activation

Onthispage:

Reactionmechanisms,molecularity

Collisiontheoryofchemicalchange

Anatomyofmoleclarcollisions

Activationenergy

Catalysts

Temperatureandkineticenergy

TheArrheniuslaw

Deteriningtheactivationenergy

Thepre-exponentialfactor

Whatyoushouldbeabletodo

Conceptmap

GeneralChemistryVirtualTextbook→kinetics/dynamics→collision/

activaton

Collisionandactivation

theArrheniusLaw

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Whyaresomereactionssomuchfaster

thanothers,andwhyarereactionrates

independentofthethermodynamic

tendencyofthereactiontotakeplace?

Thearethecentralquestionswe

gso,weopen

thedoortotheimportanttopicof

reactionmechanisms:whathappensat

themicroscopiclevelwhenchemical

reactionstakeplace?Wecanthank

Arrheniusforunlocking

thisdoor!

Tokeepthingsassimpleaspossible,we

willrestrictourlftoreactionsthat

e

principleswillapplytoreactionsin

liquidsandsolids,butwithadded

complicationsthatwewilldiscussinalaterunit.

1Reactionmechanisms

Themechanismofachemicalreactionisthequenceofactualevents

theeventsconstitutesanelementarystepthatcanbereprentedas

acoming-togetherofdiscreteparticles("collison")orasthebreaking-up

ofamolecule("dissociation")ecularentitythat

emergesfromeachstepmaybeafinalproductofthereaction,oritmight

beanintermediate—aspeciesthatiscreatedinoneelementarystep

anddestroyedinasubquentstep,andthereforedoesnotappearinthe

netreactionequation.

Stepbystep...

Areactionmechanismmustultimatelybeunderstoodasa"blow-by-blow"

descriptionofthemolecular-leveleventswhoquenceleadsfrom

lementarysteps(alsocalledelementary

reactions)arealmostalwaysverysimpleonesinvolvingone,two,or

[rarely]threechemicalspecieswhichareclassified,respectively,as

unimolecularA→byfarthemostcommon

bimolecularA+B→

termolecularA+B+C→veryrare

Inagasatroom

temperatureandnormal

atmosphericpressure,

therewillbeabout10

33

collisionsineachcubic

centimetreeverycond.

Ifeverycollisionbetween

tworeactantmolecules

yieldedproducts,all

reactionswouldbe

completeinafractionofa

cond.

2Collisiontheoryofchemicalchange

Moleculesmustcollidebeforetheycanreact

Thisfundamentalrulemustguideanyanalysisofanordinarychemical

reactionmechanism.

etic

theoryofgastellsusthatforevery1000binarycollisions,therewillbeonly

-way

collisionsaresoimprobablethatthisprocesshasneverbeendemonstratedin

anelementaryreaction.

Considerasimplebimolecularstep

A+B→products

Clearly,iftwomoleculesAandBaretoreact,theymustapproachcloly

enoughtodisruptsomeoftheirexistingbondsandtopermitthecreation

suchan

encounteracollision.

ThefrequencyofcollisionsbetweenAandBinagaswillbeproportional

totheconcentrationofeach;ifwedouble[A],thefrequencyofA-B

collisionswilldouble,anddoubling[B]l

collisionsleadtoproducts,thantherateofabimolecularprocesswillbe

first-orderinAandB,orcond-orderoverall:

rate=k[A][B]

but...

Notallcollisionsareequal

Whentwobilliardballscollide,

isalsothemostlikelyoutcomeifthereactionbetweenAandBrequiresa

significantdisruptionorrearrangementofthebondsbetweentheiratoms.

Inordertoeffectivelyinitiateareaction,collisionsmustbesufficiently

energetic(kineticenergy)out

thisfurtheron.

Andthereisoftenoneadditional

reactions,

especiallythoinvolvingmore

complexmolecules,thereacting

speciesmustbeorientedina

mannerthatisappropriateforthe

mple,in

thegas-phareactionof

dinitrogenoxidewithnitricoxide,

theoxygenendofN

2

Omusthitthe

nitrogenendofNO;reversingthe

orientationofeithermoleculepreventsthereaction.

