Exam Survival Guide: Physical Chemistry

388 Pages·2017·9.16 MB·English

by  Jochen Vogt (auth.)

Jochen Vogt
Exam Survival
Guide:
Physical
Chemistry
Exam Survival Guide: Physical Chemistry
Jochen Vogt
Exam Survival Guide:
Physical Chemistry
123
JochenVogt
ChemischesInstitut
derUniversitaRtMagdeburg
Magdeburg,Germany
ISBN978-3-319-49808-9 ISBN978-3-319-49810-2 (eBook)
DOI10.1007/978-3-319-49810-2
LibraryofCongressControlNumber:2017933473
©SpringerInternationalPublishingAG2017
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ForBirgit
Preface
Novel concepts in teaching stress the active role of the student in the acquisition
of competence. In this spirit, the Exam Survival Guide: Physical Chemistry was
developedas a supplementaloffer primarily to students, but also to teachers. The
bookpresentsmorethan80selectedproblems,sometypicalofphysicalchemistry
examinations;others,owingtotheirrelativecomplexity,suitableforseminarswith
the intention of reaching an in-depth understanding of the key topics in physical
chemistry. The solutions to the problems are presented in a more extensive way
compared with typical textbooks. Having worked out a solution independently,
the student is invited to follow the solution offered in the text. Alternatively, the
studentcanbenefitfroman solution,gaininsightinto solutionstrategies,methods
of calculus, and additional information that draws attention to some remarkable
points. The intention of the book is to encourage the reader to use paper, pencil,
andcomputertocultivateproblem-solvinginphysicalchemistry.
Eachchapterdealswithakeytopicandstartswith ashortsurveyofthetheory
necessarytosolvetheproblems.Thesebasicconceptsarenotintendedtoreplacethe
contentsoftried-and-testedtextbooks.Instead,theyserveasstartingpointsaround
which the topics of the exercises are developed. In addition, the book provides
an extensive appendix of the essential mathematics typical of physical chemistry
problems.
Afirstbrieflookthroughthechaptersshowsthattheemphasisofthisworkbook
isontheapplicationofmathematicalmethodsinphysicochemicalcontexts.Infact,
thereare hardlyanyquestionsthatcan simplybe answeredby “yes” or“no.”The
Chapter 1 deals with the aspects of this kind of quantitative problem-solvingand
provides a survey on the various topics, the level of difficulty, and hints on the
manifoldcross-linksamongcertainproblems.
Although I am aware of the varying curricula and examination formats, the
different approaches that students develop during their career, the lively diversity
amongstudents- hardworkers, sophisticatedthinkers, pragmatists,optimists, and
allthecombinationsinbetween-Ihopethisworkbookisuseful.
It is obvious that a book of this volume does not cover the entire field of
physical chemistry. To maintain a clear and compact form, I have omitted topics
vii
viii Preface
thatsomereadersperhapsfeelarelacking.Ifyouhaveanycomments,questions,or
suggestions,or if youwantto reporterrors,youarewelcometo contactme under
[email protected].
Magdeburg,Germany JochenVogt
September2016
Acknowledgements
I am grateful to Tobias Wassermann and the Springer Verlag for the production
and publication of this book. Furthermore, the design of the periodic system of
elementsintheappendixofthisbookisbasedonaLATEXtemplatemadeavailable
byChristophWölper.
Moreover, I am grateful to my sister Katrin Vogt, expert in the psychology of
learning, for reading and improving the chapter on problem-solving in physical
chemistry. This book would not have been possible without the motivation and
supportof my wife Birgit Vogt. As a physicist herself, she has helped to improve
thetextandthedesignoftheillustrations.Shehasaccompaniedthisprojectthrough
almostallstageswithpatienceandgoodspirit.
ix
Contents
1 QuantitativeProblemSolvinginPhysicalChemistry ................. 1
1.1 AConceptforProblem-SolvinginPhysicalChemistry............ 1
1.2 OverviewofProblems ............................................... 4
References.................................................................... 8
2 StoichiometryandChemicalReactions.................................. 9
2.1 BasicConcepts ....................................................... 9
2.1.1 ChemicalReactions........................................ 9
2.1.2 MolarMassandMolarVolume ........................... 11
2.2 Problems.............................................................. 12
Reference..................................................................... 16
3 ChangesofState............................................................ 17
3.1 Systems............................................................... 17
3.2 EquationofState,ThermalStateVariables......................... 18
3.2.1 Problems.................................................... 20
3.3 CaloricStateVariables,Entropy..................................... 29
3.3.1 InternalEnergy,Work,andEnthalpy ..................... 30
3.3.2 ReversibleandIrreversibleChangesofState,
theSecondLawandEntropy.............................. 32
3.3.3 AdiabaticChangesofStateofaPerfectGas ............. 33
3.3.4 TheThermodynamicPotentials........................... 34
3.3.5 Problems.................................................... 35
3.4 HeterogeneousSystemsandPhaseTransitions..................... 51
3.4.1 TheStandardState......................................... 53
3.4.2 RealandIdealMixtures ................................... 53
3.4.3 Problems.................................................... 54
References.................................................................... 69
4 Thermochemistry........................................................... 71
4.1 BasicConcepts ....................................................... 71
4.1.1 EnthalpiesofFormation................................... 71
xi
xii Contents
4.1.2 TheMolarReactionEnthalpyandtheMolar
ReactionEntropy........................................... 72
4.1.3 Kirchhoff’sLaw............................................ 73
4.1.4 Hess’sLaw ................................................. 73
4.2 Problems.............................................................. 74
5 ChemicalEquilibrium ..................................................... 83
5.1 BasicConcepts ....................................................... 83
5.1.1 TheLawofMassAction .................................. 85
5.1.2 TemperatureDependencyoftheEquilibrium
Constant.................................................... 86
5.1.3 ChemicalEquilibriuminDiluteSolutions................ 86
5.2 Problems.............................................................. 87
6 ChemicalKinetics .......................................................... 119
6.1 BasicConcepts ....................................................... 119
6.1.1 ReactionRate .............................................. 119
6.1.2 ReactionRateLaws........................................ 120
6.2 Problems.............................................................. 122
Reference..................................................................... 145
7 KineticTheory.............................................................. 147
7.1 BasicConcepts ....................................................... 147
7.1.1 Maxwell-BoltzmannVelocityDistribution............... 147
7.1.2 Pressure..................................................... 148
7.1.3 CollisionsBetweenParticles .............................. 149
7.1.4 CollisionswithSurfaces................................... 150
7.2 Problems.............................................................. 151
8 StatisticalThermodynamics............................................... 175
8.1 BasicConcepts ....................................................... 175
8.1.1 StatisticalInterpretationofEntropy....................... 175
8.1.2 BoltzmannDistribution.................................... 176
8.1.3 CanonicalEnsemble....................................... 176
8.2 MolecularDegreesofFreedomandPartitionFunctions........... 178
8.3 Problems.............................................................. 179
References.................................................................... 211
9 QuantumMechanicsandElectronicStructure ......................... 213
9.1 BasicConcepts ....................................................... 213
9.1.1 FailureofClassicalMechanics:KeyExperiments....... 214
9.1.2 WaveMechanics........................................... 216
9.1.3 AtomicStructure........................................... 219
9.1.4 AtomicUnits............................................... 220
9.2 Problems.............................................................. 221
References.................................................................... 292