Physical Inorganic Chemistry CH3514 - Eli Zysman-Colman

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PhysicalInorganicChemistry

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Dr EliZysman-Colman

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2PhysicalInorganicChemistry

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DrEliZysman-Colman

Rm244inPurdie

[email protected]

http://www.zysman-colman.com/courses/ch3514_2017aut_en.php

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DrEliZysman-Colman

Rm244inPurdie

[email protected]


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DrEliZysman-Colman

Rm244inPurdie

[email protected]


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5CourseOutline

5

PhysicalChemistryandBonding ofTransitionMetals

Aims: Acontinuationofthechemistryofthe3dtransitionmetalswithparticularfocus

onthethermodynamics,bondingandkineticsofreactions.

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6CourseOutline

6

PhysicalChemistryandBonding ofTransitionMetals

Objectives:

• Asummaryofhowd-orbitalsaffectthepropertiesofthetransitionmetals.

• Tounderstandmetalion-ligandcomplexation equilibria;stepwiseformationandoverall

stabilityconstants.RelationshipofbML toKMLandDGoML

• TounderstandthetrendsinbML acrosstheperiodSc – ZnandtheIrvingWilliams

maximumatCu2+ duetoJahn-Tellereffectatd9

• Tounderstandhowmolecularorbitaltheorycanbeusedtoexplainthepropertiesof

metal-ligandcomplexes

• Tounderstandtheoriginsofthechelateeffect– theincreaseinbML withchelate

ligands.Toappreciateandrationalisetheentropicandenthalpic factorsinvolved–

trendsacrosstheperiod.CorrelationofKn (bn)valueswithLFSE.• Toappreciatethatthermodynamicstabilityandkineticlability areindependent

phenomena– notnecessarily correlated.Equilibriumcanberapidlyobtained

irrespectiveofthesizeofK.

• Toappreciatetherangeoflabilities on3daquametal ionsandthecorrelationwith

LFSE.Definitionofthetermsinertandlabile.CorrelationofinertnesswithhighLFAE–

linkedtoLFSE.

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7ResourceBooks

7

InorganicChemistry,6th EditionMarkWeller,TinaOverton,

JonathanRourke andFraserArmstrong

OrganotransitionMetalChemistryFromBondingtoCatalysis

JohnHartwig

InorganicChemistry,4th EditionCatherineHousecroft andAlanSharpe

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8FrontierMO’sofσ-Donor,π-Donorandπ-AcceptorLigands

8

BeforewecanunderstandMOdiagramsandbondingincomplexes,wemust

understandthenatureofthefrontierMOsofligands.

Therearethreetypesoforbitalinteractionsbetweenligandsandmetals,whichdefine

theligandtype:

• s-donors• p-donors• p-acceptors

HOMO LUMO

[Ru(bpy)3]2+

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9FrontierMO’sofσ-DonorLigands

9

These ligandsdonatetwoe–sfromanorbitalofσ-symmetry:

Examplesinclude:H-,CH3-,NR3,PR3,OH2.

Let’slookatNH3 inmoredetailasanexampleofamolecular ligand(asopposedtoasimpleatomicligand)

Thereare3N-Hs-bondsinthismolecule

andithasC3 symmetry

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10




Let’sanalyzetheSymmetryAdaptedLinearCombinations(SALC)moreclosely.

Nonodes 1node

Recall thatonlyorbitalsofthesamesymmetrycancombine

toformnewLinearCombinationsofAtomicOrbitals(LCAO)

3H’s

N

a1 e

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11




Let’sdeterminetheLinearCombinationsofAtomicOrbitals(LCAO)s

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12


Let’snowlookattheMOdiagram

Remember:• Thegreatertheoverlap,thegreaterthesplitting

• Thecloserinenergybetweenthetwosetsoforbitals,

thegreater thesplitting

Note:• TheHOMOisusedforbondingtothemetalanditis

thelonepaironNinas-orbital• MOdiagrampredictsMOsof3differentenergies,

whichisborneoutbyPES

8valencee-s

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13

HowaboutH2Owithits2lonepairs?

Note:• TheHOMOisusedforbondingtothemetalanditis

thenon-bondinglonepaironOinap-orbital• MOdiagrampredictsMOsof4differentenergies,

whichisborneoutbyPES

H O H

H O H

H O H

H O H

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14FrontierMO’sofp-DonorLigands

14

Inadditiontodonatingelectrondensitytoametalviaaσ-bond,

e–smaybeprovidedtothemetalviaaπ-symmetryinteraction.

π-donorligands includeX– (halide),amide(NR2–),sulfide(S2–),oxide(O2–),alkoxide (RO–)

h3-C3H5,h5-C5H5,h6-C6H6

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15FrontierMO’sofp-DonorLigands

15

Let’slookatNH2-,whichwecanthinkofas“planar”NH3withaLPreplacingoneoftheHatoms

theHOMOisfilledandofp-symmetry

Therearenow2extrae-s

comparedtoNH3

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16FrontierMO’sofp-AcceptorLigands

16

Thisclassofligandsdonatese–sfromaσ orbital

andthese ligandsaccepte–sfromthemetalintoanemptyπ*orbital.

COisthearchetypeofthis ligandclass.

Otherπ-acceptorsareNO+,CN–,CNR, H2,C2H4,N2,O2,PR3,BR2

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17FrontierMO’sofp-AcceptorLigands

17

Thisclassofligandsdonatese–sfromaσ orbital

andthese ligandsaccepte–sfromthemetalintoanemptyπ*orbital.

COisthearchetypeofthis ligandclass.Otherπ-acceptorsareNO+,CN–,CNR.

theHOMOisfilledandofσ-symmetry,theLUMOisemptyandofπ*symmetry

HOMO

LUMO

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18ElectronicStructureandPropertiesofComplexes:

CrystalFieldTheory

Twotheoriesarecommonlyusedtorationalizeelectronicstructure

• CrystalFieldTheory(emergedfromananalysisofthespectraofd-metalionsinthesolid)

• LigandFieldTheory(emergedfromanapplicationofMOtheorytod-metalcomplexes)

• Complexesheldtogetherviaelectrostaticforcesbetweenthepositivelychargedmetalandthe

negativelychargedorpolarizedligands

• Modelsinteractionsbasedonelectrostaticswiththevalenceelectronsofthemetalinthed-orbitalsand

theligandsasnegativecharges(ion-ioninteractions)ordipoles(ion-dipole)interactions

(IONICbondingmodel)

• Strongerinteractionsbetweenelectronsofthemetalandtheligandsresultingreaterdestabilization

• Theenergydifferenceofd-orbitalscorrelateswiththeoptical,magneticandthermodynamicproperties

ofthecomplex

CFTAssumptions

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CrystalFieldTheory

Thelobesofthedx2-y2anddz2 orbitalsliedirectlyalongthe

x,y and/or z axes

Thelobesofthedxy,dxzanddyzorbitals liebetweentheaxes

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CrystalFieldTheory

stabilization

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CrystalFieldTheory– OctahedralComplex

crystalfieldsplittingparameter

Ene

rgy

Δo3/5Δo

2/5Δo

eg

t2g

barycentre

• Theenergydifferencebetweenthetwosetsoforbitalsisthecrystalfieldsplittingenergy - denotedDO (or10Dq)

• Theeg orbitalsareraisedinenergy

• Thet2g orbitalsareloweredinenergy

Thelobesofthedx2-y2 anddz2belongtotheeg representation

Thelobesofthedxy,dxz anddyzbelongtothet2g representation

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CrystalFieldTheoryLimitations&

MO(LFT)Theory

QuestionsforwhichCrystalFieldTheoryhasnoanswers:

• WhyisKMnO4withMn7+ andnod-electronscoloured?

• WhyisOH- aweakerfield ligandthatH2O?

• WhyareneutralligandslikeCO,whichareotherwiseverypoor

Lewisbasessuchstrongfieldligands?

• WhyinEPRspectraofhighspincomplexes istherehyperfine

splitting, indicatingthatthespinisdelocalizedontothe ligands?

