Schaum’s Outline of Physical Chemistry

513 Pages·1989·32.681 MB·English

by  Clyde Metz

S C H A U M ’ S
!
ouT
PHYSICAL
CHEMISTRY
Second Edition
CLYDE R. METZ
The perfect aid for better grades!
Covers ail course fundamentals—supplements
any class text
Teaches effective problem-solving
704 fully worked problems
Ideal for self-study!
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SCHAUM'S OUTLINE OF
THEORY AND PROBLEMS
of
PHYSICAL
CHEMISTRY
SECOND EDITION
by
CLYDE R. METZ, Ph.D.
Professor of Chemistry
College of Charleston
SCHAUM’S OUTLINE SERIES
McGRAW-HILL
New York San Francisco Washington, D.C. Auckland Bogota Caracas Lisbon
London Madrid Mexico City Milan Montreal New Dehli
San Juan Singapore Sydney Tokyo Toronto
Clyde Metz, currently Professor of Chemistry at The College of Charleston,
received his Ph.D. from Indiana University. He is a coauthor of a general
chemistry textbook and related laboratory materials, solutions manuals,
and study guides and has published several student research papers. Dr.
Metz is active in the Division of Chemical Education of the American
Chemical Society; is a member of the Electrochemical Society, Alpha Chi
Sigma, Sigma Xi, Tau Beta Pi, Phi Lambda Upsilon, and the South Carolina
Academy of Science; and is a Fellow of the Indiana Academy of Science.
Schaum's Outline of Theory and Problems of
PHYSICAL CHEMISTRY
Copyright © 1989, 1976 by The McGraw-Hill Companies, Inc. All rights reserved. Printed in the
United States of America. Except as permitted under the Copyright Act of 1976, no part of this
publication may be reproduced or distributed in any form or by any means, or stored in a data base
or retrieval system, without the prior written permission of the publisher.
14 15 16 17 18 19 20 RHR 12 11 10
ISBN 41715-b
Sponsoring Editor, John Aliano
Production Editor, Leroy Young
Editing Supervisor, Marthe Grice
Project Supervision, The Total Book
Library of Congress Cataloging-in-Publication Data
Metz, Clyde R.
Schaum's outline of theory and problems of physical
chemistry.
(Schaum's outline series)
Includes index.
1. Chemistry, Physical and theoretical—Problems,
exercises, etc. ( Title. II. Title: Theory and
problems of physical chemistry.
QD45* M-S 1988 541.3 076 87-29839
:5B\ (MU-041715-6
McGraw-Hill
A Division of The McGraw-Hill Companies
Preface
This supplementary book has been written for students at all levels in physical
chemistry and contains the solved problems and additional exercises that most texts
omit because of space limitations. Each chapter is divided into three sections: The
important concepts for each subject are summarized in word and equation form,
usually followed by an example problem; a series of completely solved problems
is presented to illustrate the concepts both singly and in combination; and a set of
supplementary problems (with answers) is provided for additional drill.
Since the publication of the first edition of this book, the changeover to the SI
system of units from the modified cgs system that had been used in physical chemistry
for many years has been nearly completed. In fact, even a new thermodynamic
standard state pressure (1 bar) has been chosen. Nearly all the data in this book
are given in the newer units—the older systems are discussed briefly and conversion
factors given both in the text and in the appendix.
Data for the problems have been taken from the Handbook of Chemistry and
Physics with permission of the Chemical Rubber Company, from various original
papers, and from publications of the National Bureau of Standards. Appreciation
is extended to Chemical Education Resources, Inc. for permission to reprint several
figures and tables found in Chapters 18 and 22; to W. H. Freeman and Co., Inc.
for permission to reprint several figures in Chapter 22; to Academic Press, Inc. for
permission to use tables in the Appendix; to Mr. Thomas J. Dembofsky and Mr.
David Beckwith and their staff for their cooperation in making many improvements
in the manuscript; to Miss Linda S. Hill for reworking all the problems in the first
edition; to an anonymous reviewer who made a number of valuable suggestions, to
two outstanding teachers of physical chemistry—Dr. Oran M. Knudsen and Dr.
