CH3514 Physical Inorganic Chemistry 1 - Zysman-Colman - Physical Inorganic... · CH3514 –...

CH3514–PhysicalInorganicChemistry

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CH3514–PhysicalChemistryandBondingofTransitionMetals

EliZysman-Colman(ezc)


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1.INTRODUCTION:CoordinationChemistryofComplexesThismodulefollowsfromthetransitionmetalschemistrymoduleofCH2501.Here,therewillbeafocusonunderstandingthethermodynamicsandkineticsofreactionsinvolvingmetalaquacomplexes.Inparticular,conceptsrelatingtostepwiseandglobalequilibriumconstantsandtheirrelationshiptothefreeenergyofformationwillbediscussed.Thechelateeffectwillbeexploredasitpertainstothethermodynamicstabilityofthecomplexes.Kineticlabilityanditslinktothermodynamicstabilitywillalsobeinvestigated.Finally,therewillbeamoredetailedexplorationofbothmolecularorbitaltheoryandligandfieldtheory.

2.MOTheoryBeforewecanunderstandMOdiagramsandbondingincomplexes,wemustunderstandthenatureofthefrontierMOsofligands.Therearethreetypesoforbitalinteractionsbetweenligandsandmetals,whichdefinetheligandtype:

• s-donors• p-donors• p-acceptors

2.1MOTheory:s-DonorLigandsTheseligandsdonatetwoe–sfromanorbitalofσ-symmetry.Examplesinclude:H-,CH3

-,NR3,PR3,OH2.

2.1.1MOTheory:s-DonorLigands:NH3Let’slookmorecloselyattheMOdiagramofNH3asaprototypics-donor.ThismoleculeisC3-symmetric.Thesymmetryadaptedlinearcombinations(SALCs)ofatomicorbitalsareshownbelow.

HOMO LUMO

[Ru(bpy)3]2+


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Recallthatonlyorbitalsofthesamesymmetrycancombinetoformnewmolecularorbitals(MOs),inwhatisalsotermedlinearcombinationsofatomicorbitals(LCAOs).Sotheallin-phaseSALCofa1symmetrycanformtwocombinations,onewiththeN2pzandonewiththeN2sorbitals.EachofthetwoSALCsofesymmetry(bothcontainingonenodeandsohigherinenergythantheSALCofa1symmetry)cancombinewithoneoftheothertwoN2porbitals,asshownbelow.Noticethatineachcase,thephasingoftheorbitalsaligns(lightwithlightanddarkwithdark).

Withthesecombinationsinhand,wenextneedtoconstructtheMOdiagram.Rememberthat:

• Thegreatertheoverlap,thegreaterthesplitting• Thecloserinenergybetweenthetwosetsoforbitals,thegreaterthesplitting

RecallalsothattheHOMOisusedforbondingtothemetalanditisinthiscaserelatedtothelonepaironNinas-orbital.TheMOdiagrampredictsoccupiedMOsofthreedifferentenergies,whichisborneoutexperimentallybyphotoemissionspectra(PES).

Nonodes 1node

3H’s

N

a1 e


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2.1.2MOTheory:s-DonorLigands:OH2Howdoweanalysewater?RecallthatwesawthisMOdiagraminCH2501.TheHOMOinwater(b2)isoneofthetwonon-bondinglonepairsonoxygenanditcanbindtometals.TheMOdiagrampredictsoccupiedMOsoffourdifferentenergies,whichisalsoborneoutinthePES(shownabove).TheMOdiagramisshownbelowleftwhilebelowrightonecanseetheSALCsofthetwohydrogenatomsinteractingwiththecentralO2sandO2porbitals.

2.2MOTheory:p-DonorLigands

H O H

H O H

H O H

H O H


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Inadditiontodonatingelectrondensitytoametalviaaσ-bond,e–smaybeprovidedtothemetalviaaπ-symmetryinteraction.

π-donorligandsincludeX–(halide),amide(NR2–),sulfide(S2–),oxide(O2–),alkoxide(RO–),h3-C3H5,h5-C5H5,h6-C6H6.Noticethatinsomecasesthereisalonepairinap-orbitalthatisorthogonaltoafirstlonepairdonatingtothemetalwiths-symmetrywhileinothercases,thereisap-systemcomposedofdoublebondsthatcandonateelectrondensity.2.2.1MOTheory:p-DonorLigands:NH2

-Let’slookatNH2

-,whichwecanthinkofas“planar”NH3withalonepairreplacingoneoftheHatoms.Thissecondlonepairislocatedinap-orbital,orientedperpendiculartothefirstlonepair,whichisinansp2-hybridorbital.Below,leftisaWalshdiagram,whichshowshowtheMOdiagramismodulatedbyconvertingthetrigonalNH3toanallplanarNH3molecule.OnecanseethatintheallplanarMOthereisgreaterbondingbetweentheN2pxand2pyorbitalswiththeSALCsofesymmetry.Theseleadstoastabilizationoftheseorbitals.Conversely,inplanarizingthestructure,thereisnomorebondingbetweentheN2pzorbitalandtheSALCofa1symmetry,whichleadstoadestabilizationofthatorbital.


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WhenanalyzingNH2

-,oneofthethreehydrogenatomsisreplacedwithalonepair.TheresulthereisastrongdestabilizationoftheMOofformallyexsymmetryaswehaveremovedabondinginteractionbetweentheN2pxorbitalandoneofthethreehydrogenatoms.TheMOthatformallywasofa2symmetrydoesn’tchangeenergywiththereplacementofoneofthethreehydrogenatomswiththelonepairasthe2pzorbitalisorthogonaltotheplaneoccupiedbythelonepair.

2.3MOTheory:p-AcceptorLigandsThisclassofligandsdonatese–sfromaσorbitalandtheseligandsaccepte–sfromthemetalintoanemptyπ*orbital.COisthearchetypeofthisligandclass.Otherπ-acceptorsareNO+,CN–,CNR,H2,C2H4,N2,O2,PR3,BR2.WeanalyzedtheMOdiagramofCOindetailinCH2501.TheHOMOofCOisthelonepaironcarbonandthisiswhatbindstothemetal.TheLUMOofCOisoneofthetwodegenerate

p*orbitals.Itisintothisorbitalthatthemetalback-donatesintotheligand.2.4MOTheory:GeneralConceptsSomeimportantpointstorememberregardingMOdiagrams.TheM—LatomicorbitalmixingbetweentwoatomsMandLisproportionaltotheoverlapbetweenthetwoatoms(SML).Owingtomoredirectionalbonding(greateroverlap)alongtheseriesSML(σ)>SML(π)>SML(δ),whichleadstogreatersplittingalongtheseriesofbondingandantibondingorbitals(therefore,s-bondstendtobemorestabilizedandtheantibondingcombinationtendstobemoredestabilizedthanp-bondsandp-antibondingcombinations).M–Latomicorbitalmixingisinverselyproportionaltoenergydifferenceofmixingorbitals(i.e.ΔEML).Sothecloserinenergythetwosetsoforbitals,thegreaterthemixing(andthegreaterthesplittingofthebondingandantibondingcombinations).OnlyorbitalsofcorrectsymmetrycanmixandthetotalMOs=sumoftheprecursororbitals.Thislastpointisextremelyimportant.Formostmetalcomplexes,theorderoftheenergiesoftheligand-basedandmetal-based


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orbitalsELandEMalmostalwaysis:s(L)<p(L)<nd<(n+1)s<(n+1)p.Thep*(L)canresideanywhereabovethendorbitalsandtheenergyofthep*(L)orbitalsisdependentonthenatureofL.Somegeneralobservationsinclude:

• Thesorbitalsoftheligands(L’s)aregenerallytoolowinenergytoparticipateinbonding(ΔEML(σ)isverylarge)

• FilledporbitalsofL’sarethefrontierorbitalsoftheligands,andtheyhaveIEsthatplacethembelowthemetalorbitals

• FormolecularL’s,whosefrontierorbitalscomprisesandporbitals,heretoofilledligandorbitalshaveenergiesthatarestabilizedrelativetothemetalorbitals

• Ligandorbitalenergyincreaseswithdecreasingelectronegativity(Eneg)oftheLewisbasicbondingatomE(CH3

-)>E(NH2-)>E(OH-)

• Morbitalenergydecreaseswithincreaseoxidationstateofmetal,asyougodowntheperiodictableandasyougofromlefttorightontheperiodictable,whichisreflectiveintheionizationenergyofthemetal(seebelow)–recallthatthereisacontractionintheionicradiumacrosstherowduetoinefficientshieldingofthed-orbitalsbyd-electrons.

3LIGANDFIELDTHEORY(LFT),REVISITED.NowthatwehaveinvestigatedtheMOdiagramsoftheligands,letusnowtryandunderstandinmoredetailLFT,whichistheinteractionofligandMOswithmetalAOs.WhatisLFT?LFTisamorecompletetheoryofbondingwithincomplexes,andincorporatesaspectsofcrystalfieldtheorywithMOtheory.Ligandfieldtheoryattemptstoincorporatetheoverlapofmetal-baseddorbitalswithligandorbitalsofsuitablesymmetry.Thisapproachtriestoexplain,amongotherthings,theeffectofdifferentligandsonΔo.

