Experiment5∙Freezing‐pointdepression 5‐1

Name___________________________________________________________LabDay__________LabTime_________Experiment5∙Freezing‐pointdepressionPre‐labquestionsAnswerthesequestionsandhandthemtotheTFbeforebeginningwork.(1)Whatisthepurposeofthisexperiment?__________________________________________________________________________________________________________________________________________________________________________________________________________________(2)According toFigure5‐2atwhat temperaturedoes cyclohexane freezeat1 atmpres‐sure?__________________________________________________________________________________________________________________________________________________________________________________________________________________(3)Whatisthedefinitionof“molality”?__________________________________________________________________________________________________________________________________________________________________________________________________________________(4)Youwillmeasurethetemperatureatwhichasampleofcyclohexanefreezes.Howwillyouknowthatthesampleisatitsfreezingpoint?__________________________________________________________________________________________________________________________________________________________________________________________________________________(5)Youwillmeasurethetemperatureofasolutionofanunknowndissolvedincyclohexaneasthesolutionfreezes.Howwillyouknowthatthesampleisintheprocessoffreezing?__________________________________________________________________________________________________________________________________________________________________________________________________________________

Experiment5∙Freezing‐pointdepression 5‐2

Experiment5

Freezing‐pointdepression

PhasediagramsandphasetransitionsAphasediagramsuchasFigure5‐1 indicates themoststablestateofasubstance(solid, liquid,orvapor)atanygiventem‐perature and pressure. Phase boundaries (solid lines) on aphase diagram indicate conditions at which two or morephasescoexistinequilibrium. When temperatureandpressure change, a substancemayundergoaphasetransition,thatis,aconversionfromonestatetoanother;thenamesofthesephasetransitionsappearinFig‐ure 5‐1. Suppose that the substancewhose phase diagram isgiveninFigure5‐1is initiallyat1atmpressureandataverylowtemperature;undertheseconditions,themoststablestateofthatsubstanceisasolid.Asthesolidisheatedat1atmpres‐sure, the systemmoves to the rightalong the1‐atmpressurelineinthephasediagramuntilitreachesthesolid–liquidphaseboundary, at which point the solid and the liquid coexist atequilibrium. Inotherwords, thesolidmelts.The temperatureat whichmelting of the solid (or freezing of the liquid if thephaseboundaryisapproachedfromtheright)occursat1atmpressure is called the normal melting point (or the normalfreezingpoint).Uponfurtherheatingat1atm,thesystemcon‐tinues tomove along the 1‐atmpressure line until it reachesthe liquid–vapor phase boundary, at which point the liquid

Experiment5∙Freezing‐pointdepression 5‐3

boils. The temperature at which boiling of the liquid takesplaceat1atmpressureiscalledthenormalboilingpoint.Con‐tinuedheatingat1atmtransformstheliquidtothevapor. Althoughweareconcernedwiththeconversionofaliquidtoasolid (i.e., freezing) in thisexperiment,wemust firstdis‐cusstheconversionofaliquidtoavapor(i.e.,boiling)becausean understanding of the boiling process provides some theo‐reticalideasneededinthepresentexperiment.Vaporpressureandvapor‐pressureloweringMany liquids (e.g.,wateror alcohol) if left in abeaker that isopen to the atmosphere will, in time, completely evaporate.However, if a beaker containing sufficient liquid is placed in‐sideaclosedbox,adifferentresult isobtained:some,butnotall,oftheliquidevaporatesandtheatmospherewithintheboxbecomespermeatedwithvaporcomingofftheliquid.Theendresult of the experiment in the closed box corresponds to asituation inwhich the liquidand thevaporcoexist inequilib‐riumwitheachother.

Figure5‐1Aphasediagramshowsthemoststablestateofasubstanceatanygiventempera‐tureandpressure.Phaseboundaries(solidlines)indicateconditionsatwhichtwoormorephasescoexistinequilibrium.Tfdenotesthenormalfreezing(ormelting)point,Tbdenotesthenormalboilingpoint,andthetriplepointdenotesconditionsatwhichsolid,liquidandvaporallcoexist.

