Thermodynamics of Molecular Species

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ISBN: 9780471012542 | 0471012548
Cover: Hardcover
Copyright: 12/20/1996

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An updated and fresh perspective of the subject based on the concepts that the thermodynamic properties of a system are independent whether composition is specified in terms of formal components or molecular species and that the laws of thermodynamics are independent of the observational time-scale. By applying these concepts, the author has derived approximately 20 general theorems concerned with the thermodynamic properties of molecular species and their relationships to those of the formal components. Grunwald defines molecular species to include all participants in reaction mechanisms. Proved theories are supplemented with verbal explanations and explicit examples. Applications chapters include environmental isomers in liquids and thermodynamic properties of water and aqueous systems. Extra thermodynamic chapters feature interionic attraction theory and structure-energy correlation.

Preface

xiii

(4)

Glossary of Symbols

xvii

1. Thermodynamic Components and Molecular Species

(16)

Formal Components

(1)

Molecular Species

(3)

Distinguishability

(1)

Nomenclature: Molar versus Formal

(1)

Isomeric Species

(4)

Composition Models

(2)

Errors of Omission

(1)

Composition Trees

(2)

Observational Time Scales and Components

(4)

The Timewise Component

(3)

2. Gibbs Free Energy, Chemical Equilibrium, and Correspondence Theorems

(26)

Mathematical Analogy

(3)

Legendre Analogy for Energy Functions

(2)

Euler Equations and Solution Properties

(4)

Definition

(1)

Euler Equations

(1)

Euler Analogy

(1)

Nomenclature and Physical Significance

(1)

The Gibbs-Duhem Equation

(1)

The Free Energy

(2)

Partial Free Energies and Chemical Potentials

(1)

Being Comfortable with Partial Derivatives

(3)

Partial Derivatives as Infinitesimal Processes

(1)

Transformation of Variables

(2)

Chemical Equilibrium

(6)

Free Energy and Reaction Progress

(2)

Partial Free Energies at the Equilibrium Point

(3)

The Equilibrium Status of Thermodynamic Partial Derivatives

(3)

Concerning the Very Small Processes

(1)

The Correspondence Theorems

(5)

Application of the Second Theorem

(1)

The Correspondence Theorems and the Operational Time Scale

(1)

3. Dilute Solutions, Standard Partial Free Energies, and the Stability Theorem

(35)

Partial Free Energy in Ideal-Gas Mixtures

(2)

Dilute Liquid Solutions: Henry's Law

(4)

The Partial Free Energy of a Dilute Liquid Solute

(1)

Extension to Molecular Species

(2)

Units and Standard States

(5)

Concentration Units

(2)

Standard Partial Free Energies. Reference States and Standard States

(1)

Physical Dimensions

(1)

Change of Concentration Units

(1)

Medium Effects and Activity Coefficients

(2)

Equilibrium Constants in Dilute Solutions

(1)

The Solvent in Dilute Solutions

(4)

Reaction with the Solvent

(2)

Solute-Induced Medium Effects

(6)

Use of Dielectric Data

(1)

Carboxylic Acid Solvents

(1)

1-Octanol Solvent

(3)

Two-Component Solvents

(7)

A Two-Component Solvent with Z1 Constant

(2)

Change of Z1

(1)

Solvation Numbers

(3)

Stability Theorem

(1)

Statistical Form of the Stability Theorem

(5)

Consistency with Statistical Thermodynamics

(3)

4. Displacements from Equilibrium and Error Tolerance

(16)

Chemical Systems Off-Equilibrium

(2)

Nomenclature

(1)

Definition of Molar Strain and Molar Stress

(1)

Properties of Molar Stress

(1)

Stress-Strain Relationships in Dilute Solutions

(1)

Self-Contained Sets of Isomers

(4)

A Numerical Example

(1)

The Tolerance Theorem

(7)

Maximum or Minimum?

(1)

Theorem for Standard Partial Free Energies

(2)

5. Linear Free-Energy Relationships, Transition-State Theory, and Error Tolerance

(26)

Reaction Series and Free-Energy Perturbations

(3)

Linear Free-Energy Plots Involving Rate Constants

(7)

The Hammett Plot

(1)

Bronsted Catalysis Law

100

(2)

Correlations of Solvolysis Rates

102

(1)

Physical Problems That Must Be Faced

103

(2)

Transition-State Theory

105

(9)

Straight Passage

107

(1)

Rate Equation

108

(2)

Scope and Validity

110

(4)

Thermodynamic Properties of Transition States

114

(1)

Parameters of the Arrhenius Equation

115

(1)

Error Tolerance in Free-Energy Relationships

115

(5)

Procrustean Approach

116

(1)

Configurational Error Tolerance

117

(3)

6. Enthalpy-Entropy Compensation and Dormant Interactions

120

(17)

A Theoretical Overview

121

(3)

The Basic Term

122

(1)

Theoretical Summary

123

(1)

An Experimental Overview

124

(11)

Strong Propensities Toward Compensation

124

(4)

Enthalpy-Entropy Vector Diagrams

128

(2)

Modest or Weak Propensities Toward Compensation

130

(2)

Some Enthalpy-Entropy Patterns

132

(3)

Dormant Interactions

135

(2)

Effect of Observational Time Scale

135

(2)

7. Effects of Molar Shifts on State Functions

137

(20)

The Two Representations

137

(3)

Derivations for a Single Progress Variable

140

(6)

Partial Free Energy

141

(1)

Partial Entropy

142

(2)

Partial Enthalpy. Propensity Toward Compensation

144

(1)

Partial Volume. Interaction Coefficient

144

(1)

Partial Heat Capacity

145

(1)