2nd 1309 1414 1592 1509 1561 1644 1752 1958

3rd 2650 2828 3056 3251 2956 3231 3489 3954

4th 4173 4600 4900 5020 5510 5114 5404 5683


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LFTanalysesbondingofmetals,panddorbitalswithSALCsoftheligands,whichareusuallyformedofsandporbitals.Therearetwoprincipalbondingbonds,similartowhatwehaveseenpreviously.Theyares-andp-bonding.Newbondingbetweentwometalscanalsohaved-symmetry(seeCH2501notes).3.1LIGANDFIELDTHEORY(LFT),REVISITED–OctahedralComplexes.Sigma(s)bonding

• Neutralligands(e.g.,NH3)oranionicligands(e.g.,F-)possesslonepairsthatcanbondtometal-basedorbitals(s,px,py,pz,dxy,dyz,dxz,dx2-y2,dz2)withs-symmetry

• InanOhcomplex,6SALCsofthe6ligands-symmetryorbitalscanbeformed• MOsfortheresultingcomplexareformedbycombiningtheligandSALCsandthemetal-basedd-

orbitalsofthesamesymmetrytype(whichwillbeofegsymmetry)• With6SALCscombinedwiththemetalMOs,wewillget6bondingand6antibondingMOs–

nowcalledligandgrouporbitals(LGOs)• TheresultingMOdiagramnowgetspopulatedwiththeelectronsaccordingtotheAufbau

process,PauliexclusionprincipleandHund’srule

AboveyoucanseethedifferentSALCsinteractingwiththemetals(left),p(middle)andd(right)orbitals.FortheLigandSALCs,thesearecomposeduniquelyofsorbitalsforthesakeofsimplicityabove

butareshownassp3hybridorbitalsbelow.Thedxy,dxzanddyzorbitalsdonothavetheappropriatesymmetrytocombinetoformnewLGOs.Inaddition,theligandSALCScaninteractwiththemetalsandporbitals.IfwenowlookatthecorrespondingMOdiagram(below),weseethatthenewbonding/antibondingMOcombinationofthedx2-y2anddz2orbitalsarenowcalledegandeg*,respectively.TheegMOisveryligandbased(itiscloserinenergytotheligandSALCs)whiletheeg*ismoremetalbased.Thethreedorbitals

constitutingthet2gsetarenownon-bonding.Noticethatthed-orbitalsplittingpatternisexactlythe


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sameaswasobservedinCFTwithanenergydifferenceofDo.TheMOdiagrambelowrepresents[Co(NH3)6]3+.

Pi(p)bonding:ThepreviousMOdiagramignorespbonding.Iftheligandspossessorbitalsoflocalp-symmetrythenthesecaninteractwiththemetald-orbitalswiththesamesymmetry(i.e.thet2gsetinanoctahedralcomplex)toformnewLGOsinadditiontoalltheLGOswehavejustdiscussedthathaves-symmetry.TheseligandSALCscanactaselectrondonors(populated)orelectronacceptors(vacant).Weknowtheseasp-donorandp-acceptorligands,respectively.ThenatureofthissecondaryinteractionwillaffectDo.


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Ifthep-bondthatisformediscomposedofunoccupiedd-orbitalswithoccupiedp-orbitalsontheligands,thenthisisthecaseofp-donorligands(p-bases).AboveleftisanMOdiagramdemonstratingtheimpactofthenewbonding/antibondingcombinationoftheligandSALCsinteractingwiththemetalt2gset.Theimpactofthisnewinteractionistodestabilizetheantibondingt2g*orbitalthatcontainslargemetalcharacter,therebydecreasingDo.Thecorrespondingligand-basedt2gorbitalsarestabilized.3-dMetalcomplexeswithp-donorligandsarefrequentlyhighspinduetothesmallerDo.Anexampleofsuchacomplexis[FeCl6]3-.BelowleftisthecompleteMOdiagramforanoctahedralcomplexwithp-donorligands.

Ifthep-bondthatisformediscomposedofoccupiedd-orbitalswithunoccupiedp-orbitalsontheligands,thenthisisthecaseofp-acceptorligands(p-acids).AboverightisanMOdiagramdemonstratingtheimpactofthenewbonding/antibondingcombinationoftheligandSALCsinteractingwiththemetalt2gset.Theimpactofthisnewinteractionistostabilizethebondingt2gorbitalthatcontainslargemetalcharacter,therebyincreasingDo.Thecorrespondingt2gorbitalscontaininglargedegreesofligandcharacterarenowdestabilized(t2g*).RecallthatDorefersonlytotheenergydifferencebetweenthemetal-basedMOs.Theinteractionofthemetalt2gorbitalswithp-acceptorligandsisfrequentlycalledp-backbonding.p-Backbondingeffectivelyremoveselectrondensityfromthemetal,whichdoesnotliketohavetoohighanelectrondensity.Complexeswithp-acceptorligandsarefrequentlylowspinduetothelargerDo.Anexampleofsuchacomplexis[Cr(CO)6].ThefullMOdiagramisontherightinthelowerfigureabove.


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Takehomemessage:p-bondingandp-backbondingmodulatetheenergyofthemetalt2gorbitals.Thissecondarybondinginteractionnowexplainsthespectrochemicalseries.

3.2LIGANDFIELDTHEORY(LFT),REVISITED–SquarePlanarComplexes.HowdoweapplyLFTtocomplexeswithothergeometries?Weapplythesameprinciplesaswedidforoctahedralcomplexes.Let’slookatsquareplanarcomplexes,whichwecanthinkofasoctahedralcomplexeswithoutthetwoaxialligands.Let’suse[Pd(NH3)4]2+astheexample,wheretheligandshowsonlysigmadonation.TheresultingMOdiagramshouldthereforemirror,forthed-orbitalsplitting,thesamepatternasCFT.


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Wecannowseeintheleft-handfigureabovethatthedx2-y2MO(b1g)containsverystrongmetal−ligandantibondinginteractionsinthexyplane.ItistheLUMO.Thereisacorrespondingstabilizedb1gorbitalthathasastrongligandcharacter.Thedz2MO(a1g)containsslightmetal−ligandantibondinginteractionsinthexyplaneduetothedonutpartofthedz2orbital.ItistheHOMO.Contrastthesetwoorbitalswiththeeg*setintheoctahedralcasewhereboththedx2-y2anddz2orbitalsinteractedequallywiththeligandSALCSandsowereequallydestabilizedinthenewLGOs.Inthesquareplanarcomplex,thisisnotthecase.Thedxy,dxz,dyz,MO(eg,b2g)arenormallypresentedasdegenerateandnon-bonding(nosymmetrymatchwithligandMOs).Theobservedsplittingoftheseorbitalsintotwosets(egandb2g)isrequiredbygrouptheoryconsiderationsaccordingtotheirreduciblerepresentationsoftheD4hpointgroup,andisbeyondthescopeofthiscourse.Whataboutligandswithp-character?Includingp-interactionsresultsinare-orderingoftheenergiesoftheMOs,unlikewhatwesawwithOhcomplexes.Forcomplexeswithp-donatingligands,suchas[PdCl4]2-,theHOMOistheegMOs(dxzanddyz)andnotthea1gMOasaresultofthedestabilizationfromπ-antibondinginteractionswiththelonepairsoftheligands.Inaddition,thea1gMOisenergeticallystabilized,duetotheweakσ-donatingpropertiesofligandsinteractingwiththemetaldz2orbital.Forp-acceptingligands,suchas[Pd(CN)4]2-,theorderoftheLGOsremainsthesamebuttheegsetcontainingmainlymetalcharacterisstabilized.4WATERASALIGANDIN3-dMETALCOMPLEXES.Sincewatercanbeviewedasthemostfundamentalligand,wewilluseaqueoussolutionsandthespeciesfoundthereinasthebasisforexploringthechemistryof3-dmetalcomplexes.Thetablebelowdetailsthevariousmetalaquacomplexesthatexistasafunctionofmetalidentityandoxidationstate. II III IV V VI VII

Sc - [Sc(OH2)7]3+

d0

Ti [Ti(OH2)6]2+

d2

[Ti(OH2)6]3+

d1

V [V(OH2)6]2+

d3

[V(OH2)6]3+

d2

[VO(OH2)5]2+

d1

[VO2(OH2)4]+

[VO4]3-

d0

Cr [Cr(OH2)6]2+

d4

[Cr(OH2)6]3+

d3

[CrO(OH2)5]2+

d2

[Cr2O7]2-

[CrO4]2-

d0

Mn [Mn(OH2)6]2+ [Mn(OH2)6]

3+ - [MnO4]

3- [MnO4]

2- [MnO4]

-


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d5 d

4 d

2 d

1 d

0

Fe [Fe(OH2)6]2+

d6

[Fe(OH2)6]3+

d5

[FeO(OH2)5]2+

d4

[FeO4]2-

d2

Co [Co(OH2)6]2+

d7

[Co(OH2)6]3+

d6

-

Ni [Ni(OH2)6]2+

d8

- -

Cu [Cu(OH2)n]2+

d9(n=5or6)

- -

Zn [Zn(OH2)6]2+

d10

- -

Thosecomplexesingreenarethermodynamicallystable.Thoseinpurplearemetastable.Thoseinredarereducing(i.e.hydrogenisgeneratedthroughwaterdecomposition)andthoseinblueareoxidizing(i.e.oxygenisgeneratedthroughwaterdecomposition).Dependingontheoxidationstateandidentityofthemetal,thewaterligandcaneitherexistsasaneutralH2Oligand,M-OH2,asananionicdeprotonatedOH-ligand,M-OH,orasadoublydeprotonatedoxoligand,M=O.Themostcommongeometriesareoctahedralandtetrahedralandthisdependsbothontheidentityofthemetalandalsoontheoxidationstate.Dependingonthekineticlabilityoftheligands(moreonthisconceptlater),5-coordinatecomplexesarealsopossible,thoughunusual.ThisisthecasewithCu2+,whichshowsJahn-Tellerdistortion


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Scandium(III)isd0andsoisaparticularlylargeionanditcanaccommodate7watermoleculestoadoptapentagonalbipyramidalgeometry.[Mn(OH2)6]2+asanexampleisoctahedralwhile[MnO4]-istetrahedral,theresultofthemuchsmallerMn7+ion.Whyarethewaterligandsdeprotonatedsomuchinpermanganate?Theclueliesintheacid-basechemistryofthesecomplexes.

