IUPAC-NIST Solubility Data Series. 95. Alkaline Earth Carbonates in Aqueous Systems. Part 1

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IUPAC-NIST Solubility Data Series. 95.
Alkaline Earth Carbonates in Aqueous Systems.
Part 1. Introduction, Be and Mg
AlexDeVisscher,Editor,Evaluatora)
DepartmentofChemicalandPetroleumEngineering,andCentreforEnvironmentalEngineering
ResearchandEducation(CEERE),SchulichSchoolofEngineering,
UniversityofCalgary,Calgary,AB,T2N1N4Canada
JanVanderdeelen,Evaluatorb)
DepartmentofAppliedAnalyticalandPhysicalChemistry,FacultyofBioscienceEngineering,
GhentUniversity,B-9000Ghent,Belgium
ErichKo¨nigsberger,Compilerc)
SchoolofChemicalandMathematicalSciences,MurdochUniversity,Murdoch,WA,6150,Australia
BulatR.Churagulov,Compiler
DepartmentofChemistry,MoscowStateUniversity,Moscow,Russia
MasamiIchikuni,CompilerandMakotoTsurumi,Compiler
DepartmentofEnvironmentalChemistry,TokyoInstituteofTechnology,Nagatsuda,Yokohama,Japan
(Received2December2011;accepted6December2011;publishedonline27March2012)
Thealkalineearthcarbonatesareanimportantclassofminerals.Thisvolumecompiles
and critically evaluates solubility data of the alkaline earth carbonates in water and in
simple aqueous electrolyte solutions. Part 1, the present paper, outlines the procedure
adopted in this volume in detail, and presents the beryllium and magnesium carbonates.
For the minerals magnesite (MgCO ), nesquehonite (MgCO (cid:2)3H O), and lansfordite
3 3 2
(MgCO (cid:2)5H O),acriticalevaluationispresentedbasedoncurvefitstoempiricaland=or
3 2
thermodynamic models. Useful side products of the compilation and evaluation of the
data outlined in the introduction are new relationships for the Henry constant of CO
2
with Sechenov parameters, and for various equilibria in the aqueous phase including the
dissociation constants of CO (aq) and the stability constant of the ion pair MCO0ðaqÞ
2 3
(M¼alkalineearthmetal).Thermodynamicdataofthealkalineearthcarbonatesconsist-
ent with two thermodynamic model variants are proposed. The model variant that
describes the Mg2þ(cid:3)HCO(cid:3) ion interaction with Pitzer parameters was more consistent
3
with the solubility data and with other thermodynamic data than the model variant that
described the interaction with a stability constant.VC 2012 American Instituteof Physics.
[doi:10.1063/1.3675992]
Keywords: aqueoussolution;berylliumcarbonate;magnesiumcarbonate;solubility;thermodynamics.
CONTENTS 1.2.4. Ambient CO mole fraction and
2
altitude correction of total pressure.. 5
1. Preface.................................... 3 1.3. Evaluations............................ 6
1.3.1. Empirical equations for solubility... 6
1.1. Scope of the volume.................... 3
1.3.2. Thermodynamic model for solubility 7
1.2. Unit conversions for compilations ........ 3
1.3.2.1. Model equations for open
1.2.1. Density of pure water ............. 4
system................... 8
1.2.2. Density of electrolyte solutions..... 5
1.3.2.2. Model equations for closed
1.2.3. Influence of dissolved gases on
system................... 9
water density..................... 5
1.3.2.3. The Pitzer ion interaction
formalism ................ 10
1.3.2.4. Some thoughts on the
a)Electronicmail:[email protected]. calcium bicarbonate
b)Electronicmail:[email protected].
c)Electronicmail:[email protected]. ion pair .................. 10
VC 2012AmericanInstituteofPhysics. 1.3.3. Thermodynamic data.............. 11
0047-2689/2012/41(1)/013105/67/$47.00 013105-1 J.Phys.Chem.Ref.Data,Vol.41,No.1,2012
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013105-2 DEVISSCHERETAL.
