【doc】三水铝石在氢氧化钠溶液中的平衡溶解度热力学模型（英文）

【doc】三水铝石在氢氧化钠溶液中的平衡溶解度热力学模型（英文） 三水铝石在氢氧化钠溶液中的平衡溶解度 热力学模型(英文) 黉Availableonlineatwww.sciencedirect.corn电 ScienceDirectPressTrans.NonferrousMet.Soc.China22(2012)447-455 TransactiOU$of NonferrousMetals SocietyofChina wwvv.mmSC.Cn Thermodynamicmodelforequilibriumsolubilityofgibbsitein concentratedNaOHsolutions LIXiao—bin,YANLi,ZHOUQiu—sheng,LIUGui-hua,PENGZhi—hong SchoolofMetallurgicalScienceandEngineering,CentralSouthUniversity,Changsha410083,Chma Received4March2011;accepted12June2011 Abstract:ThethermodynamicpropertiesofthemostimportantNaOH-NaAI(OH)4-H,OsysteminBayerprocessforalumina productionwereinvestigated.Atheoreticalmodelforcalculatingtheequilibriumconstantofgibbsitedissolvedinsodiumhydroxide solutionwasproposed.NewPitzermodelparametersandmixingparametersforthesystemNaOH—NaAI(OH)4一H2Owereyielded andtestedinthetemperaturerangeof298.15-373.15K.Theresultsshowthattheproposedmodelforcalculatingtheequilibrium constantofgibbsitedissolutionisapplicableandaccurate.TheobtainedPitzermodelparametersof(NaAI(OH)4), ? ')(NaAI(OH)4),c(NaAI(OH)4)forNaAI(OH)4,thebinarymixingparameterofOHAI(OH)4一)forAI(OH)4一with0H一,andthe ternarymixingparameterof~,(Na+OH-AI(OH)4一)forAI(OH)4一withOH— andNaaretemperature.dependent.Thepredictionofthe equilibriumsolubilityofgibbsitedissolvedinsodiumhydroxidesolutionwasfeasibleinthete mperaturerangeof298.15-373.15K. Keywords:Pitzermodel;sodiumaluminatesolution;gibbsite;equilibriumconstant:equilib riumsolubility 1Introduction ThesolubilityisothermoftheNa2O—A1203一H2O systematdifferenttemperaturesistheresearch foundationoftheBayeraluminaproductionandphase equilibrium,whichplaysanimportantroleinthe industryofaluminaproduction.TheessenceoftheBayer processisthataluminahydratesdissolveandprecipitate altematelyintheNa20一A1203一H2Osystemunder differentconditions.Unfortunately,notablyconflicting objectivesbetweenproductqualityandyieldin precipitationrequireasolution.Thefocusofthisstudy, therefore.isontheequilibriumsolubilityofgibbsitein theconcentratedNaOHsolutions,whichwillfacilitate theresearchanddevelopmentofnewtechnologiesfor reducingenergyconsumptionandaluminaproduction cost. Quantitativeknowledgeonthesolubilityofgibbsite dissolvedinBayerliquorsisessentialforphase equilibriaandthermodynamicpropertiesofhydrated aluminainconcentratedNaOHsolution.Thesolubilities ofaluminahydratesdissolvedinsodiumhydroxide solutionwerereportedbyRUSSELLetal[1],APPSand NEILf2】,IKKATAIandOKADA【3】,POKROVSK? andHELGESON『41.However,manyresearchers attemptedtodevelopthethermodynamicmodelofthe NaOH_NaAl(OH)4-H2Osystemtoconvenientlyobtain seriesofsolubilitydata.sincetheexperimentaldataare limitedandhardtocollectintheliteratures.Themodel studiescanbedividedintotwocategories.11The chemica1 thermodynamicmodelsbasedonthephysico— propertiesoftheNaOH-NaAI(OH)4一H20system. ZHOUeta1『51measuredtheosmoticcoefficientsat 313.2KfortheNaOH-NaAI(OH)4一H20systemwiththe totalalkalimolalityfrom0.05to12mol/kgandakfrom 1.64tO5.53.andobtainedPitzermodelparametersby