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24MO(LFT)Theory

Theinteractionofthefrontieratomic(forsingleatomligands)or

molecular(formanyatomligands)orbitalsoftheligandandmetal leadtobondformation

Someimportantpoints:• M—Latomicorbitalmixingisproportionaltotheoverlapofthemetalandligandorbital(SML)

• Owingtomoredirectionalbonding(greateroverlap)alongtheseriesSML(σ)>SML(π)>SML(δ),

whichleadstogreatersplittingalongtheseries

• M–Latomicorbitalmixingisinverselyproportionaltoenergydifferenceofmixingorbitals(i.e.ΔEML)

• OnlyorbitalsofcorrectsymmetrycanmixandthetotalMOs=sumoftheprecursororbitals

• TheorderoftheELandEM energylevelsalmostalwaysis:

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25MO(LFT)Theory



Somegeneralobservations:• ThesorbitalsofL’saregenerallytoolowinenergytoparticipateinbonding(ΔEML(σ)isverylarge)

• FilledporbitalsofL’sarethefrontierorbitals,andtheyhaveIEsthatplacethembelowthemetalorbitals

• FormolecularL’s,whosefrontierorbitalscomprisesandporbitals,heretoofilledligandorbitals

haveenergiesthatarestabilizedrelativetothemetalorbitals

• LigandorbitalenergyincreaseswithdecreasingEneg ofLewisbasicbondingatomE(CH3-)>E(NH2

-)>E(OH-)

• Morbitalenergydecreaseswithincreaseoxidationstateofmetal,asyougodowntheperiodictableand

asyougofromlefttorightontheperiodictable

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26MO(LFT)Theory



Somegeneralobservations:• ThesorbitalsofL’saregenerallytoolowinenergytoparticipateinbonding(ΔEML(σ)isverylarge)

• FilledporbitalsofL’sarethefrontierorbitals,andtheyhaveIEsthatplacethembelowthemetalorbitals

• FormolecularL’s,whosefrontierorbitalscomprisesandporbitals,heretoofilledligandorbitals

haveenergiesthatarestabilizedrelativetothemetalorbitals

• LigandorbitalenergyincreaseswithdecreasingEneg ofLewisbasicbondingatomE(CH3-)>E(NH2

-)>E(OH-)

• Morbitalenergydecreaseswithincreaseoxidationstateofmetal,asyougodowntheperiodictableand

asyougofromlefttorightontheperiodictable

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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LFTTheory

WhatisLigandFieldTheory?

Itis:

• Asemi-empiricaltheorythatappliestoaclassofsubstances(transitionmetal

complexes)

• Alanguage inwhichavastnumberofexperimental observationscanberationalizedand

discussed

• Amodelthatappliesonlytoarestrictedpartofreality

Itisnot:

• Anabinitiotheorythatletsonepredictthepropertiesofacompound

• Aphysicallyrigoroustreatmentoftheelectronicstructureoftransitionmetalcomplexes

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LFTTheory

Sigma(s)bonding

• Neutralligands(e.g.,NH3)oranionic ligands(e.g.,F-)possess lonepairsthatcanbondto

metal-basedorbitals (s,px,py,pz, dxy,dyz,dxz,dx2-y2,dz2)withs-symmetry

• InanOh complex,6symmetry-adaptedlinearcombinations(SALCs)ofthe6ligands-symmetryorbitalscanbeformed

• MOsfortheresultingcomplexareformedbycombiningtheligandSALCsandthemetal-

basedd-orbitalsofthesamesymmetrytype

• With6SALCscombinedwiththemetalMOs,wewillget6bondingand6antibonding

MOs– nowcalled ligandgrouporbitals(LGOs)• TheresultingMOdiagramnowgetspopulatedwiththeelectronsaccordingtothe

Aufbau process,PauliexclusionprincipleandHund’srule

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LFTTheory– OctahedralComplexes

Sigma(s)bonding:Simpleexampleshowinginteractionofligands-orbitalswithmetal-

basedorbitals

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Sigma(s)bonding:Simpleexampleshowinginteractionofligands-orbitalswithmetal-

basedorbitalsnotpropersymmetrysono interaction

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Sigma(s)bonding:• Formost ligands,theirSALCs

arelowerinenergythanthe

metal-basedd-orbitals

• Thereforethe6bonding MOs

ofthecomplexwillbemostly

ligand-based incharacter

• Thed-electronsofthemetalwill

occupythesame orbitalsasinCFT

• UnlikeCFT,thet2g orbitalsarenon-bonding andtheegorbitalsareanti-bonding

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ExampleTake[Co(NH3)6]

3+

NH3 cans-bondthroughits lonepair

Tosummarize:• Of9valenceorbitals(5xd,3xp,1xs)

only6aresuitablefors-bonding• Thecombinationoforbitalsfromligandsand

frommetalarecalled

LigandGroupOrbitals(LGOs)• TheDO hereisthesameasinCFT

• Co3+ isd6 andthereare12e- from

the6NH3 ligands

• Asthisisadiamagnetic

LScomplex,the

6-delectronsoccupy

onlythet2g set

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3+


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3+


ligand-basedbondingMOswith

strongligandcontributions

metal-basednon-bondingAOs

metal-basedanti-bondingMOswith

strongmetalAOcontributions

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Pi(p)bonding:• ThepreviousMOdiagramignoresp bonding.Ifthe ligandspossessorbitalsoflocalp-

symmetrythenthesecaninteractwiththemetald-orbitalswiththesamesymmetry(i.e.

thet2g set)toformnewLGOs

• These ligandSALCscanactaselectrondonors(populated)orelectronacceptors(vacant)

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Pi(p)bonding:• ThepreviousMOdiagramignoresp bonding.Ifthe ligandspossessorbitalsoflocalp-

symmetrythenthesecaninteractwiththemetald-orbitalswiththesamesymmetry(i.e.

thet2g set)toformnewLGOs

• These ligandSALCscanactaselectrondonors(populated)orelectronacceptors(vacant)

• ThenatureofthissecondaryinteractionwillaffectDo

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Pi(p)donorligands:(akap-bases)

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ExampleTake[FeCl6]

3-

Clcans-bondthroughitslonepairAND

p-bondthroughitsp-orbitals

TheCl- porbitalscannowinteract

withtheFet2g,whicharedestabilized

Thesecomplexesarenowlargely

highspin

Highoxidationstatecomplexes

arepossiblewithp-base ligandse.g.,[MnO4]

-

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ExampleTake[FeCl6]

3-






highspin

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ExampleTake[FeCl6]

3-






highspin

BothFe-centered

t2g andeg

areantibonding!

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Pi(p)acceptorligands:(akap-acids)

p-backbonding effectivelyremoveselectrondensityfromthemetal,whichdoesnotliketohavetoohighanelectrondensity.

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ExampleTake[Cr(CO)6]

COcans-bondthroughitslonepaironCAND

p-bondthroughitsp-orbitalsAND

itsp*orbitalscanform

bondinginteractions

withmetaldorbitals

• NowtheCot2gorbitals

arestabilized

• Thesecomplexesarenow

largelylowspin

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ExampleTake[Cr(CO)6]

COcans-bondthroughitslonepaironCAND

p-bondthroughitsp-orbitalsAND

itsp*orbitalscanform

bondinginteractions

withmetaldorbitals

Co-centeredeg

isantibondingwhile

t2g

isbondingwith

thep*ofCO!

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CrystalFieldTheoryLimitations&

MO(LFT)Theory

Summary: p-bondingandp-backbondingmodulatetheenergyofthemetalt2g orbitals

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45MO(LFT)Theory

Summary: p-bondingandp-backbondingmodulatetheenergyofthemetalt2g orbitals

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46MO(LFT)Theory:AQuickLookatSquarePlanarComplexes

HowwouldtheoctahedralMOdiagrambeperturbedifweremovedtheaxialligands?

ExampleTake[Pd(NH3)4]

2+

i.e.onlys-donation

Thedx2-y2 MO(b1g)contains

verystrongmetal−ligand

antibondinginteractions

inthexy plane.ItistheLUMO

Thedz2 MO(a1g)contains

slightmetal−ligand

antibondinginteractions

inthexy plane.ItistheHOMO

Thedxy,dxz,dyz,MO(eg,b2g)

arenormallypresentedas

degenerateandnon-bonding

(nosymmetrymatchwith

ligandMOs)

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47MO(LFT)Theory:AQuickLookatSquarePlanarComplexes

HowwouldtheoctahedralMOdiagrambeperturbedifweremovedtheaxialligands?

Whataboutligandswithp-character?

Includingp-interactionsresultsinare-orderingoftheenergiesoftheMOs,

unlikewhatwesawwithOh complexes.

Forcomplexeswithp-donatingligands,the

HOMOistheeg MOsandnotthea1gMOasa

resultofthedestabilizationfromπ-antibonding

interactionswiththe lonepairsoftheligands.

Inaddition,thea1g MOisenergeticallystabilized,

duetotheweakσ-donatingpropertiesofligands

interactingwiththemetaldz2 orbital

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48Water– TheMostFundamental Ligand

Sincewatercanbeviewedasthemostfundamentalligandwewilluseaqueoussolutions and

thespecies foundthereinasthebasisforexploringthechemistry

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49ASummaryofMetalAquaComplexes

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+

d5[Mn(OH2)6]3+

d4- [MnO4]3-

d2[MnO4]2-

d1[MnO4]-

d0

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 = 5 or 6)- -

Zn [Zn(OH2)6]2+

d10- -

green – stable

red – reducing

blue – oxidising

purple - metastable

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50CoordinationGeometries

Common

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51CoordinationGeometries

Unusual

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52HydrolysisChemistry

WhydoesMnII existasanaquacomplex[Mn(OH2)6]2+

whileMnVII existsasanoxo complex[MnO4]- ?