Owingtotheextensiverandomizationofmolecularmotionsinagasorliquid,

therearealwaynoughcorrectly-orientedmoleculesforsomeofthe

our,themorecriticalthisorientational

requirementis,thefewercollisionswillbeeffective.

Anatomyofacollision

Energeticcollisionsbetweenmoleculescauinteratomicbondstostretch

andbendfarther,temporarilyweakeningthemsothattheybecomemore

tionofthebondscanexpotheir

associatedelectroncloudstointeractionswithotherreactantsthatmight

leadtotheformationofnewbonds.

Chemicalbondshavesomeofthepropertiesof

mechanicalsprings,whopotentialenergy

dependsontheextenttowhichtheyare

om-to-atom

bondcanbedescribedbyapotentialenergy

diagramthatshowshowitnergychanges

ebondabsorbnergy

(eitherfromheatingorthroughacollision),itis

elevatedtoahigherquantizedvibrationalstate

(indicatedbythehorizontallines)thatweakens

thebondasitslengthoscillatesbetweenthe

extendedlimitscorrespondingtothecurve.

Aparticularcollisionwilltypicallyexcitea

about10–13condthixcitation

getsdistributedamongtheotherbondsinthemoleculeinrathercomplex

andunpredictablewaysthatcanconcentratetheaddedenergyata

ectedbondcanstretchandbend

farther,thebonddoesnot

breakbypurestretching,itcanbecomedistortedortwistedsoasto

exponearbyelectroncloudstointeractionswithotherreactantsthat

mightencourageareaction.

Consider,forexample,theisomerizationofcyclopropanetopropenewhich

takesplaceatfairlyhightemperaturesinthegaspha.

Wecanimaginethecollision-to-productquenceinthefollowing[grossly

oversimplified]way:

Notethat

Tokeepthingssimple,

reasonablebecauC–CbondsareweakerthenC–Hbondsandthuslesslikely

tobeaffected.

Thecollisionatwillusuallybewithanothercyclopropanemolecule,but

becaunopartofthecollidingmoleculegetsincorporatedintotheproduct,it

caninprinciplebeanoblegasorsomeothernon-reactingspecies;

AlthoughtheC–Cbondsincyclopropaneareallidenticial,theinstantaneous

localizationofthecollisionalenergycandistortthemoleculeinvariousways(

),leadingtoaconfigurationsufficientlyunstabletoinitiatethe

rearrangementtotheproduct.

Unimolecularprocessalsobeginwithacollision

Thecyclopropaneisomerizationdescribedaboveistypicalofmany

decompositionreactionsthatarefoundtofollowfirst-orderkinetics,

bout1921,chemistsdid

sout

thatthemechanismsofsuchreactionsarereallyrathercomplicated,and

Thechemicalreactions

associatedwithmostfood

spoilagearecatalyzedby

enzymesproducedbythe

bacteriawhichmediate

theprocess.

HereisashortYouTube

videoonactivation

energy.

The"reactioncoordinate"plottedalongtheabscissa

reprentsthechangesinatomiccoordinatesasthe

ery

simplestelementaryreactionsitmightcorrespondtothe

stretchingortwistingofaparticularbond,andbeshown

ral,however,thereactioncoordinateis

aratherabstractconceptthatcannotbetiedtoany

singlemeasurableandscaleablequantity.

Theactivatedcomplex(alsoknownasthetransition

state)reprentsthestructureofthesystemasitexists

not

correpondtoanidentifiableintermediatestructure(which

wouldmoreproperlybeconsideredtheproductofa

parateelementaryprocess),butrathertowhatever

configurationofatomxistsduringthecollision,which

lastsforonlyabout0.1picocond.