regressingthedata.KONIGSBERGEReta1『61 measuredtheisopiesticofmixedelectrolytesolutions involvingsodiumhydroxideandothercomponentsof Bayer1iquorsat323.15Kand373.15Kfollowing Zdanovskii'srule.andestablishedapredictive thermodynamicmodelbasedonPitzer'sequations. CAIANIetal『71measuredtheapparentmolarheat capacitiesofaqueousalkalinesolutionsofaluminumion inexcessNaOHattemperaturesbetween323.15and 523.15Kinthetota1molalityrangeof0.3-1.7mog' andalsodevelopedtheparametersofthePitzerionic Foundationitem:Project(2005CB6237)supportedbytheNationalBasicResearchProgram ofChina Correspondingauthor:ZHOUQiu— sheng;Tel:+86-731-88830453;E-mail:qszhou@csu.edu.cn DOI:10.1016/S1003—6326(I1)61197—7 448LIXiao—bin,etal/Trans.NonferrousMet.Soc.China22(2012)447—455 interactionmode1.MAGALHAESetal『8]measuredthe specificheatcapacitiesofaqueousNaOH/NaAI(OH)4 solutionsattotalstoichiometricionicstrengthsofupt06 mol/kgat298.15Kandverifledtheaccuracyand adaptabilityofPitzermode1.2,Thermodynamicmodels developedonthesolubilitydataofgibbsitedissolvedin NaOHsolutions.WES0LOWSKIf91gaveasetof approximatevaluesofpureelectrolytePitzermodel parametersforNaAl(OH)4(aq)inthetemperaturerange of273.15-373.15K.aswellasthemixingparameters forAI(OH)4一withOH—andOH一+Na十,bymodelingthe solubilityofgibbsitewiththePitzerioninteraction treatment.LIeta1『10,111introducedtheapparent dielectricconstantofsodiumaluminatesolution,and thenestablishedacalculationmodelofactivity coefficientsaccordingtoDebye—Hackeltheory. Despiteofthewealthofexperimentaldataforthe NaOH_A1,O3_】}I,Osystem.fewdirectstudiesofthe equilibriumconstantareavailable.Consensushasnot beenreachedcompletelyonthevaluesofequilibrium constant,andthereisnotheoreticalmodeltoaccurately describetheequilibriumconstant.Moreover,the equilibriumconstantScalculatedfromsolubilitydataare notexactlyequaltothetrueones.Forexample.the calculatedequilibriumconstantvaluesby WES0L0WSK【『91agreedwellwithmostofthe experimentalvaluesofRUSSELLetal『11,buttheywere obviouslygreaterthanthoseofIKK(rlAIandOKADA 『3].P0KROVSK?andHELGESON『41modeledallof thepreviousexperimentalworkandcalculatedthevalues ofequilibriumconstant,whichisequivalenttothe calculatedmeanvaluebyZHOUetal『51.Inthiswork, theobjectivewastodevelopathermodynamicmodelto predictthebehaviorofgibbsiteinhighlyaqueous sodiumhydroxideelectrolytessolutions,andtoprovidea theoreticalbasisofdevelopingnewtechniquesfor industrialaluminaproduction.Underthese considerations.weattempttol1developa thermodynamicmodeltodescribetheequilibrium constantofgibbsitedissolvedinNaOHsolutions,21 determinePitzermodelparametersandmixing parametersfortheNaOH-NaAI(OH)4一H20system,and 3,assesstheapplicabilityofthemodelproposed. 