Ralph L. Seifert; and to my family—Jennie, Curtis, and Michele.
Clyde R. Metz
Contents
Chapter / GASES AND THE KINETIC-MOLECULAR THEORY.................................. 1
TEMPERATURE AND PRESSURE 1.1 Temperature 1.2 Pressure
LAWS FOR IDEAL GASES 1.3 Boyle’s or Mariotte’s Law 1.4 Charles’s
or Gay-Lussac’s Law 1.5 Ideal Gas Law 1.6 Molar Mass of an Ideal Gas
MIXTURES OF IDEAL GASES 1.7 Dalton’s Law of Partial Pressures
1.8 Amagat’s Law of Partial Volumes 1.9 Molar Mass of a Gaseous
Mixture REAL GASES 1.10 Critical Point 1.11 Compressibility Factor
1.12 Virial Equations 1.13 Van der Waals Equation 1.14 Molar Mass of a
Real Gas KINETIC-MOLECULAR THEORY (KMT) 1.15 KMT
Postulates for Gases 1.16 P-V-KE Relationships
Chapter 2 TRANSLATION AND TRANSPORT PHENOMENA .................................. 21
VELOCITY AND ENERGY DISTRIBUTIONS OF GASES 2.1 Velocity
Distribution 2.2 Energy Distribution COLLISION PARAMETERS
2.3 Collision Numbers of Gases 2.4 Mean Free Path TRANSPORT
PROPERTIES 2.5 General Transport Law 2.6 Viscosity 2.7 Fluid Flow
2.8 Diffusion
Chapter 3 FIRST LAW OF THERMODYNAMICS............................................................... 41
INTERNAL ENERGY AND ENTHALPY 3.1 Internal Energy, U 3.2 Enthalpy, H
3.3 Thermal Energy of an Ideal Gas 3.4 Thermal Enthalpy of an Ideal Gas
HEAT CAPACITY 3.5 Definitions 3.6 Relationship Between CP and Cv
3.7 Empirical Heat-Capacity Expressions 3.8 Cv for Ideal Gases 3.9 Cv for
Condensed States INTERNAL ENERGY, WORK, AND HEAT 3.10 Work, w
3.11 Heat, q 3.12 Statement 3.13 General A U and AH Calculations SPECIFIC
APPLICATIONS OF THE FIRST LAW 3.14 Reversible Isothermal Expansion of
an Ideal Gas 3.15 Isothermal Isobaric Expansion of an Ideal Gas 3.16 Isothermal
Isobaric Phase Change 3.17 Reversible Adiabatic Expansion of an Ideal Gas
3.18 Isobaric Adiabatic Expansion of an Ideal Gas 3.19 Joule-Thomson Effect
Chapter 4 THERMOCHEMISTRY ............................................................................................. 67
HEAT OF REACTION 4.1 Introduction 4.2 Temperature Dependence of the Heat
of Reaction 4.3 Calorimetry CALCULATIONS INVOLVING
THERMOCHEMICAL EQUATIONS 4.4 Law of Hess 4.5 Enthalpy of Formation
4.6 Enthalpy of Combustion 4.7 Bond Enthalpy 4.8 Thermal Energies and
Enthalpies APPLICATIONS TO SELECTED CHEMICAL REACTIONS
4.9 Ionization Energy and Electron Affinity 4.10 Lattice Energy 4.11 Enthalpy of
Neutralization 4.12 Enthalpy of Solution 4.13 Enthalpy of Dilution
APPLICATIONS TO PHYSICAL CHANGES 4.14 States of Matter
4.15 Approximate Values of Enthalpies of Transition 4.16 Enthalpy of Heating
4.17 Clapeyron Equation 4.18 Enthalpy of Formation Diagram
Chapter 5 ENTROPY ...................................................................................................................... 92
THE SECOND LAW OF THERMODYNAMICS 5.1 Statements 5.2 The Carnot
Cycle 5.3 Efficiency of a Heat Engine 5.4 Refrigerators ENTROPY
CALCULATIONS 5.5 Definition of Entropy 5.6 AA(system) for Heat Transfer
5.7 AA(system) for Volume-Pressure-Temperature Changes 5.8 A A (system) for
CONTENTS
Isothermal Mixing 5.9 AS(surroundings) THE THIRD LAW OF
THERMODYNAMICS 5.10 Statement 5.11 Values of S°r AS FOR CHEMICAL
REACTIONS 5.12 ArS°T from Third Law Entropies 5.13 Temperature Dependence
