Essentials of Physical Chemistry

504 Pages·2011·5.563 MB·English

by  Shillady, Don

K11901 Cover 6/9/11 2:29 PM Page 1
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Physical Chemistry ESSENTIALS OF Shillady
PHYSICAL
ESSENTIALS OF
CHEMISTRY E
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PHYSICAL
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Don Shillady
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At a time when U.S. high school students are producing low scores in T
mathematics and science on international examinations, a thorough grounding IA CHEMISTRY
in physical chemistry should not be considered optional for science under-
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graduates. Based on the author’s thirty years of teaching, Essentials of Physical
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Chemistry merges coverage of calculus with chemistry and molecular physics

in a friendly yet thorough manner. Reflecting the latest ACS guidelines, the O
book can be used as a one or two semester course, and includes special topics
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suitable for senior projects.

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The book begins with a math and physics review to ensure all students start
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on the same level, and then discusses the basics of thermodynamics and
kinetics with mathematics tuned to a level that stretches students’ abilities.
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It then provides material for an optional second semester course that
shows students how to apply their enhanced mathematical skills in a brief S
historical development of the quantum mechanics of molecules. Emphasizing
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spectroscopy, the text is built on a foundation of quantum chemistry and more
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mathematical detail and examples. It contains sample classroom-tested exams
to gauge how well students know how to use relevant formulas and to display
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successful understanding of key concepts.
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• Coupling the development of mathematical skills with chemistry concepts