1.3.3.1. Solubility of CO .......... 11 3. Sechenov coefficients for CO in various
2 2
1.3.3.2. Salting out of CO ......... 12 electrolyte solutions,34 together with fitted
2
1.3.3.3. Fugacity of the gas phase... 13 values.................................... 12
1.3.3.4. Dissociation constants of 4. Single-ion Sechenov coefficients and Pitzer k
carbonic acid ............. 15 parameters for CO in electrolytes, with
2
1.3.3.5. Ionization constant of temperature dependence .................... 13
water .................... 18 5. Enthalpy and entropy of the first dissociation
1.3.3.6. Metal-carbonate ion of CO at 298.15 K estimated from different
2
pairing................... 18 sources................................... 15
1.3.3.7. Other ion pairs............ 23 6. Values of (cid:3)lg(K ) from the Harned and
1
1.3.4. Independent thermodynamic data ... 25 Davis50 experiments obtained with different
1.3.5. Solubility in salt solutions: a SIT data analysis techniques .................... 17
approach ........................ 26 7. Enthalpy and entropy of the second
1.4. Remaining issues....................... 26 dissociation of CO at 298.15 K estimated
2
2. Solubility of Beryllium Carbonate ............ 27 from different sources...................... 18
2.1. Critical evaluation of the solubility of 8. Stability constants of alkaline earth
beryllium carbonate in aqueous systems... 27 bicarbonate ion pairs....................... 19
2.2. Data for the solubility of beryllium 9. Stability constants of alkaline earth carbonate
carbonate in aqueous systems............ 27 ion pairs.................................. 21
3. Solubility of Magnesium Carbonate........... 27 10. Pitzer parameters for M(HCO ) ............. 22
3 2
3.1. Critical evaluation of the solubility of 11. Stability constants of alkaline earth hydroxide
magnesium carbonate in aqueous ion pairs.................................. 24
systems ............................... 27 12. Single-electrolyte Pitzer parameters for
3.1.1. Overview of solubility data ........ 28 M(OH)2.................................. 25
3.1.2. Analytical methods used for 13. Two-electrolyte ion interactions ............. 25
dissolved magnesium 14. Overview of magnesium carbonate solubility
determination .................... 30 data in aqueous systems.................... 28
3.1.3. Magnesite ....................... 30 15. Data collected for the evaluation of the
3.1.3.1. MgCO þH OþCO ...... 30 solubility of magnesite in the system
3 2 2
3.1.3.2. MgCO þH OþCO MgCO þH OþCO ...................... 31
3 2 2 3 2 2
þNaCl .................. 33 16. Evaluation of magnesite solubility in the
3.1.3.3. MgCO þH O............ 33 system MgCO þH OþCO ................ 32
3 2 3 2 2
3.1.3.4. MgCO þH Oþsalt....... 34 17. Data collected for the evaluation of the
3 2
3.1.4. Nesquehonite..................... 35 solubility of MgCO in the system
3
3.1.4.1. MgCO (cid:2)3H OþH O MgCO þH OþCO þNaCl ............... 33
3 2 2 3 2 2
þCO ................... 35 18. Data collected for the evaluation of the
2
3.1.4.2. MgCO (cid:2)3H OþH OþCO solubility of magnesite in the system
3 2 2 2
þsalt.................... 39 MgCO þH O ............................ 33
3 2
3.1.4.3. MgCO (cid:2)3H OþH O....... 39 19. Comparison of magnesite solubility in the
3 2 2
3.1.4.4. MgCO (cid:2)3H OþH O system MgCO þH O with model
3 2 2 3 2
þsalt.................... 42 predictions................................ 34
3.1.5. Lansfordite ...................... 42 20. Data collected for the evaluation of the
3.1.5.1. MgCO (cid:2)5H OþH O solubility of MgCO in the system
3 2 2 3
þCO ................... 42 MgCO þH OþNaCl ..................... 34
2 3 2
3.1.6. Conclusion....................... 44 21. Data collected for the evaluation of the
3.2. Data for the solubility of magnesium solubility of MgCO in the system
3
carbonate in aqueous systems............ 45 MgCO þH OþNa SO ................... 34
3 2 2 4
Acknowledgments .......................... 66 22. Data collected for the evaluation of the
4. References................................. 66 solubility of MgCO3 in the system
MgCO þH OþNa CO ................... 35
3 2 2 3
