Essentials of Physical Chemistry

504 Pages·2011·5.56 MB·English

by  Shillady

K11901 Cover 6/9/11 2:29 PM Page 1
C M Y CM MY CY CMY K
Physical Chemistry ESSENTIALS OF Shillady
PHYSICAL
ESSENTIALS OF
CHEMISTRY E
S
PHYSICAL
S
E
Don Shillady
N
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-
L
graduates. Based on the author’s thirty years of teaching, Essentials of Physical
S
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
F
suitable for senior projects.

P
The book begins with a math and physics review to ensure all students start
H
on the same level, and then discusses the basics of thermodynamics and
kinetics with mathematics tuned to a level that stretches students’ abilities.
Y
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
I
spectroscopy, the text is built on a foundation of quantum chemistry and more
C
mathematical detail and examples. It contains sample classroom-tested exams
to gauge how well students know how to use relevant formulas and to display
A
successful understanding of key concepts.
L
• Coupling the development of mathematical skills with chemistry concepts

encourages students to learn mathematical derivations
C
• 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
E
provides a pedagogically useful technique
M
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
I
text highlights applications across the range of chemistry, forensic science, S
pre-medical science and chemical engineering. In a presentation of fundamental
T
topics held together by clearly established mathematical models, the book
R
supplies a quantitative discussion of the merged science of physical chemistry.
Y
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
TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk
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
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
© 2012 by Taylor & Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business
No claim to original U.S. Government works
Version Date: 20110804
International Standard Book Number-13: 978-1-4398-9693-8 (eBook - PDF)
This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been
made to publish reliable data and information, but the author and publisher cannot assume responsibility for the valid-
ity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright
holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this
form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may
rectify in any future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or uti-
lized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopy-
ing, microfilming, and recording, or in any information storage or retrieval system, without written permission from the
publishers.
For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://
www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923,
978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For
organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for
identification and explanation without intent to infringe.
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the CRC Press Web site at
http://www.crcpress.com
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