Activationenergydiagramsalwaysincorporatethe

energetics(ΔUorΔH)ofthenetreaction,butitis

importanttounderstandthatthelatterquantitiesdepend

solelyonthethermodynamicsoftheprocesswhichare

ans

thatthesamereactioncanexhibitdifferentactivation

energiesifitcanfollowalternativepathways.

Withafewexceptionsforverysimpleprocess,

activationenergydiagramsarelargelyconceptual

constructsbadonourstandardcollisionmodelfor

dbeunwitoreadtoomuch

intothem.

ails

arebeyondthescopeofthiscour,butagoodintroductioncanbefound

apage.

Activationenergy

Highertemperatures,fasterreactions

Itiscommonknowledgethatchemicalreactionsoccurmorerapidlyat

neknowsthatmilkturnssourmuchmore

rapidlyifstoredatroomtemperatureratherthaninarefrigerator,butter

goesrancidmorequicklyinthesummerthaninthewinter,andeggs

same

reason,cold-bloodedanimalssuchasreptilesandinctstendtobe

noticeablymorelethargiconcolddays.

lenergyrelates

emperatureris,

moleculesmovefasterandcollidemorevigorously,greatlyincreasingthe

likelyhoodofbondcleavagesandrearrangemensasdescribedabove.

Activationenergydiagrams

Mostreactionsinvolvingneutralmoleculescannottakeplaceatalluntil

theyhaveacquiredtheenergyneededtostretch,bend,orotherwi

iticalenergyisknownastheactivation

tionenergydiagramsofthekindshown

belowplotthetotalenergyinputtoareactionsystemasitproceedsfrom

reactantstoproducts.

Inexaminingsuchdiagrams,takespecialnoteofthefollowing:

Galleryofactivationenergyplots

Activationenergydiagramscandescribebothexothermicandendothermic

reactions:

...andtheactivationenergiesoftheforwardreactioncanbelarge,small,

orzero(independently,ofcour,ofthevalueofΔH):

Processwithzeroactivationenergymost

commonlyinvolvethecombinationof

oppositely-chargedionsorthepairingupof

electronsinfreeradicals,asinthe

dimerizationofnitricoxide(whichisanodd-

electronmolecule).

Inthisplotforthedissociationof

bromine,theE

a

isjusttheenthalpy

ofatomization

Br

2

(g)→2Br·(g)

andthereactioncoordinate

correspondsroughlytothe

stretchingofthevibrationally-

"activated

complex",ifitisconsideredto

exist,isjustthelast,longest

"stretch".Thereverreaction,

beingtherecombinationoftwo

radicals,occursimmediatelyon

contact.

Wheredoestheactivationenergycomefrom?

Inmostcas,theactivationenergyis

suppliedbythermalenergy,either

throughintermoleculrcollisionsor(in

thecaofthermaldissocation)by

thermalexcitationofabond-stretching

Areviewoftheprinciplesof

gasmolecularvelocitiesand

theBoltzmanndistribution

canbefoundonthe"KMT-

classic"page.

vibrationtoasufficientlyhighquantum

level.

Asproductsareformed,theactivation

energyisreturnedintheformof

vibrationalenergywhichisquickly

degradedtoheat.

It'sworthnoting,however,thatothersourcesofactivationenergyare

sometimesapplicable:

Absorptionoflightbyamolecule(photoexcitation)canbeaverycleanand

efficient,butitdoesn''snotenoughthatthewavelengthofthe

lightcorrespondtotheactivationenergy;itmustalsofallwithintheabsorption

spectrumofthemolecule,and(inacomplexmolecule)enoughofitmustend

upintherightpartofthemolecule,suchasinaparticularbond.

lescapableoflosingorgainingelectrons

atthesurfaceofanelectrodecanundergoactivationfromanextrapotential

(knownastheovervoltage)

electrodesurfaceoftenplaysanactiverole,sotheprocessisalsoknownas

electrocatalysis.

