IChO41th理论试题及答案.docx

IChO41th理论试题及答案.docx

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IChO41th理论试题及答案

ProblemAuthors

StephenAshworthUniversityofEastAnglia

JonathanBurtonUniversityofOxford

JonDilworthUniversityofOxford

NicholasGreenUniversityofOxford

PhilipMountfordUniversityofOxford

WilliamNolanUniversityofCambridge

JeremyRawsonUniversityofCambridge

KathrynScottUniversityofOxford

MalcolmSeddonUniversityofEastAnglia

SimonTitmussUniversityofOxford

ClaireVallanceUniversityofOxford

PeterWothersUniversityofCambridge

FieldsofAdvancedDifficulty

Theoretical

Kinetics:

integratedfirst-orderrateequation;analysisofmoderatelycomplexreactionsmechanismsusingthesteadystateapproximation,theuseoftheArrheniusequation,simplecollisiontheory

Thermodynamics:

electrochemicalcells,therelationshipbetweenequilibriumconstants,electromotiveforceandstandardGibbsenergy,thevariationoftheequilibriumconstantwithtemperature

Quantummechanics:

calculationoforbitalandspinangularmomentum,calculationofthemagneticmomentusingthespin-onlyformula

Spectroscopy:

interpretationofrelativelysimple13Cand1HNMRspectra;chemicalshifts,multiplicities,couplingconstantsandintegrals

Massspectrometry:

molecularionsandbasicfragmentation

Theoreticalproblems

Problem1Datingmoonrock

TheageofrockscollectedfromthemoonontheApollo16missionhasbeendeterminedfromthe87Rb/86Srand87Sr/86Srratiosofdifferentmineralsfoundinthesample.

Mineral

87Rb/86Sr

87Sr/86Sr

A（Plagioclase）

0.004

0.699

B（Quintessence）

0.180

0.709

a）87Rbisa–emitter,writedowntheequationofnucleardecay.Thehalf-lifeforthisdecayis4.8×1010years.

b）Calculatetheageoftherock.Youcanassumethattheinitial87Sr/86SristhesameinAandBandthat87Srand86Srarestable.

Problem2Snorkelling

Thepressureofagasmaybethoughtofastheforcethegasexertsperunitareaonthewallsofitscontainer,oronanimaginarysurfaceofunitareaplacedsomewherewithinthegas.Theforcearisesfromcollisionsbetweentheparticlesinthegasandthesurface.Inanidealgas,thecollisionfrequency（numberofcollisionspersecond）withasurfaceofunitareaisgivenby:

WherepisthepressureandTthetemperatureofthegas,misthemassofthegasparticles,andkBistheBoltzmann’sconstant（kB=1.38×10–23JK–1）.

Atsealevel,atmosphericpressureisgenerallyaround101.3kPa,andtheaveragetemperatureonatypicalBritishsummerdayis15°C.

a）Usingtheapproximationthatairconsistsof79%nitrogenand21%oxygen,calculatetheweightedaverage massofamoleculeintheair.

b）Humanlungshaveasurfaceareaofapproximately75m2.Anaveragehumanbreathtakesaround5seconds.EstimatethenumberofcollisionswiththesurfaceofthelungsduringasinglebreathonatypicalBritishsummerday.Youshouldassumethatthepressureinthelungsremainsconstantatatmosphericpressure;thisisareasonableapproximation,asthepressureinthelungschangesbylessthan1%duringeachrespiratorycycle.

Thehumanlungscanoperateagainstapressuredifferentialofuptoonetwentiethofatmosphericpressure.Ifadiverusesasnorkelforbreathing,wecanusethisfacttodeterminehowfarbelowwaterthesurfaceofthewatershecanswim.

Thepressureexperiencedbythediveradistancedbelowthesurfaceofthewaterisdeterminedbytheforceperunitareaexertedbythemassofwateraboveher.TheforceexertedbygravityonamassmisF=mg,whereg=9.8ms–2istheaccelerationduetogravity.

c）WritedownanexpressionforthemassofavolumeofwaterwithcrosssectionalareaAanddepthd.

d）Deriveanexpressionfortheforceexertedonthediverbythevolumeofwaterin（c）,andhenceanexpressionforthedifferenceinpressuresheexperiencesatdepthdrelativetothepressureatthewater’ssurface.

e）Calculatethemaximumdepththedivercanswimbelowthewatersurface,whilestillbreathingsuccessfullythroughasnorkel.

Problem3Idealandnot-so-idealgases

Theforceagasexertsonthewallsofitscontainerarisesfromcollisionsbetweentheparticlesinthegasandthesurface.Inasinglecollision,themagnitudeoftheimpulsiveoftheforceexertedonthesurfaceisequaltothechangeinthemomentumnormaltothesurface,m∆v.Theforceonthesurfaceisthentheimpulse,multipliedbytherateatwhichtheparticlescollidewiththesurface.

Sincethemotionofparticleswithinagasisrandom,thenumberofcollisionsoccurringperunittimeisaconstantforagasatconstanttemperature.

Thetemperatureofagasreflectsthedistributionofparticlevelocitieswithinthegas.Foragivengas,theparticlespeedswillbehigher,onaverage,athighertemperatures.

a）Giventheaboveinformation,andassumingthegasisinitiallyatroomtemperatureandatmosphericpressure,considerhowcarryingoutthefollowingactionswouldbelikelytoaffectthepressure.Wouldthepressuredouble,halve,increaseslightly,decreaseslightly,orremainunchanged?

i）Doublingthenumberofparticlesinthegas.

ii）Doublingthevolumeofthecontainerinwhichthegasisconfined.

iii）Doublingthemassoftheparticlesinthegas（assumethattheparticlevelocitiesremainconstant）.

iv）Increasingthetemperatureby10°C.