encourages students to learn mathematical derivations
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• Mini-biographies of famous scientists make the presentation more
interesting from a “people” point of view H
• Stating the basic concepts of quantum chemistry in terms of analogies
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provides a pedagogically useful technique
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Covering key topics such as the critical point of a van der Waals gas, the
Michaelis–Menten equation, and the entropy of mixing, this classroom-tested
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text highlights applications across the range of chemistry, forensic science, S
pre-medical science and chemical engineering. In a presentation of fundamental
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topics held together by clearly established mathematical models, the book
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supplies a quantitative discussion of the merged science of physical chemistry.
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K11901
Don Shillady
6000 Broken Sound Parkway, NW
Suite 300, Boca Raton, FL 33487
270 Madison Avenue
an informa business New York, NY 10016
2 Park Square, Milton Park
Abingdon, Oxon OX14 4RN, UK
ESSENTIALS OF
PHYSICAL
CHEMISTRY
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ESSENTIALS OF
PHYSICAL
CHEMISTRY
Don Shillady
Boca Raton London New York
CRC Press is an imprint of the
Taylor & Francis Group, an informa business
CRC Press
Taylor & Francis Group
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Boca Raton, FL 33487-2742
© 2012 by Taylor & Francis Group, LLC
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No claim to original U.S. Government works
Version Date: 20110804
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Contents
Preface............................................................................................................................................xiii
Author...........................................................................................................................................xvii
List of Constants............................................................................................................................xix
PeriodicTableof theElements......................................................................................................xxi
Introduction:Mathematics and Physics Review..........................................................................xxiii
Chapter 1 Ideal and Real Gas Behavior.......................................................................................1
Introduction tothe ‘‘First Encounter with Physical Chemistry’’................................1
Phenomenological Derivationof theIdeal Gas Equation...........................................1
Charles’(Jacques-Alexandre-César Charles)Law......................................................4
Useful Units.................................................................................................................8
Molecular Weightfrom Gas Density (the DumasBulb Method)............................10
Dalton’sLaw ofPartial Pressures.............................................................................11
Nonideal Gas Behavior.............................................................................................13
Supercritical Fluid Chromatography.........................................................................18
Fluids....................................................................................................................19
Supercritical Fluid Instrumentation......................................................................20
Supercritical Mobile Phase...................................................................................21
SampleSCF Separations......................................................................................21
Summary....................................................................................................................22
Problems....................................................................................................................23
References.................................................................................................................24
Chapter 2 Viscosityof LaminarFlow........................................................................................25
Introduction...............................................................................................................25
Measurement ofViscosity.........................................................................................28
Viscosityof Blood.....................................................................................................30
Staudinger’s Rule forPolymerMolecular Weight....................................................31
Summary....................................................................................................................34
Problems....................................................................................................................35
References.................................................................................................................35
Chapter 3 The KineticMolecular Theory ofGases...................................................................37
Introduction...............................................................................................................37
KineticAssumptions of theTheory ofGases...........................................................37
WeightedAveraging: AVeryImportant Concept....................................................39
Summary....................................................................................................................50
Problems....................................................................................................................51
References.................................................................................................................51
Chapter 4 The First Law ofThermodynamics...........................................................................53
Introduction...............................................................................................................53
Historical Developmentof Thermodynamics...........................................................53
Definitions.................................................................................................................54
First Law ofThermodynamics..................................................................................55
v
vi Contents
IsothermalProcesses.................................................................................................57
Enthalpy andHeat Capacities...................................................................................59
AdiabaticProcesses...................................................................................................61
AdiabaticNozzleExpansionSpectroscopy...............................................................64
Diesel EngineCompression......................................................................................65
Calorimetry andThermochemistry............................................................................67
Hess’sLaw of Heat Summation................................................................................71
Standard Heats of Formation at298.158K and1 bar Pressure.................................72
Temperature Dependence ofReaction Enthalpies....................................................73
Polynomial Curve Fitting..........................................................................................74
Application to DH0 (T>298:15(cid:1)K)........................................................................75
rxn
Other Types ofThermochemistry.............................................................................78
Perspective.................................................................................................................78
Key Formulas and Equations....................................................................................78
Problems....................................................................................................................79
Testing,Grading, and Learning?...............................................................................79
References.................................................................................................................80
Chapter 5 The Second and Third Laws of Thermodynamics....................................................81
Introduction...............................................................................................................81
Carnot Cycle=Engine.................................................................................................81
Carnot Cycle.........................................................................................................83
Carnot Efficiency..................................................................................................85
Efficiency ofRealHeat Engines...............................................................................86
Entropy andSpontaneity...........................................................................................87
Summaryof theSecondLaw of Thermodynamics..................................................88
Eight BasicEquations ofThermodynamics..............................................................88
Third Lawof Thermodynamics................................................................................90
Entropy ofReactions............................................................................................92
Entropy Changes atT>298.158K.......................................................................93
Trouton’sRule=Observation.................................................................................94
SimpleStatisticalTreatmentof Liquidsand Gases..................................................95
Summary....................................................................................................................99
Testing,Grading, and Learning?.............................................................................100
Problems..................................................................................................................101
Bibliography............................................................................................................102
References...............................................................................................................102
Chapter 6 Gibbs’FreeEnergyand Equilibria..........................................................................103
Introduction.............................................................................................................103
Temperature Dependence ofEquilibriumConstants..............................................106
van’tHoffEquation.................................................................................................106
VaporPressure ofLiquids.......................................................................................108
Phase Equilibria.......................................................................................................112
How IceSkates Work.............................................................................................113
Gibbs Phase Rule....................................................................................................113
IodineTriple Point..................................................................................................115
(C –C )for Liquidsand Solids..............................................................................117
P V
Open Systems:Gibbs–DuhemEquation forPartial MolalVolumes.....................119
ChemicalPotential forOpen Systems.....................................................................123
Contents vii
ModelingLiquids....................................................................................................125
Summary..................................................................................................................128
Problems..................................................................................................................129
Testing,Grading, and Learning?.............................................................................129
Bibliography............................................................................................................130
References...............................................................................................................130
Chapter 7 Basic Chemical Kinetics.........................................................................................133
Introduction.............................................................................................................133
First-Order Reactions..............................................................................................133
Promethium: An Introductionto Nuclear Chemistry..............................................135
MadameCurieand Radioactivity............................................................................137
Radium....................................................................................................................139
Second-Order Rate Processes: [A]¼[B]................................................................139
Second-Order Rate Processes: [A] 6¼ [B]...............................................................139
Arrhenius Activation Energy...................................................................................145
The ClassicA !B! CConsecutive First-Order Reaction.................................147
Splittingthe Atom...................................................................................................150