Catalystscanreduceactivationenergy

Acatalystisusuallydefinedasasubstancethatspeedsupa

ecifically,a

catalystprovidesanalternative,loweractivationenergy

,theyare

vitallyimportanttochemicaltechnology;approximately95%

ofindustrialchemicalprocessinvolvecatalystsofvarious

tion,mostbiochemicalprocessthatoccurin

livingorganismsaremediatedbyenzymes,whicharecatalysts

madeofproteins.

Itisimportanttounderstandthatacatalystaffectsonlythe

kineticsofareaction;itdoesnotalterthethermodynamic

ereisasinglevalue

ofΔHforthetwopathwaysdepictedintheplotontheright.

Temperatureandkineticenergy

Inthevastmajorityofcas,wedependonthermal

actvation,sothemajorfactorweneedtoconsideris

whatfractionofthemoleculespossnoughkinetic

energytoreactatagiventemperature.

Accordingtokineticmoleculartheory,apopulationofmoleculesatagiven

temperatureisdistributedoveravarietyofkineticenergiesthatis

describedbytheMaxwell-Boltzmandistributionlaw.

Thetwodistributionplotsshownhereareforalower

temperatureT

1

andahighertemperatureT

2

.Thearea

undereachcurvereprentsthetotalnumberof

moleculeswhoenergiesfallwithinparticularrange.

Theshadedregionsindicatethenumberofmolecules

whicharesufficientlyenergetictomeettherequirements

dictatedbythetwovaluesofE

a

thatareshown.

Itisclearfromtheplotsthatthefractionofmolecules

whokineticenergyexceedstheactivationenergy

thereasonthatvirtuallyallchemicalreactions(andall

elementaryreactions)aremorerapidathigher

temperatures.

2TheArrheniuslaw

By1890itwascommonknowledgethathigher

temperaturesspeedupreactions,oftendoublingtherate

fora10-degreeri,butthereasonsforthiswerenot

y,in1899,theSwedishchemistSvante

Arrhenius(1859-1927)combinedtheconceptsofactivation

energyandtheBoltzmanndisributionlawintooneofthe

mostimportantrelationshipsinphysicalchemistry:

Takeamomenttofocusonthemeaningofthiquation,neglectingtheAfactor

forthetimebeing.

First,notethatthisisanotherformoftheexponentialdecaylawwediscusdin

"decaying"hereisnottheconcentration

ofareactantasafunctionoftime,butthemagnitudeoftherateconstantasa

functionoftheexponent–E

a

/tisthesignificanceofthisquantity?If

yourecallthatRTistheaveragekineticenergy,itwillbeapparentthatthe

exponentisjusttheratiooftheactivationenergyEatotheaveragekineticenergy.

Thelargerthisratio,thesmallertherate(hencethenegativesign.)Thismeans

thathightemperatureandlowactivationenergyfavorlargerrateconstants,and

authetermsoccurinanexponent,their

effectsontheratearequitesubstantial.

Thetwoplotsbelowshowtheeffectsoftheactivationenergy(denoted

herebyE‡)odestactivationenergyof

50kJ/molreducestheratebyafactorof108.

Thelogarithmicscaleintheright-handplotleadstonicestraightlines,as

describedunderthenextheadingbelow.

Lookingattheroleof

temperature,weea

similareffect.

(Ifthex-axiswerein

"kilodegrees"theslopeswouldbe

morecomparableinmagnitude

withthoofthekilojouleplotat

theaboveright.)

Determiningtheactivationenergy

TheArrheniuquation

canbewritteninanon-exponentialformwhichisoftenmoreconvenient

thelogarithmsofbothsides

andparatingtheexponentialandpre-exponentialtermsyields

whichistheequationofastraightlinewhoslopeis–E

a

/fords

asimplewayofdeterminingtheactivationenergyfromvaluesofk

obrvedatdifferenttemperatures;wejustplotlnkasafunctionof1/T.