List of Tables 23. Data collected for the evaluation of the
1. Thermodynamic properties of the dissolution solubility of MgCO in the system
3
of CO at 25 (cid:4)C derived from different semi- MgCO þH OþNaNO .................... 35
2 3 2 3
empirical equations ........................ 11 24. Data collected for the evaluation of the
2. Henry constant of CO predicted in this study solubility of MgCO in the system
2 3
and by Crovetto32 ......................... 12 MgCO þH OþMgCl .................... 35
3 2 2
J.Phys.Chem.Ref.Data,Vol.41,No.1,2012
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IUPAC-NISTSOLUBILITYDATASERIES.95-1 013105-3
25. Data collected for the evaluation of the system 1. Preface
MgCO (cid:2)3H OþH OþCO , and fit with
3 2 2 2
empirical model........................... 36 1.1. Scopeofthevolume
26. Evaluation of nesquehonite solubility in the
Solubilities of alkaline earth metal carbonates in water
system MgCO (cid:2)3H OþH OþCO .......... 40
3 2 2 2 and aqueous solutions are of interest in many areas such as
27. Data collected for the evaluation of the
biology, geology, hydrology, medicine, and environmental
solubility of MgCO in the system
3 sciences.Ofparticularsignificanceistheinteractionbetween
MgCO (cid:2)3H OþH OþCO þNa CO ....... 42
3 2 2 2 2 3 alkaline earth metal carbonates and carbon dioxide during
28. Data collected for the evaluation of the
CO storageinundergroundaquifers.
2
solubility of nesquehonite in the system
This volume contains compilations and evaluations of the
MgCO (cid:2)3H OþH O....................... 42
3 2 2 solubilitiesofthealkalineearthcarbonatesinwaterandsim-
29. Comparison of nesquehonite solubility in the
ple electrolyte solutions. Solid phases containing mixed car-
system MgCO (cid:2)3H OþH O with model
3 2 2 bonates or mixed carbonates and hydroxides, solubilities in
predictions................................ 42
mixed or non-aqueous solvents, solubilities in supercritical
30. Data collected for the evaluation of the
water,andsolubilitiesinseawaterareexcluded.Thevolume
solubility of lansfordite in the system
isorganizedasfollows:
MgCO (cid:2)5H OþH OþCO ................. 43
3 2 2 2
31. Evaluation of lansfordite solubility in the Part1(thispaper):Introduction,Be,Mg
system MgCO (cid:2)5H OþH OþCO .......... 44 Part2:Ca
3 2 2 2
Part3:Sr,Ba,Ra
Literature through 2009 was searched. For each of beryl-
List of Figures lium carbonate and radium carbonate, only one reference is
1. Solubility of magnesite in MgCO þH O
3 2 available, and the solubilities given are doubtful. For magne-
þCO systems divided by the cubic root of
2 sium carbonate about 25 references are available. Data are
the equilibrium CO partial pressure.......... 31
2 available for three mineralogical types: the anhydrous salt
2. Solubility constants of magnesite derived from
MgCO (magnesite), the trihydrate MgCO (cid:2)3H O (nesque-
3 3 2
solubility data in the system
honite),andthepentahydrateMgCO (cid:2)5H O(lansfordite).For
MgCO þH OþCO with Model 1.......... 31 3 2
3 2 2 calcium carbonate, about a hundred references were found
3. Solubility constants of magnesite derived from
covering three well-defined crystallographical forms of anhy-
solubility data in the system
drous salt (calcite, aragonite, and vaterite) and two hydrates,
MgCO þH OþCO with Model 2.......... 32
3 2 2 the monohydrate (monohydrocalcite) and the hexahydrate
4. Solubility of magnesite in the system
(ikaite).Therearefewerthan20referenceseachforstrontium
MgCO þH O measured and predicted with
3 2 carbonate(strontianite)andbariumcarbonate(witherite).
Model 1 and Model 2...................... 33
5. Solubility of nesquehonite in MgCO (cid:2)3H O
3 2
1.2. Unitconversionsforcompilations
þH OþCO systems divided by the cubic
2 2
root of the equilibrium CO2 partial The general equations for unit conversions are given in
pressure................................... 38 the Introduction to the Solubility Data Series.1,2 For many
6. Solubility constants of nesquehonite derived conversions, like from mol l(cid:3)1 to mol kg(cid:3)1,a density of the
from solubility data in the system liquidsolutionisneeded.