of ArS°T 5.14 Pressure Dependence of ArS°T
Chapter 6 FREE ENERGY.............................................................................................................117
FREE ENERGY 6.1 Definition and Significance 6.2 Pressure Dependence of G
6.3 Temperature Dependence of G 6.4 Free Energy Calculations 6.5 Temperature
Dependence of A,G° 6.6 Chemical Potential ACTIVITIES 6.7 Introduction
6.8 Activities for Ideal Gases 6.9 Activities for Real Gases 6.10 Activities for
Liquids and Solids 6.11 Activities for Electrolytic Solutions 6.12 Reaction
Quotient THERMODYNAMIC RELATIONS 6.13 Maxwell Relations
6.14 Transformations
Chapter 7 CHEMICAL EQUILIBRIUM ....................................................................................141
EQUILIBRIUM CONSTANTS 7.1 Equilibrium Constant Expressions
7.2 Temperature Dependence of K 7.3 Free Energy Curves EQUILIBRIUM AND
GASES 7.4 Gaseous Equilibrium Constants 7.5 Calculations for Heterogeneous
Systems 7.6 Le Chatelier’s Principle EQUILIBRIUM IN AQUEOUS SOLUTIONS
7.7 Monoprotic Acids and Conjugate Bases 7.8 Aqueous Solutions of Weak Acids
7.9 Aqueous Solutions of Weak Bases 7.10 Buffer Solutions 7.11 Solutions of
Ampholytes 7.12 Hydrolysis of Ions 7.13 Consecutive Equilibria 7.14 Slightly
Soluble Salts
Chapter 8 STATISTICAL THERMODYNAMICS...................................................................162
ENSEMBLES 8.1 Introduction 8.2 Ensemble Energy States and Probabilities
8.3 Most Probable Distribution IDEAL-GAS PARTITION FUNCTIONS
8.4 Introduction 8.5 Molecular Translational Partition Function 8.6 Molecular
Rotational Partition Function 8.7 Molecular Vibrational Partition Function
8.8 Molecular Electronic Partition Function 8.9 Molecular Nuclear Partition
Function APPLICATION TO THERMODYNAMICS INVOLVING IDEAL
GASES 8.10 General Thermodynamic Functions 8.11 Molar Thermal Energy
8.12 Molar Entropy 8.13 Free Energy Function MONATOMIC CRYSTALS 8.14
Partition Functions and Molar Heat Capacities 8.15 Other Thermodynamic
Properties
Chapter 9 ELECTROCHEMISTRY .............................................................................................178
OXIDATION-REDUCTION 9.1 Stoichiometry 9.2 Galvanic and Electrolytic
Cells CONDUCTIVITY 9.3 Molar Conductivity 9.4 Transport Numbers 9.5 Ionic
Mobilities 9.6 Ionic Molar Conductivity ELECTROCHEMICAL CELLS 9.7 Sign
Convention and Diagrams 9.8 Standard State Potentials 9.9 Nonstandard State
Potentials 9.10 Concentration Cells and Thermocells
Chapter 10 HETEROGENEOUS EQUILIBRIA ........................................................................197
PHASE RULE 10.1 Phases 10.2 Components 10.3 Degrees of Freedom
(Variance) 10.4 Gibbs Phase Rule PHASE DIAGRAMS FOR
ONE-COMPONENT SYSTEMS 10.5 Introduction PHASE DIAGRAMS FOR
TWO-COMPONENT SYSTEMS 10.6 Introduction 10.7 Liquid-Liquid and
Liquid-Vapor Diagrams 10.8 Solid-Liquid Diagrams PHASE DIAGRAMS FOR
THREE-COMPONENT SYSTEMS 10.9 Introduction
CONTENTS
Chapter 11 SOLUTIONS ..................................................................................................................213
CONCENTRATIONS 11.1 Introduction 11.2 Concentration Units 11.3 Dilutions
11.4 Henry’s Law 11.5 Distribution Coefficients THERMODYNAMIC
