EXPERIMENT B8: EFFECT OF TEMPERATURE ON EQUILIBRIUM .equilibrium is established ... A saturated...

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Transcript of EXPERIMENT B8: EFFECT OF TEMPERATURE ON EQUILIBRIUM .equilibrium is established ... A saturated...

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    EXPERIMENTB8:EFFECTOFTEMPERATUREONEQUILIBRIUMCONSTANT

    LearningOutcomesUponcompletionofthislab,thestudentwillbeableto:

    1) Predicttheeffectoftemperatureontheequilibriumconstant.2) Designanexperimenttomeasurethethermodynamicparametersforthe

    dissolvingofmetalhydroxidesinwater.IntroductionWhenioniccompoundsaredissolvedinwater,itisgenerallyassumedthatincreasingthetemperaturewillcausemoreofthesolidtodissolve.However,thisassumptionisnotalwaystrue,aswillbedemonstratedinthisexperiment.Inthisexperiment,calciumhydroxidewillbedissolvedinwaterandtheeffectoftemperatureonthisprocesswillbestudied.Thedatafromtheexperimentwillnotonlybeusedtodeterminetheeffectoftemperatureontheequilibriumconstant,butalsotodeterminethermodynamicparameterssuchasH,S,andGfortheprocess.Severalconceptsdiscussedthroughoutthisclasswillbeexaminedinthisexperiment.Theseinclude:

    a. Effectoftemperatureonequilibriumb. RelationshipbetweenpHandequilibriumconstantforasaturatedsolutionc. DeterminationofthermodynamicparameterssuchasHandS.

    EffectoftemperatureonequilibriumAccordingtoLeChateliersprinciple,whenasystematequilibriumissubjectedtochangeinconcentration,temperature,volume,orpressure,thenthesystemreadjustsitselfto(partially)counteracttheeffectoftheappliedchangeandanewequilibriumisestablished.Inthissection,theeffectoftemperatureontheequilibriumprocesswillbefurtherexamined.Theeffectoftemperatureontheequilibriumprocessdependsonwhetherthereactionisexothermicorendothermic.Exothermicreactionsarethoseinwhichthesystemgeneratesheatandasaresultheatmaybeconsideredasaproduct(anoutput)ofthesereactions.Ontheotherhand,endothermicreactionsarethoseinwhichthesystemabsorbsheatandasaresultheatmaybeconsideredasareactant(aninput)ofthesereactions.

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    ConsidertheexothermictransformationofAtoB.Sinceheatisgeneratedinthisreaction,theequationcanbewrittenas:

    A

    B+heatIfheatisaddedtothisreaction,i.e.,ifthetemperatureisincreased,theequilibriumwillshiftleftandproducemoreA.Conversely,ifheatisremovedfromthisreaction,i.e.,ifthetemperatureisdecreased,theequilibriumwillshiftrightandproducemoreB.Therefore,ingeneral,increasingthetemperatureofanexothermicreactionshiftstheequilibriuminthedirectionofthereactantsandviceversa.Now,considertheendothermictransformationofCtoD.Sinceheatisabsorbedinthisreaction,theequationcanbewrittenas:

    C+heat

    D

    Ifheatisaddedtothisreaction,i.e.,ifthetemperatureisincreased,theequilibriumwillshiftrightandproducemoreD.Conversely,ifheatisremovedfromthisreaction,i.e.,ifthetemperatureisdecreased,theequilibriumwillshiftleftandproducemoreC.Therefore,ingeneral,increasingthetemperatureofanendothermicreactionshiftstheequilibriuminthedirectionoftheproductsandviceversa.RelationshipbetweenpHandequilibriumconstantforasaturatedsolutionAsaturatedsolutionisobtainedwhenthemaximumamountofsolutehasbeendissolvedinagivenamountofsolvent.Inasaturatedsolutionofanionicsubstanceinwater,thesoluteisinequilibriumwiththeaqueousions.Forinstance,inasaturatedsolutionofcalciumhydroxide:

    Ca(OH)2(s)

    Ca2+(aq)+2OH(aq)

    Theequilibriumconstantforthisprocessisgivenby:

    K=[Ca2+][OH]2

    NotetheabsenceofCa(OH)2(s)intheexpressionfortheequilibriumconstant.Sincetheamountofasolidisgenerallythoughttobeunchanged,itisexcludedfromtheequilibriumconstantexpression.Thefollowingequilibriumtableshowshowtheequilibriumconstantiscalculatedforsuchaprocess.Inthetable,Iisassumedtobesomeinitialamountofthesolid

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    calciumhydroxide,andxistheamountofthesolidthatdissolvesinwatertoformtheaqueousions.

