第38届ICHO理论试题及答案.docx

第38届ICHO理论试题及答案.docx

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第38届ICHO理论试题及答案

ChemistryforLife,

ChemistryforbetterLife

TheoreticalTest

GeneralDirections

-Writeyournameandcodenumberoneachpageoftheanswersheet.

-Youhave5hourstofinishthetask.FailuretostopaftertheSTOPcommandmayresultinzeropointsforthetask.

-Writeanswersandcalculationswithinthedesignatedbox.

-Useonlythepenandthecalculatorprovided.

-Thereare23pagesofProblemsand19pagesofAnswerSheet.

-AnEnglish-languageversionisavailable.

-Youmaygototherestroomwithpermission.

-Afterfinishingtheexamination,placeallsheetsincludingProblemsandAnswerSheetintheenvelopeandseal.

-Remainseateduntilinstructedtoleavetheroom.

Constantsandusefulformulas

GasconstantR=8.314JK-1mol-1

FaradayconstantF=96485Cmol-1

Useasstandardpressure:

p=1.013∙105Pa

Useasstandardtemperature:

T=25°C=298.15K

Avogadro’snumberNA=6.022∙1023mol-1

Planckconstanth=6.626∙10-34Js

Speedoflightc=3.00∙108ms-1

G=H-TSG=-nFE

G0=-RT∙lnKG=G0+RT∙lnQwithQ=

H（T1）=H0+（T1-298.15K）∙Cp（Cp=constant）

Arrheniusequationk=A∙

IdealgaslawpV=nRT

NernstequationE=E0+

Beer-LambertLawA=log

=∙c∙d

V（cylinder）=r2h

A（sphere）=4r2

V（sphere）=

r3

1J=1Nm1N=1kgms-21Pa=1Nm-2

1W=1AV=1Js-11C=1As

1.Avogadro'snumber（5pts）

Sphericalwaterdropletsaredispersedinargongas.At27oC,eachdropletis1.0micrometerindiameterandundergoescollisionswithargon.Assumethatinter-dropletcollisionsdonotoccur.Theroot-mean-squarespeedofthesedropletswasdeterminedtobe0.50cm/sat27oC.Thedensityofawaterdropletis1.0g/cm3.

1-1.Calculatetheaveragekineticenergy（mv2/2）ofthisdropletat27oC.Thevolumeofasphereisgivenby（4/3）πr3whereristheradius.

Ifthetemperatureischanged,thendropletsizeandspeedofthedropletwillalsochange.Theaveragekineticenergyofadropletbetween0oCand100oCasafunctionoftemperatureisfoundtobelinear.Assumethatitremainslinearbelow0oC.

Atthermalequlibrium,theaveragekineticenergyisthesameirrespectiveofparticlemasses（equipartitiontheorem）.

Thespecificheatcapacity,atconstantvolume,ofargon（atomicweight,40）gasis0.31Jg-1K-1.

1-2.CalculateAvogadro'snumberwithoutusingtheidealgaslaw,thegasconstant,Boltzmann’sconstant）.

2.DetectionofHydrogen（5pts）

Hydrogenisprevalentintheuniverse.Lifeintheuniverseisultimatelybasedonhydrogen.

2-1.Thereareabout1023starsintheuniverse.Assumethattheyarelikeoursun（radius,700,000km;density,1.4g/cm3;3/4hydrogenand1/4heliumbymass）.Estimatethenumberofstellarprotonsintheuniversetoonesignificantfigure.

Inthe1920s,CeciliaPaynediscovered,byspectralanalysisofstarlight,thathydrogenisthemostabundantelementinmoststars.

2-2.Theelectronicenergyofahydrogenatomisgivenby-C/n2relativetozeroenergyatinfiniteseparationbetweentheelectronandtheproton（nistheprinciplequantumnumber,andCisaconstant）.Fordetectionofthen=2→n=3transition（656.3nmintheBalmerseries）,theelectroninthegroundstateofthehydrogenatomneedstobeexcitedfirsttothen=2state.Calculatethewavelength（innm）oftheabsorptionlineinthestarlightcorrespondingtothen=1→n=2transition. 

2-3.AccordingtoWien'slaw,thewavelength（λ）correspondingtothemaximumlightintensityemittedfromablackbodyattemperatureTisgivenbyλT=2.9×10-3mK.Calculatethesurfacetemperatureofastarwhoseblackbodyradiationhasapeakintensitycorrespondingtothen=1→n=2excitationofhydrogen.

Thegroundstateofhydrogenissplitintotwohyperfinelevelsduetotheinteractionbetweenthemagneticmomentoftheprotonandthatoftheelectron.In1951,Purcelldiscoveredaspectrallineat1420MHzduetothehyperfinetransitionofhydrogenininterstellarspace.

2-4.Hydrogenininterstellarspacecannotbeexcitedelectronicallybystarlight.However,thecosmicbackgroundradiation,equivalentto2.7K,cancausethehyperfinetransition.Calculatethetemperatureofablackbodywhosepeakintensitycorrespondstothe1420MHztransition.

2-5.Wiengeneratedhydrogenionsbydischargeofhydrogengasataverylowpressureanddeterminedthee/m（charge/mass）value,whichturnedouttobethehighestamongdifferentgasestested.In1919,Rutherfordbombardednitrogenwithalpha-particlesandobservedemissionofapositivelychargedparticlewhichturnedouttobethehydrogenionobservedbyWien.Rutherfordnamedthisparticlethe“proton”.Fillintheblankintheanswersheet.

