Concise Physical Chemistry E-Book

Donald W. Rogers

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Veröffentlichungsjahr: 2011

Beschreibung

This book is a physical chemistry textbook that presents the essentials of physical chemistry as a logical sequence from its most modest beginning to contemporary research topics. Many books currently on the market focus on the problem sets with a cursory treatment of the conceptual background and theoretical material, whereas this book is concerned only with the conceptual development of the subject.  Comprised of 19 chapters, the book will address ideal gas laws, real gases, the thermodynamics of simple systems, thermochemistry, entropy and the second law, the Gibbs free energy, equilibrium, statistical approaches to thermodynamics, the phase rule, chemical kinetics, liquids and solids, solution chemistry, conductivity, electrochemical cells, atomic theory, wave mechanics of simple systems, molecular orbital theory, experimental determination of molecular structure, and photochemistry and the theory of chemical kinetics.

Leseprobe

CONTENTS

COVER

HALF TITLE PAGE

TITLE PAGE

COPYRIGHT PAGE

FOREWORD

PREFACE

CHAPTER 1: IDEAL GAS LAWS

1.1 EMPIRICAL GAS LAWS

1.2 THE MOLE

1.3 EQUATIONS OF STATE

1.4 DALTON’S LAW

1.5 THE MOLE FRACTION

1.6 EXTENSIVE AND INTENSIVE VARIABLES

1.7 GRAHAM’S LAW OF EFFUSION

1.8 THE MAXWELL–BOLTZMANN DISTRIBUTION

1.9 A DIGRESSION ON “SPACE”

1.10 THE SUM-OVER-STATES OR PARTITION FUNCTION

PROBLEMS AND EXERCISES

CHAPTER 2: REAL GASES: EMPIRICAL EQUATIONS

2.1 THE VAN DER WAALS EQUATION

2.2 THE VIRIAL EQUATION: A PARAMETRIC CURVE FIT

2.3 THE COMPRESSIBILITY FACTOR

2.4 THE CRITICAL TEMPERATURE

2.5 REDUCED VARIABLES

2.6 THE LAW OF CORRESPONDING STATES, ANOTHER VIEW

2.7 DETERMINING THE MOLAR MASS OF A NONIDEAL GAS

PROBLEMS AND EXERCISES

CHAPTER 3: THE THERMODYNAMICS OF SIMPLE SYSTEMS

3.1 CONSERVATION LAWS AND EXACT DIFFERENTIALS

3.2 THERMODYNAMIC CYCLES

3.3 LINE INTEGRALS IN GENERAL

3.4 THERMODYNAMIC STATES AND SYSTEMS

3.5 STATE FUNCTIONS

3.6 REVERSIBLE PROCESSES AND PATH INDEPENDENCE

3.7 HEAT CAPACITY

3.8 ENERGY AND ENTHALPY

3.9 THE JOULE AND JOULE–THOMSON EXPERIMENTS

3.10 THE HEAT CAPACITY OF AN IDEAL GAS

3.11 ADIABATIC WORK

PROBLEMS AND EXAMPLE

CHAPTER 4: THERMOCHEMISTRY

4.1 CALORIMETRY

4.2 ENERGIES AND ENTHALPIES OF FORMATION

4.3 STANDARD STATES

4.4 MOLECULAR ENTHALPIES OF FORMATION

4.5 ENTHALPIES OF REACTION

4.6 GROUP ADDITIVITY

4.7 ΔfH298(g) FROM CLASSICAL MECHANICS

4.8 THE SCHRÖDINGER EQUATION

4.9 VARIATION OF ΔH WITH T

4.10 DIFFERENTIAL SCANNING CALORIMETRY

PROBLEMS AND EXAMPLE

CHAPTER 5: ENTROPY AND THE SECOND LAW

5.1 ENTROPY

5.2 ENTROPY CHANGES

5.3 SPONTANEOUS PROCESSES

5.4 THE THIRD LAW

PROBLEMS AND EXAMPLE

CHAPTER 6: THE GIBBS FREE ENERGY

6.1 COMBINING ENTHALPY AND ENTROPY

6.2 FREE ENERGIES OF FORMATION

