaction catalyzed by an acid is proportional to some power of the dissociation equilibrium constant of the acid used as catalyst. 

Group contributions or additivity principle Extrathermodynamic relationships between rate and equilibrium parameters Poianyi and Brpnsted relations Hammett relationship for dissociation constants... 

The rate constant k is thus a measure of the efficiency of the base as a catalyst and is therefore called the catalytic constant. One might expect k to be bigger, the stronger B is as a base. Not only is this the case, but there is also a quantitative relation between catalytic activity and basicity, i.e., the Brpnsted relation,... 

The resulting relation is of course equation (5.69). Reversing the argument that led to it, we immediately recover the Brpnsted relation of equation (5.65). 

Brpnsted and Pederson (1924) showed that for a series of acids of similar nature, for example, carboxylic acids, their catalytic constants k for a particular reaction are related to their dissociation constants according to Equation 3.14 (a or b), called the Brpnsted relation ... 

Figure 8.6 Schematic free-energy diagram for slow proton-transfer reactions. Interpretation of the Brpnsted relation.

The Equation (9.50) corresponds to a linear dependence of AG, on AG , analogous to the Brpnsted relation. The more general relation (9.48) corresponds to a plot that is curved, concave downwards, the more steeply as A/AG increases. 

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