TheClueliesintheacid-basechemistry

Housecroft andSharpe,Chapter7,page191-193

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• ThemetalactsasaLA.WhenH2Ocomplexestothemetal,theO-Hbondispolarizedandthe

protonbecomesacidicandsocanbeabstractedbysolventmolecules

• Asthechargedensity increasesonthemetal, theO-Hbondbecomesmorepolarizedand

theprotonacidityincreasesandmoreprotonsareabstractedintosolutionandtheOH2 ligand

becomesanOH- ligand,reducingtheoverallchargeofthecomplex.• Thesolutionthusbecomesmoreacidic

Hydrolysisreaction

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• IfnowastrongerLBisusedthenmoreandmoreprotonscanbeabstractedfrommetalaqua

complexes

Hydrolysisreaction

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Wecandetermine therelativeacidities of[M(OH2)6]2+ and[M(OH2)6]

3+ ions

canbeseenbelowintermsoftherespectivepKa values

ForFespecies:

ThepKa for[Fe(OH2)6]3+ issimilartothatofformicacid(2.0)– itwillliberateCO2 fromcarbonate

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56HydrolysisChemistry– pKa Trends

=Z2/relectrostaticparameter

Empiricalrelationshipthatisalsobasedontheelectronegativityofthemetal

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Ifweincreasetheoxidationstateonthemetal further(andhencethechargedensity)

wecanevenrendertheprotonofthehydroxideligand,O-H-acidic

Astheoxidationstateonthemetal increasesfurtherwecanobtainmultiple oxo groups

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AtOS6+andgreatertheionicradiusbecomestoosmalltoaccommodate

6ligandsandthusa4-coordinatetetrahedralcomplexispreferred.

Oxogroupspossessothertraitsthathelptostabilizetheresultingmetalcomplex

• O2- helpstoneutralizehighchargeonthemetalfromhighOS

• Formetalswithlowd-electroncount,strongp-donorabilityhelpstostabilizet2g orbital

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Afurtherreactioncantakeplacewiththetrivalenthydroxo ions.Theycan‘condense’

togetherinaprocesscalled ‘hydrolyticpolymerisation’

HeretheOH- ligandretainsadegreeofnucleophilicity andsubstitutes awateronan

adjacention

Housecroft andSharpe,Chapter7,page192c

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Thisprocesscancontinue- buildinguphugeOH- bridged polynuclear structuresuntil

solubility limitsareexceededresultinginprecipitationofthehydroxide;M(OH)3 aq.

Accompanyingdehydrationcanalsooccurleadingtooxy-hydroxideoroxide(M2O3)

formsprecipitating

Fe(III)hydrolysishasbeenwellstudiedandpolymericnanostructurescontainingover100iron

atomshavebeencharacterizedbeforeFe(OH)3 precipitation.

StructureofaFe19 clusterwithtriplyoxideandhydroxidebridgesanddoublybridginghydroxides

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FeHydrolysisinActioninvivo

Ferritinisaproteinthatstoresironinourbodybyconcentratingitviacontrolledhydrolysisof

Fe3+aq toyieldhugeoxy-hydroxy bridgednanostructurescontainingupto4500ironatoms.

Movementofironinandoutoftheproteinis

achievedviareductiontoFe2+aq whichdoesn’t

hydrolyseatpH7andpassesthroughspecific

M2+-sensingchannels

Housecroft andSharpe,Chapter29,page966

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Ferritinisaproteinthatstoresironinourbodybyconcentratingitviacontrolledhydrolysisof

Fe3+aq toyieldhugeoxy-hydroxy bridgednanostructurescontainingupto4500ironatoms.

Movementofironinandoutoftheproteinis

achievedviareductiontoFe2+aq whichdoesn’t

hydrolyseatpH7andpassesthroughspecific

M2+-sensingchannels


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TheinstabilityofFe3+aq solutionsatpH7withrespecttohydrolysistoinsolubleFe(OH)3

(Ksp =2.6x10-39)makesitachallenge forbiologytoconcentrateironinthebody.

Ksp =[Fe3+aq][OH

-]3

Toachievethis,Naturehasevolvedverypowerfulagentsthatbindandsolubilizeallformsof

Fe(III)evenFe(OH)3 toenableefficient ironuptake.Thesecompoundsarecalledsiderophores(Greek- ironcarrier)

Someofthesehavethehighestmeasuredequilibriumconstantsforametalion- ligand

combination.Therecordvalueisheldbyenterobactin

catecholateFe3+

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siderophore donorset logK

aerobactin hydroxamate,carboxylate 22.5

coprogen hydroxamate 30.2

deferrioxamine B hydroxamate 30.5

ferrichrome hydroxamate 32.0

Enterobactin catecholate 49.0

aerobactin

Coprogen

ferrichrome

Deferrioxamine B

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65Thermodynamicsofmetalcomplexformation


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Thismeansprocessesatequilibrium. e.g.,hydrolysis,Fe3+ complexation withsiderophores

Let’slookatligandexchangeinmoredetailbylookingat

[M(OH2)6]n+ +mL�[M(OH2)6-mmL]n+�� [M(L)6]

n+(Lisaneutralligand)

K1-K6 areknowasstepwisestabilityconstants

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Thismeansprocessesatequilibrium. e.g.,hydrolysis,Fe3+ complexation withsiderophores

Let’slookatligandexchangeinmoredetailbylookingat

[M(OH2)6]n+ +mL�[M(OH2)6-mmL]n+�� [M(L)6]

n+(Lisaneutralligand)

b6 =K1*K2*K3*K4*K5*K6log(b6)=log(K1)+log(K2)+log(K3)+log(K4)+log(K5)+log(K6)

Weandefineanoverallstabilityconstant,b,forthecompleteexchangeofH2OligandsforL

Whatthisimplies isthatb6 >b5 >b4 >b3 >b2 >b1 andsotherewillalwaysbecomplete

substitution ofLforH2O

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Anexample:NH3replacingH2Oon[Ni(OH2)6]2+

-LogK1 -LogK2 -LogK3 -LogK4 -LogK5 -LogK6

-2.79 -2.26 -1.69 -1.25 -0.74 -0.03

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 =5.75x108

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Withknownequilibriumconstants,Kn,wecandeterminefreeenergyDGn

DGn=-RTln(Kn),whereRisthegasconstant8.314Jmol-1 K-1

Soat303K,DG1=-(8.314x10-3*303)ln(102.79)=-16.2KJmol-1

DGn=DHn –TDSn

IfDH1 =-16.8KJmol-1

DS1 =(DH1-DG1)/T=[-16.8-(-16.2)]/303=-1.98Jmol-1 K-1

Quitesmall– nochangein#molecules

Thereforesubstitution isprimarilyanenthalpic effect(DHisgoverningtheprocess)ThisisduetothestrongerNi2+-NbondsbeingformedcomparedtotheNi2+-Obonds

(moreexothermic)

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HSABTheory


NowwhyisNamorepreferreddonorthanOforNi2+?

Theanswerlies inHard-SoftAcidandBaseTheory(HSAB)


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HSABTheory


Salem-KlopmanEquation (simplified)

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HSABTheorySalem-KlopmanEquation (simplified)

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HSABTheorySalem-KlopmanEquation (simplified)

Considerthefollowingexamples involvingreplacementofwaterbyhalide ions

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

NotethevastlydifferenttrendsinlogKvalues!

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HSABTheory

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

NotethevastlydifferenttrendsinlogKvalues!

Fe3+ aq isHARD

Hg2+ aq isSOFT

Halidesgetharderassizegetssmaller

Thegoldenrule:StrongestM-LinteractionsrequireHHorSSmatch

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HSABTheory

Fe3+ aq isHARD

Hg2+ aq isSOFT



Thebehaviour ofFe3+aq isparalleledbysimilarbehaviour shownbytheGroup1and2

metalsandtheearly3dtransitionelements totheleft

Thebehaviour ofHg2+aq isparalleledbysimilarbehaviour shownbytheheavierp–block

elements andtheheaviertransitionelements totheright

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HSABTheory

Fe3+ aq isHARD

Hg2+ aq isSOFT



Orderofincreasingstability incomplexesforHardmetalions: O>> S>Se>Te

N>>P>As>Sb

Orderofincreasingstability incomplexesforSoftmetalions: O<< S>Se~Te

N<<P>As>Sb

Orderofdecreasinghardnessbasedonelectronegativity:

F>O>N>Cl >Br>C~I~S>Se>P>As>Sb


CH3514


HSABTheory

Orderofincreasingstability incomplexesforHardmetalions: O>> S>Se>Te

N>>P>As>Sb

Orderofincreasingstability incomplexesforSoftmetalions: O<< S>Se~Te

N<<P>As>Sb

Orderofdecreasinghardnessbasedonelectronegativity:

F>O>N>Cl >Br>C~I~S>Se>P>As>Sb


CH3514


HSABTheory

Ligandsdisplacewaterinacompetitiveprocess– notasimple combination

IftheMn+ isahard metal- itisalreadyassociatedwithhardH2O ligands.Thus

reactionwithanotherhardligandmaynotbefavourable– onlyasmallexothermic

enthalpyeffectmightbeseen.