14N+4He→（）+1H

3.InterstellarChemistry（5pts）

EarlyinterstellarchemistryisthoughttohavebeenapreludetolifeonEarth.Moleculescanbeformedinspaceviaheterogeneousreactionsatthesurfaceofdustparticles,oftencalledtheinterstellaricegrains（IIGs）.ImaginethereactionbetweenHandCatomsontheIIGsurfacethatformsCH.TheCHproductcaneitherdesorbfromthesurfaceorfurtherreact,throughsurfacemigration,withadsorbedHatomstoformCH2,CH3,etc.

Dependingonhowenergeticallyamolecule“jumps”fromitsanchoredsite,iteitherleavesthesurfacepermanently（desorption）orreturnstoanewpositionatthesurface（migration）.TheratesofdesorptionandmigratoryjumpfollowtheArrheniusformula,k=Aexp（-E/RT）,wherekistherateconstantfordesorptionormigratoryjump,Athejumpingfrequency,andEtheactivationenergyfortherespectiveevent.

3-1.DesorptionofCHfromtheIIGsurfacefollowsfirst-orderkinetics.CalculatetheaverageresidencetimeofCHonthesurfaceat20K.AssumethatA=1x1012s-1andEdes=12kJmol-1.

3-2.ConsidertheshortesttimeitwouldtakeforoneCHunittomovefromitsinitialpositiontotheoppositesideofanIIGbysuccessivemigratoryjumps.Assumethattheactivationenergyformigration（Emig）is6kJmol-1,andtheIIGisaspherewitha0.1μmradius.Eachmigratoryjumplaterallyadvancesthemoleculeby0.3nm.Showworkandchooseyouranswerfrom（a）-（e）below.

（a）t≤1day（b）10day≤t≤102yr（c）103yr≤t≤106yr

（d）107yr≤t≤1010yr（e）t≥1011yr

3-3.ConsiderthereactionofCOwithH2toformH2CO.Theactivationenergyonametalcatalystis20kJmol-1,whichproducesformaldehydeatarateof1molecule/spersiteat300K.Esitmatetherateofformaldehydeformationpersiteifthereactiontakesplaceat20K.

3-4.Whichisasetofalltruestatements?

Circleone.

（a）MostCHspeciesdesorbfromtheIIGsurfacebeforeencounteringotherreactantsbysurfacemigration.

（b）IIGscanassisttransformationofsimplemoleculestomorecomplexonesininterstellarspace.

（c）ForareactionontheIIGtooccuratanappreciablespeedduringtheageoftheUniverse（1x1010yr）,thereactionenergybarriermustbeabsentornegligible.

（a）（b）（c）（a,b）（a,c）（b,c）（a,b,c）

4.TheChemistryofDNA（5pts）

4-1.In1944OswaldAveryisolatedageneticmaterialandshowed,byelementalanalysis,thatitwasasodiumsaltofdeoxyribonucleicacid.AsegmentofDNAwithformulamassof1323.72isshown.

AssumingthatequimolaramountsofthefourbasesarepresentinDNA,writethenumberofHatomsperPatom.Calculate,to3significantfigures,thetheoreticalweightpercentageofHexpecteduponelementalanalysisofDNA.

4-2.ChargaffextractedtheseparatedbasesanddeterminedtheirconcentrationsbymeasuringUVabsorbance.TheBeer-Lambertlawwasusedtoobtainthemolarconcentration.ChargaffdiscoveredthefollowingmolarratioforbasesinDNA:

       adeninetoguanine=1.43        thyminetocytosine=1.43

       adeninetothymine=1.02        guaninetocytosine=1.02

Chargaff’sdiscoverysuggestedthatthebasesmightexistaspairsinDNA.WatsonandCrickmentionedintheircelebrated1953paperinNature:

"Ithasnotescapedournoticethatthespecificpairingwehavepostulatedimmediatelysuggestsapossiblecopyingmechanismforthegeneticmaterial."

DrawstructuresofthespecificpairingfoundinDNA.Indicatehydrogenbonds.Omitthesugar-phosphatebackbone.

4-3.Mutationcanoccurthroughbasepairingsdifferentfromtheabove.Drawstructuresofanythreealternativebasepairs.

4-4.TheplausibilityoftheformationofpurineandpyrimidinebasesintheprebioticatmosphereoftheEarthfromHCN,NH3,andH2Ohasbeendemonstratedinthelaboratory.WritetheminimumnumberofHCNandH2Omoleculesrequiredforformationofthefollowingcompounds.

5.Acid-BaseChemistry（5pts）

5-1.Calculate[H+],[OH-],[HSO4-],and[SO42-]ina1.0x10-7Msolutionofsulfuricacid（Kw=1.0x10-14,K2=1.2x10-2at25oC）.Inyourworkyoumayusemass-andcharge-balanceequations.Answerwithtwosignificantfigures.

5-2.Calculatethevolumeof0.80MNaOHsolutionthatshouldbeaddedtoa250mLaqueoussolutioncontaining3.48mLofconcentratedphosphoricacidinordertoprepareapH7.4buffer.Answerwiththreesignificantfigures.（H3PO4（aq）,purity=85%wt/wt,density=1.69g/mL,FW=98.00）（pK1=2.15,pK2=7.20,pK3=12.44）.

5-3.Theefficacyofadrugisgreatlydependentonitsabilitytobeabsorbedintothebloodstream.Acid-basechemistryplaysanimportantroleindrugabsorption.

Assumethattheionicform（A-）ofaweaklyacidicdrugdoesnotpenetratethemembrane,whereastheneutralform（HA）freelycrossesthemembrane.AlsoassumethatequilibriumisestablishedsothattheconcentrationofHAisthesameonbothsides.Calculatetheratioofthetotalconcentration（[HA]+[A-]）