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Schaum’s Outline of Physical Chemistry PDF

513 Pages·1989·32.681 MB·English
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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! USB With tllBSB GOllPS6S: [^Biochemistry [^Molecular Biology [^Thermodynamics □ Health Science □ Analytical Chemistry ^Electrochemistry □ Medicine Organic Chemistry □ Intensive General Chemistry 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.

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