PROPERTIES OF SOLUTIONS 11.6 Ideal Solutions 11.7 Vapor Pressure
11.8 AS, AH, and AG of Mixing 11.9 Activities and Activity Coefficients
COLLIGATIVE PROPERTIES OF SOLUTIONS CONTAINING
NONELECTROLYTIC SOLUTES 11.10 Vapor Pressure Lowering 11.11 Boiling
Point Elevation 11.12 Freezing Point Depression 11.13 Osmotic Pressure
SOLUTIONS OF ELECTROLYTES 11.14 Conductivity 11.15 Colligative
Properties of Strong Electrolytes 11.16 Colligative Properties of Weak Electrolytes
PARTIAL MOLAR QUANTITIES 11.17 Concept
Chapter 12 RATES OF CHEMICAL REACTIONS ...............................................................236
RATE EQUATIONS FOR SIMPLE REACTIONS 12.1 Reaction Rate
12.2 Concentration Dependence 12.3 Zero-Order Reactions 12.4 First-Order
Reactions 12.5 Second-Order Reactions 12.6 Third-Order Reactions 12.7 Pseudo-
Order Reactions DETERMINATION OF REACTION ORDER AND RATE
CONSTANTS 12.8 Differential Method 12.9 Integral Methods 12.10 Half-Life
Method 12.11 Powell-Plot Method 12.12 Relaxation Methods 12.13 Experimental
Parameters RATE EQUATIONS FOR COMPLEX REACTIONS
12.14 Differential Rate Equations 12.15 Steady-State Approximations 12.16 Opposing
Reactions and Equilibrium 12.17 Consecutive First-Order Reactions
12.18 Competing (Parallel) Reactions RADIOACTIVE DECAY 12.19 Decay
Constant and Half-Life 12.20 Successive Decays 12.21 Radioactive Dating
Chapter 13 REACTION KINETICS .............................................................................................263
INFLUENCE OF TEMPERATURE 13.1 Arrhenius Equation REACTION RATE
THEORY 13.2 Collision Theory of Bimolecular Reactions 13.3 Transition-State
Theory 13.4 Thermodynamic Considerations CATALYSIS 13.5 Homogeneous
Catalysis PHOTOCHEMISTRY 13.6 Introduction
Chapter 14 INTRODUCTION TO QUANTUM MECHANICS ..........................................279
PRELIMINARIES 14.1 Electromagnetic Radiation 14.2 De Broglie Wavelength
14.3 Heisenberg Uncertainty (Indeterminacy) Principle 14.4 Rydberg Equation
14.5 Bohr Theory for Hydrogenlike Atoms POSTULATES OF QUANTUM
MECHANICS 14.6 Wave Functions 14.7 Operators 14.8 Eigenfunctions and
Eigenvalues 14.9 Expectation Values 14.10 Time Dependence 14.11 The
Correspondence Principle APPROXIMATION METHODS 14.12 The Variation
Method 14.13 Nondegenerate Perturbation Theory
Chapter IS ATOMIC STRUCTURE AND SPECTROSCOPY..............................................299
HYDROGENLIKE ATOMS 15.1 System Description 15.2 The Angular Function
15.3 The Radial Function 15.4 Electron Position 15.5 Energy Values QUANTUM
THEORY OF POLYELECTRONIC ATOMS 15.6 Electron Spin Wave Functions
15.7 Hamiltonian Operator and Wave Function 15.8 Energy Levels ATOMIC TERM
SYMBOLS 15.9 Russell-Saunders Coupling 15.10 Polyelectronic Atom Term
Symbols SPECTRA OF POLYELECTRONIC ATOMS 15.11 Selection Rules
15.12 The Normal Zeeman Effect
CONTENTS
Chapter 16 ELECTRONIC STRUCTURE OF DIATOMIC MOLECULES.....................319
QUANTUM THEORY OF DIATOMIC MOLECULES 16.1 Hamiltonian Operator
16.2 Wave Functions APPLICATION OF THE VARIATION METHOD
16.3 Energy 16.4 Molecular Orbitals BOND DESCRIPTION 16.5 Electronegativity
16.6 Dipole Moment 16.7 Ionic Character MOLECULAR TERM SYMBOLS
16.8 Classification of Electronic States 16.9 Term Symbols for Electronic
Configurations