Leadsonlytomoderatelystablecomplexes(-DGo small)

e.g.,withL=RCO2-,F-,Cl- etc.

NowifMn+ isasoftmetalandLasoftbase thereaction isnowhighlyfavouredsince itremovestwounfavourable soft-hardinteractions- fromwatersolvation

HereasignificantDHo effect(largeandnegative)isseenwhenthesoft-soft

interactionresults - leadstostablecomplexeswith DGo thatisalsolargeand

negative(DSo smallasbefore)- highKn

e.g.,Hg2+aq andS2-aq � HgS(s)precipitates

CH3514


WehaveexaminedthevaluesoflogKn (bn)forthesuccessivereplacementofH2O

onNi2+aqbyNH3

Whathappensalongthe3dseriesfromSc – Zn?

ThistrendshowingamaximuminlogK1 valuesfor

Cu2+ istermedtheIrving-Williamsseries

WhythemaximumatCu2+?

CH3514


OctahedralComplexes

TheIrving-WilliamsSeries

TheIrving-WilliamsSeries(IWS)describes anempirical increaseinstabilityofM2+ octahedral

complexesasafunctionofatomicradius,regardlessofthenatureofLforthefollowing

reaction:

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

2+ +H2O

Kf variesalong:Ba2+ <Sr2+ <Ca2+ < Mg2+ < Mn2+ < Fe2+ < Co2+ < Ni2+ <Cu2+ >Zn2+

CH3514


OctahedralComplexes

TheIrving-WilliamsSeries

TheIrving-WilliamsSeries(IWS)describes anempirical increaseinstabilityofM2+ octahedral

complexesasafunctionofatomicradius,regardlessofthenatureofLforthefollowing

reaction:

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

2+ +H2O

Kf variesalong:Ba2+ <Sr2+ <Ca2+ < Mg2+ < Mn2+ < Fe2+ < Co2+ < Ni2+ < Cu2+ > Zn2+

reflectselectrostatic effects

smallermetalwithsamecharge=

greaterchargedensity

Basedpurelyonelectrostatics

wewouldexpectstabilities tovaryas

Mn2+ <Fe2+ <Co2+ <Ni2+ >Cu2+ >Zn2+

Exception:Cu2+ isactuallymorestablethanNi2+

andthisisduetotheJahnTeller Distortion

CH3514

82Jahn-TellerDistortion– AShortOverview

Highspind4 t2g3eg

1

Lowspind7 t2g6eg

1ord9 t2g6eg

3

Let’slookatthecaseforLSd9 t2g6eg

3

Ifthereare2eindz2 and1eindx2-y2

thengreaterrepulsionalongthez-axis

� elongationoftheseM-Lbonds

alongthez-axistocompensate,

leadingtostabilizationofthedz2

orbital– mostcommondistortionE

Occurswhenyoucanasymmetrically fillorbitalsthataredegenerateinanon-linearcomplex.

Thegeometryofthecomplexthendistortstoreachamorestableelectronicconfiguration

netstabilizationof½E

CH3514


Highspind4 t2g3eg

1

Lowspind7 t2g6eg

1ord9 t2g6eg

3

Let’slookatthecaseforLSd9 t2g6eg

3

Ifthereare2eindz2 and1eindx2-y2

thengreaterrepulsionalongthez-axis

� elongationoftheseM-Lbonds

alongthez-axistocompensate,

leadingtostabilizationofthedz2

orbital– mostcommondistortion



Ifthereare2eindx2-y2 and1eindz2

thengreaterrepulsionalongthexy-

plane

� effectivecompressionoftheM-L

bondsalongthez-axistocompensate,

leadingtostabilizationofthedx2-y2

orbital

CH3514




CH3514


TheImpactofJahn-TellerDistortion

Thepresenceofonlyoneelectroninthedx2-y2 orbitalstrengthensthewaterligandattractionintheequatorialplaneduetolowere-erepulsionwiththedonorOelectrons

TheresultisaraisinginlogK1-4 andaloweringinlogK5 andK6 forwatersubstitution compared

tothetwoionseitherside;Ni2+ (d8)andZn2+ (d10)wherethere isnosuchextrastabilization


ReplacementofsuccessivewatersonM2+aq byNH3

CH3514


TheChelateEffect

Let’snowconsiderthesituationwhentheligandLreplacingcoordinatedwater

possesses twodonoratomsthatleadtotheformationofachelate ring

EDTAcomplex with Cu2+

CH3514


TheChelateEffect

Let’snowconsiderthesituationwhentheligandLreplacingcoordinatedwater

possesses twodonoratomsthatleadtotheformationofachelate ring

Theincrease inlogK1 aschelateringsare

formedisareflectionofamore

negativevalueofDGo1

Itis largelyduetoanincreaseintheentropyofreactioni.e.DSo1 islargeandpositive

DGo1=DHo

1- TDSo1

Thefigureshowsthatthereplacementof

NH3 onM2+aq bythechelatesen andEDTA is

thermodynamicallyfavourable.

Thisisageneralphenomenoncalled

thechelateeffect

CH3514


TheChelateEffect

Let’slookataspecificexample:Ca2+aq +EDTA4-

DGo1=-60.5KJmol-1;DSo1=117Jmol-1 K-1

At300K, DHo1=-25.4KJmol-1(DHo

1=DGo1+TDSo1)

Thereforethiscomplexation ismostlyentropydriven(TDSo1=-35.1KJmol-1)

Thoughthereisafavourableenthalpic termaswell(HSABandchelateeffect).

Whyentropycontrolled?Thereisanincrease inentropyduetoreleaseof6watermolecules – increase indisorderofthesystem

CH3514


TheChelateEffect


DGo1=-60.5KJmol-1;DSo1=117Jmol-1 K-1

At300K, DHo1=-25.4KJmol-1(DHo

1=DGo1+TDSo1)

WecannowcalculateK1asDGo1=-RTln (K1)

log(K1)=log(e-DG1/RT)=10.53

Wecannowaddthispointtothepreviousfigure!

CH3514


TheChelateEffect


Thefigureshowsthatthereplacementof

NH3 onM2+aq bythechelatesen andEDTA is

thermodynamicallyfavourable.

Thisisageneralphenomenoncalled

thechelateeffect

CH3514


TheChelateEffect

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

DGo1=-57.2KJmol-1;DHo

1=-16.6KJmol-1;-TDSo1=-36.1KJmol-1

bothenthalpyandentropyeffectsreinforce

Theenthalpic effect onchelationfromen arisesfromstrongerbonds

totheN donorsofthechelateasaresultoftheformationofthering

CH3514


TheChelateEffect

Let’slookatanotherspecificexamplewheretheenthalpyandentropy

termsdonot reinforceeachother:Mg2+ +EDTA4-

DGo1=-51.2KJmol-1;DHo

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

Heretheendothermicenthalpytermarisesfromtheunfavourablereplacementof

twohard waterligandsontheextremelyhard Mg2+ bythesofter N donorsofEDTA4-

(HSAB).

Formationofthechelate ishoweverstillhighlyfavouredduetothefavourable

entropycontribution

CH3514

93

HARD SOFT

Thermodynamicsofmetalcomplexformation

TheChelateEffect

ThisbegsthequestionwhyisMg2+ harderthanCa2+?

Mg2+ issmaller(chargemoreconcentrated)thanCa2+,whichwillreinforcethe

electrostatic interaction(Hard-Hard)interactionwithH2O

Salem-KlopmanEquation (simplified)

CH3514


TheChelateEffect

Wecanalsoprobetheeffectofthenatureofthedonoratomonthebindingstrength

tothemetal.

OrderoflogK1reflectsHSABtheory

ForNi2+ toZn2+ (soft metals):(soft)N^N>NÔ>OÔ(hard)

ForMn2+(hardmetal):

(hard) OÔ>NÔ>N^N(soft)

CH3514


TheChelateEffect

Wecanalsoprobetheeffectofthenatureofthedonoratomonthebindingstrength

tothemetal.

CH3514

96


TheChelateEffect

Bindingstrengthisalso influencedbythenumberofdelectronsonthemetal (LFSE)

IgnoringLFSE,increasingK1

reflectsstrongerM-Lbonding

asafunctionofincreasing

chargedensityontheMastheionic

radiusdecreases alongtheperiod

CH3514

97


TheChelateEffect

Whydoestheionicradiusdecreasealongtheperiod?

