Solutions manual to accompany Atkins physical Chemistry-11th-ed

675 Pages·2018·3.82 MB·English

Instructor Solutions
Manual to
Accompany Atkins’
Physical Chemistry
ELEVENTHEDITION
Peter Bolgar
Haydn Lloyd
Aimee North
Vladimiras Oleinikovas
Stephanie Smith
and
James Keeler
DepartmentofChemistry
UniversityofCambridge
UK
OUPlegalpage
Table of contents
Preface vii
1 Thepropertiesofgases 1
1A Theperfectgas 1
1B Thekineticmodel 10
1C Realgases 19
2 Internalenergy 35
2A Internalenergy 35
2B Enthalpy 40
2C Thermochemistry 43
2D Statefunctionsandexactdifferentials 49
2E Adiabaticchanges 55
3 Thesecondandthirdlaws 63
3A Entropy 63
3B Entropychangesaccompanyingspecificprocesses 68
3C Themeasurementofentropy 80
3D Concentratingonthesystem 87
3E CombiningtheFirstandSecondLaws 92
4 Physicaltransformationsofpuresubstances 99
4A Phasediagramsofpuresubstances 99
4B Thermodynamicaspectsofphasetransitions 101
5 Simplemixtures 115
5A Thethermodynamicdescriptionofmixtures 115
5B Thepropertiesofsolutions 126
5C Phasediagramsofbinarysystems:liquids 141
5D Phasediagramsofbinarysystems:solids 148
5E Phasediagramsofternarysystems 154
5F Activities 158
6 Chemicalequilibrium 171
6A Theequilibriumconstant 171
iv TABLEOFCONTENTS
6B Theresponseofequilibriatotheconditions 179
6C Electrochemicalcells 190
6D Electrodepotentials 197
7 Quantumtheory 215
7A Theoriginsofquantummechanics 215
7B Wavefunctions 223
7C Operatorsandobservables 227
7D Translationalmotion 236
7E Vibrationalmotion 248
7F Rotationalmotion 257
8 Atomicstructureandspectra 271
8A HydrogenicAtoms 271
8B Many-electronatoms 277
8C Atomicspectra 279
9 MolecularStructure 287
9A Valence-bondtheory 287
9B Molecularorbitaltheory:thehydrogenmolecule-ion 292
9C Molecularorbitaltheory:homonucleardiatomicmolecules 298
9D Molecularorbitaltheory:heteronucleardiatomicmolecules 302
9E Molecularorbitaltheory:polyatomicmolecules 307
10 Molecularsymmetry 321
10A Shapeandsymmetry 321
10B Grouptheory 329
10C Applicationsofsymmetry 337
11 MolecularSpectroscopy 349
11A Generalfeaturesofmolecularspectroscopy 349
11B Rotationalspectroscopy 357
11C Vibrationalspectroscopyofdiatomicmolecules 371
11D Vibrationalspectroscopyofpolyatomicmolecules 384
11E Symmetryanalysisofvibrationalspectroscopy 385
11F Electronicspectra 388
11G Decayofexcitedstates 398
TABLEOFCONTENTS v
12 Magneticresonance 409
12A Generalprinciples 409
12B FeaturesofNMRspectra 412
12C PulsetechniquesinNMR 421
12D Electronparamagneticresonance 429
13 Statisticalthermodynamics 435
13A TheBoltzmanndistribution 435
13B Partitionfunctions 439
13C Molecularenergies 449
13D Thecanonicalensemble 456
13E Theinternalenergyandentropy 457
13F Derivedfunctions 473
14 MolecularInteractions 485
14A Electricpropertiesofmolecules 485
14B Interactionsbetweenmolecules 496
14C Liquids 504
14D Macromolecules 506
14E Self-assembly 517
15 Solids 523
15A Crystalstructure 523
15B Diffractiontechniques 526
15C Bondinginsolids 534
15D Themechanicalpropertiesofsolids 539
15E Theelectricalpropertiesofsolids 541
15F Themagneticpropertiesofsolids 543
15G Theopticalpropertiesofsolids 546
16 Moleculesinmotion 551
16A Transportpropertiesofaperfectgas 551
16B Motioninliquids 558
16C Diffusion 563
17 Chemicalkinetics 573
17A Theratesofchemicalreactions 573
vi TABLEOFCONTENTS
17B Integratedratelaws 579
17C Reactionsapproachingequilibrium 593
17D TheArrheniusequation 597
17E Reactionmechanisms 601
17F Examplesofreactionmechanisms 607
17G Photochemistry 614
18 Reactiondynamics 621
18A Collisiontheory 621
18B Diffusion-controlledreactions 626
18C Transition-statetheory 629
18D Thedynamicsofmolecularcollisions 639
18E Electrontransferinhomogeneoussystems 640
19 Processesatsolidsurfaces 647
19A Anintroductiontosolidsurfaces 647
19B Adsorptionanddesorption 650
19C Heterogeneouscatalysis 660
19D Processesatelectrodes 662
Preface
Thismanualprovidesdetailedsolutionstothe(b)Exercisesandtheeven-numberedDiscus-
sionquestionsandProblemsfromthe11theditionofAtkins’PhysicalChemistry.