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Experiment5∙Freezing‐pointdepression 5‐4

Becauseitisagas,thevaporexertsapressureontheinte‐riorwallsofthebox;thispressureiscalledthevaporpressureoftheliquid.Liquidsthathaveahighvaporpressureatroomtemperature are said to be volatile, that is, they evaporatereadily, whereas liquids that have a low vapor pressure atroomtemperaturearesaidtobenon‐volatile.Ether,whoseva‐porpressureis0.703atmat25°C, isanexampleofavolatileliquid.Water(vaporpressure=0.0313atmat25°C)isconsid‐ered amoderately volatile liquid.Mercury (vapor pressure =2.4×10–6atmat25°C)isessentiallyanon‐volatileliquid. Thevaporpressureofa liquidatagiven temperaturecanbereadoffaphasediagram.Considerthephasediagramofcy‐clohexane shown in Figure 5‐2. Suppose that a sample of cy‐clohexane is at1atmpressureand20 °C;under these condi‐tions,themoststablestateofcyclohexaneistheliquid.Itsva‐porpressureat20°Cisfoundbyfollowingthe20°Clineuntilthe liquid–vapor phase boundary is encountered: the figureshows that the vapor pressure of cyclohexane at 20 °C is0.1atm. Boilingoccurswhen thevaporpressureof a liquidequalsthepressureofthesurroundingatmosphere.Cyclohexaneboils

Figure5‐2Phasediagramofcyclohexane.

Experiment5∙Freezing‐pointdepression 5‐5

at 20 °C if the special arrangement is made so that the sur‐roundingatmosphereisat0.1atm.However,inabeakeropento theatmosphereat theordinary conditionsof1 atm, cyclo‐hexaneboilsat80°C. In the 1880s the French chemist François–Marie Raoultdiscovered thatdissolvingasubstance(thesolute) ina liquid(the solvent) lowers the vaporpressure of the liquid solvent.Raoult’sobservationcanperhapsbebestappreciatedbylook‐ingatFigure5‐3inwhichwehaveplottedthephasediagramofapuresubstance(solidline)andthephasediagramofaso‐lutioninwhichthatpuresubstanceisthesolvent(dottedline). In accord with Raoult’s findings, the liquid–vapor phaseboundarybelongingtothesolutionislowerateverypointthanthe liquid–vaporphaseboundarybelongingtothepure liquidsolvent.Aconsequenceofthisbehavioristhephenomenonofboiling‐pointelevation:thesolutionboilsatahighertempera‐turethanthepureliquidsolvent. Therequirementthatthevaporpressureofthesolutionbe

Figure5‐3Phasediagramofapureliquid(solidline)andofasolution(dottedline)inwhichtheliquidisthesolvent.Dissolvingasubstance(thesolute)intheliquidlowersthevaporpressureoftheliquidsolvent.Thiseffectresultsinboiling‐pointelevationandfreezing‐pointdepression.

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Experiment5∙Freezing‐pointdepression 5‐6