Thedecreasingmetalionradiusalongtheperiodisaresultofthepoor

shieldingofthenuclearchargebytheadditionofthesuccessived–electrons

Thed-orbitalsdonotpenetrate intothenucleusbecausethedorbitalwave

functiongoestozerobeforethenucleus isreached

CH3514

98


TheChelateEffect

Thesamephenomenonisseen inotherpropertiesof3d-metalcomplexes

Latticeenergiesofdivalentoxides

CH3514

99

ChelateRingFormationinApplications

Chelationtherapyhasbeenusedtotreatdiseases andconditionsrelatingtometaloverload

Wilson�sdisease isarecessivegeneticdisorderthatcausesepilepsyamongstother

neurologicalsymptomsandisduetoanoverloadofcopper

ChelatingagentssuchasthosebelowthatbindCu2+ ions

stronglyhavebeensuccessfullyusedclinicallytotreat

thecondition

AKayser-Fleischerring

CH3514

100



Apotentially fatalconditioncalledhemosiderosis occurswhenthenaturallyoccurringiron

carrierprotein transferrinbecomessaturatedandironbecomesdepositedwithinthebody.

Incasesofsevereironoverload,deposition intheheart,liverandendocrinesystemsleadsto

functionalimpairmentofthese organs,andreducedlifeexpectancy.

Hemosiderosis oftheliver

CH3514

101



Apotentially fatalconditioncalledhemosiderosis occurswhenthenaturallyoccurringiron

carrierprotein transferrinbecomessaturatedandironbecomesdepositedwithinthebody.

Incasesofsevereironoverload,deposition intheheart,liverandendocrinesystemsleadsto

functionalimpairmentofthese organs,andreducedlifeexpectancy.

Hemosiderosis oftheliver

CH3514

102



ThereexistsotherclinicallyprovenagentsfortheremovalofFe3+fromthebody

NotetheaffinityofthehardFe3+ forhardO donors

CH3514

103



ThereexistsotherclinicallyprovenagentsfortheremovalofFe3+fromthebody

TheseareallagentsbasedonEDTAderivatives

CH3514

104

StabilitiesofOxidationStates

Thehigherstatesbecomemoreoxidisingandthe

lowerstates lessreducingtotheright

Why?

Duetothepoorshielding ofthenucleusbytheadditionofsuccessived-electrons,the

effectivepositivechargefeltbyanouterelectronincreasesfromlefttoright.

Thishastwoconsequences:

• Decreaseinionicradiustotheright.

• Valenceelectronsbecomehardertolose/sharethemoretotherightyougo.

– thehigheroxidationstatesbecomemoreoxidizingandthelowerstates lessreducing

CH3514

105


Buthowdowetrulydefinetheterm“oxidationstate”?

Innomenclaturetermsthisisdonebyassumingoctetconfigurationstodefinethecharge

ontheatomsattachedtothemetalintheionorcomplex

Complex Ligand TotalCharge

onLigand

OverallChargeon

Complex

OxidationStateof

Metal

[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]+ NH3

RCO2-

Cl-

0

1-

1-

+1 III

Inreality,oxidationstatesareaformalismandareonlytrueiftheM-Lbondingishighlyionic

(electrostatic).

e.g., [Mn(OH2)6]2+whereMn istrulyisMn2+

(independentevidenceexistsfromopticalspectroscopyandmagnetismthatitishighspind5)

CH3514

106


ButwhataboutthecaseofMnO4- wheretheMn-Obondsarehighlycovalent(Mn-Obond

lengthislessthansumofionicradii)

Sowherenowaretheelectrons?

Hereopticalspectroscopyandmagnetism areless informative:

• spectraisdominatedbyOàMnchargetransferbands

• itisdiamagnetic

SowewriteasMnVII(O-II)4

CH3514

107

QuantificationofOxidizingandReducingStrengths

WeknowthatMnO4- isapowerfuloxidantand[Cr(OH2)6]

2+ isapowerfulreductant.

Buthowdowequantifyoxidisingandreducingstrength?

Theanswer:Usingascaleofstandardredoxpotentials,Eo

Thesearebestenvisagedaspartofanelectrochemical cell– thedrivingforceinabattery

CH3514

108


Considerthe interactionofCu2+/CuandZn2+/ZnintheDaniell Cell

Reaction isspontaneousas

DGo isnegative

CH3514

109


Thisismadeupoftwohalfreactions:

Reaction isspontaneousas

DGo isnegative

Thepotentialdifference,Eocell is

measuredbythevoltmeter

CH3514

110


Thisismadeupoftwohalfreactions:

Thepotentialdifference,Eocell is

measuredbythevoltmeter

Thepotentialdifference,Eocell isdefinedasthestandardcellpotentialunderstandard

conditions:

• Unitactivity(whichmeansdilutionsolutionssoactivities approximateconcentrations)

• 1barpressureofanygaseouscomponent

• Allsolidcomponentsareintheirstandardstates

• T=298K

DGocell =-nFE

ocell

whereFistheFaradayconstant=96487Cmol-1

nisthenumberofelectronstransferredinthereaction

Eocell =Eoreduction – E

ooxidation=E

ocathode – E

oanode

ForacellreactiontobethermodynamicallyfavourableEocell mustbepositivesothat

DGocell isnegative

CH3514

111


Eocell at298K=1.10V

SoDGocell =-nFE

ocell =-2*96487*1.10=-212267Jpermol reaction=-212KJmol-1

DGocell =-RTln(Kcell)andsoKcell =1.50x10

37 - soreactionishighlyfavoured!

CH3514

112


Eocell at298K=1.10V

Thereis+0.34VdrivingthereactionduetoreductionofCu2+

Thereis+0.76VdrivingthereactionduetooxidationofZn(s)

Butwheredothesevalues

comefrom?

CH3514

113


Eocell at298K=1.10V



Butwheredothesevalues

comefrom?

AllEo valuesarerelatedonascaletothecellpotentialofthe

standardhydrogenelectrode(SHE),whichisarbitrarilysetata

valueof0.0VTheSHEconsistsofplatinumwire thatis

connectedtoaPt surfaceincontactwithan

aqueoussolutioncontaining1MH+ in

equilibriumwithH2 gasatapressureof1atm.

Half-cellpotentials areintensiveproperties,

namelyindependent oftheamountof

thereactingspecies.

CH3514

114


CH3514

115


1. AllvaluesarerelativetoSHE(=referenceelectrode)

2. Half-reactionsarewrittenasreductions

(onlyreactantsareoxidizingagentsandonlyproductsarethereducingagents)

3. ThemorepositivetheEo themorereadilythereactionoccurs

4. Half-reactionsareshownwithequilibriumarrowab/ceachcan

occurasreductionoroxidation

5. Thehalf-cellthatislistedhigheratthetableactsasthecathode

CH3514

116


Eocell at298K=1.10V



BycombiningtheSHEwithanotherhalfcell,e.g.,Cu2+aq/Cu(s),theEo canbedetermined

fromthemeasuredcellpotentialEocell

Wecanthenshow:

WecannowseewhyZn(s)readilyreducesCu2+aq andprovidesthehugedrivingforcefor

theDaniell cell

CH3514

117


Let’slookatadifferentreaction.Let’sconsiderthewellknowntitrationreactionof

thereductionMnO4- withFe2+aqunderstandardconditions(1MH+,298K)

Thehalfreactionsare:

WecannowseethatfromtherelativeE0 valuesthatthespontaneousreactionis:

Eocell =Eored– E

oox =1.51– (+0.77)=0.74V

DGocell =-357.03KJmol-1 (veryfavourable)

CH3514

118


Let’snowlookatadifferentprocess,whichistheoxidationofFe(s)byCl2aq.

Thehalfreactionsare:

Thesedataindicatethattworeactionsarepossible:

BothEocell valuesarepositiveandfromtheirmagnitudeonemightsupposethefirst

reactionisfavouredoverthesecond…

CH3514

119


ButwhatreallycountsisDGocell

Canshowthatthesecondreactionis favoured byconsidertheDGocell valuesforthetwo

processes,whichtakeintoaccountthenumberofelectronsinvolved

Thereforesecondreactionfavouredby~500kJmol-1!

CH3514

120


Sofarwehavebeenlookingatsystemsunderstandardconditions.

WhathappensifwechangethepH?

1st example:ReductionofMnO4-

HereEo referstothecondition[H+]=1mol dm-3,pH=0

BecauseoftheconsumptionofH+ ions,theaboveEo willvarywithpH.

WhatwouldbethemeasuredEvaluefortheaboveatpH2.5at298K?

CH3514

121

SoEdropsaspHincreases!


TheNernstEquation

WecancalculateEunderanyconditionsusingtheNernstEquation

ForthereductionofMnO4-:

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

Atequilibrium[Mn2+ aq]=[MnO4-]andE=Eeq

=1.27

8

8

(9.09X1019)

CH3514

122




2nd example:ReductionofZn2+ aq

No[H+]consumptionhere– sowhythechange?

ThereasonisthatatpH0theZn2+ species is[Zn(OH2)6]2+

butatpH14thespecies is[Zn(OH)4]2-

SotheZn2+ species beingreducedisdifferent!