ThemetalactsasaLewisAcid(LA).WhenH2Ocomplexestothemetal,theO-Hbondispolarizedandtheprotonbecomesacidicandsocanbeabstractedbysolventwatermolecules.Asthechargedensityincreasesonthemetal(i.e.higheroxidationstateofthemetal),theO-HbondbecomesmorepolarizedandtheprotonacidityincreasesandmoreprotonsareabstractedintosolutionandtheOH2ligandbecomesanOH-ligand,reducingtheoverallchargeofthecomplex.Thewatersolutionthusbecomesmoreacidicaswell.Incertaincases,themetalbecomessoLewisacidicthatasecondprotoncanbeabstractedbythewatersolventmoleculesandtheOH-canbecomeO2-.Oxogroupspossessothertraitsthathelptostabilizetheresultingmetalcomplex.Theytakeuplessspacethan2OH-,whichisimportantbecausethehighoxidationstatemetalcentresareverysmall.O2-helpstoneutralizehighchargeonthemetalfromhighOSduetoitshighernegativecharge.Formetalswithlowd-electroncount,strongp-donorabilityhelpstostabilizet2gorbital.


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Therefore,asetofequilibriareactionsexistsasshownbelow.Theequilibriumcanbemodulated.Additionofbasewillshifttheequilibriumtotherightwhileadditionofacidwillfavouranequilibriumtotheleft.

Wecandeterminetherelativeaciditiesof[M(OH2)6]2+and[M(OH2)6]3+ionsintermsoftherespectivepKavalues.

WecanseethatthepKafor[Fe(OH2)6]3+issimilartothatofformicacid(2.0)andthisLewisacidisacidicenoughtoreactwithcarbonatetoliberateCO2.Wecanalsoseethatastheoxidationstateincreases,thepKadecreasesquitedramatically.Understandingthismoregenerally,wecanassociateapKaofaparticularionwithanelectrostaticparameter,x,whichisequaltoZ2/r,whereZistheatomicnumberandristheionicradius.ThepKacanbederivedfromthepHofthewaterandtheoxidationstateofthemetalby:

orcanbeempiricallyderivedfromtheelectronegativityofthemetalby:


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Asidefromthedeprotonationchemistrydiscussedabove,substitutionchemistryisalsopossiblebetweentwoadjacentcomplexes,resultingintheformationofµ-OH--bridgedmetaldimerspecies.Thisprocessiscalled“olation”

Thisprocesscancontinue-buildinguphugeOH-bridgedpolynuclearstructuresuntilsolubilitylimitsareexceededresultinginprecipitationofthehydroxide;M(OH)3aq.Accompanyingdehydrationcanalsooccurleadingtooxy-hydroxideoroxide(M2O3)formsprecipitating.Fe(III)hydrolysishasbeenwellstudiedandpolymericnanostructurescontainingover100ironatomshavebeencharacterizedbeforeFe(OH)3precipitation.Theformationofoxobridgesis“oxolation”.4.1FeHYDROLYSISINVIVO.

Ferritin(left)isaproteinthatstoresironinourbodybyconcentratingitviacontrolledhydrolysisofFe3+aqtoyieldhugeoxy-hydroxybridgednanostructurescontainingupto4500ironatoms.MovementofironinandoutoftheproteinisachievedviareductiontoFe2+aq,whichdoesnothydrolyseatpH7andpassesthroughspecificM2+-sensingchannels.TheinstabilityofFe3+aqsolutionsatpH7withrespecttohydrolysistoinsolubleFe(OH)3makesitachallengeforbiologytoconcentrateironinthe

body.Notethesolubilityproductequilibriumconstantthatisveryverysmall,(Ksp=2.6x10-39).TocircumventthisissueNaturehasevolvedverypowerfulagentsthatbindandsolubilizeallformsofFe(III)evenFe(OH)3toenableefficientironuptake.Thesecompoundsarecalledsiderophores(Greek-ironcarrier).Someofthesehavethehighestmeasuredequilibriumconstantsforametalion-ligandcombination.Therecordvalueisheldbyenterobactin.Thecatecholate(dihydroxybenzene)fragmentschelatetheironverystronglyasshownschematicallybelow.Catecholatebindingisn’ttheonlymotifusedtocoordinateiron.Hydroxamate-basedsiderophoresalsoexist.


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Thetablebelowdocumentsequilibriumconstantsforthesiderophoresshownabove.siderophore donorset logK

aerobactin hydroxamate,carboxylate 22.5

coprogen hydroxamate 30.2

deferrioxamineB hydroxamate 30.5

ferrichrome hydroxamate 32.0

Enterobactin catecholate 49.0

4.2ACLOSERLOOKATTHEHYDROLYSISREACTION.Let’slookatligandexchangeinmoredetailbylookingat:[M(OH2)6]n++mL➞[M(OH2)6-mmL]n+➞➞[M(L)6]n+(Lisaneutralligand).Fromthismultipleligandexchangereaction,wecanderivestepwiseequilibriumconstants,K1-K6.


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Wecannowdefineanoverallstabilityconstant,bnforthecompleteexchangeofH2OligandsforL.

Sob

6=K

1*K

2*K

3*K

4*K

5*K

6andlog(b

6)=log(K

1)+log(K

2)+log(K

3)+log(K

4)+log(K

5)+log(K

6).

Whatthisimpliesisthatb

6>b

5>b

4>b

3>b

2>b

1andsotherewillalwaysbecompletesubstitutionofL

forH2Oiftheincomingligandbindsmorestronglytothemetalthanwater.Anexample:NH3replacingH2Oon[Ni(OH2)6]2+withstepwiseequilibriumconstantsshownbelow.NotethesteadyfallinKn.Whatthisdatameansisthat[Ni(OH2)6]2++excessNH3givesonly[Ni(NH3)6]2+.Logb6=2.79+2.26+1.69+1.25+0.74+0.03=8.76b6=5.75x108Withknownequilibriumconstants,Kn,wecandeterminefreeenergyDGn.DGn=-RTln(Kn),whereRisthegasconstant8.314Jmol-1K-1Soat303K,DG1=-(8.314x10-3*303)ln(102.79)=-16.2kJmol-1DGn=DHn–TDSnIfDH1=-16.8kJmol-1DS1=(DH1-DG1)/T=[-16.8-(-16.2)]/303=-1.98Jmol-1K-1.Onecanseethattheentropictermisnegligible.Therefore,substitutionisprimarilyanenthalpiceffect(DHisgoverningtheprocess).ThisisduetothestrongerNi2+-NbondsbeingformedcomparedtotheNi2+-Obonds(moreexothermic).


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5HARD-SOFTACIDBASETHEORY.

HSABTheoryisaconceptthatisusedtorationalizethestabilityofcertaininteractionsbetweenatoms.'Hard'appliestospeciesthataresmall,havehighchargestatesandareeitherveryelectropositiveorveryelectronegative(orangeelementsbelow),andareweaklypolarizable.'Soft'appliestospeciesthatarebig,havelowchargestatesandarestronglypolarizable(blueelementsbelow).

Thetotalenergyofaninteraction,asdefinedbytheSalem-Klopmanequation,isgovernedbyseveralterms,includinganelectrostaticterm(secondterm)andamolecularoverlapterm(thirdterm).

Thus,Hard-Hard(HH)interactions,whichmaximizetheelectrostaticinteractionsorSoft-Soft(SS)interactions,whichmaximizethemolecularorbitalinteraction,providemorestablecompounds.Hard-Softinteractionsgenerateweakerinteractionsbetweenthetwoatomsinthebond.Thegoldenrule:TheStrongestM-LinteractionsrequireHHorSSmatchConsiderthefollowingdataonequilibriumconstantsforthereactiontotheleft.