6.3 SOME FUNDAMENTAL THERMODYNAMIC IDENTITIES

6.4 THE FREE ENERGY OF REACTION

6.5 PRESSURE DEPENDENCE OF THE CHEMICAL POTENTIAL

6.6 THE TEMPERATURE DEPENDENCE OF THE FREE ENERGY

PROBLEMS AND EXAMPLE

CHAPTER 7: EQUILIBRIUM

7.1 THE EQUILIBRIUM CONSTANT

7.2 GENERAL FORMULATION

7.3 THE EXTENT OF REACTION

7.4 FUGACITY AND ACTIVITY

7.5 VARIATION OF THE EQUILIBRIUM CONSTANT WITH TEMPERATURE

7.6 COMPUTATIONAL THERMOCHEMISTRY

7.7 CHEMICAL POTENTIAL: NONIDEAL SYSTEMS

7.8 FREE ENERGY AND EQUILIBRIA IN BIOCHEMICAL SYSTEMS

PROBLEMS AND EXAMPLES

CHAPTER 8: A STATISTICAL APPROACH TO THERMODYNAMICS

8.1 EQUILIBRIUM

8.2 DEGENERACY AND EQUILIBRIUM

8.3 GIBBS FREE ENERGY AND THE PARTITION FUNCTION

8.4 ENTROPY AND PROBABILITY

8.5 THE THERMODYNAMIC FUNCTIONS

8.6 THE PARTITION FUNCTION OF A SIMPLE SYSTEM

8.7 THE PARTITION FUNCTION FOR DIFFERENT MODES OF MOTION

8.8 THE EQUILIBRIUM CONSTANT: A STATISTICAL APPROACH

8.9 COMPUTATIONAL STATISTICAL THERMODYNAMICS

PROBLEMS AND EXAMPLES

CHAPTER 9: THE PHASE RULE

9.1 COMPONENTS, PHASES, AND DEGREES OF FREEDOM

9.2 COEXISTENCE CURVES

9.3 THE CLAUSIUS CLAPEYRON EQUATION

9.4 PARTIAL MOLAR VOLUME

9.5 THE GIBBS PHASE RULE

9.6 TWO-COMPONENT PHASE DIAGRAMS

9.7 COMPOUND PHASE DIAGRAMS

9.8 TERNARY PHASE DIAGRAMS

PROBLEMS AND EXAMPLES

CHAPTER 10: CHEMICAL KINETICS

10.1 FIRST-ORDER KINETIC RATE LAWS

10.2 SECOND-ORDER REACTIONS

10.3 OTHER REACTION ORDERS

10.4 EXPERIMENTAL DETERMINATION OF THE RATE EQUATION

10.5 REACTION MECHANISMS

10.6 THE INFLUENCE OF TEMPERATURE ON RATE

10.7 COLLISION THEORY

10.8 COMPUTATIONAL KINETICS

PROBLEMS AND EXAMPLES

CHAPTER 11: LIQUIDS AND SOLIDS

11.1 SURFACE TENSION

11.2 HEAT CAPACITY OF LIQUIDS AND SOLIDS

11.3 VISCOSITY OF LIQUIDS

11.4 CRYSTALS

11.5 BRAVAIS LATTICES

11.6 COMPUTATIONAL GEOMETRIES

11.7 LATTICE ENERGIES

PROBLEMS AND EXERCISES

CHAPTER 12: SOLUTION CHEMISTRY

12.1 THE IDEAL SOLUTION

12.2 RAOULT’S LAW

12.3 A DIGRESSION ON CONCENTRATION UNITS

12.4 REAL SOLUTIONS

12.5 HENRY’S LAW

12.6 VAPOR PRESSURE

12.7 BOILING POINT ELEVATION

12.8 OSMOTIC PRESURE

12.9 COLLIGATIVE PROPERTIES

PROBLEMS, EXAMPLES, AND EXERCISE

CHAPTER 13: COULOMETRY AND CONDUCTIVITY

13.1 ELECTRICAL POTENTIAL

13.2 RESISTIVITY, CONDUCTIVITY, AND CONDUCTANCE

13.3 MOLAR CONDUCTIVITY

13.4 PARTIAL IONIZATION: WEAK ELECTROLYTES

13.5 ION MOBILITIES

13.6 FARADAY’S LAWS

13.7 MOBILITY AND CONDUCTANCE

13.8 THE HITTORF CELL

13.9 ION ACTIVITIES

PROBLEMS AND EXAMPLES

CHAPTER 14: ELECTROCHEMICAL CELLS

14.1 THE DANIELL CELL

14.2 HALF-CELLS

14.3 HALF-CELL POTENTIALS

14.4 CELL DIAGRAMS

14.5 ELECTRICAL WORK

14.6 THE NERNST EQUATION

14.7 CONCENTRATION CELLS

14.8 FINDING E°

14.9 SOLUBILITY AND STABILITY PRODUCTS

14.10 MEAN IONIC ACTIVITY COEFFICIENTS

14.11 THE CALOMEL ELECTRODE

14.12 THE GLASS ELECTRODE

PROBLEMS AND EXAMPLES

CHAPTER 15: EARLY QUANTUM THEORY: A SUMMARY

15.1 THE HYDROGEN SPECTRUM