Thusfortheisomerizationofcyclopropanetopropene

thefollowingdatawereobtained(calculatedvaluesshadedinpink):

T,°C477523577623

1/T,K–1×1031.331.251.181.11

k,s–10.000180.0027

0.0300.26

lnk–8.62–5.92–3.51–1.35

Fromthecalculatedslope,wehave

–(E

a

/R)=–3.27×104K

E

a

=–(8.314Jmol–1K–1)(–3.27×104K)=273kJmol–1

Comment:Thisactivationenergyisratherhigh,whichisnotsurprisingbecaua

carbon-carbonbondmustbebrokeninordertoopenthecyclopropanering.(C–Cbond

energiesaretypicallyaround350kJ/mol.)Thisiswhythereactionmustbecarriedoutat

hightemperature.

Youdon'talwaysneedaplot

(...ifyouarewillingtoliveabitdangerously!)Sincethelnk-vs.-1/Tplot

yieldsastraightline,itisoftenconvenienttoestimatetheactivation

owthisis

done,considerthat

(...inwhichwehavemadetheln-Atermdisappearbysubtractingthe

expressionsforthetwoln-kterms.)Solvingtheexpressionontherightfor

theactivationenergyyields

ProblemExample1

Awidelyudrule-of-thumbforthetemperaturedependenceofareaction

rateisthataten-C°riinthetemperatureapproximatelydoublestherate.

(Thisisobviouslynotgenerallytrue,especiallywhenastrongcovalentbond

mustbebroken.)Butforareactionthatdoesshowthisbehavior,whatwould

theactivationenergybe?

Solution:tutinginto

theaboveexpressionyields

=(8.314)(0.693)/(.00339-0.00328)

=(5.76Jmol–1K–1)/(0.00011K–1)=52400Jmol–1=52.4kJmol–1

ProblemExample2

Ittakesabout3.0minutestocookahard-boiledegginLosAngeles,butat

thehigheraltitudeofDenver,wherewaterboilsat92°C,thecookingtimeis

sinformationtoestimatetheactivationenergyforthe

coagulationofeggalbuminprotein.

Solution:TheratiooftherateconstantsattheelevationsofLAandDenver

is4.5/3.0=1.5,

thesubscripts2and1referringtoLAandDenverrespectively,wehave

E

a

=(8.314)(ln1.5)/(1/365–1/273)=(8.314)(.405)/(0.00274–

0.00366)

=(3.37Jmol–1K–1)/(0.000923K–1)=3650Jmol–1=3.65kJmol–1

Comment:Thisratherlowvalueemsreasonablebecauproteindenaturationinvolvesthe

disruptionofrelativelyweakhydrogenbonds;nocovalentbondsarebroken.

Thepre-exponentialfactor

Itisnowtimetofocusinonthepre-exponentialtermAin

beenneglectingitbecau

itisnotdirectlyinvolvedinrelatingtemperatureand

activationenergy,

sinceAmultipliestheexponentialterm,itsvalueclearlycontributestothe

valueoftherateconstantandthusoftherate.

RecallthattheexponentialpartoftheArrheniuquationexpressthe

fractionofreactantmoleculesthatpossnoughkineticenergytoreact,

actioncanrunfrom

zerotonearlyunity,dependingonthemagnitudesofE

a

andofthe

temperature.

Ifthisfractionwereunity,theArrheniuslawwouldreduceto

k=A

Inotherwords,Aisthefractionofmoleculesthatwouldreactifeitherthe

activationenergywerezero,orifthekineticenergyofallmolecules

exceededE

a

—admittedly,anuncommonscenario.

It'sallaboutcollisions

Sowhatwouldlimittherateconstantiftherewerenoactivationenergy

requirements?Themostobviousfactorwouldbetherateatwhich

nbecalculatedfromkinetic

moleculartheoryandisknownasthefrequency-orcollisionfactorZ.

Insomereactions,therelativeorientationofthe

moleculesatthepointofcollisionisimportant,so

wecanalsodefineageometricalorstericfactor

(commonlydenotedbyρ(Greeklowercarho).