CH3514

123




3rd example:Mn3+/Mn2+ aq – anexamplewherepHaffectsredoxbehaviour

AtpH0:Mn3+ existsas[Mn(OH2)6]3+ andcanoxidiseH2Oà O2

Eocell =1.54- 1.23=0.31V(favourable)

DGocell =-nFE

ocell =-4*96487*0.31Jmol-1=-120KJmol-1

CH3514

124




3rd example:Mn3+/Mn2+ aq – anexamplewherepHaffectsredoxbehaviour

AtpH14:MnIII andMnII arenowpresentasthehydroxo complexes;Mn(OH)2/3(s)

NowO2 istheoxidantandEocell =0.4– (-0.27)=0.67V(favourable)

DGocell =-nFE

ocell =-4*96487*0.67Jmol-1=-259KJmol-1

[OH-]=1mol dm-3,pH=14

CH3514

125


LatimerDiagrams

Whenseveraloxidationstatesexist foraparticularmetalaconvenientmethodof

representingtherespectiveEo values isintheformofaLatimerdiagram

pH=0

1st example: Iron

pH=14

UsingDGo valuescanshowusingtheabovethatEo(Fe3+aq/Fe(s))=-0.04V

Housecroft andSharpe,page227

RecallHess’sLaw:

CH3514

126


LatimerDiagrams

2nd example:Manganese



WithmultipleLatimerdiagrams,onecanillustratethechangeinEo withpH


pH=0

pH=14

CH3514

127


LatimerDiagrams






pH=0

Let’shaveacloser look:

Whenagivenoxidationstatehasahigher(morepositive)Eo foritsreduction thanforits

oxidationitisthermodynamicallyunstabletodisproportionationtogivethetwo

oxidationstateseitherside.

OnecanshowDGo forthisprocessisnegative

Doanyofthespecies abovesatisfythiscriterion? YES

CH3514

128


LatimerDiagrams






pH=14

Let’shaveacloser look:

Whenagivenoxidationstatehasahigher(morepositive)Eo foritsreduction thanforits

oxidationitisthermodynamicallyunstabletodisproportionationtogivethetwo

oxidationstateseitherside.

OnecanshowDGo forthisprocessisnegative

Doanyofthespecies abovesatisfythiscriterion? YES

Inthiscase:MnO42- andMn3+intheformofMn(OH)3(s),

arenowstabletowardsdisproportionation

CH3514

129


Pourbaix Diagrams

APourbaix Diagramcondenses theinformationavailable inLatimerDiagramsacross

allpHranges.

NernstEquation

CH3514

130


Frost-Ebsworth Diagrams

AconvenientwayofrepresentingredoxbehaviouristographicallyplotDGo versus

theoxidationnumber

Housecroft andSharpe,page227-230

Recall thatDGo =- nFEo

SoDGo/F=-nEo

SoifweplotnEo vs oxidationnumberthentheslopeofthelinedrawnbetween

twooxidationstates,separationn,willgiveEo forthatprocess.

TheFEdiagramscanbeusedtopredictredoxbehaviour

CH3514

131

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



Example1:Mn atpH0


Thefurtherupthediagram

themoreoxidizingthestate

increasingStability

CH3514

132



Example1:Mn atpH0


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-

-1.19 V+1.54 V

+2.10 V

+0.90 V

+0.95 V

Go/F for disproportionationof MnO4

2- into MnO4

- and MnO2

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

Eodisp

= 2.10 - 0.90 = + 1.20 V

Godisp = -231.5 kJ mol-1

DGo =-nFEo =-2*96487*1.2=-231.5KJmol-1

CH3514

133



Example1:Mn atpH0andpH14

Wecanalso illustratetheeffectsof

pHontheredoxbehaviour

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-

pH=0

pH=14

MnO4- is

lessoxidizing

Mn(OH)3 isnowthemoststablestate

CH3514

134



WhichpHconditionisbestforMnO4- titrations?

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

pH=0 UseofacidsolutionavoidsMnO2(s)production

Noteinair(O2)

pH=14MnO4

- aq + 4 H2O + 5 e- Mn(OH)2(s) + 6 OH-aq + 0.34 -164

MnO2(s) + 4 OH-aqMnO4

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

Noteinair(O2)

O2 + 2 Mn(OH)2(s) 2 MnO2(s) + 2 H2O + 0.44 -169.8

ReductiontoMn2+aq favoured

ReductiontoMnO2 favoured

CH3514

135


Frost-Ebsworth Diagramsalongthe3dSeries

6

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+

Notehowthelowerstates

becomemorestableandless

reducingalongtheperiod

CH3514

136


Frost-Ebsworth Diagramsalongthe3dSeries

6

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+

Notethatcopperisthefirst

trulyinert3dmetal (allEo

valuesarepositive– typical

ofcoinagemetals

• Cuistheonly3dmetal

foundnaturally

• Cu+aq isunstableWRT

disproportionation

CH3514

137


M(s) M(g) atomization Hoa

M2+(g) M2+aq hydration Ho

hyd

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

consistsofthethreeprocesses:

M2+aq + 2 e- M(s)

Eo

CH3514

138


M2+aq + 2 e- M(s)

Eo

DoanyofthetrendsinEo valuescorrelateanyoftheseprocesses? YES

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

WefindthatthevaluesofEo (-DGo/nF)

correlatewithIP1 andIP2

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139


Eo (M2+/M) / volts

IE / kJ mol-1

0 1 2 3 4 5 6 7 8 9 10


-3

-2

-1

0

1

2

3

1750

2000

2250

2500

2750

3000

3250

3500

1500

IP1 + IP2

IP3

WefindthatthevaluesofEo (-DGo/nF)

correlatewithIP1 andIP2

TheexpectedvariationofDHohyd withLFSE(formingtheaquacomplexes)

doesnotcontributesignificantly.

ThelowEo forZn2+/Zndoescorrelatehoweverwithanunusuallylowvalue

ofDHoaforZn(s)

CH3514

140


Furthermore,Eo(M3+/M2+)correlateswithIP3

OnceagainthevariationinrespectiveDHohyd valuesofM

2+ andM3+ isnot

significant

Eo (M3+/M2+) / volts

IE / kJ mol-1

0 1 2 3 4 5 6 7 8 9 10


-3

-2

-1

0

1

2

3

1750

2000

2250

2500

2750

3000

3250

3500

1500

IP3

VCr

Mn

Fe

Co

WefindthatthevaluesofEo (M3+/M2+)

correlatewithIP3 exceptforCr

CH3514

141




2+ andM3+ isnot

significant

WefindthatthevaluesofEo (M3+/M2+)

correlatewithIP3 exceptforCr

OnthebasisofIP3,oxidationofCr2+(g)shouldbemoredifficultthanwith

V2+ (g)byca.165KJmol-1

YetCr2+aq isamorepowerfulreductant (morenegativeEo)thanV2+aq

WHY?

ThereasonistheconsiderablegaininLFSE(0.6Do)onformingthed3 Cr3+

ion(t2g3 eg

0 configuration)

OxidationofV2+aq toV

3+aq (t2g

3 eg1 configuration)actuallyresultsinalossof

LFSEof0.4DocomparedtoV2+aq

InthiscaseLFSEfactorsaresignificant

CH3514

142




2+ andM3+ isnot

significant

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

0.6 o

-0.4 o

Cr2+

LFSE-0.6 o

t2g (dxy,xz,yz)

eg (dz2, x2-y2)


CH3514

143


Insummary,Eo valuesinsolution largelycorrelatewiththerelevantionization

potential, IPn

OnlyincertainextremecasesdoLFSEfactorsplayasignificantparte.g., Cr2+aq/Cr3+aq

Eo (M2+/M) / volts

IE / kJ mol-1

0 1 2 3 4 5 6 7 8 9 10


-3

-2

-1

0

1

2

3

1750

2000

2250

2500

2750

3000

3250

3500

1500

IP1 + IP2

IP3

CH3514

144

RatesofReactionsInvolving3dTransitionMetalIons

inAqueousSolution

Kineticsversusthermodynamics– dotheycorrelate?

CH3514

145


inAqueousSolution

Considerthefollowingprocess:

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

Thisisoneofthelargestlogbn valuesknownforamonodentate ligandreplacingH2O

Whatthismeans isthat[Ni(CN)4]2- isverystablethermodynamically

b

b

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146


inAqueousSolution

Considertherateofthereactionforthefollowingprocess:

[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

Whatthismeans isthat[Ni(CN)4]2- isverylabile!