15.2 EARLY QUANTUM THEORY

15.3 MOLECULAR QUANTUM CHEMISTRY

15.4 THE HARTREE INDEPENDENT ELECTRON METHOD

15.5 A DIGRESSION ON ATOMIC UNITS

PROBLEMS AND EXAMPLES

CHAPTER 16: WAVE MECHANICS OF SIMPLE SYSTEMS

16.1 WAVE MOTION

16.2 WAVE EQUATIONS

16.3 THE SCHRÖDINGER EQUATION

16.4 QUANTUM MECHANICAL SYSTEMS

16.5 THE PARTICLE IN A ONE-DIMENSIONAL BOX

16.6 THE PARTICLE IN A CUBIC BOX

16.7 THE HYDROGEN ATOM

16.8 BREAKING DEGENERACY

16.9 ORTHOGONALITY AND OVERLAP

16.10 MANY-ELECTRON ATOMIC SYSTEMS

PROBLEMS

CHAPTER 17: THE VARIATIONAL METHOD: ATOMS

17.1 MORE ON THE VARIATIONAL METHOD

17.2 THE SECULAR DETERMINANT

17.3 A VARIATIONAL TREATMENT FOR THE HYDROGEN ATOM: THE ENERGY SPECTRUM

17.4 HELIUM

17.5 SPIN

17.6 BOSONS AND FERMIONS

17.7 SLATER DETERMINANTS

17.8 THE AUFBAU PRINCIPLE

17.9 THE SCF ENERGIES OF FIRST-ROW ATOMS AND IONS

17.10 SLATER-TYPE ORBITALS (STO)

17.11 SPIN–ORBIT COUPLING

PROBLEMS AND EXAMPLES

CHAPTER 18: EXPERIMENTAL DETERMINATION OF MOLECULAR STRUCTURE

18.1 THE HARMONIC OSCILLATOR

18.2 THE HOOKE’S LAW POTENTIAL WELL

18.3 DIATOMIC MOLECULES

18.4 THE QUANTUM RIGID ROTOR

18.5 MICROWAVE SPECTROSCOPY: BOND STRENGTH AND BOND LENGTH

18.6 ELECTRONIC SPECTRA

18.7 DIPOLE MOMENTS

18.8 NUCLEAR MAGNETIC RESONANCE (NMR)

18.9 ELECTRON SPIN RESONANCE

PROBLEMS AND EXAMPLES

CHAPTER 19: CLASSICAL MOLECULAR MODELING

19.1 ENTHALPY: ADDITIVE METHODS

19.2 BOND ENTHALPIES

19.3 STRUCTURE

19.4 GEOMETRY AND ENTHALPY: MOLECULAR MECHANICS

19.5 MOLECULAR MODELING

19.6 THE GUI

19.7 FINDING THERMODYNAMIC PROPERTIES

19.8 THE OUTSIDE WORLD

19.9 TRANSITION STATES

PROBLEMS AND EXAMPLES

CHAPTER 20: QUANTUM MOLECULAR MODELING

20.1 THE MOLECULAR VARIATIONAL METHOD

20.2 THE HYDROGEN MOLECULE ION

20.3 HIGHER MOLECULAR ORBITAL CALCULATIONS

20.4 SEMIEMPIRICAL METHODS

20.5 AB INITIO METHODS

20.6 THE GAUSSIAN BASIS SET

20.7 STORED PARAMETERS

20.8 MOLECULAR ORBITALS

20.9 METHANE

20.10 SPLIT VALENCE BASIS SETS

20.11 POLARIZED BASIS FUNCTIONS

20.12 HETEROATOMS: OXYGEN

20.13 FINDING ΔfH298 OF METHANOL

20.14 FURTHER BASIS SET IMPROVEMENTS

20.15 POST-HARTREE–FOCK CALCULATIONS

20.16 PERTURBATION

20.17 COMBINED OR SCRIPTED METHODS

20.18 DENSITY FUNCTIONAL THEORY (DFT)

PROBLEMS AND EXAMPLES

CHAPTER 21: PHOTOCHEMISTRY AND THE THEORY OF CHEMICAL REACTIONS

21.1 EINSTEIN’S LAW

21.2 QUANTUM YIELDS

21.3 BOND DISSOCIATION ENERGIES (BDE)

21.4 LASERS

21.5 ISODESMIC REACTIONS

21.6 THE EYRING THEORY OF REACTION RATES

21.7 THE POTENTIAL ENERGY SURFACE

21.8 THE STEADY-STATE PSEUDO-EQUILIBRIUM

21.9 ENTROPIES OF ACTIVATION

21.10 THE STRUCTURE OF THE ACTIVATED COMPLEX

PROBLEMS AND EXAMPLES

REFERENCES

ANSWERS TO SELECTED ODD-NUMBERED PROBLEMS

INDEX

CONCISE PHYSICAL CHEMISTRY

Copyright © 2011 by John Wiley & Sons, Inc. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.Published simultaneously in Canada.