MgCO3(cid:2)3H2OþH2OþCO2 with Model 1.... 39 The conversion from amount concentration to molality in
7. Solubility constants of nesquehonite derived an aqueous system containing a dissolved salt and dissolved
from solubility data in the system CO isgivenby
2
MgCO (cid:2)3H OþH OþCO with Model 2.... 39
3 2 2 2
8. Solubility of nesquehonite in the system 1000 csalt
MgCO3(cid:2)3H2OþH2O measured and predicted msalt ¼ moll(cid:3)1 ;
with Model 1 and Model 2.................. 42 molkg(cid:3)1 qsolution(cid:3) Msalt csalt (cid:3) MCO2 cCO2
9. Solubility of lansfordite in kgm(cid:3)3 kgkmol(cid:3)1moll(cid:3)1 kgkmol(cid:3)1moll(cid:3)1
MgCO3(cid:2)5H2OþH2OþCO2 systems divided (1)
by the cubic root of the equilibrium CO
2
partial pressure. ........................... 43 with m the molality of the salt, c its amount concentra-
salt salt
10. Solubility constants of lansfordite derived tion,q thesolutiondensity,M themolarmassofthe
solution salt
from solubility data in the system salt,M themolarmassofCO ,andc itsconcentration.
CO2 2 CO2
MgCO (cid:2)5H OþH OþCO with Model 1.... 43 If multiple salts are dissolved, each salt will result in a term
3 2 2 2
11. Solubility constants of lansfordite derived inthedenominatorofEq.(1).
from solubility data in the system InsystemsopentoCO (g),thedominantdissolvedspecies
2
MgCO (cid:2)5H OþH OþCO with Model 2.... 44 inequilibriumwithanalkalineearthcarbonateisthealkaline
3 2 2 2
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013105-4 DEVISSCHERETAL.
earth metal ion, and bicarbonate, unlike systems in the ab- excess of 5%, when the partial pressure is 40 bar. Even
sence of added CO , where the dominant species are the saltingoutneedstobeaccountedforinsomeextremecases,
2
metal and the carbonate ions. Hence, in open systems the especially when working with nesquehonite or lansfordite.
valueofM applicableinEq.(1)is62gmol(cid:3)1largerthan Not accounting for this effect would overestimate the
salt
the value of the metal carbonate. Improper use of Eq. (1) dissolved CO concentration, and the molality. If none of
2
leads to errors in excess of 5% at a concentration of these precautions are taken, the error made can be in excess
1moll(cid:3)1,whichoccursinthecaseofnesquehoniteandlans- of 10%. Hence, the nature of the dissolved salt, the dissolu-
forditeathighCO partialpressures. tionof CO andits salting out were appropriately accounted
2 2
The dissolved CO concentration in open systems is on for.