2Generalresearchthinking ItisknownthattheBayerprocesscanbeconsidered anindustrialscalerecrystallizationofgibbsiteinthe presenceofvariousorgamc(e.g.,oxalate,succinate, acetate)andinorganic(e.g.,carbonate,chloride,sulphate) impurities.Thecompositionandstructureofaluminate complexesinBayer1iquorshavebeeninvestigated intensivelyoverthepast120years.Themajorityof publishedworksreachtheagreementthatthepureBayer liquorsconsistonlyofthreecomponents[12]:H20, NaOHanddissolvedAI(III).Severalaluminatespecies, suchasAI(OH)4一,A102一,AIO(OH)2一,AI(OH)4-.2HzO, AI(OH)5一,AI(OH)6一,AI(OH)4一OH一,A120(OH)6一, [A1(OH)416andNaAI(OH)4havebeenpostulatedinthe literatures.Accordingtothepreviousstudies[13—15],it isgenerallyagreedthatthetetrahedralaluminateion AI(OH)d—isthepredominantspeciesinsodium aluminatesolutionofmoderateconcentrationof2-4 mol/kgbelow373.15K.Therefore.onthebasisofthe possibleequilibriumamongthevariOUSspecies,the actuallyexistingspeciesareNa,AI(OH)4一,0H—and H2Oinaninfinitelydilutesodiumaluminatesolution『5]. Thedissolvingreactionofgibbsiteandsodium hydroxidesolutionscanbeexpressedasfollows: AI(OH)3(cr)+NaOH(aq)=NaAI(OH)4(aq) Theequilibriumconstant,Kis 一(NaAI(OH)4) aOH1 一 g2(NaAI(OH)4)?(Na)?m(AI(OH)4) y2(NaOH).m(Na).m(OH一) 一 y2(NaAI(OH)4).m(Al(OH)4) where y2(NaOH).m(OH一)(1) m=m(NaOH+NaAI(OH)4) =m(AI(OH)4)+m(OH一)(2) m(NaAI(OH)4)=m(Al(OH)4):my(3) m(NaOH)=m(OH一)=m(1一Y)(4) SubstitutionofEqs.(2-4)intoEq.(1)yields :— r2 =.. (N— a — A — I(O— H — )— 4)一 . my (NaOH)?m(1一)(5) Equation(5)isaconciseexpressionthatcombines theequilibriumconstantwiththemolalityofNaAI(OH)4 andNaOH.LogarithmictransformationofEq.(5)and rearrangementyields ln[z(NaAI(OH)4)卜ln[r(NaOH)】= — InK+lnm(1— - y)-Inmyf61 Nowdays,Pitzerandtheimprovedequationsarethe mostwidelyusedmodelsofaqueouselectrolytesandthe resultsofPitzertheoryinstudyingthermodynamic propertiesaresatisfying.Accordingtotheion-interaction approachdevelopedbyPitzerandcoworkers[16],the activitycoefficientoftheNaOH-NaAI(OH)4——H20 systemiSgivenby: ln+lnm(1一y),Inmy一 2 LIXiao-bin,etal/Trans.NonferrousMet.Soc.China22(2012)447—455449 (0)(NaAI(OH)4)+ — 2 — 11— - — (1 — + — a — lm — l — /Z 了 )e — xp — ( — - — oq — m — l/ 一 2)l'1(NaA1(.H)4)+ — 2D—— - — (1 — + — a2 — m — l/ — Z)ex — p — (- — o — ~2m — l 一 /2)l(2(N(.H)4)一 (0)(NaOH)一 — 2 — ~1— - — (1 — + — a — lm — l/2)e — xp — (- — o — qm —一 l/2)l((Na.H)一 — 2D—— - — (1 — + — ot2 — m — l/ — 2)ex — p — (- — a — 2m — l 一 /2)l(z,(Na.H)+ c(NaAl(oH)(oH)m2C~(NaOH)+ (一2my)O(OH—Al(0H))+ (-~-m2y)(Na+OH-Al(oH)D(7) AsshowninEq.(7,,thereisamathematical relationshipbetweenthevaluesofmandyonthe assumptionthatotheritemsarefixedvalues.IfthePitzer modelparameters,mixingparametersforthesystem NaOH-NaAI(OH)4一H,Oandtheequilibriumconstant f0rthedissolvingreactionareknown.wecancalculate thevalueofyforanappointedvalueofmatvarious temperatureswiththeassistanceofcomputer. Consequentl~preciseknowledgeoftheequilibrium constant.Pitzermodelparametersandmixingparameters forthesystemNaOH-NaAI(OH)4一H20areessentialfor predictionoftheequilibriumsolubilityofAI(OH)3in concentratedNaOHsolutions. 