lowerthanthatofthepureliquidsolventimpliesthatthesolu‐tionhasadifferenttriplepointfromthatofthepuresubstance:thetriplepointofthesolutionisfartherdownthesolid–vaporphase boundary. Because the solid–liquid phase boundaryoriginates at the triplepoint, Figure5‐3 indicates that vapor‐pressureloweringalsoresultsinthephenomenonoffreezing‐pointdepression: thesolution freezesata lower temperaturethanthepureliquidsolvent.Molarmassdeterminationsfromfreezing‐pointdepressiondataTheadditionofantifreezetothewaterintheradiatorofacaris perhaps themost familiar practical applicationof freezing‐pointdepression(seethepost‐labquestions). Freezing‐pointdepressiondataalsoallowus todeterminethemolarmassofasolute.Theincrementbywhichthefreez‐ingpointofasolvent is loweredbytheadditionofasolute isproportionaltotheamountofsolutepresentinthesolvent.Inequationform ΔTf=Tf,solvent–Tf,solution=Kfm (Eqn.5‐1)whereΔTfistheamountbywhichthefreezingpointofthesol‐ventisloweredinunitsofdegreesCelsius,Tf,solventisthefreez‐ingpointofthesolventinunitsofdegreesCelsius,Tf,solutionisthefreezingpointofthesolutioninunitsofdegreesCelsius,Kfisthefreezing‐pointdepressionconstantofthesolventinunitsofdegreesCelsius–kilogramofsolventpermoleofsolute,andmisthemolalityofthesolutioninunitsofmolesofsoluteperkilogram of solvent. (The units in Eqn. 5‐1 are awkward, butit’s important tokeep trackof theminorder toavoidmakinganerrorofseveralordersofmagnitude.) Whenwecombinethedefinitionofmolalitym

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m=nsolutemsolvent

wherensolute is thenumberofmolesof solute in thesolutionandmsolvent is the mass of the solvent in units of kilogramswiththedefinitionofthemolarmassofthesoluteMsolute

Experiment5∙Freezing‐pointdepression 5‐7

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Msolute =msolutensolute

wheremsoluteisthemassofthesoluteinunitsofgrams,wecanrewritetheexpressionformolalitymas

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m=msolute

Msolutemsolvent

PluggingthisexpressionintoEqn.5‐1andrearranginggives

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Msolute =K fmsolutemsolventΔTf

Ifthesolventisaliquid,weemploythesubstitution

msolvent=ρsolventVsolventwhereρsolventisthedensityofthesolventinunitsofgramspermilliliterandVsolventisthevolumeofsolventinunitsofmillili‐ter.Weatlastarriveatacomputationalformulafordetermin‐ing themolarmass of the soluteMsolute from freezing‐pointdepressiondata:

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Msolute =K fmsolute

ρsolventVsolventΔTf (Eqn.5‐2)

Youwill useEqn. 5‐2 to determine themolarmass of anun‐knownsolute.ProcedureDeterminationofthefreezingpointofpurecyclohexaneObtainorassembleanapparatusformeasuringfreezing‐pointdepression(seeFigure5‐4).Theapparatusconsistsofa largePyrex test tube sealed off with a neoprene stopper that hasbeenfittedwithathermometer.Clamptheapparatustoaringstand.Do notwash or rinse the test tubewithwater nor

Experiment5∙Freezing‐pointdepression 5‐8

allowanywetobject tocomeintocontactwiththe insideof the test tube: water will contaminate the liquid you areabouttopourintothetesttube. Using a graduated cylinder, measure out about 15 mL ofcyclohexane. Record the volume you take in your notebook.Pour thecyclohexane into the test tubeandreseal itwith thestopper.Besurethatthetipofthethermometerisdippingintothemiddleofthecyclohexaneandthatthetip isnottouchingthesidesorbottomofthetesttube. You will now prepare a cold bath. Obtain a second ther‐mometer anda600‐mLbeaker;place about300mLof ice inthebeaker.Usingacleananddry250mLbeaker,measureoutabout50mLofNaCl(s).Gradually add theNaCl(s) to the ice.Stirthemixtureconstantlyusingaspatula.Afteraboutamin‐uteofconstantstirring,theNaClsolutionshouldgetverycold.Youcancheckitstemperatureusingthesecondthermometer.

Figure5‐4Apparatusformeasuringfreezing‐pointdepression.