Problems..................................................................................................................153
References...............................................................................................................154
Chapter 8 More Kinetics and Some Mechanisms....................................................................155
Introduction.............................................................................................................155
Beyond Arrhenius tothe Eyring Transition State...................................................155
Example...................................................................................................................159
Graphical–AnalyticalMethodfor DHz and DSz.....................................................161
Summaryof Graphical Method Resultsat T¼258C..............................................163
FurtherConsiderationof SN1 Solvolysis...............................................................164
Chain Reactionsand the Steady State.....................................................................165
Steady-State Example No. 1: H þBr ! 2HBr...............................................165
2 2
Steady-State Example No. 2: Thermal Cracking ofAcetaldehyde....................167
Steady-State Example No. 3: The LindemannMechanism...............................168
Enzyme Kinetics......................................................................................................169
Basic Michaelis–Menten Equation.....................................................................171
Example:AHypothetical Enzyme..........................................................................172
Michaelis–MentenwithCompetitive Inhibitor..................................................174
Michaelis–MentenSummary..............................................................................176
KineticsConclusions...............................................................................................178
Problems..................................................................................................................178
Testing,Grading, and Learning?.............................................................................179
Bibliography............................................................................................................180
References...............................................................................................................180
Chapter 9 Basic Spectroscopy..................................................................................................181
Introduction.............................................................................................................181
Planck’sDiscovery..................................................................................................181
Radio Waves.......................................................................................................183
Balmer’s IntegerFormula........................................................................................184
AVeryUseful Formula...........................................................................................189
PreliminarySummary ofthe Bohr Atom................................................................190
viii Contents
Significance ofthe Bohr Quantum Numbern........................................................192
OrbitalScreening.....................................................................................................192
X-Ray Emission......................................................................................................193
Forensic=AnalyticalUse of AugerX-Rays.............................................................196
X-Ray Fluorescence................................................................................................198
X-Ray Diffraction....................................................................................................199
Electronic Absorption Spectroscopy=Spectrophotometry.......................................202
InterpretingElectronic Spectra................................................................................204
General Principles ofSpectroscopy........................................................................209
Problems..................................................................................................................210
Bibliography............................................................................................................210
References...............................................................................................................211
Chapter 10 Early Experiments inQuantum Physics..................................................................213
Introduction.............................................................................................................213
Stefan–Boltzmann Law: Relating Heat and Light—PartI.....................................213
Blackbody Radiation: Relating Heat and Light—Part II........................................214
Photoelectric Effect.................................................................................................221
De Broglie Matter Waves........................................................................................225
Davisson–Germer Experiment................................................................................226
Summary..................................................................................................................230
Problems..................................................................................................................231
References...............................................................................................................232
Chapter 11 The Schrödinger WaveEquation............................................................................233
Introduction.............................................................................................................233
Definition ofa Commutator....................................................................................242
Postulates ofQuantum Mechanics..........................................................................243
Particle on aRing....................................................................................................244
Comparison of PIB and POR Applications............................................................247
Additional Theorems inQuantum Mechanics........................................................247
Summary..................................................................................................................249
Problems..................................................................................................................250
Study, Test, and Learn?...........................................................................................251
References...............................................................................................................252
Chapter 12 The Quantized Harmonic Oscillator:Vibrational Spectroscopy.............................253
Introduction.............................................................................................................253
Harmonic Oscillator Details....................................................................................255
Harmonic Oscillator Results....................................................................................258
Reduced Mass.........................................................................................................262
Isotope Shift in theVibrational Fundamental Frequency.......................................264
HermiteRecursion Rule..........................................................................................265
InfraredDipole SelectionRule................................................................................265
3N(cid:3)6or 3N(cid:3)5 Vibrations?.................................................................................267
Raman Spectroscopy...............................................................................................271
Summary..................................................................................................................274
Problems..................................................................................................................275
References...............................................................................................................275
Contents ix
Chapter 13 The Quantized Rigid Rotorand theVib-Rotor.......................................................277
Introduction.............................................................................................................277
Three-DimensionalParticle-in-a-Box......................................................................277
Rigid Rotor..............................................................................................................279
Key Step!............................................................................................................281
Rigid RotorWave Functions..............................................................................283
Rigid RotorResults............................................................................................285
Angular Wave Functions.........................................................................................285
Angular Momentum................................................................................................286
Rotational Spectrumof CO.....................................................................................289
FourierTransform Spectrometry.............................................................................291
FT-IR Imagingand Microscopy..............................................................................292
Dipole Requirement................................................................................................294
Vib-Rotor Infrared Spectroscopy............................................................................295
Bond Lengthof H-35Cl...........................................................................................302
17
Summary..................................................................................................................303
Problems..................................................................................................................304
References...............................................................................................................305
Chapter 14 The Schrödinger Hydrogen Atom...........................................................................307
Introduction.............................................................................................................307
Strategy to Solve the Problem.................................................................................307
AssociatedLaguerre Polynomials...........................................................................310
Interpretation...........................................................................................................311
Picturesof Angular Orbitals....................................................................................316
Powell Equivalentd-Orbitals..................................................................................319
Unsöld’sTheorem...................................................................................................323
Aufbau Principleand theScaled HAtom...............................................................323
Term Symbols and SpinAngular Momentum........................................................324
Hund’s Rule.............................................................................................................325
jL, Si versus jJ, JiCoupling.................................................................................326
z z
Summary..................................................................................................................328
Problems..................................................................................................................329
References...............................................................................................................329
Chapter 15 Quantum Thermodynamics.....................................................................................331
Introduction.............................................................................................................331
(Energy) PartitionFunction.....................................................................................333
Average Translation Energyin One Dimension.....................................................334
Average Rotational Energyof a Diatomic Molecule..............................................334
Average Vibrational Energy....................................................................................335
High-TemperatureLimitfor Vibrational Heat Capacity.........................................337
Heat Capacity ofa Polyatomic Species:Water......................................................337
CombiningPartition Functions...............................................................................339
Statistical Formulas forOtherThermodynamic Functions.....................................340
Statistical Formulafor S(T).....................................................................................340
Sakur–Tetrode Formulafor Absolute Entropy of aGas.........................................341
Summary..................................................................................................................343
Problems..................................................................................................................344
References...............................................................................................................344