3Calculationofequilibriumconstantof gibbsitedissolvedinsodiumhydroxide solution Theusualways『17-191aretodevelopanempirica1 equationtocalculatealargenumberofsystematicdata coveringawiderangeoftemperatures,sincethe measureddataofequilibriumsolubilityarelimitedand dimculttocollect.Inourearlystudy『ll1,anempirica1 equationforcalculatingequilibriumconstantofgibbsite dissolvedinsodiumhydroxidesolutionhasbeen proposed.ItshouldbenotedthatourearlierPaDerhad somemistakesandlackedtheoreticalbasistosome extent.Soitisnecessarytodevelopanapplicableand e衔cientmodelforcalculatingtheequilibriumconstant otglbbSltedissolution.Ihet011owingextendedDebye. HfickelequationreportedbyHELGESONetal[20]is takenastheobjectofthisstudy: 一? where 4:(9)— = (10) AccordingtoEq.(1)andEq.(8),thefollowing equationfortheNaOH-NaAI(OH)4——H20systemis derived: l— m(AI(O— H)4)一2A.1,2. , I m(OH一,' 『!一!]一l 1+a(NaAI(OH)4)BrI1/21+(NaoH)"j lgK一2[(NaAI(OH)4)一b~(NaOH)]I(11) wherea(NaOH)=3.31A,~(NaAI(OH)4)=3.595A; 卢(Na+)+m(AI(OH)4一)+m(OH-)]/2=m(Na十);ATand canbeobtainedthroughEq.(9)andEq.(10).Asshown inEq.(11),providingtheinfluenceofpressureis neglected,thetermoflgKcanbeexpressedasafunction oftemperature,socanthetermof 【br(NaAI(OH)4)一bv(NaOH)].Thus,thefightpartof Eq.(11)canbeexpressedasafunctionoftemperature( andionicstrength?. Accordingtothegeneraltemperature—dependent equ~ionsemployedbyPABALANandPITZER【211, andSIMONSONetal[22],thePitzermodelparameters m , n ,,)forNaOHandNaAI(OH)4inmixed aqueouselectrolytesareappliedtothefollowing algorithm: f(T)=A1+A2/T+-43InT+(12) Accordingly,theequationsofactivitycoefficientfor NaOHandNaAI(OH)4transformintothetemperature— dependentexpressions.Then,substitutionofEq.(12) intoEq.(1)andrearrangementyield 1g=lg+2(c+c/+c3lI1+c) (13) SubstitutionofEq.(13)intoEq.(11)yields [bv(NaAI(OH)4)一b~(NaOH)]I: [c+C2/T+C3In+C4]+,"- 450LIXiao—bin,etal/Trans.NonferrousMet.Soc.China22(2012)447—455 [一1———1+a(NaO— H)B~,I1/21'1bylinearregressingtheselectedsolubilitydatainthe(14)temperaturerangeof2 98.15-373.15K[1,9]. Equations(13)and(14)aretemperature—dependent. AsthemolalitiesofAI(OH)4-andOH—arefixedvalues intheNaOH—NaAl(OH14-H20systemforaspecific temperature,theitemoflg[m(Al(OH)4一)/m(OH-)]in Eq.f13)isaconstant.Furthermore.theseconditernin therighttermofEq.(141canalsobeexpressedasa constant.Equations(13)and(14)arethen仃ansformed intoEq.(15)andEq.(16),respectively lgK=P1+P2/T+p31nT+P4T br(NaAI(OH)4)一br(NaOH)= P5+P6/T+P7In+P8T (15) (16) AsshowninEq.(15)andEq.(16),theequilibrium constantandthemodifiedparameterbTareexpressedby thetemperature-dependentequations.Substitutionof Eq.(15)andEq.(16)intoEq.(11)andrearrangement yieldthefinalequation: 1] 1+a(NaOH)Bj?.j P1+P2/T+P3InT+一 [P5+P6/T+P7InT+P8r]i(17) Equation(17)isafiringequationcorrespondingto equilibriumsolubilitydataofgibbsite,whereTis absolutetemperature(K),andPfisafixedvaluewhichis obtainedby1inearregressing.Thefittingmodelhas definitetheoreticalbasiswhichwastestedandverified byliterature『11].Furthermore,thenewmodelobtained isbetterthanthepreviousoneduetoitsbriefand improvedcharacteristics.Thefixedvaluesofparameters correspondingtoEq.f17)areobtaInedandlistedinTable1 Table1FixedvaluesofparametersofpltoPsinEq.