    Ca(OH)2(s)

    Ca2+(aq) + 2OH(aq)Initialconcentrations I 0 ~0Amountthatdissolves -x +x +2xEquilibriumamount Ix x 2xTherefore:

    K = [Ca2+][OH ]2

    K = x (2x)2 = 4x 3

    InordertodeterminetheequilibriumconstantK,xmustbeknown.Howcanxbedeterminedexperimentally?Inapreviousexperiment(ExperimentB4),xwasdeterminedspectrophotometrically.Inthatcase,theproductwascoloredandsuchadeterminationwasthereforepossible.Inthissituationhowever,spectrophotometricdeterminationisnotasimpleoption.Acloseexaminationoftheequilibriumtableaboveshowsthat:

    2x=[OH]

    Therefore:

    x = [OH]

    2

    Theconcentrationofhydroxide,[OH],isrelatedtothehydrogenionconcentration,[H+],andthereforetothepHofthesolution,bytheionicproductofwater.

    KW=1.010-14=[H+][OH]

    pH=-log[H+]

    Insummary,ifthepHofthesaturatedsolutionisdetermined,the[H+]canbeascertained.Usingtheionicproductofwater,onecanthendeterminethe[OH].Knowingthe[OH]onecancalculatexandthereforeK.

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    DeterminationofthermodynamicparameterssuchasH,S,andGAsdiscussedearlier,chemicalequilibriumisimpactedbychangesintemperature.Therelationshipbetweentheabsolutetemperature,T,andtheequilibriumconstant,K,forareactionisgiveninEquation1below: G=-RTlnK Equation1InEquation1,GisthestandardfreeenergychangeandRistheuniversalgasconstant(8.314J/mol-K).Bydefinition,thestandardfreeenergychange,Gisalsorelatedtothestandardenthalpychange,Handthestandardentropychange,SaccordingtoEquation2. G=H-TS Equation2Inthermodynamics,thevaluesofHandSmaygenerallybeconsideredtobeinvariablewhenthetemperatureischangedandthevalueofGontheotherhandchangeswithtemperature.Therefore,Equations1and2maybecombinedasfollows: RTlnK=HTS Equation3Equation3canfurtherbemanipulatedtoisolatethedependentvariablesandtheconstants.Dividingbothsidesoftheequationby-RTresultsinEquation4.

    lnK = H!

    R1T

    +

    S !

    R Equation4

    InEquation4,H,S,andRareconstantsandKandTarevariables.AcomparisonofEquation4withtheequationofastraightline,y=mx+b,indicatesthefollowing:

    lnKisanalogoustoy

    1Tisanalogoustox

    H !

    Risanalogoustom

    S !

    Risanalogoustob

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    ThereforealinearregressionofaplotoflnKvs.

    1Tshouldresultinastraightline

    whoseslopewillbe

    H !

    Randwhosey-interceptwillbe

    S !

    R.SinceRisthe

    universalgasconstant,thevaluesofHandScanbedeterminedfromtheslopeandtheintercept,respectivelyofthebestfitline.

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    ExperimentalDesignAsaturatedsolutionofcalciumhydroxidewillbeprovidedforthisexperiment.Thissolutionwillbeheatedtoabout70CandthepHofthesolutionwillbedeterminedusingapHmeter.Thesolutionshouldthenbecooledinabout5Cintervalsdowntoabout5CandthepHdeterminedateachintermediatetemperature.ThepHofthesolutionwillbeusedtodeterminethe[H+]ateachtemperature.Thiswillthenbeconvertedto[OH]andthenKateachtemperature.AplotoflnKvs.1/Twillbeusedtodeterminethevariousthermodynamicparameters.ReagentsandSuppliesSaturatedsolutionofCa(OH)2,pHmeter,hotplate,thermometer(SeepostedMaterialSafetyDataSheets)

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    Procedure1. ReadthecompleteinstructionmanualfortheoperationofapHmeter.

