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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. 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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