Muromachi-2011-Phase equilibrium for clathrate(3)

148S.Muromachietal./FluidPhaseEquilibria

305 (2011) 145–151

Fig.2.Schematicillustratingtheprocedurefordeterminingthephase-equilibriumpressurepeqfortheO3+O2+CCl4+H2OorO3+O2+CH3CCl2F+H2Osystem.Weassumedtheminimumpvalueatthepointindicatedbyabroadverticalarrow(i.e.,thelowestoftheminimumpvaluesobservedintheindividualpressure-relaxationperiodseachborderedbytwosuccessivegasdischarging/rechargingoperations)asthetargetpeqvalueofthissearchprocedure,thereasoningofwhichisdescribedinthetextwiththeaidofFigs.3and4.

vailedonlyduringpart(orparts)oftheperiod.Inthe?rstpart,CCl4musthavecontinuedtovaporize,therebyincreasingitspar-tialpressureintherenewedgasphasetothesaturationpressurelevelcorrespondingtothesystemtemperatureT.Simultaneously,theresidueofthehydrateformedintheperiodbeforethelastgasdischarging/rechargingoperationwaspossiblydissociating,whilethepartialpressureofCCl4inthegasphasewasinsuf?cienttobeequilibratedwiththehydrate.TheCCl4vaporizationandthehydratedissociationinevitablyincreasedthesystempressurep.Thehydratedissociationshouldhaveceasedandthenswitchedtothehydrateformation,asthegasphasebecameequilibrated

and

Fig.3.Conceptualillustrationofthefourrateprocessesthatsimultaneouslyoralter-nativelyprogressinthetestcellduringtherelaxationperiodsubsequenttoagasdischarging/rechargingoperation.Illustratedisthecasethatthepressurepexhibitsbothamaximumandminimumduringtherelaxation

period.

Fig.4.Recordsofpressurechangesactuallyobservedduringthe?verelaxationperiodswhichfollowedoneafteranother(intheorderofthenumbersindi-catedonthepressurecurves)inanequilibrium-pressure-searchprocedureforO3+O2+CCl4+H2OsystemheldattemperatureT=276.62K.Notethatthetimet=0foreachpressurecurverepresentstheinstantwhenthelastgasdischarg-ing/rechargingoperationwasperformed.

thenoversaturatedwiththehydrateasaresultoftheincreasesinboththepartialpressureofCCl4andthesystempressurep.Sub-sequently,thesystempressureppeakedduetotheoffsetoftheeffectsoftheCCl4vaporizationandthehydrateformation(pointAindicatedinFig.3).Beyondthisstage,pcontinuouslydecreasedwiththeprogressofthehydrateformationuntilitceasedastheresultofthedecreaseinpaswellasthatintheozoneconcentra-tioninthegasphaseduetothepreferentialozoneuptakeintothehydrateandalsotheozone-to-oxygendecay.Asthehydrateforma-tionceased,pleveledoff(pointBindicatedinFig.3),thenturnedtoanincreaseduetorestartingofthehydratedissociation.Basedontheabove-statedinterpretationoftheevolutioninpwithtwopointsofin?ection(pointsAandBinFig.3),wecanassumethattheminimumofpatpointBrepresentstheequilibriumpressurecorrespondingtotheinstantaneousozoneconcentrationinthegasphase.Duringtheequilibrium-pressuresearchprocedureactuallyperformedateachsystemtemperatureT,wenotedsuchmini-mumppointsinseveralperiodseachborderedbytwosuccessivegasdischarging/rechargingoperations.Fig.4showsthechangesinpactuallymeasuredduring?vesuccessivesystem-relaxationperiodsinaspeci?cequilibrium-pressure-searchprocedureper-formedatT=276.62K.Theminimumpvaluesatthetroughsofcurves1,2and5(indicatedbyverticalarrows)areconsideredtoapproximatethephase-equilibriumpressurescorrespondingtotheinstantaneousozoneconcentrationsinthegasphase.Amongtheseminimumpvalues,weusedtheoneforcurve2,i.e.,thelowest“minimump”value,asthephase-equilibriumpressurecorrespond-ingtothehighestozoneconcentrationinthegasphase.Inpractice,wedidnotmeasuretheozoneconcentrationinthegasphaseattheminimumppoints.Thisisbecausetheoccurrenceofeachminimumppointwasrecognizedafterphadexhibitedasubsequentincreaseoveratimeof～1–2h.Therefore,wesubstitutedtheozoneconcen-trationofthegasmixturedischargedfromthetestcellattheendofeachsystem-relaxationperiodfortheconcentrationinthegasphaseinequilibriumwiththehydrateattheminimumppointdur-ingtheperiod.Becausetheincreaseinpfromitsminimumvaluetothe?nalvaluejustbeforethegasdischargewasonly～1kPa,weassumedthatthecompositionalchangeinthegasphaseinthistimewasinsigni?cant.