Chapter 17 SPECTROSCOPY OF DIATOMIC MOLECULES ..........................................335
ROTATIONAL AND VIBRATIONAL SPECTRA 17.1 Rotational Spectra
17.2 Vibrational Spectra 17.3 Anharmonic Oscillator 17.4 Vibrational-Rotational
Spectra 17.5 The Raman Effect ELECTRONIC SPECTRA 17.6 Selection Rules
17.7 Deslandres Table
Chapter 18 ELECTRONIC STRUCTURE OF POLYATOMIC MOLECULES . . . . 348
HYBRIDIZATION 18.1 Angular Wave Functions 18.2 Relative Bond Strength
LOCALIZED MULTIPLE BONDS 18.3 Molecular Orbital Theory CONJUGATED
BONDS 18.4 Chain Molecules 18.5 Cyclic Molecules 18.6 Bond Order and Length
COORDINATION COMPOUNDS 18.7 Valence Bond Theory 18.8 Crystal Field
Theory 18.9 Molecular Orbital Theory for Complexes SPATIAL RELATIONSHIPS
18.10 Introduction 18.11 Lewis Structures 18.12 Structure Number and Shape
Chapter 19 SPECTROSCOPY OF POLYATOMIC MOLECULES ..................................377
ROTATIONAL SPECTRA 19.1 Moments of Inertia for a Rigid Molecule
19.2 Spherical Top Molecules 19.3 Symmetrical Top Molecules 19.4 Asymmetrical
Top Molecules VIBRATIONAL SPECTRA 19.5 Degrees of Freedom 19.6 Infrared
Spectra ELECTRON MAGNETIC PROPERTIES 19.7 Magnetic Susceptibility
19.8 Electron Spin (Magnetic or Paramagnetic) Resonance NUCLEAR MAGNETIC
RESONANCE 19.9 Introduction 19.10 Chemical Shifts 19.11 Spin-Spin Splittings
Chapter 20 SYMMETRY AND GROUP THEORY ...............................................................390
SYMMETRY OPERATIONS AND ELEMENTS 20.1 Introduction 20.2 Identity
20.3 Axis of Proper Rotation 20.4 Center of Symmetry and Inversion 20.5 Mirror
Plane 20.6 Rotoreflection 20.7 Rotoinversion 20.8 Translation 20.9 Screw Axis
20.10 Glide Planes POINT GROUPS 20.11 Concept 20.12 Mathematical Properties
of a Point Group 20.13 Determination of a Point Group REPRESENTATION OF
GROUPS 20.14 Matrix Expressions for Operations 20.15 Representations
20.16 Character 20.17 Character Tables APPLICATIONS OF GROUP THEORY TO
MOLECULAR PROPERTIES 20.18 Optical Activity 20.19 Dipole Moment
20.20 Molecular Translational Motion 20.21 Molecular Rotational Motion
20.22 Vibrational Motion for Polyatomic Molecules
Chapter 21 INTERMOLECULAR BONDING ............................................................................419
EXTENDED COVALENT BONDING 21.1 Covalent Bonding 21.2 Hydrogen
Bonding METALLIC BONDING 21.3 The Free-Electron Model 21.4 The Band
Theory IONIC BONDING 21.5 Born-Haber Cycle 21.6 Potential-Energy Functions
VAN DER WAALS FORCES 21.7 Dipole Moments 21.8 Potential-Energy Functions
CONTENTS
Chapter 22 CRYSTALS ......................................................................................................................431
UNIT CELL 22.1 Introduction 22.2 Unit Cell Content 22.3 Unit Cell Coordinates
22.4 Crystallographic Projections 22.5 Coordination Number 22.6 Theoretical
Density 22.7 Crystal Radii 22.8 Separation of Atoms CRYSTAL LORMS
22.9 Metallic Crystals 22.10 Covalently Bonded Crystals 22.11 Ionic Crystals
22.12 Molecular Crystals CRYSTALLOGRAPHY 22.13 Miller Indices
22.14 d-Spacings 22.15 Point Group Symmetry X-RAY SPECTRA 22.16
Bragg Equation 22.17 Extinctions 22.18 Method of Ito 22.19 Intensities
Chapter 23 PHENOMENA AT INTERFACES............................................................................455