2
theorder of 0.035moll(cid:3)1perbar ofCO partialpressureat When mass concentrations analyzed as MCO
2 3
25 (cid:4)C, and is strongly temperature dependent. Hence, not (M¼alkalineearthmetal)aretobeconvertedtomolalitiesin
accounting for dissolved CO can also generate errors in systemsopentoCO (g),theappropriateequationis
2 2
q (cid:2)M
1000 MCO3 MCO3
mmMoðlHkCgO(cid:3)3Þ12 ¼qsolution(cid:3)MMðHCO3Þ2qMgClO(cid:3)31(cid:2)MgMmCoOl3(cid:3)(cid:3)1 MCO2 cCO2 : (2)
gl(cid:3)1 gmol(cid:3)1 gl(cid:3)1 gmol(cid:3)1 gmol(cid:3)1moll(cid:3)1
Solubility of CO2 and salting out are discussed in later q¼ qsat : (4)
sections. Aq (cid:5)ðkgm(cid:3)3Þ
1(cid:3) sat lnð1þBðp=kPa(cid:3)p =kPaÞÞ
v
B
1.2.1. Densityofpurewater
The saturated vapor pressure p in Eq. (4) was also taken
v
Astandardequationofstateforfluidwaterwasdeveloped fromWagnerandPruß,3
byWagnerandPruß3thataccuratelypredictsallwaterprop-
eardtvieasntiangaewofidtehirsanagpeproofatcehmipsetrhaatturtehseaenqduaptrieosnsuforersd.eTnhseitdyisis- pv ¼pcexp(cid:3)Tc(cid:6)a1hþa2h1:5þa3h3þa4h3:5
T
an implicit one, making density calculations inconvenient
(cid:4)
forcompilationpurposes.Therefore,anapproximateexplicit þa h4þa h7:5(cid:7) ; (5)
5 6
equation was developed. The starting point of the approach
is the explicit equation suggested by Wagner and Pruß3 for
with
the density of liquid water at the saturated vapor pressure,
p ¼22064kPa(criticalpressure)
q ,asafunctionoftemperature,whichisvalidfromthetri- c
sat
T ¼647.096K(criticaltemperature)
plepointtothecriticalpointofwater, c
a ¼(cid:3)7.85951783
1
(cid:3) a ¼1.84408259
2
qsat ¼qc 1þb1h1=3þb2h2=3þb3h5=3þb4h16=3 a3¼(cid:3)11.7866497
a ¼22.6807411
(cid:4) 4
þb5h43=3þb6h110=3 ; (3) a5¼(cid:3)15.9618719
a ¼1.80122502
6
Equation (4) with 4th-order polynomials in h for A and B
where were fitted to predictions of the Wagner and Pruß3 equation
q ¼322kgm(cid:3)3(criticaldensity)
c of state in the temperature range 273.15–473.15 K and the
h¼1(cid:3)T=T
c pressurerangefromp to20000kPa.ThecoefficientsAand
v
T ¼647.096K(criticaltemperature)
c BinEq.(4)resultingfromthisfitare
b ¼1.99274064
1
b2¼1.09965342 A¼a0þa1hþa2h2þa3h3þa4h4; (6)
b ¼(cid:3)0.510839303
3
b ¼(cid:3)1.75493479 with
4
b ¼(cid:3)45.5170352 a ¼7.4242997(cid:5)10(cid:3)9
5 0
b ¼(cid:3)6.74694450(cid:5)105 a ¼(cid:3)5.3019784(cid:5)10(cid:3)8
6 1
Thewaterdensitywasthencorrectedforpressureusingan a ¼1.6188583(cid:5)10(cid:3)7
2
equationbasedonTait’slaw,butwithtemperature-dependent a ¼(cid:3)2.3371482(cid:5)10(cid:3)7
3
coefficientsAandB, a ¼1.3239697(cid:5)10(cid:3)7
4
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IUPAC-NISTSOLUBILITYDATASERIES.95-1 013105-5
B¼b þb hþb h2þb h3þb h4 (7) 1.2.3. Influenceofdissolvedgasesonwater
0 1 2 3 4
density
b ¼6.1180105(cid:5)10(cid:3)5
0 Kell7 investigated the influence of dissolved N , O , Ar,
b ¼(cid:3)4.4068335(cid:5)10(cid:3)4 2 2
1 and CO on the densityof water.The combinedeffect of N ,
b ¼1.3633547(cid:5)10(cid:3)3 2 2
2 O , and Ar was found to be about 0.0003% and can be
b ¼(cid:3)2.0035442(cid:5)10(cid:3)3 2
3 ignored.TheeffectofCO onthesolutiondensitydependson
b ¼1.1496256(cid:5)10(cid:3)3 2
4 the temperature and the CO partial pressure. Its estimation
The consistency of Eq. (4) with the Wagner and Pruß3 2
requiresavalueoftheapparentmolarvolumeofCO (aq).As
equation of state is 0.004% (0.04 kg m(cid:3)3) or better in the 2
CO isafairlyidealsoluteinthepressurerangeofinterest,it
entirerangetested. 2
is assumed that apparent molar volume equals partial molar
volume. Kell7 reviewed the literature available at the time,
1.2.2. Densityofelectrolytesolutions andtentativelyputforwardavalueof38cm3mol(cid:3)1,withlit-
erature values ranging from 28 to 38 cm3 mol(cid:3)1. This range
Densities of electrolyte solutions were calculated with the
was confirmedbyHne˘dkovsky` et al.,9whoreportedapparent
methodofKrumgalzetal.,4basedonthePitzermodel.When
molar volumes for a wide temperature range. However, they
datawasunavailableinRef.4,dataofKrumgalzetal.5valid
found a pronounced temperature dependence. Their values
at 25 (cid:4)C were used, with pure water density data at the tem-
compare well with other studies in the literature and are
peratureofinterest.Intheirmodel,Krumgalzetal.4usedthe
largely consistent with the Wagner and Pruß3 equation of
somewhat obsolete pure water density calculations of Kell6
state.10Whentheirdataat25–200(cid:4)Carefittedtoaparabolic
because those data or very similar values were used in most
equationinT=K,thefollowingisobtained:
experimental determinations of electrolyte solution densities.