Theidealgasmodelassumesthattherearenointeractionsbetweengasparticles.Particlesinarealgasdointeractthrougharangeofforcessuchasdipole–dipoleforces,dipole–induced–dipoleforces,andvanderWaalsinteractions（induced–dipole–induced–dipoleforces）.Atypicalcurveshowingthepotentialenergyofinteractionbetweentwoparticlesisshownright:

Theforcebetweentwoparticlesinagasatagivenseparationrmaybecalculatedfromthegradientofthepotentialenergycurvei.e.F=–dV/dr.

b）WhatistheforceatthefourpointsmarkedA,B,CandDonthefigure?

（attractive/repulsive/approximatelyzero）

Thedeviationfromnon-idealityinagasisoftenquantifiedintermsofthecompressionratio,Z.

where

isthemolarvolumeofthe（real）gas,and

isthemolarvolumeofanidealgasunderthesameconditionsoftemperature,pressureetc.

c）MatchthefollowingvaluesofZwiththedominanttypeofinteractioninthegas.

[Z=1][Z<1][Z>1]

Attractiveforcesdominate

Repulsiveforcesdominate

Nointermolecularforces,idealgasbehaviour

d）Thecompressionratioispressuredependent.Considertheaverageseparationbetweenparticlesinagasatdifferentpressures（rangingfromextremelylowpressuretoextremelyhighpressure）,andtheregionsoftheintermolecularpotentialthattheseseparationscorrespondto.Sketchthewayinwhichyouthinkthecompressionratiowillvarywithpressureonthesetofaxesbelow.[Note:

donotworryabouttheactualnumericalvaluesofZ;thegeneralshapeofthepressuredependencecurveisallthatisrequired.]

Problem4

Coalgasification

Intheprocessofcoalgasificationcoalisconvertedintoacombustiblemixtureofcarbonmonoxideandhydrogen,calledcoalgas

H2O（g）+C（s）CO（g）+H2（g）

a）Calculatethestandardenthalpychangeforthisreactionfromthefollowingchemicalequationsandstandardenthalpychanges

2C（s）+O2（g）2CO（g）∆rH=–221.0kJmol–1

2H2（g）+O2（g）2H2O（g）∆rH=–483.6kJmol–1

Thecoalgascanbeusedasafuel:

CO（g）+H2（g）+O2（g）CO2（g）+H2O（g）

b）Giventheadditionalinformation,calculatetheenthalpychangeforthiscombustion

C（s）+O2（g）CO2（g）∆rH=–393.5kJmol–1

Coalgascanalsoundergotheprocessofmethanation.

3H2（g）+CO（g）CH4（g）+H2O（g）

c）Determinethestandardenthalpychangeforthemethanationreactionusingtheadditionaldata.

CH4（g）+2O2（g）CO2（g）+2H2O（g）∆rH=–802.7kJmol–1

Problem5Theindustrialpreparationofhydrogen

Hydrogengasmaybepreparedindustriallybyheatinghydrocarbons,suchasamethane,withsteam:

CH4（g）+H2O（g）

3H2（g）+CO（g）A

a）Giventhefollowingthermodynamicdata,calculatethe∆rGforreactionAat298Kandhenceavaluefortheequilibriumconstant,Kp.

∆fH（298）/kJmol–1

S（298）/JK–1mol–1

CH4（g）

–74.4

186.3

H2O（g）

–241.8

188.8

H2（g）

130.7

CO（g）

–110.5

197.7

b）Howwilltheequilibriumconstantvarywithtemperature?

Theindustrialpreparationcanbecarriedoutatatmosphericpressureandhightemperature,withoutacatalyst.Typically,0.2vol%ofmethanegasremainsinthemixtureatequilibrium.

c）Assumingthereactionstartedwithequalvolumesofmethaneandsteam,calculatethevalueofKpfortheindustrialprocesswhichgives0.2vol%methaneatequilibrium.

d）Useyouranswerfrom（c）togetherwiththeintegratedformofthevan’tHoffisochoretoestimatethetemperatureusedinindustryforthepreparationofhydrogenfrommethane.

Problem6Thebondsindibenzyl

Thisquestionisatypicalapplicationofthermodynamiccyclestoestimateabonddissociationenthalpy.

Thefirststepinthepyrolysisoftoluene（methylbenzene）isthebreakingoftheC6H5CH2–Hbond.Theactivationenthalpyforthisprocess,whichisessentiallythebonddissociationenthalpy,isfoundtobe378.4kJmol–1.

a）Writeabalancedequationforthecompletecombustionoftoluene.

Standardenthalpiesaregivenbelow,usingtherecommendedIUPACnotation（i.e.f=formation,c=combustion,vap=vaporisation,at=atomisation）

∆fH（CO2,g,298K）=–393.5kJmol–1

∆fH（H2O,l,298K）=–285.8kJmol–1

∆cH（C7H8,l,298K）=–3910.2kJmol–1

∆vapH（C7H8,l,298K）=+38.0kJmol–1

∆atH（H2,g,298K）=+436.0kJmol–1.

i）Calculate∆fH（C7H8,l,298K）

ii）Estimate∆fHforthebenzylradicalC6H5CH2·（g）at298K.

b）Thestandardentropyofvapori