SURFACE TENSION OF LIQUIDS 23.1 Measurement of Surface Tension
23.2 Temperature Dependence 23.3 Vapor Pressure of Droplets 23.4 Parachor
SURFACE TENSION IN BINARY SYSTEMS 23.5 Interfacial Tension 23.6 Surface
Excess Concentration ADSORPTION 23.7 Adsorption Isotherms
23.8 Heterogeneous Catalysis
Chapter 24 MACROMOLECULES.................................................................................................469
MOLAR MASS 24.1 Average Molar Mass 24.2 Distribution Functions SOLUTIONS
OF MACROMOLECULES 24.3 Thermodynamic and Colligative Properties
24.4 Osmotic Pressure 24.5 Viscosity 24.6 Ultracentrifugation 24.7 Light Scattering
THERMODYNAMIC PROPERTIES 24.8 General Properties 24.9 Fusion of
Polymers
APPENDIXES..................................................................................................................485
Base Units Derived Units Fundamental Constants Periodic Table of the Elements
INDEX 489
Chapter 1
Gases and the Kinetic-Molecular Theory
Temperature and Pressure
1.1 TEMPERATURE
A thermal equilibrium exists between two systems provided no change in any observable property
occurs when the systems are in thermal contact. The “zeroth law of thermodynamics” states that “two
systems that are separately in thermal equilibrium with a third system are in thermal equilibrium with
each other.” This law implies that there must be a property of a system that signifies the existence of
a condition of thermal equilibrium that is independent of the composition and size of the system. This
property is called temperature.
The thermodynamic temperature (T) is defined by assigning the exact value 273.16 K to the triple
point of water, and the unit of thermodynamic temperature, the kelvin (K), is the fraction 1/273.16 of
the thermodynamic temperature of the triple point of water. The Celsius temperature (t) is defined as
f/(°C) = 7/(K)- 273.15 (1.1)
EXAMPLE 1.1. The freezing point of a saturated NaCl-water solution is - 17.78 °C = 0.00 °F, and the freezing
point of pure water is 0.0 °C = 32.00 °F. Derive an equation relating the Celsius and Fahrenheit temperature scales.
The relative sizes of the respective degrees are found by comparing the numbers of degrees for the same span,
giving
32.00 °F - 0.00 °F
1.800 °F °C“l
0.00 °C-(- 17.78 °C)
The general form of the desired relation between the scales is
t/(°F) = 1.800t/(°C) + k
where k corrects for the difference between the zero points of the scales. This constant can be evaluated by
substituting the freezing point data for the pure water, giving
32.00 = (1.800)(0) + fc
fc =32.00
The desired equation is
f/(°F) = 1.800//(°C) + 32.00 (1.2)
1.2 PRESSURE
Pressure (P) is defined as a force distributed over an area. The SI unit for expressing pressure is
the pascal (Pa), which is equal to 1 N m-2 or 1 kg nT1 s-2. Because a pressure of 1 Pa is very small,
the more convenient bar (lbar=105Pa) is commonly used for expressing pressures near normal
atmospheric pressure, and 1 bar has been chosen as the standard pressure for reporting various
thermodynamic data. Other pressure units with appropriate conversion factors are given in Table 1-1.
The absolute pressure of a system is defined as the gauge pressure plus the ambient atmospheric pressure.