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[AMERICANJOURNALOFSCIENCE,VOL.274,DECEMBER,1974, P. 1089-1198]American JournalofScienceDECEMBER1974THEORETICALPREDICTIONOFTHETHERMODYNAMICBEHAVIOR OFAQUEOUSELECTROLYTESATHIGHPRESSURESANDTEMPERATURES: I. SUMMARY OFTHETHERMODYNAMIC/ELECTROSTATICPROPERTIESOFTHESOLVENTHAROLDC.HELGESONandDAVIDH.I{.IRKHAl\IDepartmentofGeologyandGeophysics,UniversityofCalifornia,Berkeley,California94720ABSTRACT.Thermodynamic/electrostaticpropertiesofH20athighpressuresandtemperatureswerecalculatedfromregressionequationsrepresentingdielectricconstantdatareportedbyOshry(ms),Owenandothers(1961),andHeger(lllS)fortemperaturesandpressuresfroln0°to550°Cand0.001to5kbtogetherwithfinitedifferencederiva-tivescomputedfromspecific vC9lulllesgivenbyBurnham,Hollo,vay,andDavis(1969b)for20°to900°Cand1to10kb.Correspondingpropertiesbelo'vakilobar,vere conl-putedwiththeaidoftheequationofstatedevelopedbyKeenanandothers(1969),'which describesthethermodynamicbehaviorofI-I~Oincloseaccord,viththetolerancesoftheInternationalSkeletonTablesof1963.Theresultsofthecalculationsaregiveninequations,tables,anddiagramsdepictingisothenns,isobars,andisoplethsofspecificvolume,entropy,enthalpy,internalenergy,HelmholtzandGibbsfreeenergies,fu-gacity,andheatcapacity,togetherwiththedielectricconstant,coefficientsofisobaricthermalexpansionandisothermalcompressibility,theBorn(1920)freeenergyfunc-tion,andtheirpartialderivatives.Perturbationofthethermodynanlic/electrostaticbe-haviorofH20bythecriticalphenomenonlead·~tosignificantdifferencesinthede-pendenceofitspropertiesontemperature,pressure,anddensityaboveandbelow---'400°Cand~1to2kb.ThecalculationspermitpredictionoftheconsequencesofthesedifferencesonthechemicalinteractionofInineralsandaqueouselectrolytesolu-tionsingeochemicalprocesses.INTRODUCTIONRecentadvancesinsolutionchemistry,thernl0dynamics,andCOln-putertechnologymakeitpossibletodescribequantitativelyequilibriunlandmasstransferamongmineralsandaqueouselectrolytesingeochemi-cal processesinvolvinglargenumbersofcOlnponents, phases,andchelni-cal speciesatbothhighandlowtemperat.uresandpressures.Thepresentseriesofcommunicationsisintendedtoprovideacomprehensivesetofequationsanddatatofacilitatesuchcalculations.Theoreticalandexperimentalstudiesofhydrothernlalsystelnsoverthepast50 years leavelittledoubtthatInineralsolubilitiesandthechemicalandthermodynamicbehaviorofsolutespeciesinaqueouselectrolytesarecontrolledtoalargeextentbythethermodynamic/elec-trostaticpropertiesofthesolvent,whichchangedramaticallywithin-creasingtemperatureandpressure.Theequations,tables,anddiagralnspresentedbelo,vconstituteaninternallyconsistentsunlmaryoftheseproperties,basedoncriticalevaluationandregressionofdensityanddielectricconstantdatareportedintheliteraturefortemperaturesand10891090H.C.HelgesonandD.H.KiTkha172-Theoreticalpredictionpressuresfrom0°to900°Cand0.001to10kb.TheseconditionsbracketthosefoundintheEarthfromitssurfacetoalithostaticdepthof~35km,whichisequivalentinpressuretoahydrostaticdepthof~100km.Thetemperaturespanrangesfrolllthestabilityfieldsofice IandVItothelow-pressuremeltingtemperaturesofhydroussilicaterocks.Thethermodynamicpropertiesof1-120havelongbeenofinteresttoengineersresponsibleforpowergenerationandinrecentdecadestogeologistsconcernedwithgeochenlicalandgeophysicalprocessesathightemperaturesandpressures.As