Inthis work,thenewlyderivedequationswere usedbecause
V =ðcm3mol(cid:3)1Þ¼58:309(cid:3)0:19758ðT=KÞ
theKell6equationislimitedto1atmpressure. /
At 273.15–373.15 K and 101.325 kPa, the deviation þ0:00038030ðT=KÞ2: (8)
between the Wagner and Pruß3 equation of state and the
Kell6 equation is up to about 0.015 kg m(cid:3)3 (standard devia- When this equation is applied at 0 (cid:4)C and 25 (cid:4)C, values of
tion0.0061kgm(cid:3)3).ThedeviationbetweentheWagnerand 32.7 and 33.2 cm3 mol(cid:3)1 are obtained, respectively. These
Pruß3 equation of state and the new equation is up to about valuescomparewellwithvaluesofthepartialmolarvolume
0.0062kgm(cid:3)3(standarddeviation0.0046kgm(cid:3)3).Thedif- suggested by Weiss11 (32.360.5 cm3 mol(cid:3)1), Barbero
ference betweentheKell6model andthenewequationisup et al.12 (32.861.2 cm3 mol(cid:3)1), and Spycher et al.13
to about 0.017 kg m(cid:3)3 (standard deviation 0.0090 kg m(cid:3)3). (32.661.3 cm3 mol(cid:3)1). Based on these values, densities
Hence, the choice to use the new equation for water density were calculated at 0 (cid:4)C (CO solubility at partial pressure 1
2
with the Krumgalzet al.4 model for electrolyte solution den- bar about 0.075 mol kg(cid:3)1) and at 25 (cid:4)C (CO solubility at
2
sity introduces a negligible inconsistency. Kell7 presented a partial pressure 1 bar about 0.033 mol kg(cid:3)1). At 0 (cid:4)C, the
comprehensive equation for water density, including pres- density effect is negligible (<0.1 kg m(cid:3)3) for partial pres-
sureeffectsforupto10atm.Becauseofthelimitedpressure suresbelow0.12bar,but isashighas0.85kgm(cid:3)3ata par-
range,thisequationwasnotinvestigatedinanydetail. tial pressure of 1 atm. At p(CO )¼12.5 bar, the error
2
To test the error introduced by applying the Krumgalz introduced by ignoring the density effect is as large as 1%.
model tohighpressures,predictions withthe model for NaCl At 25 (cid:4)C, the density effect is negligible (<0.1 kg m(cid:3)3) for
solutionswerecomparedwithvaluestabulatedbyRogersand partialpressuresbelow0.28bar,andis0.36kgm(cid:3)3atapar-
Pitzer.8Atatmosphericpressure,themodelpredicteddensities tialpressureof1bar.
upto0.16kgm(cid:3)3lowerthanthevaluesaretabulatedbyRog- The calculation of the solubility of CO is discussed in
2
ersandPitzer.8At20000kPa,themodelpredictionswereup Sec.1.3.3.