Conventionsusedispresentingthesolutions
Wehaveincludedpage-specificreferencestoequations,sections,figuresandotherfeatures
ofthemaintext.Equationreferencesaredenoted[14B.3b–595],meaningeqn14B.3blocated
onpage595(thepagenumberisgiveninitalics). Otherfeaturesarereferredtobyname,
withapagenumberalsogiven.
Generallyspeaking,thevaluesofphysicalconstants(fromthefirstpageofthemaintext)
are used to 5 significant figures except in a few cases where higher precision is required.
In line with the practice in the main text, intermediate results are simply truncated (not
rounded)tothreefigures,withsuchtruncationindicatedbyanellipsis,asin0.123...; the
valueisusedinsubsequentcalculationstoitsfullprecision.
Thefinalresultsofcalculations,generallytobefoundin abox,aregiventotheprecision
warrantedbythedataprovided.Wehavebeenrigorousinincludingunitsforallquantities
so that the units of the final result can be tracked carefully. The relationships given on
thebackofthefrontcoverareusefulinresolvingtheunitsofmorecomplexexpressions,
especiallywhereelectricalquantitiesareinvolved.
Someoftheproblemseitherrequiretheuseofmathematicalsoftwareoraremucheasier
withtheaidofsuchatool. InsuchcaseswehaveusedMathematica(WolframResearch,
Inc.) inpreparingthesesolutions,buttherearenodoubtotheroptionsavailable. Someof
theDiscussionquestionsrelatedirectlytospecificsectionofthemaintextinwhichcasewe
havesimplygivenareferenceratherthanrepeatingthematerialfromthetext.
Acknowledgements
Inpreparingthismanualwehavedrawnontheequivalentvolumepreparedforthe10thedi-
tionofAtkins’PhysicalChemistrybyCharlesTrapp,MarshallCady,andCarmenGiunta.In
particular,thesolutionswhichusequantumchemicalcalculationsormolecularmodelling
software,andsomeofthesolutionstotheDiscussionquestions,havebeenquoteddirectly
from the solutions manual for the 10th edition, without significant modification. More
generally,wehavebenefitedfromtheabilitytorefertotheearliervolumeandacknowledge,
withthanks,theinfluencethatitsauthorshavehadonthepresentwork.
This manual has been prepared by the authors using the LATEX typesetting system, in
theimplementationprovidedbyMiKTEX(miktex.org); thevastmajorityofthefigures
andgraphshavebeengeneratedusingPGFPlots. Wearegratefultothecommunitywho
maintainanddeveloptheseoutstandingresources.
Finally, we are grateful to the editorial team at OUP, Jonathan Crowe and Roseanna
Levermore,fortheirinvaluablesupportinbringingthisprojecttoaconclusion.
viii PREFACE
Errorsandomissions
Insuchacomplexundertakingsomeerrorswillnodoubthavecreptin,despitetheauthors’
bestefforts.Readerswhoidentifyanyerrorsoromissionsareinvitedtopassthemontous
[email protected].
