System – what we care about Surroundings– everything else ... · PDF file•...

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A Chemist’s View of the Universe System – what we care about Surroundings – everything else Boundary – separates system from surroundings

Transcript of System – what we care about Surroundings– everything else ... · PDF file•...

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AChemist’sViewoftheUniverse

• System – whatwecareabout

• Surroundings – everythingelse

• Boundary – separatessystemfromsurroundings

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Somebasicdefinitions

• Work– motionagainstanopposing(external)force

• Heat– energychangeassociatedwithachangeintemperature

– Exothermic – releasesheattothesurroundings– Endothermic – absorbsheatfromthesurroundings

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InternalEnergy(UorE)

• Totalenergyofthesystem(kineticandpotential)

• Internalenergyisastatefunction,whichmeanswecandefine

achangeinitasDU=Uf – Ui.

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Enthalpy(H)

• Totalpotentialenergyofthesystem

• Enthalpyisastatefunction,whichmeanswecandefinea

changeinitasDH=Hf – Hi.

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1st LawofThermodynamics

• Theinternalenergyofanisolated systemisconstant.

• Theonlywaystochangetheinternalenergyofasystemareheatand

work

– DU=Q+W• Thechangeininternalenergyforasystemisequaland

oppositetothechangeininternalenergyforthesurroundings

– DUsys +DUsurr =DUtot =0

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1st LawofThermodynamics

• “Greedy”convention(Ch andChE’s)

– Heatabsorbed bysystemà Q>0

– Heatreleased bysystemà Q<0

–WorkdonetosystemàW>0

–Workdoneby systemàW<0

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Hess’sLaw

• Directapplicationofthepropertiesofstatefunctions.

• Thestandardenthalpyofanoverallreactionisthesumofthestandard

enthalpiesoftheindividualreactionsintowhichareactionmaybe

divided.(whethertheyarerealornot)

• ThiscanbeextendedtoANYthermodynamicvariable

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PhaseChanges(Transitions)

• Anychangeofphasewillhaveacorrespondingchangeinenthalpy

• Becauseenthalpyisastatefunction,severalusefulpropertiesemerge.

• Considerachangeofphase(orstate)fromAtoBwithachangeofenthalpy=DH.Forthereverseprocess(goingfromBtoA),thechangeinenthalpywillbe–DH.

• ConsiderachangefromAtoC.Wecanconsiderthisashappeningintwosteps:first

fromAtoBandthenfromBtoC.ThusDHAàC=DHAàB+DHBàC

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Enthalpiesofreaction

• Asimilartypeofanalysiscanbeperformedforachemicalreaction.We

candefinethestandardreactionenthalpyasthechangeinenthalpy

betweentheproductsandthereactants,inthestandardstate:

whereni referstothestoichiometriccoefficientofspeciesi,andHm,i

referstothemolarenthalpyofspeciesi(akaenthalpyofformation).

Theo indicatesstandardstate.

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The2nd LawofThermodynamics

• Usedtopredictspontaneity(tendencyforaprocessto

happennaturally)

• The1st Lawonlytalksaboutconservationofenergy,it

saysnothing aboutthedirection thataprocesswilltendtogoin!

– Whydon’tballsleavethegroundandbounceup?

– Whydoesn’tshatteredglassreform?

– Whydoesn’tgreenpigmentseparateintoblueandyellow

pigments?

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The2nd LawofThermodynamics

• The2nd Lawdescribeshowspontaneityisrelatedtothedistribution ofenergy,not tothetotal energy.

• Energytendstoflowinadirectionwhereitwillbemore“spreadout”,

ordispersed.

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SoWhat’sEntropy?

• Thisleadstoanotherviewofthe2nd law:“Theentropyofanisolated

systemincreasesinthecourseofaspontaneouschange”

– DStot>0

• Relatedtochaos,randomness,disorder

• NoticethatQisnotastatefunctionbutSis!

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Phasetransitions

• Previouslywesawthatforaphasetransitionoccurringataconstant

pressure,Q=DHtr

• ThismeansthatwecanalsocalculateDStr:whereTtr isthetemperatureatwhichthetransitionoccurs

Thusexothermicprocesses(freezing,condensing)have(-)changesin

entropy,whileendothermicprocesses(melting,boiling)have(+)

changesinentropy

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Howisentropymeasured?

• Inananalogousfashiontoenthalpy,wecandefinethe

reactionentropychangeas:

• NotethatunlikeHmo,whichcan=0forsubstancesintheir

standardstate,Smo is≠0(unlessT=0)

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Gibbsfreeenergy

• let’sdefinetheGibbsfreeenergyasG=H-TS.