MetalIon log10K1

X=F X=Cl X=Br X=I

Fe3+aq 6.0 1.4 0.5

Hg2+aq 1.0 6.7 8.9 12.9

Thehalidesgetharderasthesizegetssmaller.ThebehaviourofFe3+aqisparalleledbysimilarbehaviourshownbytheGroup1and2metalsandtheearly3dtransitionelementstotheleftoftheperiodictable.

Salem-KlopmanEquation(simplified)


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ThebehaviourofHg2+aqisparalleledbysimilarbehaviourshownbytheheavierp–blockelementsandtheheaviertransitionelementstotherightoftheperiodictable.Generaltrendsare:OrderofincreasingstabilityincomplexesforHardmetalions: O>>S>Se>Te N>>P>As>SbOrderofincreasingstabilityincomplexesforSoftmetalions: O<<S>Se~Te N<<P>As>SbOrderofdecreasinghardnessbasedonelectronegativity:F>O>N>Cl>Br>C~I~S>Se>P>As>SbLigandsdisplacewaterinacompetitiveprocessthatisatequilibrium(sounderthermodynamiccontrol).IftheMn+isahardmetal-itisalreadyassociatedwithhardH2Oligands.Thus,reactionwithanotherhardligandmaynotbefavourable–onlyasmallexothermicenthalpyeffectmightbeseen.Leadsonlytomoderatelystablecomplexes(-DGosmall) e.g.,withL=RCO2

-,F-,Cl-etc.NowifMn+isasoftmetalandLisasoftbasethereactionisnowhighlyfavouredsinceitremovestwounfavourablesoft-hardinteractions-fromwatersolvation.HereasignificantDHoeffect(largeandnegative)isseenwhenthesoft-softinteractionresults-leadstostablecomplexeswithDGothatisalsolargeandnegative(DSosmallasbefore)-highKn e.g.,Hg2+aqandS2-aq➞HgS(s)precipitates6THEIRVING-WILLIAMSSERIES.WehavepreviouslyexaminedthevaluesoflogKn(bn)forthesuccessivereplacementofH2OonNi2+aqbyNH3Whathappensalongthe3dseriesfromSc–Zn?ThefigurebelowshowstheequilibriumconstantforthefirstsubstitutionofNH3forH2O.ThistrendshowingamaximuminlogK1valuesforCu2+istermedtheIrving-Williamsseries


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TheIrving-WilliamsSeries(IWS)describesanempiricalincreaseinstabilityofM2+octahedralcomplexesasafunctionofatomicradius,regardlessofthenatureofLforthefollowingreaction:

[M(H2O)n]2++L [M(H2O)n-1L]2++H2O

K1variesalong:Ba2+<Sr2+<Ca2+<Mg2+<Mn2+<Fe2+<Co2+<Ni2+<Cu2+<Zn2+

Asisevidentfromtheaboverightfigure,thereisamaximumatCu2+,regardlessofligand.Theseriesgenerallyfollowselectrostaticeffectswherebyasmallermetalwithsamecharge=greaterchargedensityandthisleadstotighterbindingbetweentheligandandthemetal.However,ifwebasebindingstrengthpurelyonelectrostaticsthenwewouldexpectstabilitiestovaryinaccordancewithtrendsinionicradius.Sothetrendinstabiltitywouldfollow:Mn2+<Fe2+<Co2+<Ni2+>Cu2+>Zn2+.ThereasonCu2+isactuallymorestablethanNi2+isduetotheJahnTellerDistortion.6.1JAHN-TELLERDISTORTION.Jahn-Teller(J-T)distortionoccurswhenthereisthepossibilitytoasymmetricallyfillorbitalsthataredegenerateinanon-linearcomplex.Thegeometryofthecomplexthendistortstoreachamorestableelectronicconfiguration.J-Tdistortionmostcommonlyoccursforhighspind4t2g3eg1metalsandlowspind7t2g6eg1metalsorford9t2g6eg3metals,allofwhichhaveanasymmetricallyfilledegsetoforbitals.ForCu2+,whichisd9,ifthereare2electronsinthedz2and1electronsinthedx2-y2orbitalthentherewillbegreaterrepulsionalongthez-axisandthereforeelongationoftheseM-Lbondsalongthez-axistocompensate,leadingtostabilizationofthedz2orbital,whichisthemostcommonlyobserveddistortion.TheM-Lbondsalongthexyplanebycontrastcontract,whichleadstoadestabilizationofboththedxyanddx2-y2orbitals.Thisisillustratedinthefigurebelow.

Ifthereare2electronsinthedx2-y2and1electronindz2thengreaterrepulsionexistsalongthexy-planeandthereforethereiseffectivecompressionoftheM-Lbondsalongthez-axistocompensateandelongationofM-Lbondsinthexyplane,leadingtostabilizationofthedx2-y2orbitalandthedxyorbital;thedz2orbitalbycontrastisdestabilized.


Page22of43

Thepresenceofonlyoneelectroninthedx2-y2orbitalstrengthensthewaterligandattractionintheequatorialplaneduetolowere--e-repulsionwiththedonorOelectrons.TheresultisaraisinginlogK1-4andaloweringinlogK5andK6forligandsubstitutionofwatermoleculescomparedtothetwoionseitherside;Ni2+(d8)andZn2+(d10)wherethereisnosuchextrastabilization(seefigureleft).

7.THECHELATEEFFECT.Let’snowconsiderthesituationwhentheligandLreplacingcoordinatedwaterpossessestwodonoratomsthatleadstotheformationofachelatering.ThefigurebelowshowsthatthereplacementofNH3onM2+

aqbythechelatesen(ethylenediamine)andEDTA(ethylenediaminetetraacetate)isthermodynamicallyfavourable.Thisisageneralphenomenoncalledthechelateeffect.TheincreaseinlogK1aschelateringsareformedisareflectionofamorenegativevalueofDGo

1.Itislargelyduetoanincreaseintheentropyofreactioni.e.DSo1islargeandpositive(DGo

1=DHo1-TDSo1).

Let’slookataspecificexample:Ca2+aq+EDTA4-

DGo

1=-60.5KJmol-1;DSo1=117Jmol-1K-1At300K,DHo

1=-25.4KJmol-1(DHo1=DGo

1+TDSo1)Therefore,thiscomplexationismostlyentropydriven(TDSo1=-35.1KJmol-1),thoughthereisafavourableenthalpictermaswell(HSABandchelateeffect).Whyentropycontrolled?Thereisanincreaseinentropyduetoreleaseof6watermolecules,whichleadstoanincreaseindisorderofthesystem(i.e.2reactingmolecules,7productmolecules).WecannowcalculateK1asDGo

1=-RTln(K1)andlog(K1)=log(e-DG1/RT)=10.53.

Let’slookatanotherspecificexample:[Ni(NH3)6]2++3en


Page23of43

DGo1=-57.2KJmol-1;DHo

1=-16.6KJmol-1;-TDSo1=-36.1KJmol-1HerebothbothenthalpyandentropyeffectspositivelyreinforceM-Lbinding.TheenthalpiceffectonchelationfromenarisesfromstrongerbondstotheNdonorsofthechelateasaresultoftheformationofthering.Let’slookatanotherspecificexamplewheretheenthalpyandentropy termsdonotreinforceeachother:Mg2++EDTA4-DGo

1=-51.2KJmol-1;DHo1=13.8KJmol-1;-TDSo1=-65.0KJmol-1

HeretheendothermicenthalpytermarisesfromtheunfavourablereplacementoftwohardwaterligandsontheextremelyhardMg2+bythesofterNdonorsofEDTA4-(HSAB).Formationofthechelateishoweverstillhighlyfavouredduetothefavourableentropycontribution.ThisbegsthequestionwhyisMg2+harderthanCa2+?Mg2+issmaller(chargemoreconcentrated)thanCa2+,whichwillreinforcetheelectrostaticinteraction(Hard-Hard)interactionwithH2O.Wecanalsoprobetheeffectofthenatureofthedonoratomonthebindingstrengthtothemetal.ThefigureontherightillustratesthattheOrderoflogK1reflectsHSABtheory.ForNi2+toZn2+(softmetals):(soft)N^N>NÔ>OÔ(hard)ForMn2+(hardmetal):(hard)OÔ>NÔ>N^N(soft)Therefore,hardchelatingligandsprefertobindhardmetalswhilesoftchelatingligandsprefertobindsoftmetals.The“hardness”or“softness”oftheligandisbasedontheHSABofthecoordinatingatoms.ThetablebelowprovidescompellingevidenceofthisHSABeffectinchelates.


Page24of43

Bindingstrengthisalsoinfluencedbythenumberofdelectronsonthemetal(LFSE),whichisillustratedinthefiguretotheleft.HerethetrendinlogK1mirrorstheLFSEtrends.IgnoringLFSE,increasingK1reflectsstrongerM-LbondingasafunctionofincreasingchargedensityontheMastheionicradiusdecreasesalongtheperiod.Recallthattheionicradiusdecreasesalongtheperiodisaresultofthepoorshieldingofthenuclearchargebytheadditionofthesuccessived–electrons.