Theseexperimentsshowthatthermodynamicstabilitydoesnotnecessarily

correlatewithkineticinertness

Theattainmentofequilibriuminmetal ioncomplexation processescanbean

extremelyfastprocess;irrespectiveofthesizeofthestabilityconstants:Kn orbn

Infactms andµs timescale ligandexchangeeventsinvolvingmonodentate ligands

arecommonwithin3dtransitionmetalcomplexes

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147


inAqueousSolution

Awiderangeofratesisrelevantforligandexchangereactionsatmetalcomplexes

Considerwaterexchangeontheaquaspecies

Formaingroupmetal ionstheserangefromthemostlabile(Cs+aq,halflife=1ns)to

themostinert(Al3+aq,halflife=1s)- 9ordersofmagnitude

Thisismostlyasaresultofvariationsinthemetalionicradiuswhichaffectsthe

strengthofthepredominantlyionic(electrostatic)bondingtothecoordinatedwaters

[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

Group2aquaions

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148


inAqueousSolution



Formaingroupmetal ionstheserangefromthemostlabile(Cs+aq,halflife=1ns)to

themostinert(Al3+aq,halflife=1s)- 9ordersofmagnitude

Thisismostlyasaresultofvariationsinthemetalionicradiuswhichaffectsthe

strengthofthepredominantlyionic(electrostatic)bondingtothecoordinatedwaters

Group13aquaions

[Al(OH2)6]3+

[Ga(OH2)6]3+

[In(OH2)6]3+

Ionic radius / pm


54

80

1

10-6

10-362

CH3514

149

[V(OH2)6]2+

[Co(OH2)6]2+

[Ni(OH2)6]2+

Ionic radius / pm


79

69

10-2

10-4

10-675


inAqueousSolution



Howeverforthe3dtransitionmetalionssizeisnottheonlyfactor

HerethereisnocorrelationwithsizeV2+ hasthelargestradiusbutitisthemostinert

Thehalflives(rates)ofexchange,justlikethestabilityconstantswesawearlier,correlatewithLFSEnotsize

3daquaions

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150


inAqueousSolution

Valuesoflogkex (waterexchange)forM2+ ionsalongthe3dseries

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

TheanomalouslyhighratesforCr2+aq andCu2+aq reflecttherapiddynamicsattachedtothe

weakly-bondedwaterligandswithinthe

Jahn-Tellerdistortedstructures

CH3514

151


inAqueousSolution

TheJahn-TellerassisterfastexchangeprocessonCu2+ aq

Entireprocesstakesplaceonce

everynanosecond!!

CH3514

152


inAqueousSolution

Amazingly,theratesofwaterligandexchangeonaquametal ionsacrosstheperiodic

tablecover20 ordersofmagnitude

>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+

CH3514

153


inAqueousSolution



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


Ir3+ Cr3+

Pt2+

Al3+ Fe3+ Ti3+ Gd3+

Be2+ Mg2+ Cu2+

Li+ Cs+

Generally,

Lowercharge:faster;Highercharge:slower

Largersize:faster;smallersize:slower

CH3514

154


inAqueousSolution



Let’sputthisintoperspective

averagetimeintervalat25oC

beforewaterexchangeevent

OnCu2+ aq 1ns– 10-9s

OnAl3+ aq 0.1s– 10-1 s

OnCr3+ aq 1day– 86400s

OnIr3+ aq 50years– 1.58x109s

CouldenvisagestudyingtheexchangeonCr3+aq withoutproblembutwhataboutthatonIr3+aq?

glucose

crayon

~StAndrewstoEdinburgh~40%fromtheEarthtoMoon

CH3514

155


inAqueousSolution

SohowwastheexchangeonIr3+ aq measured?

SincewaterexchangeinvolvesbondbreakingfromMn+ toresidentwater,whichhas

anendothermicactivationbarrierofabout130kJmol-1,raisingthetemperaturewill

speedupthereaction

waterexchangeon[Ir(H2O)6]3+wasstudiedinpressurizedvesselsat120oC – anevent

occursnowinlessthan1hour– wecanfollowbyNMRusingenriched17O-labelled

water(17OhasanNMRsignal like1H)

Classificationforexchange reactions

onmetalions

t < 1min labile

t > 1min inert

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156


inAqueousSolution

Ofallthe3dtransitionmetalaquaionsonlyCr3+aq isclassedasinert– why?

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


Ir3+ Cr3+

Pt2+

Al3+ Fe3+ Ti3+ Gd3+

Be2+ Mg2+ Cu2+

Li+ Cs+

INERT LABILE

CH3514

157


inAqueousSolution


Octahedral[Cr(H2O)6]3+ hasahighchargecoupledwithaverystablet2g

3 configuration

with-1.2Do ofLFSE

o

-0.4 o

+0.6 o

t2g

eg

HighLFSEcorrelateswithahighligandfieldactivationenergy(LFAE)forexchange

CH3514

158


inAqueousSolution



3 configuration

with-1.2Do ofLFSE

-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+ GreatestLFSEisforCr3+

CH3514

159

-100

-200

0

-300

-400

-500

-600

LFSEkJ mol-1

0 2 4 6 8 10


M3+

M2+

V2+

Ca2+

Ni2+

Mn2+ Zn2+

Cr3+

Co3+


inAqueousSolution



3 configuration

with-1.2Do ofLFSE

InfactthehighestLFSEisforCo3+aq

andCo3+aqshouldbethemostinert

Whyisthisnotthecase?

CH3514

160


inAqueousSolution

Lowspinoctahedral[Co(H2O)6]3+ hasahighcharge(highDo)coupledwithat2g

6

configurationandthereforehasthemaximumLFSEpossible of-2.4Do

o

-0.4 o

+0.6 o

t2g

eg

SoCo3+ hasaveryhighLFAEandshouldbekinetically inert

CH3514

161


inAqueousSolution

Buthowdoweknowthatoctahedral[Co(H2O)6]3+ hasalowspint2g

6 configuration?

Thecomplexcouldbehighspin.

SoCo3+ wouldthenhaveaLFSEofonly-0.4Do

o

-0.4 o

+0.6 o

t2g

eg

CH3514

162


inAqueousSolution

Sohowdoweknow?

Ofcoursewecouldlookatthemagneticpropertiesbutwecanalsotell fromtheM-OH2

distances intheaquacomplexes

-100

-200

0

-300

-400

-500

-600

LFSEkJ mol-1

0 2 4 6 8 10


Cr3+

Co3+

210

200

190

180

M-OH2 distance / ppm in aqua salts

Fe3+Sc3+ Ga3+

Thedecrease inM-OH2 distanceonceagain

reflectsdecreasingM3+ ionicradiusacrossseries

CH3514

163


inAqueousSolution

Therateofexchangeon[Co(OH2)6]3+ hasnotbeenmeasuredhoweverbecause itisnot

stable

[Co(OH2)6]3+ spontaneouslyoxidizeswatertoO2

DGocell =-nFE

ocell =-4*96487*0.75=-386KJmol-1

Theexchangereactionobservediscatalysedbythemorelabile[Co(OH2)6]2+generated

[Co(OH2)6]3+ providesanothergoodexampleofthe lackofcorrelationbetween

thermodynamicstabilityandkineticlability

Co(OH2)6]3+ isinertyetonlymetastable

CH3514

164


inAqueousSolution

LiterallyhundredsofstableCo3+ complexesareknownwithligandsotherthanwater,

mostofthemN-donorligands.

Becauseoftheirredoxstability,coupledwithslowratesofligandexchange,manyof

thesehaveplayedahugeroleindevelopingourunderstandingofthemechanismsof

reactionsattransitionmetalcentres

CH3514

165


inAqueousSolution

LiterallyhundredsofstableCo3+ complexesareknownwithligandsotherthanwater,

mostofthemN-donorligands.

Becauseoftheirredoxstability,coupledwithslowratesofligandexchange,manyof

thesehaveplayedahugeroleindevelopingourunderstandingofthemechanismsof

reactionsattransitionmetalcentres

WhythishugedifferenceinEo values?

withCoIII stabilizedhugelywithN-donorslikeNH3

CH3514

166


inAqueousSolution


M NH

Hfilled t2g

lowspin H

empty eg

o

t2g

eg

o

t2g

eg NH3

eg

Co

s-donorligand

CH3514

167


inAqueousSolution


p-donorligandinadditiontos-donation

M OH

H

filled t2g

repulsion

O2p

lowspin

Co3+

o

t2g

eg

o

t2g

egOH2

O2p

Strongerp-donationcoupledwithweakers-donation lowersDo

Thisdecreases thestabilityofthelsd6 configurationwithrespecttothe

reductiontothehs d7 [Co(OH2)6]2+(Do <P)

CH3514

168


inAqueousSolution


M OH

H

filled t2g

repulsion

O2p

lowspin M O

H

H

vacancy in t2g O2p

highspin

reduction to Co2+

Co2+

o

t2g

eg

o

t2g

egOH2

O2p

CH3514

169


inAqueousSolution

ThereareonlytwoknownhighspinCo3+ complexes:

• [Co(OH2)3F3]

• [CoF6]3-

Thisisduetogoodp-donationfromF-,whichdramaticallydecreasesDo

AllotherCocomplexesarelowspin,whichisduetostrongers-donationoutweighingallothereffects

CH3514

170

AnIntroductiontoMechanisms inOrganicChemistry

Youallarefamiliarwithsubstitution reactionsoncarbon:SN1andSN2

Thereexistscomparablemechanismsofligandreplacementonthemetal

• Dissociative– similartoSN1

• Associative– similartoSN2

ML

L L

X

L

L

n+

ML

L L

Y

L

L

n+

Y

X

CH3514

171


TheDissociativepath:

XleavesfirstandthenYcoordinatesatthevacantsiteonthemetal

ML

L L

X

L

L

n+

ML

L LL

L

n+

- X+ X

ML

L L

Y

L

L

n+

+ Y

- Y

TheAssociativepath:

M-Ybondformsfirstfollowedbyde-coordinationofX

ML

L L

X

L

L

n+

+ YM

L

L LL

L

n+

- YY

X

ML

L L

Y

L

L

n+- X

+ X

CH3514

172


Whichpathwouldyoupredicttohavethelargest activationenergy?

