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EXPERIMENTB8:EFFECTOFTEMPERATUREONEQUILIBRIUMCONSTANT

LearningOutcomesUponcompletionofthislab,thestudentwillbeableto:

1) Predicttheeffectoftemperatureontheequilibriumconstant.2) Designanexperimenttomeasurethethermodynamicparametersforthe

dissolvingofmetalhydroxidesinwater.IntroductionWhenioniccompoundsaredissolvedinwater,itisgenerallyassumedthatincreasingthetemperaturewillcausemoreofthesolidtodissolve.However,thisassumptionisnotalwaystrue,aswillbedemonstratedinthisexperiment.Inthisexperiment,calciumhydroxidewillbedissolvedinwaterandtheeffectoftemperatureonthisprocesswillbestudied.Thedatafromtheexperimentwillnotonlybeusedtodeterminetheeffectoftemperatureontheequilibriumconstant,butalsotodeterminethermodynamicparameterssuchasΔH,ΔS,andΔGfortheprocess.Severalconceptsdiscussedthroughoutthisclasswillbeexaminedinthisexperiment.Theseinclude:

a. Effectoftemperatureonequilibriumb. RelationshipbetweenpHandequilibriumconstantforasaturatedsolutionc. DeterminationofthermodynamicparameterssuchasΔHandΔS.

EffectoftemperatureonequilibriumAccordingtoLeChatelier’sprinciple,“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,“I”isassumedtobesomeinitialamountofthesolid

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calciumhydroxide,and“x”istheamountofthesolidthatdissolvesinwatertoformtheaqueousions.

Ca(OH)2(s)

€

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

€

K = [Ca2+][OH −]2

K = x × (2x)2 = 4x 3

InordertodeterminetheequilibriumconstantK,“x”mustbeknown.Howcan“x”bedeterminedexperimentally?Inapreviousexperiment(ExperimentB4),“x”wasdeterminedspectrophotometrically.Inthatcase,theproductwascoloredandsuchadeterminationwasthereforepossible.Inthissituationhowever,spectrophotometricdeterminationisnotasimpleoption.Acloseexaminationoftheequilibriumtableaboveshowsthat:

2x=[OH−]

Therefore:

€

x =[OH −]2

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

KW=1.0×10-14=[H+]×[OH−]

pH=-log[H+]

Insummary,ifthepHofthesaturatedsolutionisdetermined,the[H+]canbeascertained.Usingtheionicproductofwater,onecanthendeterminethe[OH−].Knowingthe[OH−]onecancalculate“x”andthereforeK.

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DeterminationofthermodynamicparameterssuchasΔH,ΔS,andΔGAsdiscussedearlier,chemicalequilibriumisimpactedbychangesintemperature.Therelationshipbetweentheabsolutetemperature,T,andtheequilibriumconstant,K,forareactionisgiveninEquation1below: ΔG°=-RTlnK Equation1InEquation1,ΔG°isthestandardfreeenergychangeandRistheuniversalgasconstant(8.314J/mol-K).Bydefinition,thestandardfreeenergychange,ΔG°isalsorelatedtothestandardenthalpychange,ΔH°andthestandardentropychange,ΔS°accordingtoEquation2. ΔG°=ΔH°-TΔS° Equation2Inthermodynamics,thevaluesofΔH°andΔS°maygenerallybeconsideredtobeinvariablewhenthetemperatureischangedandthevalueofΔG°ontheotherhandchangeswithtemperature.Therefore,Equations1and2maybecombinedasfollows: −RTlnK=ΔH°−TΔS° Equation3Equation3canfurtherbemanipulatedtoisolatethedependentvariablesandtheconstants.Dividingbothsidesoftheequationby“-RT”resultsinEquation4.

€

lnK = −ΔH !

R1T⎛

⎝ ⎜ ⎞

⎠ ⎟ +

ΔS !

R Equation4

InEquation4,ΔH°,ΔS°,andRareconstantsandKandTarevariables.AcomparisonofEquation4withtheequationofastraightline,y=mx+b,indicatesthefollowing:

lnKisanalogoustoy

€

1Tisanalogoustox

€

−ΔH !