• Foramacroscopicchange,DG=DH– TDS• Thisalsoleadstothefamiliarconclusionthatfora

spontaneousprocessDG≤0• DGalsorepresentsthemaximumnon-PVwork thatcanbedonebyasystem

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HowcanDGbemeasured?

• Asfortheotherthermodynamicquantitieswehaveencountered,wecandefinethestandardfreeenergychangeforareactionas:

• Aswithenthalpyofformation,DGfo foranelement(ora

naturallyoccurringdiatomicmolecule)=0.

• ExperimentallyDGisoftenobtainedbydeterminingDHandDSseparately.

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Gibbsenergyandtheequilibriumconstant

• WhatdoesDGrxno represent?Itisthedifferenceinthe(molar)Gibbs

energiesofproductsandreactants,intheirstandardstate.

isthecruciallinkbetweenthermodynamics(energy)andchemicalequilibrium

• NoticethatifK>1thentheproductsarefavoredatequilibrium,whileifK<1thenthereactantsarefavored.

• Ingeneral, whereQisthereactionquotient

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Calculate ΔH°298 for the process Sb(s) + 5/2 Cl2(g) ⟶SbCl5(g) from the following information:Sb(s) + 3/2Cl2(g)⟶SbCl3(g) ΔH°298 = −314 kJSbCl3(s) + Cl2(g)⟶SbCl5(g) ΔH°298 = −80 kJ

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Calorimetry– it’sdabomb!• Experimentsmaybedoneatconstantvolume(bomb)orconstantpressure(coffee-cup)

• Entiresystemisadiabatic – thereisnoheatlostbetweenthesystem(sample)andthesurroundings(waterbathandmetalcasing)

• Thechangeintemperatureofthecalorimeterwillbeproportionaltotheheatthatitabsorbs:QαΔT,orQ=CΔT,whereCistheheatcapacityofthecalorimeter.

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Example

• Inapreliminaryexperiment,theheatcapacityofabombcalorimeterassemblyisfoundtobe5.15kJ/oC.Inasecondexperiment,a0.480gsampleofgraphite(carbon)isplacedinthebombwithanexcessofoxygen.Thewater,bomb,andothercontentsofthecalorimeterareinthermalequilibriumat25.00oC.Thegraphiteisignitedandburned,andthewatertemperaturerisesto28.05oC.CalculateΔHforthereaction:C(graphite)+O2(g)à CO2(g)

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Solution

• Thekeytothisproblemistorealizethatalltheheatabsorbedbythecalorimetermusthavecomefromthecombustionreaction.

• FirstcalculatetheheatabsorbedbythecalorimeterusingQ=CΔT:

• Theheatgivenupbythereactionmustbeequalandoppositetothis:Qrxn =-15.7kJ

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• WecanthenequatethistoΔUforthecombustionof1molofgraphite:

• Finally,recallthatΔH=ΔU+RTΔnforanisothermalprocess.Sincethetemperaturechangeisprettysmall(3.05oC)wecanassumethatitisisothermal.Δn=(1-1)=0soΔH≈ΔU.ThusΔH=-393kJ/mol

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Calorimetryrevisited– that’sonefancycoffeecup!

• Forisobaricmeasurements,useathermallyinsulatedvesselthatisopentotheatmosphere

• Moresophisticatedcalorimeterscanbeused–Adiabaticflamecombustion–Differentialscanning–Isothermaltitration• Forsolidsandliquids,ΔH≈ ΔUsincetheirvolumeisnegligible(atleastcomparedtogases)

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Example

• A15.5gsampleofametalalloyisheatedto98.9oCandthendroppedinto25.0gofwaterinacalorimeter.Thetemperatureofthewaterrisesfrom22.5to25.7oC.Calculatethespecificheatofthealloy.

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Solution• Thekeytosolvingthisproblemistorealizethatalltheheatlostbythehotsolidmustbegainedbythewaterinthecup.

• Firstwewillfindtheheatabsorbedbythewater:QH2O =mcΔTso

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• Thismustbeequalandoppositetotheheatlostbythealloy(rememberthesignconvention!)soQalloy =-334J

• Finallycalculatethespecificheatofthealloy:

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Example

• A50.0mLsampleof0.250MHClat19.50oCisaddedto50.0mLof0.250MNaOH,alsoat19.50oC,inacalorimeter.Aftermixing,thesolutiontemperaturerisesto21.21oC.Calculatetheheatofthisreaction.

