Rates and Equilibria of Organic Reactions

As Treated by Statistical, Thermodynamic and Extrathermodynamic Methods

John E. Leffler, Ernest Grunwald

• Publisher: Dover Publications
• Year: 2013
• Print ISBN: 9780486660684
• eBook ISBN: 9780486151427
• Topic: Physical Sciences
• Subtopic: Chemistry
• Index: Chemistry

Graduate-level text stresses extrathermodynamic approach to quantitative prediction and constructs a logical framework that encompasses and classifies all known extrathermodynamic relationships. Numerous figures and tables. Author and Subject Indexes.

7

Extrathermodynamic Free Energy Relationships. I. Substituent Effects

He was pinched perspiringly in the epistemological dilemma of the skeptic, unable to accept solutions to problems he was unable to dismiss as unsolvable. He was never without misery and never without hope.

Joseph Heller
Catch 22

In Chapter 6 we constructed a formal system for generating extrathermodynamic relationships, based on the concept of physical interaction mechanisms with scalar independent variables. We shall now apply this system to the analysis of substituent effects. We shall find that simple linear free energy relationships need not be limited to closely related reactions but in some cases encompass entire classes of reactions. Thus our formal interaction mechanisms have exact counterparts in real interactions of broad scope.

When a linear free energy relationship applies to a group of reactions, we may choose the model process to be any convenient reaction in the group under a suitable single set of conditions. Normally we would choose the model process on the basis that accurate data are already available for a large number of substituents. Yet even so, we usually find that the existing data do not cover a sufficiently long list of structural changes. We therefore supplement the data for the model process with structural parameters whose operational definition varies somewhat from one structural change to another. For example, the temperature, the solvent, or even the nature of the reaction may be different, although an attempt is made to hold these variations to a minimum. In addition, an attempt is made to show that the parameters obtained from these variants of the standard or reference process are not very different from those that would have been obtained under fixed conditions.

THE HAMMETT ρσ RELATIONSHIP

The best known of the extrathermodynamic equations relating reaction rate or equilibrium to the structure of the reagent is the Hammett ρσ equation.¹⁴⁸ It describes the effect of a meta- or para-substituent on the rate or equilibrium constant of an aromatic side-chain reaction. It is based on the fact that, as the substituent is varied, the logarithms of the rate or equilibrium constants for a large number of aromatic side-chain reactions are linearly related to one another. Although any one of these reactions could have been used to define a set of substituent parameters in terms of which the free energy changes of the others might be described, the parameter σ has been defined on the basis of the acid dissociation equilibrium of benzoic acid in water at 25°.

(1)

The reason for this choice was the accessibility of the data and the belief, current at that time, that the mechanisms by which substituents exert their effects were known for this reaction. The substituents, X, must be in the meta- or para-position, since the linear relationships fail for ortho-substituents.

The effect of substitution on the rate or equilibrium constants for other benzene side-chain reactions can now be expressed as a function of σ. The resulting equation (2) is the well-known Hammett equation.

(2)

The constants k_x and k₀ (or K_x and K₀) must be for the same experimental conditions, though not necessarily the conditions used in the definition of σ. The constant ρ is a function of the reaction and will also vary with the reaction conditions.

Values of the parameter σ for use in the Hammett equation are listed in Table 7-1.¹⁴⁹,¹⁵⁰ Whenever possible, the values have been based on data for the standard model process, as defined in equation 1. Values obtained in this way will be referred to as primary σ-values. When the required data for the standard process are not available, the σ-value for that substituent is obtained from some secondary reference process, chosen to resemble the ionization of benzoic acid in water at 25° as closely as possible. The procedure for obtaining such a secondary σ-value is as follows. First, a number of known primary σ-values are used to evaluate...

Table of contents

• Title Page
• Copyright Page
• Apologia
• Preface
• Table of Contents
• Glossary of Symbols
• I - Equilibrium from the Statistical Point of View
• 2 - Equilibrium and the Gibbs Free Energy
• 3 - Free Energy, Enthalpy, and Entropy
• 4 - Concerning Rates of Reaction
• 5 - Rates of Interconversion of Subspecies
• 6 - Theoretical Introduction to Extrathermodynamic Relationships
• 7 - Extrathermodynamic Free Energy Relationships. I. Substituent Effects
• 8 - Extrathermodynamic Free Energy Relationships. II. Medium Effects
• 9 - Extrathermodynamic Analysis of Enthalpy and Entropy Changes
• 10 - Some Mechanochemical Phenomena
• Authors Index
• Subject Index
• A CATALOG OF SELECTED DOVER BOOKS IN ALL FIELDS OF INTEREST
• A CATALOG OF SELECTED DOVER BOOKS IN ALL FIELDS OF INTEREST