Experiment5∙Freezing‐pointdepression 5‐9

Addanother300‐mLportionoficeandanother50‐mLportionofNaCl(s);stirthemixtureconstantly.Youwantthetempera‐tureoftheNaClsolutiontoreachandstayatabout–15°C. Youarenowreadytocarryoutyourfirstdeterminationofthefreezingpointofpurecyclohexane.Placethetesttubecon‐tainingthecyclohexaneintothecoldbath.Immediatelyrecordthetemperatureofthecyclohexanewhenyouimmerseitinthecoldbath(callthist=0 sec)andevery20 secthereafter. You should observe three separate régimes of cooling be‐havior(seeFigure5‐5):(1)arapiddecreaseintemperatureascylcohexane cools after its immersion in the cold bath; (2) aplateauascyclohexane freezes; (3)aseconddecrease in tem‐perature as cyclohexane(s) cools.The freezingpoint of cyclo‐hexane(Tf,solvent inEqn.5‐1)correspondsto the temperatureat the plateau. Continue taking time‐versus‐temperature datauntil you have positively identified the third régime of tem‐perature decrease (the entire run from beginning to endshouldtakenomorethan10min).Beawareofthepossibilitythattheremaybeasignificantwobbleinthedata:donotlosepatienceandabandontherununtilyou’resurethatthesystemhascomeoutoftheplateauandthatthetemperatureisreallyandtrulydecreasing.Successhingesinpartonmaintainingthetemperatureofthecoldbathascloseto–15 °Caspossible:youmayhavetostirthecoldbaththroughouttherun.Inanyevent,

Figure5‐5Coolingcurveofapureliquidundergoingfreezing.ThefreezingpointoftheliquidTfcorrespondstothetemperatureattheplateau.

Experiment5∙Freezing‐pointdepression 5‐10

check the temperatureof the coldbathbetween timedmeas‐urementsusingthesecondthermometer. Afterthecompletionoftherun,removethetesttubefromthe cold bath and gently heat it under a stream ofwarm tapwater until the cyclohexane(s) melts. Remember that waterwillcontaminatethecyclohexane:donotpourwaternearthetopofthetesttubeanddonotdelugethetesttubeinaragingtorrentofhotwater!Allow the cyclohexane to come to roomtemperaturebeforecontinuing. Theresultsofyourfirstrunmaybewoefullyinaccuratebe‐cause you are just becoming familiar with the correct tech‐nique. Repeat the freezing‐point determination at least oncemore: you want the average of at least two runs. You don’thave tomeasure out new cyclohexane – just reuse the liquidalready in the test tube.Before each run (1)be sure that thetemperature of the cyclohexane has stabilized around roomtemperature,thatis,donotbeginthenextrunwithhotorevenwarmcyclohexane;(2)checkthatthetemperatureofthecoldbathisaround–15 °C:ifitisnot,mixitagainwithaspatulaordispose of the cold bath in the sink and prepare a fresh coldbath if stirringdoesnot bring the temperaturebackdown tonear–15 °C.DeterminationofthefreezingpointofasolutionofanunknowndissolvedincyclohexaneWeighoutabout0.5gofunknownsolid.Recordtheexactmassinyournotebook.Transferthesolidtothecyclohexaneinthetest tube, being careful to avoid losses during the transfer.Shakethetesttubegentlytodissolvealltheunknownandtakecarethatnounknownstickstothewallsofthetesttube.Afterall theunknownhasdissolved,waitabout2min for the tem‐peratureofthesolutiontostabilize. Place the test tube containing the solution into the coldbath.Immediatelyrecordthetemperatureofthesolutionwhenyou immerse it in thecoldbath(call thist=0 sec)andevery20 secthereafter.

Experiment5∙Freezing‐pointdepression 5‐11

You should once again observe three separate régimes ofcoolingbehavior,butthefreezingofasolutionismorecomplexthanthefreezingofapuresubstance(seeFigure 5‐6).Immedi‐ately after its immersion in the coldbath, the temperatureofthesolutionrapidlydecreases.Asthesolutionfreezes,therateatwhichthetemperaturedecreasesshouldslowdownsignifi‐cantly,butitdoesnotreachatemperatureplateauinthewaythat pure cyclohexane does. After the solution is completelyfrozen,thetemperaturedecreaseresumesatafasterrate.Thefreezingpointofthesolution(Tf,solutioninEqn.5‐1)isthetem‐peratureatwhichthesolutionjustbeginstofreeze.Thequan‐tity Tf,solution is best found by plotting the time‐versus‐temperaturedata,drawinga linethroughthedatapointscor‐respondingtotheinitialrapidcoolingstageanddrawingasec‐ondlinethroughthepointscollectedduringthequasi‐plateaucooling stage: Tf,solution is identified with the temperature atwhichthetwolinesintersect. Ideally, you should continue taking time‐versus‐temperaturedatauntilyouhavepositivelyidentifiedthethirdrégimeoftemperaturedecrease,butthisisnotalwayseasyto