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Solution• Firstrecognizethereactionthatistakingplace:HCl(aq)+NaOH(aq)à NaCl(aq)+H2O

• Nowlet’smakeafewassumptions/simplifications:–Takesolutionvolumestobeadditivesothetotalvolumeofsolutionis50.0+50.0=100.0mL–ConsidertheNaCl(aq)solutiontobesufficientlydilutethatthedensityandspecificheatarethesameasthoseforpurewater(1.00g/mLand4.184J/goC)–Thesystemisperfectlyinsulated,sonoheatescapesfromthecalorimeter–Theheatrequiredtowarmanypartofthecalorimeter(otherthantheNaClsolution)isnegligible)

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• Findtheheatretainedinthecalorimeter:

• Finallyfindtheheatofreaction:Qrxn =Qp =-Qcal =-715J

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ChemicalKinetics

• Studyoftheratesofchemicalreactions– Howquicklyaprocesscantakeplace

• Understandingofthemechanismofareaction– How(onamolecularlevel)aprocesscantakeplace

• Becausethesemeasurementsarechangingwithrespecttotimeandaresensitivetomanyvariables,theyarenotoriouslydifficultexperimentstocarryout!

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Factorsaffectingtherateofachemicalreaction

• Concentration• Pressure(gasesonly)• Temperature• Presenceofacatalyst• Understandingthedependenceofareactiononthesefactorscanaidouroptimizationofachemicalprocess

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Measuringtherateofareaction

• Wecandefinetherateintermsofthelossofareactantortheformationofaproduct:

– Noticethatthismeanstherateisrelatedtotheslope(tangentline)tothecurve

• Howeverthisdoesn’ttakeintoaccountthestoichiometryofthereaction(i.e.ifthereactionisRà2Ptherateofformationofaproductwillbetwiceasgreatasthelossofreactant).

• Intermsofagivencomponenti, whereni isthestoichiometric number.

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Inpictures

http://textbook.s-anand.net/ncert/class-xii/chemistry/4-chemical-kinetics

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Ratelaws• Itisfoundexperimentallythattherateofareactionisusuallyproportionaltothe

concentrationofeachreactant,raisedtoacertainpower:wherexandyaretheorders ofthereactionwithrespecttoAandB,respectively.Theordersmaybeanyrealnumber(including0andfractions).Theoverallorderisgivenbyx+y.

• IngeneraltheordersmustbedeterminedexperimentallyandareNOTnecessarilythestoichiometriccoefficientsofthereaction(unlessthereactioniselementary).

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Determinationoftheratelawforareaction

• Isolationmethod– systematicallyvarytheconcentrationsofthereactantssothatallareinalargeexcessexceptforone.Thisallowsthedeterminationoftheorderofthatonespecies.

• Forexample,ifthegeneralratelawisandBispresentinalargeexcess,thenitsconcentrationcanbeassumedtobeconstantasthereactionproceeds,whichmeansthatd[B]/dtà0.Thuswecanwritetheratelawas whereandwecanfindthevaluesofk’andxbycurve-fitting.

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Determinationoftheratelawforareaction

• Typicallytheinitial ratesaremeasured.ForexampleifBisinexcessthentheinitialratecanbewrittenas

• Thuswecanplotvo vs.[A]o andgetk’andxbyfittingthedatanonlinearly(powerlaw),orwecanlinearizetheequationbytakingthelogofbothsides:

• WecanrepeatthisprocesswhereAisheldinexcess,anddetermineanewpseudo-rateconstantk’’( )andy,andthereforealsogettheoriginalrateconstantk.

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Example

• Therecombinationofiodineatomsinthegasphaseinthepresenceofargonwasinvestigatedandtheorderofthereactionwasdeterminedbythemethodofinitialrates.Theinitialratesofthereaction2I(g)+Ar(g)àI2(g)+Ar(g)wereasfollows:

[I]o (10-5 mol/L) 1.0 2.0 4.0 6.0vo (mol/L*s) a)8.70X10-4 3.48X10-3 1.39X10-2 3.13X10-2

b)4.35X10-3 1.74X10-2 6.96X10-2 1.57X10-1c)8.69X10-3 3.47X10-2 1.38X10-1 3.13X10-1

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Example

• TheArconcentrationsarea)1.0mmol/L,b)5.0mmol/Landc)10.0mmol/L.DeterminetheordersofreactionwithrespecttotheIandAratomconcentrationsandtherateconstant.

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Solution• Sincetheratelawwillbeoftheform

,weneedtoplotthedependenceoftherateonboth[I]o and[Ar]o.Alog-logplotwillbehelpfulastheslopewillgiveustheorderwithrespecttothatsubstance.

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Solution• Fromthefirstgraph,theslopeis2whichmeansthatthereactionis2nd orderwithrespecttoI.Fromthesecondgraph,theslopeis1whichmeansthatthereactionis1st orderwithrespecttoAr.Thustheratelawis

• Noticethatthisistheratelawonlyfortheinitialrate– itispossiblethatthereactionhasadifferentratelawasthereactionproceeds.