Thed-orbitalsdonotpenetrateintothenucleusbecausethedorbitalwavefunctiongoestozerobeforethenucleusisreached.Thisiscalledthed-blockcontraction.7.1THECHELATEEFFECT-APPLICATIONS.Chelationtherapyhasbeenusedtotreatdiseasesandconditionsrelatingtometaloverload.OneexampleisWilson’sdisease.Wilson’sdiseaseisarecessivegeneticdisorderthatcausesepilepsyamongstotherneurologicalsymptomsandisduetoanoverloadofcopper.ChelatingagentssuchasthosetotherightthatbindCu2+ionsstronglyhavebeensuccessfullyusedclinicallytotreatthecondition.


Page25of43

AnotherexampleinvolveschelationofFe3+.Apotentiallyfatalconditioncalledhemosiderosisoccurswhenthenaturallyoccurringironcarrierproteintransferrinbecomessaturatedandironbecomesdepositedwithinthebody.Incasesofsevereironoverload,depositionintheheart,liverandendocrinesystemsleadstofunctionalimpairmentoftheseorgans,andreducedlifeexpectancy.ThereexistotherclinicallyprovenagentsfortheremovalofFe3+fromthebody,suchasdeferoxamineanddeferiproneandtheexamplesshownbelow,whichareallagentsbasedonEDTAderivatives.NoteineachexampletheaffinityofthehardFe3+forhardOdonors.

8.STABILITIESOFOXIDATIONSTATES.Thehigheroxidationstatesbecomemoreoxidisingandtheloweroxidationstateslessreducingasonemovestotherightofthed-block.Whyisthisso?Itisduetothepoorshieldingofthenucleusbytheadditionofsuccessived-electrons(dblockcontraction),wheretheeffectivepositivechargefeltbyanouterelectronincreasesfromlefttoright.Thishastwoconsequences:

• Generaldecreaseinionicradiusfromlefttotheright.• Valenceelectronsbecomehardertolose/sharethemoretotherightonegoes.

Therefore,thehigheroxidationstatesbecomemoreoxidizingandthelowerstateslessreducing.Buthowdowetrulydefinetheterm“oxidationstate”?Innomenclaturetermsthisisdonebyassumingoctetconfigurationstodefinethechargeontheatomsattachedtothemetalintheionorcomplex.Thetablebelowprovidessomeexampleswithdifferentmetalsandligandforwhatthecalculatedoxidationstateonthemetalwouldbe.Complex Ligand TotalChargeon

LigandOverallChargeonComplex

OxidationStateofMetal


Page26of43

[Mn(OH2)6]2+ H2O 0 +2 II

MnO4- O2- 8- -1 VII

[Fe(CN)6]4- CN- 6- -4 II

[Co(NH3)4(O2CR)Cl]+ NH3RCO2

-Cl-

01-1-

+1 III

Inreality,oxidationstatesareaformalismandareonlytrueiftheM-Lbondingishighlyionic(electrostatic). e.g.,[Mn(OH2)6]2+whereMntrulyisMn2+whereindependentevidenceexistsfromopticalspectroscopy&magnetismthatMn2+ishighspind5.

Butwhataboutthecaseof[MnO4]-wheretheMn-Obondsarehighlycovalent(Mn-Obondlengthislessthansumofionicradii).Sowherenowaretheelectrons(seethethreeresonancestructurestotheleft)?

Hereopticalspectroscopyandmagnetismarelessinformative:• TheabsorptionspectrumisdominatedbyOàMnligand-to-metalchargetransferbands• Thecomplexisdiamagnetic

SowewriteasMnVII(O-II)48.1QUANTIFICATIONOFOXIDIZINGANDREDUCINGSTRENGTHS.WeknowthatMnO4

-isapowerfuloxidantand[Cr(OH2)6]2+isapowerfulreductant.Buthowdowequantifyoxidisingandreducingstrength?Theanswer:Usingascaleofstandardredoxpotentials,Eo.Thesearebestenvisagedaspartofanelectrochemicalcell–thedrivingforceinabattery(showntotheright).ConsidertheinteractionofCu2+/CuandZn2+/ZnintheDaniellCell.ThereactionisspontaneousasDGoisnegative.Thiselectrochemicalcellcanbethoughtofastwohalfreactions.Thepotentialdifference,Eocellismeasuredbythevoltmeter.Thepotentialdifference,Eocellisdefinedasthestandardcellpotentialunderstandardconditions,whichare:


Page27of43

• Unitactivity(whichmeansdilutionsolutionssoactivitiesapproximateconcentrations)• 1barpressureofanygaseouscomponent• Allsolidcomponentsareintheirstandardstates• T=298K

Thefreeenergyofthecell,DGo

cell=-nFEocell whereFistheFaradayconstant=96,487Cmol-1 nisthenumberofelectronstransferredinthereactionForacellreactiontobethermodynamicallyfavourableEocellmustbepositivesothatDGo

cellisnegative.IntheDaniellCell,Eocellat298K=1.10V(seefigureonpreviouspage).This1.10Viscomprisedof:+0.34VdrivingthereactionduetoreductionofCu2+and+0.76VdrivingthereactionduetooxidationofZn(s).Wheredothesevaluescomefrom?Firstly,DGo

cell=-nFEocell=-2*96,487*1.10=-212267Jpermolreaction=-212kJmol-1,whichdemonstratesthatthereactionfortheoxidationofthezincandthereductionofthecopperisspontaneous.AllEovaluesarerelatedonascaletothecellpotentialofthestandardhydrogenelectrode(SHE),whichisarbitrarilysetatavalueof0.0V(thinkofthisasanalogousto1HNMRwhereeveryotherresonanceisreportedrelativetoTMS).TheSHEconsistsofplatinumwirethatisconnectedtoaPtsurfaceincontactwithanaqueoussolutioncontaining1MH+inequilibriumwithH2gasatapressureof1atm.Thehalf-cellpotentialsareintensiveproperties,namelyindependentoftheamountofthereactingspecies.Allhalf-reactionsarewrittenasreductions(onlyreactantsareoxidizingagentsandonlyproductsarethereducingagents).ThemorepositivetheEovaluethemorereadilythereactionoccurs.Thehalf-cellthathasthemorepositiveEovalueactsasthecathode.BycombiningtheSHEwithanotherhalf-cell,e.g.,Cu2+aq/Cu(s)asintheDaniellcell,theEocanbedeterminedfromthemeasuredcellpotentialEocell.Thus,intheDaniellcell:

WecannowseewhyZn(s)readilyreducesCu2+aqandprovidesthehugedrivingforcefortheDaniellcell.Zn(s)thusisthestrongerreducingagentandCu2+isthestrongeroxidizingagent.Let’slookatadifferentreaction.Let’sconsiderthewell-knowntitrationreactionofthereductionMnO4

-withFe2+aqunderstandardconditions(1MH+,298K).Thehalfreactionsare:


Page28of43

WecannowseethatfromtherelativeE0valuesthatthespontaneousreactionis:

AsEocell=Eored–Eoox=1.51–(+0.77)=0.74VandDGo

cell=-357.03kJmol-1(soisveryfavourable).Let’snowlookatadifferentprocess,whichistheoxidationofFe(s)byCl2aq.Thehalfreactionsare:

Thesedataindicatethattworeactionsarepossible:

BothEocellvaluesarepositiveandfromtheirmagnitudeonemightsupposethefirstreactionisfavouredoverthesecondbutwhatreallycountsisthesignofDGo

cell.ItcanbeshownthatthesecondreactionisfavouredbyconsidertheDGo

cellvaluesforthetwoprocesses,whichtakeintoaccountthenumberofelectronsinvolved.Thefirstreactioninvolvestwoelectronswhilethesecondreactioninvolvessixelectrons.RecallthatDGo

cell=-nFEocell.


Page29of43

Thereforesecondreactionfavouredby~500kJmol-1!8.1.1QUANTIFICATIONOFOXIDIZINGANDREDUCINGSTRENGTHSUNDERNON-STPCONDITIONS.Sofarwehavebeenlookingatsystemsunderstandardconditions.WhathappensifwechangethepH?Letlookatthisfirstexample:ReductionofMnO4

-.

HereEoreferstothecondition[H+]=1moldm-3,pH=0.BecauseoftheconsumptionofH+ions,theaboveEowillvarywithpH.WhatwouldbethemeasuredEvaluefortheaboveatpH2.5at298K?WecancalculateEunderanyconditionsusingtheNernstEquation.

ForthereductionofMnO4

-:

AtpH=2.5=-log10([H+]);[H+]=3.2x10-3M:

8


Page30of43

Atthemidpoint[Mn2+aq]=[MnO4

-]andE=Eeq

=1.27.ThisimpliesthatEcelldropsasthepHincreases.Let’slookatasecondexample:ReductionofZn2+aq

Inthisreactionthereisno[H+]consumption.Sowhyisthereachangeinthecellpotential?ThereasonisthatatpH0theZn2+speciesis[Zn(OH2)6]2+butatpH14thespeciesis[Zn(OH)4]2-.SotheZn2+speciesbeingreducedisdifferent!Let’snowlookatathirdexample:Mn3+/Mn2+aq–anexamplewherepHaffectsredoxbehavior.AtpH0:Mn3+existsas[Mn(OH2)6]3+andcanoxidiseH2OàO2.