Partial Properties for Multiple Progress Variables

146

(4)

Uncoupling Theorem

147

(1)

Partial Free Energy

148

(1)

Partial Entropy

148

(2)

Other Second Derivatives. Partial Enthalpy

150

(1)

Interconnections

150

(3)

Permutation of Subscripts

150

(1)

Separateness of Isomolar/Molar-Shift Parts

151

(2)

Molar-Shift Terms and Tradition

153

(5)

Some Benchmarks

153

(3)

Further Questions

156

(1)

8. Molar-Shift Terms in Dilute Solutions

157

(30)

A Renewed Look at the Dilute-Solution Model

158

(4)

Molar-Shift Categories

158

(1)

Additional Solute

158

(1)

Active Solute

159

(1)

Solvent Species

160

(1)

The Well-Behaved Dilute Solute

161

(1)

Molar-Shift Terms Based on the Law of Mass Action

162

(5)

Dimerization of the Solute

162

(2)

The Curve of V2 Versus m2

164

(2)

Related Matters

166

(1)

Solute-Induced Molar Shifts in the Solvent

167

(6)

Necessary Conditions

168

(1)

Derivation of Molar-Shift Terms

169

(2)

Standard Partial Properties of Solute

171

(1)

Standard Changes in Chemical Reactions

172

(1)

Water and Nonpolar Solutes

173

(9)

Nature of the Solvent Species

175

(3)

Molar Shifts Induced by Nonpolar Solutes

178

(1)

Delphic Dissection of the Entropy of Solvation

179

(3)

Alcohols and Alcohol-Water Solvents

182

(5)

9. Hard-Sphere and Potential Energy Cages Around Molecules in Liquids

187

(30)

Hard-Sphere Simulation

189

(2)

Hard-Sphere Encounters

191

(1)

A Medley of Model-Encounter Results

191

(4)

Hard-Sphere Collision Rate Z

192

(1)

Estimates for s and z

192

(1)

Hard-Sphere Packing Fraction f

193

(1)

Equilibrium for Forming an Encounter Pair

193

(1)

Dynamics of Forming an Encounter Pair

194

(1)

Collisions per Encounter. Diffusion-Controlled Reactions

195

(1)

Some Chemical Evidence

195

(2)

The Potential-Energy Cage

197

(8)

The Cage-Packing Theorem

199

(3)

Containment Controversy and Radial Distribution Function

202

(3)

The Cage Potential from Pair Potentials

205

(4)

The Additivity Theorem

206

(1)

Potential at Cage Center

207

(1)

Displacements from the Cage Center

208

(1)

Properties of Cage Potentials

209

(5)

Half-Width

211

(1)

Potential Shape at the Cage Center

211

(1)

Quasi-Harmonic Treatment of In-Cage Libration

212

(1)

Amplitude of Potential-Energy Noise

212

(2)

Cage Potentials and Discrete Solvates

214

(3)

10. Environmental Isomers, Molecular Complexes, and Cage Exchange in Liquids

217

(20)

Time Scales

218

(3)

Cage Lifetimes

218

(1)

Correlation/Relaxation Times for Brownian Motions

218

(3)

Transit Times in Cage Switching

221

(1)

Relaxation of Electron Distributions

221

(1)

Frequency Switching in Schrodinger Wave Trains

221

(7)

Mean Time of Exchange and Power Spectrum

224

(1)

Exchange and Distinguishability

225

(3)

Real Distinguishability. Effect of Brownian Motions

228

(3)

Encounter Pairs, Linkage Pairs, and Molecular Complexes

231

(6)

Modes of Motion for [A, X] and [A-X]

233

(1)

Approximate Threshold for [A, X] --> [A-X]

234

(3)

11. Solvation in Dilute Solutions

237

(22)

Nominal and Environmental Equations

238

(3)

Thermodynamic Formulation

241

(2)

Standard Enthalpy-Entropy Compensation

243

(5)

Magnitudes

244

(2)

Examples

246

(2)

Enthalpies of Water Subspecies in Presence of Nonpolar Solutes

248

(3)

Solvation Complexes

251

(3)

Solvation Mechanisms

254

(5)

Partial Volumes

257

(2)

12. Thermodynamics of Ionic Species

259

(48)

Thermodynamic Coupling

260

(2)

Modes of Coupling

260

(2)

Electrochemical Potential

262

(2)

Electric Potential

262

(1)

The Term for Chemical Work

263

(1)

Activity Coefficients

264

(8)

Catchall Property

265

(1)

Activities and Mean-Ion Properties of Electrolytes

266

(1)

Some Results for Acqueous Soutions

267

(2)

Empirical Propensities

269

(3)

Debye-Huckel Theory

272

(9)

Digression on Electrical Units

272

(1)

Electric Potential Due to an Ion Atmosphere

273

(4)

The Activity Coefficient Due to an Ion Atmosphere

277

(1)

A Quantitative Test

278

(1)

Some Corollaries

279

(2)

Electrostatic Ionic Solvation

281

(13)

Born's Explanation

281

(2)

The Born Radius

283

(4)

Specific Dissection

287

(4)

Change of Solvent

291

(4)

Ion Pairs

294

(13)

Some Experimental Facts

295

(2)

Ionic Association in a Dielectric Continuum

297

(6)

Ion Pairs Regarded as Molecular Species

303

(2)

Solvent-Separated Ion Pairs

305

(2)

References

307

(12)

Index

319

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Thermodynamics of Molecular Species

Summary

Author Biography

Table of Contents

Supplemental Materials

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Thermodynamics of Molecular Species

Summary

Author Biography

Table of Contents

Supplemental Materials

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