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Solution• Wecangettherateconstantfromtheinterceptsofeithersetoflines.Inthefirstexperiment,k’=k[Ar]0.Inthesecondexperiment,k’’=k[I]02.Ineithercase,k≈8.6*109 L2/mol2s.

logk' k' [Ar]0 k6.9365 8639727 0.001 86397266077.6439 44045343 0.005 88090686747.9326 85624885 0.01 8562488476

logk‘’ k‘’ [I]0 k-0.0616 0.867761 0.00001 86776074500.5387 3.457005 0.00002 86425123471.1363 13.68674 0.00004 85542121601.4969 31.39786 0.00006 8721626801

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How will each of the following affect the rate of the reaction: CO(g) + NO2(g) ⟶CO2(g) + NO(g) if therate law for the reaction is rate = k [NO2] [CO] ?

(a) Increasing the pressure of NO2 from 0.1 atm to 0.3 atm(b) Increasing the concentration of CO from 0.02 M to 0.06 M.

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TheArrheniusequation

• Aplotoflnkvs1/Tshouldgiveastraightline,withaslopeofEa/RandaninterceptoflnA:

• AsTà∞,kàko (orA),whichiscalledthefrequencyfactor.Itisalsocalledthepre-exponentialfactorsincetheaboveequationcanbewrittenas

http://chemistry.tutorvista.com/inorganic-chemistry/arrhenius-equation.html

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MoreontheArrheniusequation• Thepre-exponentialfactorA representsthefastestpossiblerateforareaction,

whichwouldonlybelimitedbydiffusion.Thiscanbeinterpretedasbeingrelatedtotherateofsuccessfulcollisionsbetweenreactantmoleculestoyieldproductmolecules.

• NoticethatthefractionofmoleculeswithanenergygreaterthanEa isgivenbyanexponentialdecay,knownasaBoltzmanndistribution.Onlythosemoleculeswithanenergythatexceedstheactivationenergywillbeabletoreacttoformproducts.

• Thehighertheactivationenergy,themoretherateconstantwilldependonT.

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Temperaturedependenceofthereactionrate

Arrheniusequation

Ea istheactivationenergyofthereaction.

http://www.wiley.com/college/boyer/0470003790/reviews/kinetics/kinetics_stability.htm

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Roleofacatalyst• Acceleratetherateofareaction– Loweractivationenergy– Providealternatepath• Doesnotchangethethermodynamicsorequilibriumofareaction– ΔG,ΔH,ΔSandKareallthesameasfortheuncatalyzedreaction

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Describe how graphical methods can be used to determine the activation energy of a reaction from a series of data that includes the rate of reaction at varying temperatures.

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Theoreticaldescriptionoftheratelaws

• Althoughtheparametersforaratelawareexperimentallydetermined,itis

sometimespossibletocalculate(orpredict)themfromfirstprinciples.Thisrequires

aknowledgeofthewayinwhichthereactiontakesplace,alsoknownasthe

mechanism.

• Mostreactionsarethoughttooccurinaseriesof(relatively)wellunderstoodsteps,

eachofwhichisknownasanelementaryreaction.

• Inanelementaryreaction,typicallyasmallnumber(1-3)atoms,moleculesorions

collidewitheachotherandformaproduct.

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Theoreticaldescriptionoftheratelaws

• Molecularity – thenumberofmolecules(oratomsorions)

thatcometogetherinanelementaryreaction

– Unimolecular- oneparticlebreaksapartorrearranges,i.e.dissociationorisomerization

– Bimolecular- twoparticlescollidewitheachother– Termolecular (rare)-threeparticlessimultaneously collidewitheachother

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Theoreticaldescriptionoftheratelaws

• Becauseelementaryreactionsareofaknownmolecularity,wecan

writedowntheratelawsforthemsimplybylookingathowmany

speciesarepresent:

– AàP v=k[A]

– A+Bà P v=k[A][B]

• Amechanism isacombinationofelementaryreactionsthattriesto

explainthesequenceofevents(steps)ofachemicalreaction

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• Therate-determiningstepistheslowest

“relevant”stepinachemicalreaction,and

determinestheoverallrateofthereaction.It

alsodictateshowmuchproductcanbe

formed.

• Typicallythesloweststepinachemical

reactionhasthehighestactivationenergy

since

• Inthediagramontheright,thelocalminima

correspondtointermediates – thismeansthat

theycanbe(theoretically)isolated.

• Themaximacorrespondtotransitionstates–theyareveryunstableandnotisolable

Rate-determiningstep

http://chemwiki.ucdavis.edu/Wikitexts/UC_Davis/UCD_Chem_2C%3A_Larsen/Chem_2C%3A_H

omework/Team_1/Chapter_24%3A_Kinetics