Ingeneral,wecanexpressAastheproductofthe

twofactors:

A=Zρ

Valuesofρaregenerallyverydifficulttoasss;theyaresometime

Cricketsandpopcorn

Manybiologicalprocesxhibitatemperaturedependence

thatfollowstheArrheniuslaw,andcanthusbecharacterized

sinterestingDartmouthU.

pagethatlooksatthekineticsofcricketchirps.

InanarticleontheKineticsofPoppingofPopcorn(Cereal

Chemisty82(1):53-59),foundthat

poppingfollowsafirst-orderratelawwithanactivation

energyof53.8kJ/mol.

Thiskindofelectrophilic

additionreactioniswell-

knowntoallstudentsof

nice(butnot-for-

beginners)discussionof

suchreactionsandtheir

mechanismscanbefound

here.

estimatedbycomparingtheobrvedrateconstantwiththeoneinwhich

AisassumedtobethesameasZ.

Directionmakesadifference

Themorecomplicatedthestructuresofthereactants,themorelikelythat

thevalueoftherateconstantwilldependonthetrajectoriesatwhichthe

reactantsapproacheachother.

Weshowedoneexampleofthisnearthetopofthepage,butforanother,

considertheadditionofahydrogenhalidesuchasHCltothedoublebond

ofanalkene,convertingittoachloroalkane.

ExperimentshaveshownthatthereactiononlytakesplacewhentheHCl

moleculeapproachesthealkenewithitshydrogen-end,andinadirection

thatisapproximatelyperpendiculartothedoublebond,asshownat

below.

Thereasonforthisbecomesapparentwhenwerecallthat

HClishighlypolarowingtothehighelectronegativityof

chlorine,sothatthehydrogenendofthemoleculeis

slightlypositive.

Thedoublebondofetheneconsistsoftwocloudsof

negativechargecorrespondingtotheσ(sigma)andπ(pi)

ter,whichextendsaboveand

belowtheplaneoftheC

2

H

4

molecule,interactswithand

attractstheHClmolecule.

If,instead,theHClapproacheswithitschlorineend

leadingasin

,electrostaticrepulsionbetweenthelikechargescausthe

twomoleculestobounceawayfromeachotherbeforeanyreactioncantake

ethinghappensin

;theelectronegativitydifferencebetween

carbonandhydrogenistoosmalltomaketheC–Hbondsufficientlypolarto

attracttheincomingchlorineatom.

Nowthatyouknowwhatittakestogetareactionstarted,youareready

forthenextlessonthatdescribestheiractualmechanisms.

Whatyoushouldbeabletodo

Thelessonyoushouldtakefromthixampleisthatonceyoustart

combiningavarietyofchemicalprinciples,yougraduallydevelopwhatmight

becalled"chemicalintuition"whichyoucanapplytoawidevarietyof

farmoreimportantthanmemorizingspecificexamples.

Makesureyouthoroughlyunderstandthefollowingesntialideaswhich

peciallyimortantthatyouknowthe

precimeaningsofallthegreen-highlightedtermsinthecontextofthis

topic.

Explainthemeaningofareactionmechanismanddefineelementarystepand

intermediate.

Describetheroleofcollisionsinreactionmechanisms,andexplainwhynotall

collisionsleadtotheformationofproducts.

Sketchoutactivationenergydiagramsforsimplereactionsthatare

endothermicorexothermic,

Explainhowanactivatedcomplexdiffersfromanintermediate.

Definecatalyst,andsketchoutanactivationenergydiagramthatillustrates

howcatalystswork.

ExplainthesignificanceofthevarioustermsthatappearintheArrheniusLaw.

SketchoutatypicalArrheniusLawplotforahypotheticalreactionathigherand

lowertemperatures.

Explainhowtheactivationenergyofareactioncanbedetermined

experimentally.

Explainthesignificanceofthevarioustermsthatappearinthepre-exponential

factoroftheArrheniuquation.

ConceptMap

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