Theproceduresforsystems(3)and(4)weregenerallythesameasthoseforsystems(1)and(2),respectively.Thetestcellwas?rstchargedwith20gofwaterand10gofR141b.Thisinitialquantity

S.Muromachietal./FluidPhaseEquilibria305 (2011) 145–151

149

Table1

H+G+Lg+Lwfour-phaseequilibriump–TconditionsinO2+CCl4+H2Osystem(theuncertaintiesforTandpareestimatedtobe±0.11Kand±1.0kPa,respectively).T(K)p(kPa)275.53212.9275.73240.7276.04280.1276.33323.4276.63364.1276.84399.8277.04432.5277.23

463.8

ofR141bisabout30%greaterthanthequantityrequiredforfullyoccupyingthe51264cagesofansIIhydrateformedfrom10gofwater.TheselectionofsuchanR-141b-richproportionbetweenthetwoliquidswastoprepareforthelossofthevolatileR141bduringthesubsequentgas-discharging/rechargingoperations.InordertopreventR141binthetestcellfromsigni?cantlyvaporizing,wedidnotdecreasethepressureinsidethetestcellbelow50kPaduringtheprocessof?ushingthecellwithpureoxygenortheO3+O2gasmixturesuppliedfromtheozonegenerator.The?ushingofthecellwithpureoxygenprecedingthemeasurementsforsystem(3)wasmadebyrepeatingeighttimestheoxygenchargingat0.2MPaandthedischargingtoapressureof50kPa.(Assumingthecompletemixingofgaseousspeciesinsidethetestcell,weestimatedthatthepartialpressureoftheresidualairdecreasedto～1Paorlessthroughsuchmultiple?ushingoperations.)

Weperformedthephase-equilibriummeasurementsforsys-tems(3)and(4)muchlessextensively,comparedtothoseforsystems(1)and(2).Infact,weobtainedtheequilibrium-pressuredataonlyattwotemperaturesforbothsystems(3)and(4).ThisisbecausewefoundtheslightdecompositionofR141binsystem(4),whichpossiblydetractedfromthereliabilityofthemeasurements.Somedetailsofthisissuearedescribedinthenextsection.3.Resultsanddiscussion

Thefour-phase-equilibriump–TdatathatweobtainedwiththeO2+CCl4+H2OandO3+O2+CCl4+H2OsystemsareseparatelycompiledinTables1and2,andplottedtogetherinFig.5.Indi-catedinTable2andFig.5arenotonlythepandTvalues,butalsotherelevantvaluesofxO3,themolefractionofozoneinthegasmixturedischargedfromthetestcelljustafterdeterminingeachp–Tdatapoint.AlthoughwedidnotdirectlycontrolxO3duringthep–Tmeasurements,wesucceededincollectingthephase-equilibriumdatafornearlythesamegas-phasecompositionsinwhichxO3×100=6.9±0.8.AsrecognizedinFig.5,allthep–TdatapointsfortheO3+O2+CCl4+H2Osystemarealignedonasinglesmoothcurve,whichisapparentlysimilarto,andnaturallydeviat-ingfrom,thecurveonwhichthedatapointsfortheO2+CCl4+H2Osystemlie.Themoderatereductioninpoftheformersystemascomparedtothelattersystemisconsistentwithourexpectation

Table2

H+G+Lg+Lwfour-phaseequilibriump–TconditionsinO3+O2+CCl4+H2Osystem(theuncertaintiesforT,p,andxO3×100areestimatedtobe±0.11K,±1.0kPa,and±0.1,respectively).T(K)p(kPa)xO3×100275.53167.26.6275.73188.76.5276.03217.17.3276.33248.57.7276.62290.36.2276.83311.96.7277.03340.46.6277.24

360.7

7.5

Fig.5.Four-phaseequilibriump–TdataforO2+CCl4+H2Osystem(??)andO3+O2+CCl4+H2Osystem(?).Theerrorbaroneachdatapointindicatestheuncer-taintyinthemeasuredtemperatureT.ThenumericalvalueonthesideofeachdatapointforO3+O2+CCl4+H2OsystemindicatesxO3×100speci?edinTable2,i.e.,theozoneconcentration(molebasis)inthegasmixturedischargedfromthetestcelljustafterthep–Tmeasurement.

thatozonebetter?tsintothe512cagesofthesIIhydratesthanoxygen(seefootnote2).

Tofurtherevaluatetheirself-consistency,thephase-equilibriump–TdataforboththeO2+CCl4+H2OandO3+O2+CCl4+H2OsystemsarereplottedonthelnpversusT?1planeinFig.6.Thedataforeachsystemarealmostlinearlyalignedonthisplane,beingconsistentwiththeClausius–Clapeyronequationwritteninthefollowingform:d(lnp)

??h?d(1/T)=?

?(1)

where??h

?istheenthalpyofhydratedissociationper1molofthegas-phase-forminghydrate-guestmolecules(i.e.,the

enclathrated

Fig.6.Four-phaseequilibriump–TdataforO2+CCl4+H2Osystem(??)andO3+O2+CCl4+H2Osystem(?)replottedonthelnpversusT?1plane.ThestraightsolidlineforeachgroupofdatapointsrepresentsalinearlnpversusT?1correlationpreparedbyapplyingaregressionanalysistoEq.(1),basedonwhichtherelevant???h

valuegiveninTable3wasdeduced.

150S.Muromachietal./FluidPhaseEquilibria305 (2011) 145–151

Table3

EnthalpyofhydrateformationdeducedfromtheH+G+Lg+Lwfour-phaseequilib-riump–TdatausingtheClausius–Clapeyronequation.System