Answer:Thedissociative path.Why?

Thismechanism involvesabond-breakingstep(M-Xbond)intheRDS,whichwillbe

endothermicbeforethenewbondisformed– formallytwostepreaction

Similarly,SN1reactionsarefrequentlyslowerthanSN2reactionsforthesamereason

Theassociative pathinvolvesabond-makingstep(M-Y),whichwillbeexothermicprior

tobondbreaking(M-X)andsoshouldpossessaloweractivationenergy.

Additionally,thepresenceofthenewM-Ybondmaylowertoenergyrequiredtobreak

theM-Xbond

CH3514

173


TheactivationenergyEa canbedeterminedfromthetemperaturedependence ofthe

reactionrateaccordingtotheArrheniusorEyring equation.

reactant

product

Go

reaction coordinate

Energy

favourable negative Go

(spontaneous reaction)

activation energy Ea

CH3514

174


TheArrheniusequation:

ln k = ln A -Ea

RTor k = A e

-Ea

RT

TheEyring equation:

ln k = lnRT

or k = ek' T

h

G k' T

hRT

G

-

k’andharetheBoltzmannandPlanck’sconstants

DD

CH3514

175


TheEyring equation,rearranginggives

ln k = lnRT

k' T

h

G- ln k = ln

k'

h+ lnT

RT

G-

ln =k'

h+ ln

RT

G-k

T

Recall thatDG‡ =DH‡ – TDS‡

ln =k'

h+ ln-k

T R

S+

RT

HSo

WecanthereforemakeanEyring plotofln (k/T)vs 1/Tandshouldobtainalinear

relationship

D D

D

D D

‡ ‡

‡

‡ ‡

CH3514

176


TheEyring Plot

ln

k'

h+ ln

-

kT

R

S

RT

H

1T0

• DS‡obtainedfrom

ExtrapolationtoinfiniteT

• Thiscanonlydetermine

mathematically

• DH‡canbeaccurately

determinedfromthe

slope

D ‡

D ‡

CH3514

177


Thisenergydiagramrepresentsaconcertedreactionwithoutintermediates

reactant

product

Go

reaction coordinate

Energy

favourable negative Go

(spontaneous reaction)

activation energy Ea

D

CH3514

178


Thisenergydiagramrepresentsatwo-stepreactionwithanintermediate

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

D D

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179


Let’slookatthedifferencebetweenassociativeanddissociativeprocesses

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

reactants

intermediate

products

transition state

transition state

G 1

G 2

MLL L

X

L

L

n+

MLL L

Y

L

L

n+

An associative process

Energy

Reaction coordinate

MLL L

X

L

L

n+

Y

MLL L

X

L

L

n+

Y

MLL L

X

L

L

n+

Y

D DD

D

CH3514

180


Let’slookatsomeexamples

Waterexchangeonaquametalions

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

• Increasingeg occupancyleadstohigherlability (smallerDH‡)butdoesn’t

changethemechanism

• Increasingt2g occupancycorrelateswithanincrease inDH‡ andamore

positiveDS‡andleadstodissociative behaviour

D D‡ ‡

CH3514

181




• DH‡ correlateswithLFSE,whichisameasureofthestrengthoftheM-OH2

bond

• However,DH‡ isoflimiteduseasamechanistic indicator


[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




associativet2g3 eg

2

t2g4 eg

2

t2g5 eg

2

t2g6 eg

2

LFSE

-1.2

kJ mol-1 J K-1 mol-1 units of o

0

-0.4

-0.8

-1.2

D‡

D‡

CH3514

182


Wesawpreviouslythatkex correlateswithLFSEWecannowdeducethatkex correlateswithDH‡

Thisisentirelyexpectedas,regardlessofmechanism,therewillbeabond-breaking

eventalongthereactioncoordinate(mostendothermicstepofthereaction,most

impactingtherate) 10

5

0

log kex (s-1)

0 1 2 3 4 5 6 7 8 109

LFSE

d electron number

Ca2+

Mn2+

Zn2+

V2+

Ni2+

Fe2+

Co2+

0

1.2 o

CH3514

183




• DS‡ toacertainextentcorrelateswithwiththemechanistic trendBUTthisvalueis

pronetolargeerrorsbasedonthemathematicalextrapolationtoinfiniteT

• Isthereanotherparameteravailablethatwecanuseasanindicatorofthe

mechanistic pathway?


[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




associativet2g3 eg

2

t2g4 eg

2

t2g5 eg

2

t2g6 eg

2

LFSE

-1.2

kJ mol-1 J K-1 mol-1 units of o

0

-0.4

-0.8

-1.2

YES

D‡ D

‡

CH3514

184


Theactivationvolume:DV‡

Considerthetwopathwaysagain:

ML

L L

X

L

L

n+

ML

L LL

L

n+

- X+ X

X

DISSOCIATIVE

• Thedissociative processwithhavea

positiveDV‡

• Theincrease inDV‡correspondstothe

volumeoffreeX

ML

L L

X

L

L

n+

Y

+ YM

L

L LL

L

n+

- YY

X

• Theassociativeprocesswithhavea

negativeDV‡

• Thedecrease inDV‡correspondstothe

volumeoffreeY

ASSOCIATIVE

CH3514

185


HowdowemeasureDV‡?

Fromthepressuredependenceofthereactionrate:

Aplotofln kvs Pwillprovideaslopeof-DV‡/RT

d (ln k)dP

= - VRT

Housecroft andSharpe,page883P

ln k

positive slope so V negative- associative mechanism

rate increases with pressure

P

ln k

rate decreases with pressure

negative slope so V positive- dissociative mechanism

D ‡

CH3514

186


Housecroft andSharpe,page883P

ln k

positive slope so V negative- associative mechanism

rate increases with pressure

P

ln k

rate decreases with pressure

negative slope so V positive- dissociative mechanism

P

ln k

no change - concerted mechanismtermed interchange I

D‡

D‡

CH3514

187


Wecannowappreciatewhyvariousmechanismswouldhavesuchrate/pressure

dependencies

Adissociative processinvolvestheexpulsionof theleavingligandX(expansive)so

wouldbeexpectedtoberetardedbyapplyingpressure

negative slope- positive activationvolume

Anassociative processinvolvesthetakeupofY(compressive)sowouldbeexpectedto

beacceleratedbyapplyingpressure

positive slope- negativeactivationvolume

CH3514

188


Let’sgobacktothepreviousexample:

• DV‡ isagoodindicatorofmechanism

• Increaseineg occupancylowersDH‡ butdoesn’tchangethemechanism

– stillassociative

• Increaseint2g occupancyincreasesDH‡ANDgivespositivevaluesforDV‡

– moredissociative


[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




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-1D ‡ D ‡ D ‡

CH3514

189


WecanunderstandthesetrendsfromanMOperspective

Increasingeg occupancyweakens(lengthens)theresidentM-OH2 bonds– lowersLFSE

andDH‡ andincreasestherateofexchange

However,increasingt2g occupancywillrepeltheelectronsontheentering ligandY-

facilitatingthedissociative pathway

M

L

L L

L

Y

repulsion

filled t2g

CH3514

190

Summary

ü LFTandinparticulars-donor,p-donorandp-acceptorsandhowtheyinfluenceDo

ü Hydrolysischemistryofmetalcomplexes

ü Thermodynamicsofmetalcomplexformation(K,b,DGo)

ü HSABchemistry

ü Theoriginsofthe Irving-WilliamsSeriesandtheJTeffect

ü Thechelateeffect

ü Thefactorsgoverningthestabilities ofoxidationstates

ü Quantificationofoxidizingandreducingstrengthbyelectrochemistry (Eocell,DGocell)

ü Delineation betweenthermodynamicstabilityandkineticinertness

Physical Inorganic Chemistry CH3514 - Eli Zysman-Colman

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Transcript of Physical Inorganic Chemistry CH3514 - Eli Zysman-Colman