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Don Rogers is an amateur jazz musician and painter who lives in Greenwich Village, NY.

Library of Congress Cataloging-in-Publication Data:

Rogers, Donald W.Concise physical chemistry / by Donald W. Rogers.p. cm.Includes index.Summary: “This book is a physical chemistry textbook that presents the essentials of physical chemistry as a logical sequence from its most modest beginning to contemporary research topics. Many books currently on the market focus on the problem sets with a cursory treatment of the conceptual background and theoretical material, whereas this book is concerned only with the conceptual development of the subject. It contains mathematical background, worked examples and problemsets. Comprised of 21 chapters, the book addresses ideal gas laws, real gases, the thermodynamics of simple systems, thermochemistry, entropy and the second law, the Gibbs free energy, equilibrium, statistical approaches to thermodynamics, the phase rule, chemical kinetics, liquids and solids, solution chemistry, conductivity, electrochemical cells, atomic theory, wave mechanics of simple systems, molecular orbital theory, experimental determination of molecular structure, and photochemistry and the theory of chemical kinetics”– Provided by publisher.ISBN 978-0-470-52264-6 (pbk.)1. Chemistry, Physical and theoretical–Textbooks.   I. Title.QD453.3.R63 2010541–dc22

2010018380

FOREWORD

Among many advantages of being a professional researcher and teacher is the pleasure of reading a new and good textbook that concisely summarizes the fundamentals and progress in your research area. This reading not only gives you the enjoyment of looking once more at the whole picture of the edifice that many generations of your colleagues have meticulously build but, most importantly, also enhances your confidence that your choice to spend your entire life to promote and contribute to this structure is worthwhile. Clearly, the perception of the textbook by an expert in the field is quite different, to say the least, from the perception of a junior or senior undergraduate student who is about to register for a class. A simple look at a textbook that is jam-packed with complex integrals and differential equations may scare any prospective students to death. On the other hand, eliminating the mathematics entirely will inevitably eliminate the rigor of scientific statements. In this respect, the right compromise between simplicity and rigor in explaining complex scientific topics is an extremely rare talent. The task is especially large given the fact that the textbook is addressed to students for whom a particular area of science is not among their primary interests. In this respect, Professor Rogers’s Concise Physical Chemistry is a textbook that ideally suits all of the above-formulated criteria of a new and good textbook.