aconsequence,aplethoraofsteamtablesandotherconlpilationshasappearedthroughtheyears,mostofwhichcatertoengineersandaretoorestrictedinthescopeofpressures,tem-peratures,and/orthepropertiesconsideredtobegenerallyapplicableinscience. l\iIanyofthecompilationsarebasedonconventionsandexpressedinunitsthatareinconvenientinageochemicalcontext,someareinsuffi-cientlydetailed,andnoneincludesallpropertiesofinterestinsolutionchenlistry.Anl0ngthemoreimportantoftheseisthedielectricconstantanditspartialderivativeswithrespecttopressureandtemperature.Thelattervariablescanbeusedinconjunctionwithexpansibilities,com-pressibilities,andothertherlllodyl1cllllicpropertiesofH20tocomputeelectrostaticparanletersintheDebye-Hiickeltheory,evaluateBornchargingequations,andformulatealgorithnlsandequationsofstateforpredictingandcorrelatingthethernlodynanlicpropertiesofaqueouselectrolytesathighpressuresandtenlperatures.REVIEWOFPREVIOUSWORKAlllultitudeofexperimentalandtheoreticalstudiesofthethermo-dynaillicpropertiesofsteam,water,andicehasaccumulatedinthecen-turyandahalfsinceCarnot(1824)publishedhisfaillousnlemoironthepOvverofheat,butonlyinthelast50yearshavesystenlaticandcoordi-natedeffortsbeennladetocOlllpileaccuratedataofhighprecisioninacOlllprehensiveandorganizedprogranlofresearch.Followingtheappear-anceoftheInternationalCriticalTablesin1928,theFirstInternationalConferenceonthePropertiesofSteaHl ,vasorganizedtoestablishtoler-ancesandcOInpileasetofskeletontableslistingacceptedvaluesforthethernlodynamicpropertiesofH20.Theskeletontablescompiledatthisconferenceprovidedthebasis fortheAS~/IEsteamtablesof1930(!(eenan,1930).Twoyears1atef, j\/[ollier's (1932)tablesanddiagramsappearedalnlostsi111ultaneouslywiththoseofKnoblauchandothers(1932).AttheThirdInternationalConferenceonthePropertiesofSteanlin1934,agreelnentwasreachedonarevisedandexpandedsetofskeletontablesandtolerancesfortelllperatures~550°Candpressures~300 bars.Shortlythereafter,!(eenanandKeyes (1936)producedthefirst co111pre-hensivesetofsteallltablesfortelnperaturesandpressuresfrolll 0°to871°Cand0to380bars.Thelattertables,whichprovedtobehighlyreliableandwidelyused,werebasedonacriticalreviewoftheliteratureandanequationofstatederivedfronlprecisepressure-volu11le-tempera-turenleasurenlentsfrom0°to460°Cand0to350atm(SmithandKeyes,ofthetherlnodynamicbehaviorofaqueouselectrolytes:I.10911934; Keyes,Smith,andGerry, 1936).Thesedata,togetherwithmanyothers, werereportedinDorsey's (1940)exhaustivereviewandcompila-tionofthepropertiesofH20,",vhichhasbeencomplementedrecentlyby extensivecritiquesofthephysical chelnistryofwater(Horne,1969,1972;Franks,1972).Internationalconferencesonthepropertiesofsteamhavebeenlleldintermittentlysince 1934,butitwasnotuntilthesixthconferencein1963thatagreementwasreachedonarevisedandenlargedsetofskele-tontablesextendingfrom0°to8000eandfrom0to1kb.Theadventofhigh-speed conlputersandtheskeletontablescompiledatthethirdandsixthinternationalconferencesonthepropertiesofsteamgeneratedanlyriadofregressionandinterpolationformulas,equationsofstate,andsteanl tables,whichhaveappearedinsteady succession sinceWorldWarII(forexample,CallendarandEgerton,1944, 1958; Schall,


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