to2.5kgm(cid:3)3abovethetabulatedvalues(NaCl(aq)hasaneg-
ative apparent compressibility). Hence, unit conversions for
1.2.4. AmbientCO molefractionandaltitude
concentrated electrolyte solutions at high pressures should be 2
correctionoftotalpressure
made with great care. However, in dilute solutions (m<0.1
molkg(cid:3)1)theerrorisacceptable(<0.11kgm(cid:3)3). In many studies total pressure is not reported, or simply
Even when solubilities of alkaline earth carbonates in pure reported as atmospheric pressure. Neither is CO mole frac-
2
water are converted from mol l(cid:3)1 to mol kg(cid:3)1, it is useful to tion in the gas phase mentioned in some older studies, or
accountforchangesinsolutiondensity.Forinstance,thesolu- merely indicated as “ambient.” However, barometric pres-
bility of the anhydrous CaCO polymorphs is around suredependsonaltitude,andtheambientCO molefraction
3 2
0.01 mol kg(cid:3)1 at 25 (cid:4)C and p(CO )¼1 atm. The dominant has increased considerably in the last 150 years. Hence,
2
ions in solution are Ca2þ and HCO (cid:3). The density of a 0.01 approximationswererequiredtodealwithsuchcases.
3
molkg(cid:3)1Ca(HCO ) solutionisabout998.33kgm(cid:3)3,whereas Barometric pressure p can be estimated with reasonable
32
thedensityofpurewaterisabout997.04kgm(cid:3)3.Notaccount- accuracy using a single, constant temperature, using the fol-
ingforthiseffectwouldintroduceanerrorofabout0.13%. lowingequation:
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013105-6 DEVISSCHERETAL.
(cid:3) (cid:4)
Mgh themetalcarbonatetoeliminateCO .Thismethodhasthe
p¼p exp (cid:3) ; (9) 2
0
RT potential toeliminateCO evolved fromthe dissolution of
2
the metal carbonate, or, conversely, trap CO dissolved
2
in which p is the barometric pressure at sea level (assumed prior to adding the metal carbonate due to the alkaline na-
0
to be 101 325 Pa), M is the molar mass of air (0.029 ture of the minerals. Either way, the system is undefined
kg mol(cid:3)1), g is the acceleration due to gravity (9.80665 m becausethetotalcarbonateconcentrationisunknown.
s(cid:3)2), h is the altitude of the measurement (m), and R is the • Empirical equations were fitted to the data, and outliers
idealgasconstant(8.314472Jmol(cid:3)1K(cid:3)1).Usingatempera- weredetectedandeliminated.
tureof15(cid:4)C(288.15K)leadstotheapproximateequation, • A simple thermodynamic model was developed for the
MCO þH OandMCO þH OþCO data(M¼Mg,Ca,
3 2 3 2 2
p=kPa¼101:325 expð(cid:3)0:00012h=mÞ: (10) Sr,Ba).Themodelwasusedtoderiveasolubilityconstant
of the alkaline earth carbonate for each measurement. The
Unlessambienttemperatures areextreme,thepotentialerror
solubility constants are then plotted versus temperature.
of Eq. (10) is less than the natural variation of the ambient
Outliers and data with spurious trends were eliminated.
barometricpressuresuptoaltitudesofwellabove1000m.
Some data points rejected by the empirical model turned
Ambient CO concentrations have been measured at
2 outtobefairlyaccuratewhenconsideredwiththethermo-
Mauna Loa, Hawaii, since 1958,14 and from Antarctic ice
dynamic model. In such cases, the data points were
cores by Etheridge et al.15 Recently the validity of the ice
reverted to accepted status. The MCO þH O data were
core measurements was confirmed by Siegenthaler et al.16 3 2
more difficult to evaluate than the MCO þH OþCO
IcecoredataofEtheridgeetal.15weresystematicallybelow 3 2 2
data. Hence, the MCO þH OþCO data were evaluated
3 2 2
the Mauna Loa data by about 0.5–1 ppm (parts per million
first, and thermodynamic solubility constant correlations
by mole fraction). The standard deviation between the ice
were fitted. These were introduced in the MCO þH O
3 2
coredataandtheMaunaLoadatawastypicallyabout1–1.5
model, and the data were evaluated by comparison with
ppm.Thedatafrombothsourceswere pooledandempirical
themodelresults.
equations were fitted to the concentration to obtain relation-
• For some cases, the consistency between the data sets was
shipswithyear.Theresultswereasfollows:
checked against independent thermodynamic data. For the
specific case of calcite, aragonite, and vaterite, all data
1800(cid:3)1939: yðCO Þ=ppm
2 were treated as a single data set, using thermodynamic
¼274:70þ5:803 datatoconvertallsolubilityconstantstocalcite.