Eocell=1.54-1.23=0.31V(favourable)andDGo

cell=-nFEocell=-4*96487*0.31Jmol-1=-120kJmol-1AtpH14:MnIIIandMnIIarenowpresentasthehydroxocomplexes;Mn(OH)2/3(s)andsothespeciationisdifferentunderbasicconditionscomparedtoacidicconditions.RecallthatatpH=14[OH-]=1moldm-3.

NowO2istheoxidantandEocell=0.4–(-0.27)=0.67V(favourable)andDGo

cell=-nFEocell=-4*96487*0.67Jmol-1=-259kJmol-18.1.2LATIMERDIAGRAMS.

8


Page31of43

WhenseveraloxidationstatesexistforaparticularmetalaconvenientmethodofrepresentingtherespectiveEovaluesisintheformofaLatimerdiagram.WithmultipleLatimerdiagrams,onecanillustratethechangeinEowithpH.ThefirstexampleisforFeatpH=0(left)andpH=14(right).

UsingDGovaluesforeachstepwecanshowusingtheaboveleftLatimerdiagramthatEo(Fe3+aq/Fe(s))=-0.04V.SeeifyoucancalculatewhatEo(FeO4

2-/Fe(s)shouldbe.RecallHess’law:

ThesecondexampleisforMnwherethetopLatimerdiagramisatpH=0andthebottomLatimerdiagramisatpH=14.Whenagivenoxidationstatehasahigher(morepositive)Eoforitsreduction(i.e.thenumbertotherightofthecomplex)thanforitsoxidation(i.e.thenumbertotheleftofthecomplex)itisthermodynamicallyunstabletodisproportionationtogivethetwospeciesoneithersideofthecomplexintheLatimerdiagram.OnecanshowthatDGoforthisprocessisnegative.AtpH=0,MnO4

2-andMn3+arebothunstabletodisproportionationwhileatpH=14MnO4

3-willdisproportionatetoMnO42-and

MnO2.8.1.2FROST-EBSWORTHDIAGRAMS.Latimerdiagramsaregreatandverydescriptive.AnotherconvenientwayofrepresentingredoxbehaviouristographicallyplotDGoversustheoxidationnumber.


Page32of43

RecallthatDGo=-nFEoandsoDGo/F=-nEoSoifweplotnEovsoxidationnumberthentheslopeofthelinedrawnbetweentwooxidationstates,separationn,willgiveEoforthatprocess.TheFrostEbsworthdiagramisaverygoodgraphicaltoolthatcanbeusedtopredictredoxbehaviour.

Let’snowlookatMnatpH=0.AsnEobecomesmorenegativethestabilityofthespeciesincreases.ThefurtherpositivethenEoisthemoreoxidizingthecomplexis.SoMnO4

-isthemostoxidizingandMn2+isthemoststable.Compoundsthatshowadecreaseconvexbehaviour(i.e.adecreaseintheslopetotherightofthecomplexcomparedtotheleft)arepronetodisproportionation.NoticethatthisisthecaseforMn3+andMnO4

2-.Let’slookmorecloselyatthecaseforMnO4

2-(rememberwewritetheredoxreactionsasreductions).

Thethirdequationshowstheoverallbalancedequation,

whichisequation1+2*equation2(equation2isinvertedandsoEobecomes-0.9V).SoEodisp=2.10–0.90=1.20VandDGo=-nFEo=-2*96487*1.2=-231.5KJmol-1.Let’snowlookathowtheredoxbehaviourchangesatpH=14.WecannowobservethatMnO4ismuchlessoxidizingunderbasicconditionswhileMn(OH)3becomesthemoststablespecies.

WhichpHconditionisbestforMnO4

-titrations?AtpH=0theuseofacidsolutionavoidsMnO2(s)production.

MnO42- + 4 H+ + 2 e- MnO2 + 2H2O Eo = + 2.10V

MnO4- + e- MnO4

2- Eo = + 0.90V

3 MnO42- + 4 H+ MnO2 + 2 MnO4

- + 2H2O

6

5

4

3

1

0

-1

-2

-3

2

0 1 2 3 4 5 6 7

n Eo

oxidation state

Mn

Mn2+

Mn3+

MnO2

MnO42-

MnO4-

most stable stateis Mn2+

aq. (sits in energy minimum)

-1.19 V+1.54 V

+2.10 V

+0.90 V

+0.95 V

6

5

4

3

1

0

-1

-2

-3

2

0 1 2 3 4 5 6 7

n Eo

oxidation state

Mn

Mn(OH)2

MnO2

MnO42- MnO4

-

-4Mn(OH)3

MnO43-

6

5

4

3

1

0

-1

-2

-3

2

n Eo

Mn

Mn2+

Mn3+

MnO2

MnO42-

MnO4-


Page33of43

SoatpH=14

FromtheretwoequationswecanseethatthereductiontoMn2+(aq)isfavoured.Notethatinair(sowithO2)

AtpH=14

FromtheretwoequationswecanseethatthereductiontoMnO2isfavoured.Notethatinair(sowithO2)Let’snowlookataFrostEbsworthdiagramalongthe3dseriesoftheperiodictable.Notehowtheloweroxidationstatesbecomemorestableandlessreducingalongtheperiod.Notethatcopperisthefirsttrulyinert3dmetal(allEovaluesarepositive.Thisistypicalofcoinagemetals.Cuistheonly3dmetalfoundnaturallyinitselementalform.WecanalsoobservethatCu+(aq)willdisproportionate.

8.1.3THELINKBETWEENOXIDATIONPOTENTIALANDIONIZATIONPOTENTIAL.

Thereductionofametalinsolutionactuallyconsistsofthreeprocesses. Firstly,themetalsolidneedstobeatomized(orvapourized),forwhichthereisanassociatedenergyrequiredtodoso.Then,ifwearediscussingatwoelectronprocess,theatomizedmetalneedstobeionizedtwice(i.e.twoelectronsareremoved).Thiscorrespondstothefirstandsecondionizationpotentials.Finally,thisoxidizedspeciesneedstobesolvated.Aswearediscussingchemistryinwater,thissolvationiscalledahydration.Thereisanenergyrequirementwiththisprocessaswell.

MnO4- aq + 8 H+

aq + 5 e- Mn2+aq + 4 H2O (l) + 1.51

Eo / V Go / kJ mol-1

-728.5

MnO4- aq + 4 H+

aq + 3 e- MnO2(s) + 2 H2O (l) + 1.69 -489.2

O2 + 2 Mn2+aq + 2 H2O 2 MnO2(s) + 4 H+

aq 0.0 0

MnO4- aq + 4 H2O + 5 e- Mn(OH)2(s) + 6 OH-

aq + 0.34 -164MnO2(s) + 4 OH-

aqMnO4- aq + 2 H2O + 3 e- + 0.59 -170.8

M2+aq + 2 e- M(s)

Eo

O2 + 2 Mn(OH)2(s) 2 MnO2(s) + 2 H2O + 0.44 -169.86

5

4

3

1

0

-1

-2

-3

2

0 1 2 3 4 5 6 7

n Eo

oxidation state

-4

6

5

4

3

1

0

-1

-2

-3

2

n Eo

M

Mn2+

Mn3+

MnO2

MnO42-

MnO4-

Cr2O72-

Cr3+

Cr2+

V2+V3+

VO2+

VO2+

Fe2+

Fe3+

FeO42-

Co2+

Co3+

Ni2+

Cu2+Cu+

Ti2+

Ti3+ TiO2+

M(s) M(g) atomization Hoa

M(g) M2+(g) ionization (IP1 + IP2)


Page34of43

SodoanyoftheseprocessescorrelatewithtrendsinEo?TheansweristhatthevaluesofEocorrelatewiththeionizationpotentials(IP1+IP2),asshownbelow.TheexpectedvariationofDHo

hydwithLFSE(formingtheaquocomplexes)doesnotcontributesignificantly.ThelowEoforZn2+/ZndoescorrelatehoweverwithanunusuallylowvalueofDHo

aforZn(s).

Furthermore,Eo(M3+/M2+)correlateswithIP3,withtheexceptionofchromium(seefigureabove,right).OnceagainthevariationinrespectiveDHo

hydvaluesofM2+andM3+isnotsignificant.OnthebasisofIP3,oxidationofCr2+(g)shouldbemoredifficultthanofV2+(g)byca.165kJmol-1YetCr2+aqisamorepowerfulreductant(morenegativeEo)thanV2+aq.ThereasonistheconsiderablegaininLFSE(0.6Do)onformingthed3Cr3+ion(t2g3eg0configuration).OxidationofV2+aqtoV3+aq(t2g3eg1configuration)actuallyresultsinalossofLFSEof0.4DocomparedtoV2+

aq.