Risanalogoustom

€

ΔS !

Risanalogoustob

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ThereforealinearregressionofaplotoflnKvs.

€

1Tshouldresultinastraightline

whoseslopewillbe

€

−ΔH !

Randwhosey-interceptwillbe

€

ΔS !

R.SinceRisthe

universalgasconstant,thevaluesofΔH°andΔS°canbedeterminedfromtheslopeandtheintercept,respectivelyofthebestfitline.

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ExperimentalDesignAsaturatedsolutionofcalciumhydroxidewillbeprovidedforthisexperiment.Thissolutionwillbeheatedtoabout70°CandthepHofthesolutionwillbedeterminedusingapHmeter.Thesolutionshouldthenbecooledinabout5°Cintervalsdowntoabout5°CandthepHdeterminedateachintermediatetemperature.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.Heatthewatertoabout70-75°C.Monitorthetemperaturewithathermometer.

5. Obtainabout10mLofsaturatedCa(OH)2solutioninalargetesttube.Adda

smallamountofsolidCa(OH)2tothetesttubetoensurethatthesolutionisindeedsaturated.

6. Obtainaringstandandaclampandsuspendthetesttubecontainingthe

Ca(OH)2intothewaterbathensuringthatthesolutioniscompletelysubmergedinsidethewater.

7. MeasureandrecordthetemperatureoftheCa(OH)2solution.Aimtostart

measurementsataround70°C.8. MeasureandrecordthepHoftheCa(OH)2solution.9. Coolthewaterbathbyabout5°Cusingroomtemperaturewateratfirstandthen

coldwaterorice.Repeatsteps7and8andobtainmeasurementsinabout5°Cintervalsuntilthetemperaturehasreached5°C.

10. DiscardtheCa(OH)2solutioninanappropriatewastecontainerprovidedbythe

instructor.

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DataTable

Temperature,°C

pH

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DataAnalysis1. Calculatethe[H+]fromthepHmeasuredateachtemperature.

€

[H +] =10−pH 2. Calculatethe[OH−]

€

[OH −] =1.0 ×10−14

[H +]

3. Calculate“x”.

€

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,calculatethevalueofΔH°.

€

slope(m) = −ΔH !

RΔH ! = − slope × R( )

10. Usingthey-intercept,calculatethevalueofΔS°.

€

y − intercept = ΔS!

RΔS ! = R × (y − intercept)

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NOTE:Steps1through7ofthedataanalysismaybecompletedusingaspreadsheetprogramsuchasMicrosoftExcel.

1. Enterthedata(temperaturein°CandpH)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. Click“Insert”andthen“Chart”.Choose“XY”scatterandselect“MarkedScatter”6. Whenthegraphisdisplayed,clickonanydatapointonthechartandfromthe

toolbar,select“Chart”andthen“InsertTrendline”.7. Fromthepop-upbox,selectthe“Options”tabandchecktheboxes: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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Results1. Whathappenstotheequilibriumconstantfortheprocessofdissolving

Ca(OH)2(s)inwater,whenthetemperatureisincreased?2. Basedontheobservationreportedinquestion1,commentontheeffectof

temperatureonthesolubilityofcalciumhydroxide.3. Theexperimentalvaluesofthethermodynamicparametersforthedissolvingof

Ca(OH)2(s)inwaterare:

ΔH°=_______________________kJ/mol

ΔS°=______________________J/mol-K

4. Aretheresultsconsistentwiththeobservations?

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5. Usethermodynamictablestodeterminethetheoreticalvaluesofthethermodynamicparameters.ThetheoreticalvaluesofthethermodynamicparametersfordissolvingofCa(OH)2(s)inwaterare(showeachcalculation):

ΔH°=_______________________kJ/mol

ΔS°=______________________J/mol-K

6. Thepercentageerrorintheexperimentalresultsare:

ΔH°=_______________________

ΔS°=_______________________

7. Whatarethesourcesoferrorinthisexperiment?