    2. ObtainapHmeter,thermometer,andahotplatefromthestockroom.3. TheinstructorwilldemonstratetheproperuseandcalibrationofthepHmeter.

    TheinstructorwillalsodemonstratehowtoadjustthetemperaturesettingofthepHmeter.ThissettingmustbeadjustedforeachtemperatureatwhichthepHwillbemeasured.

    4. Setupahotwaterbath.Inordertodothis,halffillalargebeakerwithtapwater

    andplaceonahotplate.Heatthewatertoabout70-75C.Monitorthetemperaturewithathermometer.

    5. Obtainabout10mLofsaturatedCa(OH)2solutioninalargetesttube.Adda

    smallamountofsolidCa(OH)2tothetesttubetoensurethatthesolutionisindeedsaturated.

    6. Obtainaringstandandaclampandsuspendthetesttubecontainingthe

    Ca(OH)2intothewaterbathensuringthatthesolutioniscompletelysubmergedinsidethewater.

    7. MeasureandrecordthetemperatureoftheCa(OH)2solution.Aimtostart

    measurementsataround70C.8. MeasureandrecordthepHoftheCa(OH)2solution.9. Coolthewaterbathbyabout5Cusingroomtemperaturewateratfirstandthen

    coldwaterorice.Repeatsteps7and8andobtainmeasurementsinabout5Cintervalsuntilthetemperaturehasreached5C.

    10. DiscardtheCa(OH)2solutioninanappropriatewastecontainerprovidedbythe

    instructor.

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    DataTable

    Temperature,C

    pH

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    DataAnalysis1. Calculatethe[H+]fromthepHmeasuredateachtemperature.

    [H +] =10pH 2. Calculatethe[OH]

    [OH ] = 1.0 1014

    [H +]

    3. Calculatex.

    x = [OH]

    2

    4. CalculateK.

    K = 4x 3

    5. CalculatelnK(naturallogarithmofK)

    6. ConvertalltemperaturestotheKelvinscaleandcalculate

    1T

    7. PlotagraphoflnK(y-axis)vs.

    1T(x-axis).

    8. Useregressionanalysestofindtheequationofthebestfitlinearequationforthe

    dataandobtaintheslope(m)andthey-intercept(b).9. Usingtheslope,calculatethevalueofH.

    slope(m) = H!

    RH ! = slope R( )

    10. Usingthey-intercept,calculatethevalueofS.

    y intercept = S!

    RS ! = R (y intercept)

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    NOTE:Steps1through7ofthedataanalysismaybecompletedusingaspreadsheetprogramsuchasMicrosoftExcel.

    1. Enterthedata(temperatureinCandpH)incolumnsAandB.UseRow1for

    columnheadings.

    2. EnterformulasinRow2foreachcalculation,asshowninthetableabove.3. Ineachcolumn,pointthecursortothebottomrightcornerofacell(sayC2)and

    dragdown(tillRow15)theplussigntocopytheformulatotheothercells.RepeatthisforallthecolumnsDthroughI.

    4. Todrawagraph,selectthexandydata,whichwouldbedatainfieldsH:2-15

    andI:2-15.5. ClickInsertandthenChart.ChooseXYscatterandselectMarkedScatter6. Whenthegraphisdisplayed,clickonanydatapointonthechartandfromthe

    toolbar,selectChartandthenInsertTrendline.7. Fromthepop-upbox,selecttheOptionstabandchecktheboxes:1)Display

    equationand2)DisplayR-squaredvalueandclickOK.

    A B C D E F G H I1 Temperature,T

    C pH [H+] [OH] x K T,Kelvin 1/T ln(K)2 70 pH1 =10^(-B2) =(1.0E-14)/C2 =D2/2 =4*((E2)^3) =A2+273.15 =1/G2 =LN(F2)3 65 pH2 4 60 pH3 5 55 pH4 6 50 pH5 7 45 pH6 8 40 pH7 9 35 pH8 10 30 pH9 11 25 pH10 12 20 pH11 13 15 pH12 14 10 pH13 15 5 pH14

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