SointhiscaseLFSEfactorsaresignificant.Mostly,LFSEfactorsdonotplayasignificantroleindeterminingtrendsinEo.9RATESOFREACTIONSINVOLVING3DTRANSITIONMETALIONSINAQUEOUSMEDIA.Upuntilwehaveconcentratedonthermodynamicstability.Let’snowturnourfocustounderstandingthekineticsofthesereactionsandassesswhetherthekineticsofthereactioncorrelatewiththethermodynamicsofthereaction.Considerthefollowingprocesses:

LFSEunits of o

LFSEunits of o

Change in LFSE M2+->M3+

units of oM3+ M2+M

V -0.8 -1.2 0.4 loss

Cr -1.2 -0.6 -0.6 gain

M2+(g) M2+aq hydration Ho

hyd

Eo (M2+/M) / volts

IE / kJ mol-1

0 1 2 3 4 5 6 7 8 9 10

number of d electrons for M2+

-3

-2

-1

0

1

2

3

1750

2000

2250

2500

2750

3000

3250

3500

1500

IP1 + IP2

IP3 Eo (M3+/M2+) / volts

IE / kJ mol-1

0 1 2 3 4 5 6 7 8 9 10

number of d electrons for M2+

-3

-2

-1

0

1

2

3

1750

2000

2250

2500

2750

3000

3250

3500

1500

IP3

VCr

Mn

Fe

Co


Page35of43

Inbothreactions,regardlessofwhethertheligandisachelatecyclamorjustwater,thesereactionshaveoneofthelargestlogbnvaluesknownforamonodentateligandreplacingH2O.Whatthismeansisthat[Ni(CN)4]2-isverystablethermodynamically.Nowconsidertherateofthereactionforthefollowingprocess:

Therateconstant,k,isverylargeandwhatthismeansisthat[Ni(CN)4]2-isverylabile!Theseexperimentsshowthatthermodynamicstabilitydoesnotnecessarilycorrelatewithkineticinertness.Theattainmentofequilibriuminmetalioncomplexationprocessescanbeanextremelyfastprocess;irrespectiveofthesizeofthestabilityconstants:Knorbn.Infact,msandµstimescaleligandexchangeeventsinvolvingmonodentateligandsarecommonwithin3dtransitionmetalcomplexes.Awiderangeofratesisrelevantforligandexchangereactionsatmetalcomplexes.Let’sconsiderwaterexchangeontheaquaspecies.Formaingroupmetalions(shownbelow)theserangefromthemostlabile(Cs+aq,half-life=1ns)tothemostinert(Al3+aq,half-life=1s),whichcorrespondsto9ordersofmagnitudechangeinhalflife.Thisismostlyasaresultofvariationsinthemetalionicradiuswhichaffectsthestrengthofthepredominantlyionic(electrostatic)bondingtothecoordinatedwaters.

N

N

N

NH H

H H

cyclam(macrocycle)

+ [Ni(OH2)6]2+

N

N

N

NH H

H H

Ni

log 1 = 19.4

+ 4 CN-

N

N

N

NH H

H H

+ [Ni(CN)4]2-

log 4 = 22

[Ni(OH2)6]2+ + 4 CN-log 4

[Ni(CN)4]2- + 6 H2O log 4 = 22

[Ni(CN)4]2- + *CN- [Ni(*CN)(CN)3]2- + CN-k

k = 2.3 x 106 M-1 s-1

- representing an exchange event every microsecond!!!

exchange of CN- ligand

[Be(OH2)4]2+

[Mg(OH2)6]2+

[Ca(OH2)7]2+

Ionic radius / pm

Water exchange half life / s

27

105

10-2

10-7

10-572

[Ba(OH2)8]2+ 142 10-9

[Al(OH2)6]3+

[Ga(OH2)6]3+

[In(OH2)6]3+

Ionic radius / pm


54

80

1

10-6

10-362

b

b

b


Page36of43

However,forthe3dtransitionmetalionssizeisnottheonlyfactor.Herethereisnocorrelationwithsize.V2+hasthelargestradiusbutitisthemostinert.Thehalf-lives(relatedtotherates)ofexchange,justlikethestabilityconstantswesawearlier,correlatewithLFSEnotsize.

Let’snowlookattheexchangeratesforM2+ionsalongthe3dseries.TheanomalouslyhighratesforCr2+aqandCu2+aqreflecttherapiddynamicsattachedtotheweakly-bondedwaterligandswithintheJahn-Tellerdistortedstructures(seebelow).Theexchangeinthesesystemsissofastthatexchangeoccurseverynanosecond.

Amazingly,theratesofwaterligandexchangeonaquametalionsacrosstheperiodictablecover20ordersofmagnitude(seeright).Generally:Lowerchargeleadstofasterexchangewhilehigherchargeleadstoslowerexchange.Similarly,largerionsizeleadstofasterexchangewhilesmallerionsizeleadstoslowerexchange.Ir3+isratherlarge

[V(OH2)6]2+

[Co(OH2)6]2+

[Ni(OH2)6]2+

Ionic radius / pm


79

69

10-2

10-4

10-675

10

5

0

log kex (s-1)

0 1 2 3 4 5 6 7 8 109

LFSE

d electron number

Jahn-Teller

Ca2+

Mn2+

Zn2+

V2+

Ni2+

Fe2+

Co2+

Cr2+ Cu2+

0

1.2 o

>200 y 1 day 1 h 1 s 1 ms 1 s 1 ns

water ligand residence time (= 1/kex)

Ir3+ Cr3+

Pt2+

Al3+ Fe3+ Ti3+ Gd3+

Be2+ Mg2+ Cu2+

Li+ Cs+


Page37of43

andsodoesn’tfitwithintheaforementionedtrend!Whyisligandexchangethensoslowforthision?Becauseitisinthe3rdrow(5dmetalcomplex)andsoDoisverylargeandsotheCFSEislikewiseverylargeleadingtoaveryhighligandfieldactivationenergy(LFEA).Ligandswithexchangehalf-livesoflessthanaminutearenormallylabelledaslabilewhilethosewithexchangehalf-livesofgreaterthanaminutearelabelledasinert.SohowwastheexchangeonIr3+aqmeasured?SincewaterexchangeinvolvesbondbreakingfromMn+toresidentwater,whichhasanendothermicactivationbarrierofabout130kJmol-1,raisingthetemperaturewillspeedupthereaction.Infact,waterexchangeon[Ir(H2O)6]3+wasstudiedinpressurizedvesselsat120oCwhereaneventoccursnowinlessthan1hour.ThereactioncanbefollowedbyNMRusingenriched17O-labelledwater(17OhasanNMRsignallike1H).Ofallthe3dtransitionmetalaquaionsonlyCr3+aqisclassedasinert.Whyisthat?Octahedral[Cr(H2O)6]3+

hasahighchargecoupledwithaverystablet2g3configurationwith-1.2DoofLFSE.HighLFSEcorrelateswithahighligandfieldactivationenergy(LFAE)forexchange,whichtranslatestoslowexchange.Wecanseethisgraphicallytotheright.Fromthegraph,

Co3+aqshouldbethemostinert.Whyisthisnotthecase.Thevalueshowninthegraphabovepresumesthat[Co(H2O)6]3+hasalowspinconfigurationwhereithasahighcharge(highDo)coupledwithat2g6configurationandthereforehasthemaximumLFSEpossibleof-2.4DoandthereforealsoahighLFAE.ThecomplexcouldhaveahighspinconfigurationandsoCo3+wouldthenhaveaLFSEofonly-0.4Do.OfcoursewecouldlookatthemagneticpropertiestodeterminetheelectronicconfigurationofthecobaltionbutwecanalsotellfromtheM-OH2distancesintheaquacomplexes(seethegraphtotheleft).ThedecreaseinM-OH2distanceonceagainreflectsdecreasingM3+ionicradiusacrossseries.Therateofexchangeon[Co(OH2)6]3+hasnotbeenmeasuredhoweverbecauseitisnotstableas[Co(OH2)6]3+spontaneouslyoxidizeswatertoO2.WecanassessthisfromtheEovaluesandDGo

cell=-nFEocell=-4*96487*0.75=-386kJmol-1.

Theexchangereactionobservediscatalysedbythemorelabile[Co(OH2)6]2+generatedfromtheredoxreactionshownabove.[Co(OH2)6]3+providesanothergoodexampleofthelackofcorrelationbetween

-100

-200

0

-300

-400

-500

-600

LFSEkJ mol-1

0 2 4 6 8 10

number of d electrons

M3+

M2+

V2+

Ca2+

Ni2+

Mn2+ Zn2+

Cr3+

Co3+-100

-200

0

-300

-400

-500

-600

LFSEkJ mol-1

0 2 4 6 8 10

number of d electrons

Cr3+

Co3+

210

200

190

180

M-OH2 distance / ppm in aqua salts

Fe3+Sc3+ Ga3+


Page38of43

thermodynamicstabilityandkineticlability.[Co(OH2)6]3+isinertyetonlymetastable.LiterallyhundredsofstableCo3+complexesareknownwithligandsotherthanwater.MostoftheligandsN-donorligands.Becauseoftheirredoxstability,coupledwithslowratesofligandexchange,manyofthesehaveplayed

ahugeroleindevelopingourunderstandingofthemechanismsofreactionsattransitionmetalcentres.WhyistheresuchahugedifferenceinEovaluesbetweenthetwocomplexesontheleftwithCoIIIstabilizedhugelywithN-donorslikeNH3?Thereasonrelatesbacktothedifferentligands

used.NH3(andotherN-donorligands)ares-donorswhilewaterisas-donorp-donorligand.Theaddedp-donationraisestheenergyofthet2gorbitalsandreducesDo.Moreover,waterisaweakers-donorthanNH3giventhemoreelectronegativecoordinatingoxygenatom.Theseeffectsdecreasethestabilityofthelowspind6configurationof[Co(OH2)6]3+(belowleft)withrespecttoitreductiontothehighspind7[Co(OH2)6]2+(Do<P)(belowright),therebyprovidingavacancyinthet2gsetforanadditionalelectron.