Although the fundamental laws and basic principles of physical chemistry were formulated long ago, research in the area is continuously widening and deepening. As a result, the original boundaries of physical chemistry as a science become more and more vague and difficult to determine. During the last two decades, physical chemistry has made a tremendous progress mainly boosted by a spectacular increase in our computational capabilities. This is especially visible in quantum molecular modeling. For instance, on my first acquaintance with physical chemistry about 30 years ago, the only molecule that could be quantitatively treated with an accuracy close to experimental data by wave mechanics was the hydrogen molecule. In a lifetime, I have witnessed a complete change of the research picture in which thermodynamic and kinetic data are theoretically obtained routinely with an accuracy often exceeding the experimental one. Quite obviously, to keep the pace with the progress in research, textbooks should be permanently updated and revised. In his textbook Professor Rogers sticks to the classical topics that are conventionally considered as part of physical chemistry. However, these classical topics are deciphered from a modern point of view, and here lies the main strength of this textbook as well as what actually makes this textbook different from many other similar textbooks.

Traditionally, physical chemistry is viewed as an application of physical principles in explaining and rationalizing chemical phenomena. As such, the powerful principles and theories that physical chemistry borrows from physics are accompanied by an advanced and mandatory set of mathematical tools. This makes the process of learning physical chemistry very difficult albeit challenging, exciting, and rewarding. The level of mathematics used by Professor Rogers to formulate and prove the physicochemical principles is remarkably consistent throughout the whole text. Thus, only the most general algebra and calculus concepts are required to understand the essence of the topics discussed. Professor Rogers’s way of reasoning is succinct and easy to follow while the examples used to illustrate the theoretical developments are carefully selected and always make a good point. There is no doubt that this textbook is a work of great value, and I heartily recommend it for everybody who wants to enter the wonderful world of physical chemistry.

ILIE FISHTIK

Worcester Polytechnic InstituteWorcester, MAJuly 2010

PREFACE

Shall I call that wise or foolish, now; if it be really wise it has a foolish look to it; yet, if it be really foolish, then has it a sort of wiseish look to it.

Moby-Dick    (Chapter 99)    —Herman Melville

Physical chemistry stands at the intersection of the power and generality of classical and quantum physics with the minute molecular complexity of chemistry and biology. Any molecular process that can be envisioned as a flow from a higher energy state to a lower state is subject to analysis by the methods of classical thermodynamics. Chemical thermodynamics tells us where a process is going. Chemical kinetics tells us how long it will take to get there.

Evidence for and application of many of the most subtle and abstract principles of quantum mechanics are to be found in the physical interpretation of chemical phenomena. The vast expansion of spectroscopy from line spectra of atoms well known in the nineteenth century to the magnetic resonance imaging (MRI) of today’s diagnostic procedures is a result of our gradually enhanced understanding of the quantum mechanical interactions of energy with simple atomic or complex molecular systems.

Mathematical methods developed in the domain of physical chemistry can be successfully applied to very different phenomena. In the study of seemingly unrelated phenomena, we are astonished to find that electrical potential across a capacitor, the rate of isomerization of cyclopentene, and the growth of marine larvae either as individuals or as populations have been successfully modeled by the same first-order differential equation.

Many people in diverse fields use physical chemistry but do not have the opportunity to take a rigorous three-semester course or to master one of the several ∼1000-page texts in this large and diverse field. Concise Physical Chemistry is intended to meet (a) the needs of professionals in fields other than physical chemistry who need to be able to master or review a limited portion of physical chemistry or (b) the need of instructors who require a manageable text for teaching a one-semester course in the essentials of the subject. The present text is not, however, a diluted form of physical chemistry. Topics are treated as brief, self-contained units, graded in difficulty from a reintroduction to some of the concepts of general chemistry in the first few chapters to research-level computer applications in the later chapters.

I wish to acknowledge my obligations to Anita Lekhwani and Rebekah Amos of John Wiley and Sons, Inc. and to Tony Li of Scientific Computing, Long Island University. I also thank the National Center for Supercomputing Applications and the National Science Foundation for generous allocations of computer time, and the H. R. Whiteley Foundation of the University of Washington for summer research fellowships during which part of this book was written.

Finally, though many people have helped me in my attempts to better appreciate the beauty of this vast and variegated subject, this book is dedicated to the memory of my first teacher of physical chemistry, Walter Kauzmann.

DONALD W. ROGERS