Figure5‐6Thecoolingcurveofasolutionundergoingfreezingexhibitsthreerégimesofde‐creasingtemperature:(1)aninitialrapidrateofcoolingfollowedby(2)aquasi‐plateauoverwhichtherateofcoolingdecreasesbutdoesnotleveloffthen(3)asecondrapidrateofcool‐ing.ThefreezingpointofthesolutionTfcorrespondstothetemperatureatwhichalinedrawnthroughthedatapointspertainingtothefirstcoolingrégimeintersectsalinedrawnthroughthedatapointspertainingtothesecondcoolingrégime.

Experiment5∙Freezing‐pointdepression 5‐12

dobecausetherecanbesignificantwobble in thedata.Checkthetemperatureofthecoldbathbetweentimedmeasurementsusingthesecondthermometer: inordertosuccessfullydetectthe third régimeof temperaturedecrease, thecoldbathmustbeascloseto–15 °Caspossible. Afterthecompletionoftherun,removethetesttubefromthe cold bath and gently heat it under a stream ofwarm tapwateratthesinkuntilthesolutionmelts.Reusingthesameso‐lution, repeat the freezing‐point determination twice more:youwanttheaverageofthreeruns. Itmightbeagoodideatoplotthedatacollectedinatleastthe first run immediately inorder togetabetter ideaofhowthesolutionisbehaving;yourplotshouldresembleFigure 5‐6.Clean‐upWhenyouhavefinishedallexperimentalwork,disposeofthecyclohexanesolutioninaspecialcontainerfororganicwaste.Itgoeswithout saying that the cyclohexane solution shouldnotbepoureddownthedrain.

Experiment5∙Freezing‐pointdepression 5‐13

Name___________________________________________________________LabDay__________LabTime_________Experiment5∙Freezing‐pointdepressionLabreportform Page1Youareaskedtosubmitseveralplotsaspartofthislabreport.Prepareaseparateplotforeach run.Giveeachplot a truly informative title (i.e., don’t just call it “Plot1”), label theaxes,andincludeappropriateunitsanddivisionsofthoseaxes.Donotsubmitsmallplots:useawholesheetofpaper.Scalethehorizontalandverticalaxessothatthedatapointsoc‐cupymostoftheareaoftheplot.(I.A)Prepareplotsof thedatacollected inthemeasurementof thefreezingpointofpurecyclohexaneTf,solvent.Drawalinethroughthedatapointsthatcorrespondtotheplateauinthecoolingcurve;Tf,solventcorrespondstothetemperatureoftheplateau.(I.B)Prepareplotsofthedatacollectedinthemeasurementofthefreezingpointoftheso‐lutionof theunknown incyclohexaneTf,solution.Drawa line through thedatapoints thatcorrespondtotheinitialrapidrateofcoolinganddrawalinethroughthedatapointsthatcorrespondtothequasi‐plateauoverwhichtherateofcoolingdecreases;Tf,solutioncorre‐spondstothetemperatureatwhichthetwolinesintersect.(I.C)Reporttheresultsinthetablebelow.UsingtheformulasgiveninAppendixA“Statisti‐calTreatmentofData”of this labmanual, calculate themeanvalueofTf,solvent, themeanvalueofTf,solution,andthestandarddeviationofthemeans.