ThereareonlytwoknownhighspinCo3+complexes:

• [Co(OH2)3F3]• [CoF6]3-

Thisisduetogoodp-donationfromF-,whichdramaticallydecreasesDo.AllotherCo3+complexesarelowspin,whichisduetostrongers-donationoftheligandsoutweighingallothereffects.10LIGANDEXCHANGEMECHANISMS.Youallarefamiliarwithsubstitutionreactionsoncarbon:SN1andSN2.Thereexistcomparablemechanismsforligandreplacementonthemetal

• Dissociative–similartoSN1• Associative–similartoSN2

TheDissociativepath:Xleavesfirst,generatingacoordinativelyunsaturatedcomplex,andthenYcoordinatesatthevacantsiteonthemetal(shownbelow).TheAssociativepath:M-Ybondformsfirst,generatingacongestedcomplex,followedbyde-coordinationofX.

o

t2g

eg

o

t2g

egOH2

O2p

o

t2g

eg

o

t2g

egOH2

O2p

ML

L L

X

L

L

n+

ML

L L

Y

L

L

n+

Y

X

ML

L L

X

L

L

n+

ML

L LL

L

n+

- X+ X

ML

L L

Y

L

L

n+

+ Y

- Y


Page39of43

Whichpathwouldyoupredicttohavethelargestactivationenergy?Answer:Thedissociativepath.Why?Thismechanisminvolvesabond-breakingstep(M-Xbond)intheratedeterminingstep(RDS),whichwillbeendothermicbeforethenewbondisformed–formallythisisatwo-stepreaction.Analogously,SN1reactionsarefrequentlyslowerthanSN2reactionsforthesamereason.Theassociativepathinvolvesabond-makingstep(M-Y),whichwillbeexothermicpriortobondbreaking(M-X)andsoshouldpossessaloweractivationenergy.Additionally,thepresenceofthenewM-YbondmaylowertoenergyrequiredtobreaktheM-XbondTheactivationenergyEacanbedeterminedfromthetemperaturedependenceofthereactionrateaccordingtotheArrheniusorEyringequations.

TheArrheniusequationisshownbelow,withthelinearizedformtotheleft.NoticethattheslopeisEa/R,whereRisthegasconstant:

reactant

product

Go

reaction coordinate

Energy

favourable negative Go

(spontaneous reaction)

activation energy Ea

ln k = ln A -Ea

RTor k = A e

-Ea

RT

ML

L L

X

L

L

n+

+ YM

L

L LL

L

n+

- YY

X

ML

L L

Y

L

L

n+- X

+ X

D


Page40of43

TherelatedEyringequationisshownbelow,wherek’andharetheBoltzmannandPlanck’sconstants,respectively:

WecanrearrangetheEyringequationtogive:

RecallthatDG‡=DH‡–TDS‡andsotheEyringequationcannowberewrittenintermsofenthalpyandentropyofactivation.

Ifwenowplotthisequation,weseethat–DH‡/RTistheslowwhileDS‡+ln(k’/h)isthey-intercept.

Thereactioncoordinatediagramontheprecedingpagerepresentsaconcertedreaction,proceedingviaatransitionstate(likeanSN2reaction).Theenergydiagramtotheleftrepresentsatwo-stepreactionwithanintermediate.Let’snowlookinmoredetailatthedifferenceinreactionprogressionbetweenanassociativeandadissociativemechanism.Inadissociativeprocess,thefirststepistheratedeterminingstepwhileinanassociativeprocess,thesecondstepisratedetermining.

ln k = lnRT

or k = ek' T

h

G k' T

hRT

G

-

ln k = lnRT

k' T

h

G- ln k = ln

k'

h+ lnT

RT

G-

ln =k'

h+ ln

RT

G-k

T

ln =k'

h+ ln-k

T R

S+

RT

H

D ‡D ‡

D ‡ D ‡

D ‡

D ‡ D ‡

reactants

intermediate

products

transition state

transition state

G 1 G 2

MLL L

X

L

L

n+

MLL L

L

L

n+

MLL L

X

L

L

n+

MLL L

Y

L

L

n+

MLL L

Y

L

L

n+

A dissociative process

Energy

Reaction coordinate


Page41of43

Let’slookatsomeexamplesandreturntowaterexchangeonaquametalions.

Fromthisdatawecanseethatincreasingegoccupancyleadstohigherlability(smallerDH‡)butdoesn’tchangethemechanismwhileincreasingt2goccupancycorrelateswithanincreaseinDH‡andamorepositiveDS‡andleadstodissociativebehaviour.DH‡correlateswithLFSE,whichisameasureofthestrengthoftheM-OH2bond.However,DH‡isoflimiteduseasamechanisticindicatorasallvaluesarepositive.WesawpreviouslythatkexcorrelateswithLFSE.WecannowdeducethatkexcorrelateswithDH‡.Thisisentirelyexpectedas,regardlessofthemechanism,therewillbeabond-breakingeventalongthereactioncoordinate(mostendothermicstepofthereaction,mostimpactingtherate).Whatabouttheentropyofactivation?DS‡toacertainextentcorrelateswiththemechanistictrendBUTthisvalueispronetolargeerrorsbasedonthemathematicalextrapolationtoinfinitetemperature.

Metal ion Mechanism H S

[V(H2O)6]2+

[Fe(H2O)6]2+

[Ni(H2O)6]2+

dn config

t2g3 eg

0 associative 62 ~0

41 +21

46 +37

57 +32

[Co(H2O)6]2+

[Mn(H2O)6]2+ 33 +6

increasing t2g occupancy

increasing eg occupancy

increasingly dissociative

associativet2g3 eg

2

t2g4 eg

2

t2g5 eg

2

t2g6 eg

2

kJ mol-1 J K-1 mol-1

D ‡ D ‡D ‡

D ‡

D ‡ D ‡


Page42of43

Isthereanotherparameteravailablethatwecanuseasanindicatorofthemechanisticpathway?TheanswerisYESanditistheactivationvolume,DV‡.Let’snowconsiderthetwopossiblepathwaysagain.

ThedissociativeprocesswithhaveapositiveDV‡.TheincreaseinDV‡correspondstothevolumeoffreeX.TheassociativeprocesswithhaveanegativeDV‡.ThedecreaseinDV‡correspondstothevolumeoffreeY.HowdowemeasureDV‡?Fromthepressuredependenceofthereactionrate:AplotoflnkvsPwillprovideaslopeof-DV‡/RT.A positiveslope(soDV‡isnegative)representsanassociativemechanismwhileanegativeslope(soDV‡ispositive)representsadissociativemechanism.Nochangeinsloperepresentsaconcertedmechanismandaninterchange(I)mechanism.Wecannowappreciatewhyvariousmechanismswouldhavesuchrate/pressuredependencies.AdissociativeprocessinvolvestheexpulsionoftheleavingligandX(expansive)sowouldbeexpectedtoberetardedbyapplyingpressure:negativeslope-positiveactivationvolume.AnassociativeprocessinvolvesthetakeupofY(compressive)sowouldbeexpectedtobeacceleratedbyapplyingpressure:positiveslope-negativeactivationvolume.Let’sgobacktothepreviousexample:

WecannowseethatDV‡isagoodindicatorofthemechanism.

Metal ion Mechanism H S

[V(H2O)6]2+

[Fe(H2O)6]2+

[Ni(H2O)6]2+

dn config

t2g3 eg

0 associative 62 ~0

41 +21

46 +37

57 +32

[Co(H2O)6]2+

[Mn(H2O)6]2+ 33 +6

increasing t2g occupancy

increasing eg occupancy

increasingly dissociative

associativet2g3 eg

2

t2g4 eg

2

t2g5 eg

2

t2g6 eg

2

V

-4.1

kJ mol-1 J K-1 mol-1

-5.4

+3.7

+6.1

+7.2

cm3 mol-1

d (ln k)dP

= - VRTD ‡

D ‡ D ‡ D ‡


Page43of43

IncreaseinegoccupancylowersDH‡butdoesn’tchangethemechanism,whereitremainsassociativewhileanincreaseint2goccupancyincreasesDH‡ANDgivespositivevaluesforDV‡,therebyalteringthemechanismtoonethatbecomesmoredissociative.WecanunderstandthesetrendsfromanMOperspective.Increasingegoccupancyweakens(lengthens)theresidentM-OH2bonds–decreasingLFSEandloweringDH‡–andincreasestherateofexchange.However,increasingt2goccupancywillrepeltheelectronsontheenteringligandY-facilitatingthedissociativepathway.Asthemetalcentregetssmaller,thereactionbecomesmoredissociative.Jahn-Tellerdistortionwillalsofavouradissociativemechanismofthefirsttwowatermolecules.

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