1
The properties of gases
1A Theperfectgas
Answerstodiscussionquestions
D1A.2 ThepartialpressureofgasJ,pJ,inamixtureofgasesisgivenby[1A.6–9],pJ =
xJp,wherepisthetotalpressureandxJisthemolefractionofJ.
Ifthegasesareperfect,thepartialpressureisalsothepressurethegaswould
exertifitoccupiedonitsownthesamecontainerasthemixtureatthesame
temperature.ThisleadstoDalton’slaw,whichisthatthepressureofamixture
ofgasesisthesumofthepressuresthateachonewouldexertifitoccupiedthe
containeralone.
Dalton’slawisalimitinglawbecauseitholdsexactlyonlyinthelimitthatthere
arenointeractionsbetweenthemolecules,whichforrealgaseswillbeinthe
limitofzeropressure.
Solutionstoexercises
E1A.1(b) Frominsidethefrontcovertheconversionbetweenpressureunitsis: 1atm≡
101.325kPa≡760Torr.
(i) Apressureof22.5kPaisconvertedtoatmasfollows
1atm
22.5kPa× = 0.222atm
101.325kPa
(ii) Apressureof770TorrisconvertedtoPaasfollows
1atm 101.325kPa
770Torr× × =103kPa= 1.03×105Pa
760Torr 1atm
E1A.2(b) The perfect gas law [1A.4–8], pV = nRT, is rearranged to give the pressure,
p=nRT/V.Theamountnisfoundbydividingthemassbythemolarmassof
Ar,39.95gmol−1.
n
‡„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„•„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„(cid:181)
(25g) (8.3145×10−2dm3barK−1mol−1)×(303.15K)
p=
(39.95gmol−1) 1.5dm3
=10.4bar
So no,thesamplewouldnotexertapressureof2.0bar,but 10.4bar ifitwere
aperfectgas.
2 1THEPROPERTIESOFGASES
E1A.3(b) Because the temperature is constant (isothermal) Boyle’s law applies, pV =
const.ThereforetheproductpV isthesamefortheinitialandfinalstates
pfVf = piVi hence pi = pfVf/Vi
Theinitialvolumeis1.80dm3greaterthanthefinalvolumesoVi =2.14+1.80=
3.94dm3.
pi = VVfi ×pf = 23..1944ddmm33 ×(1.97bar)=1.07bar
(i) Theininitialpressureis 1.07bar
(ii) Because1atmisequivalentto1.01325barandalsoto760Torr,theinitial
pressureexpressedinTorris
1atm 760Torr
× ×1.07bar= 803Torr
1.01325bar 1atm
E1A.4(b) Ifthegasisassumedtobeperfect,theequationofstateis[1A.4–8],pV =nRT.
In this case the volume and amount (in moles) of the gas are constant, so it
followsthatthepressureisproportionaltothetemperature:p∝T.Theratioof
thefinalandinitialpressuresisthereforeequaltotheratioofthetemperatures:
pf/pi = Tf/Ti. Solving for the final pressure pf (remember to use absolute
temperatures)gives
pf = Tf ×pi
Ti
(11+273.15)K
= ×(125kPa)= 120kPa
(23+273.15)K
E1A.5(b) TheperfectgaslawpV =nRTisrearrangedtogiven= pV/RT.
pV
n=
RT
(1.00×1.01325×105Pa)×(4.00×103m3)
= = 1.66...×105mol
(8.3145JK−1mol−1)×([20+273.15]K)
where1J=1kgm2s−2and1Pa=1kgm−1s−2havebeenused.
ThemolarmassofCH is12.01+4×1.0079=16.0416gmol−1,sothemassof
4
CH is(1.66...×105mol)×(16.0416gmol−1)=2.67×106gor 2.67×103kg.
4
E1A.6(b) Thevapourisassumedtobeaperfectgas,sothegaslawpV =nRTapplies.The
taskistousethisexpressiontorelatethemeasuredmassdensitytothemolar
mass.
First,theamountnisexpressedasthemassmdividedbythemolarmassMto
give pV = (m/M)RT;divisionofbothsidesbyV gives p = (m/V)(RT/M).