Run Tf,solvent[°C] Run Tf,solution[°C]1 1 2 2 3

mean[°C] mean[°C] standarddeviation[°C] standarddeviation[°C] (I.D) Report the freezing‐point depression ΔTf using Eqn. 5‐1 and the mean values ofTf,solventandTf,solutionreportedin(I.C). ΔTf=Tf,solvent–Tf,solution (Eqn.5‐1)ΔTf=_______________________________________________________________________________________________°C

Experiment5∙Freezing‐pointdepression 5‐14

Name___________________________________________________________LabDay__________LabTime_________Experiment5∙Freezing‐pointdepressionLabreportform Page2(II)ThemeasurementofΔTfhasanuncertaintyσΔTfgivenby

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σΔTf = σTf ,solvent( )2 + σTf ,solution( )2 whereσTf,solventisthestandarddeviationofthemeasurementofTf,solventandσTf,solutionisthestandarddeviationofthemeasurementofTf,solutionreportedin(I.C).Showthecalcula‐tionofσΔTf;includeappropriateunitsinthefinalanswer.(III.A) Show the calculation of themolarmassMsoluteof the unknown solute in units ofgrampermoleusingEqn.5‐2:

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Msolute =K fmsolute

ρsolventVsolventΔTf (Eqn.5‐2)

Kf represents the freezing‐point depression constant of the solvent cyclohexane(20.0°C‐kgsolvent/molsolute),msoluteisthemassofunknownsolutetaken,ρsolventisthedensityofcyclohexane(0.799g/mL),Vsolventisthevolumeofcyclohexanetaken,andΔTfisthefreezing‐pointdepressionreportedin(I.D).Paycarefulattentiontounits.Massofunknowntaken=_________________________________________________________________________gVolumeofcyclohexane=_______________________________________________________________________mL

Experiment5∙Freezing‐pointdepression 5‐15

Name___________________________________________________________LabDay__________LabTime_________Experiment5∙Freezing‐pointdepressionLabreportform Page3(III.B)ThemeasurementofMsolutehasanuncertaintyσMgivenby

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σM =MsoluteσΔTf

ΔTf

(Eqn.5‐3)

whereMsolute is themolarmass of the unknown reported in (III.A),ΔTf is the freezing‐pointdepressionreportedin(I.D),andσΔTfisthestandarddeviationreportedin(II).ShowthecalculationofσM.Includeappropriateunitsinthefinalanswer.Post­labquestions(1)AssumethattheunknownhastheformulaCnH2n,thatis,theunknownisacompoundofcarbon(M=12.01g/mol)andhydrogen(M=1.01g/mol)andtherearetwiceasmanyhydrogensascarbons.Whatformulasfityourdata?Explainyouranswer.

Experiment5∙Freezing‐pointdepression 5‐16

Name___________________________________________________________LabDay__________LabTime_________Experiment5∙Freezing‐pointdepressionLabreportform Page4(2)UseEqn.5‐2tocalculatethemassoftheantifreezeethyleneglycol(Msolute=62g/mol)that must be added to 1.000 L of water (Kf = 1.86 °C‐kg solvent/mol solute, ρsolvent =1.00g/mL)tolowerthefreezingpointofthesolutionby6°C.Showallcalculationsandpayattentiontounits.(3)WhenthequantityA iscalculatedfromthemeasuredquantitiesx,y,z,etc.,theuncer‐taintyσAinAisgivenby

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σA =∂A∂x

⎛ ⎝ ⎜

⎞ ⎠ ⎟ 2σx2 +

∂A∂y

⎛ ⎝ ⎜

⎞ ⎠ ⎟ 2σ y2 +

∂A∂z

⎛ ⎝ ⎜

⎞ ⎠ ⎟ 2σz2 +

(Eqn.5‐4)

whereσxistheuncertaintyinx,σyistheuncertaintyiny,σzistheuncertaintyinz,andsoon.ShowthederivationofEqn.5‐3 fromEqn.5.2andEqn.5‐4assuming that theuncer‐taintyinMsoluteisdueonlytouncertaintyinΔTf.