(17) ParameterVlue 一 161.14950 4629.7868 26.695908 - 2.5588487x10一 一 145.48317 4327.0340 24.842.142 - 3.5592409x10-z Then,theexpressionoftheequilibriumconstantof gibbsitedissolvedinsodiumhydroxidesolutioninthe temperaturerangeof298.15—373.15Kisgivenas followsaccordingtoEq.(15)andTable1. 1gK=一161.1495+4629.7868/T+ 26.6959InT一0.0256T(18) Thevaluesofequilibriumconstantwerecalculated atvarioustemperaturesaccordingtoEq.(18),asshown inFig.1.Andthecomparisonbetweenthecalculated valuesoflgKandreferencesdatawasmade.asshownin Fig.2. Itisknownthattheequilibriumconstantismainly influencedbytemperature.Thetrendsofequilibrium constantinFig.1showthattheequilibriumsolubilityof gibbsiteincreaseswiththeincreaseoftemperaturein thesystemNaOH-NaAI(OH)4一H20,indicatingthat temperatureadjustmentisaneffectivemeasuretoenrich thecausticsolutionwithamaximumofaluminain Temperature/K Fig.1Equilibriumconstantofgibbsitedissolvedinsodium hydroxidesolution b0 Temperature/I( Fig.2Comparisonbetweencalculatedandreporteddatafor equilibriumconstantofgibbsitedissolvedinsodiumhydroxide solution 一二}' 一 一r???L 一 LIXiao?bin,etal/Trans.NonferrousMet.Soc.China22(2012)447—455451 digestionandtosubsequentlydriveoutamaximumof aluminafromthesolutioninprecipitation.Figure2 presentsthecalculatedandreporteddataofequilibrium constantofgibbsitedissolvedinsodiumhydroxide solution.Thecomparisonshowsthatthecalculated valuesagreewellwithmostofthevaluesof wEsoLOwsKI[9]9andCHANG[23],indicatingthat thefittingmodelissuitableandaccuratetopredictthe equilibriumconstantofthedissolvingreactionof gibbsite.Detailsofvalueassignmentcanbefoundinthe originalpaper[11]. 4DevelopmentofPitzermodelparameters andmixingparametersforNaOH—— NaAI(OH)4——H20system Manyresearchershaveproposeddifferentmethods tocalculatethetemperature.dependentPitzermodel parametersforthesystemNaOH-NaAI(OH)d—H20since l970s.Thebinaryandtemarymixingparametersare alsorequiredbytheion—interactionmodelforcalculation Ofthemixingelectrolytes.Intheregressionanalysis.the valuesoffl(2)aOH)and(NaAI(OH)4)aretakentobe zeroasRefs.『9,2l1.ItwasshownthattheitemsofPitzer modelparametersofNaOHaretheoppositenumberof thatofPitzermodelparametersofNaAI(OH)4inEq.(7). Therefore,theiternsof(NaOH),u(Na0H)and fNa0H)mustbeascertainedinordertoregressthe itemsof…(NaAI(OH)4),u(NaAI(OH)4)and C~(NaAI(OH)4).Furthermore,thevaluesofthebinary mixingparameterofOH-AI(OH)4-)andternary Table2PitzermodelparametersforNaOHatdifferenttemperatures mixingparameterofNaOH-AI(OH)4,),whichare usuallytakenasfixedvaluesbyresearchers『91,are limitedandappliedtoonlylowconcen打ations.Precisely, themixingparametersaretakenastheobiectof regressiontotestifytheinfluenceoftheion.interaction. Inthefollowingcalculation,Pitzermodelparametersfor NaOHreportedbyPABALANandPITZER『211,as showninle2.arefirstadoptedinthisstudy. 纬enthePitzermodelparametersforNaOHand theequilibriumconstantforthedissolvingreactionare known,thePitzermodelparametersforNaAI(OH)4and themixingparameterscanberegressedbysolving Eq.f7).TheresultsarelistedinT{le3. AsshowninT{le3.thePitzermodelparameters forNaAI(OH)4,(NaAl(OH)4),(NaAI(OH)4)and C哪(NaAI(OH)4),aretemperature—dependent,whichwas pro?