(cid:5)expð0:0131073 ðt=year(cid:3)1800ÞÞ
The empirical equations and the thermodynamic model
1940(cid:3)1952: yðCO Þ=ppm¼310:6 are discussed below. We stress that the model is used as a
2
1953(cid:3)2004: yðCO Þ=ppm toolforevaluating data,notasanendofitsown.Hence,we
2
do not recommend any model. Thermodynamic data pre-
¼277:03þ1:2806
sented are data either predicted by this particular model, or
(cid:5)expð0:0214357 ðt=year(cid:3)1800ÞÞ:
mostconsistentwiththemodel,andshouldnotbeconstrued
(11) as“reference”thermodynamicdata.
Thenumberofdatapointsforthethreeperiodsis30,3,and
68.Thestandarddeviationbetweenthemodelandthedatais
1.3.1. Empiricalequationsforsolubility
1.1 ppm, 0.75 ppm, and 1.2 ppm, respectively. When neces-
sary,theaboveequationswereusedtoestimateambientCO For an empirical equation to be a useful tool in the detec-
2
concentrations. tionofoutliersinsolubilitydata,itisnecessarythattheequa-
Johnston and Walker17 pointed out that ambient air has tionhas a realistic temperature andpressure dependencein a
variable CO concentration, which leads to a serious loss of widerangeofconditions,withalimitednumberofadjustable
2
accuracy when used in the determination of the solubility parameters. To that effect, an equation that mimics some
constantofanalkalineearthcarbonate.Theyrecommendthe thermodynamic aspects of alkaline earth carbonate solubility
use of synthetic air-CO mixtures. Hence, experiments with was selected. De Visscher and Vanderdeelen18 argued that
2
ambientairshouldbetreatedwithcautionevenwhenplausi- the solubility (s) of an alkaline earth carbonate is approxi-
bleestimatesasgivenaboveareused. matelyproportionaltothecubicrootoftheCO fugacity:
2
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
4K K K a fðCO Þ
1.3. Evaluations s=ðmolkg(cid:3)1Þ¼ 3 s c 1 w 2 ; (12)
K c c2 bar
2 M2þ HCO(cid:3)
Thecompileddatawereevaluatedinvariouswaysinclud- 3
ingthefollowing:
where K is the solubility constant of MCO , K is the solu-
s 3 c
• Data obtainedwithfaultyorsuspiciousmethodology were bility constant of CO , K and K are the first and second
2 1 2
rejected.Anexampleisboilingthesuspensionafteradding acid dissociation constant of CO =carbonic acid, f(CO ) is
2 2
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IUPAC-NISTSOLUBILITYDATASERIES.95-1 013105-7
thefugacityofCO ,andthecvaluesareactivitycoefficients. pV ¼RTð1þapÞ (15)
2 m
Hence,thelogarithmofthesolubilitycanbewrittenas
is used, then the relationship between fugacity and partial
!
(cid:3) (cid:4) (cid:3) (cid:4)
s 1 4K K K a 1 fðCO Þ pressureis
lg ¼ lg s c 1 w þ lg 2 :
molkg(cid:3)1 3 K c c2 3 bar
2 M2þ HCO(cid:3)
3 (cid:3) (cid:4) (cid:3) (cid:4)
fðCO Þ pðCO Þ a pðCO Þ
(13) lg 2 ¼lg 2 þ 2 : (16)
bar bar lnð10Þ bar
Byassuminganequationoftheformaþb=TþclgTforthe
firstlogarithmontheright-handsideofEq.(13),anequation
If it is assumed that a is linearly dependent on temperature,
ofthefollowingformisobtained:
thenthefollowingequationisobtained:
(cid:3) (cid:4) (cid:3) (cid:4) (cid:3) (cid:4)
s fðCO Þ c T
lg ¼aþblg 2 þ þdlg : (cid:3)fðCO Þ(cid:4) (cid:3)pðCO Þ(cid:4)
molkg(cid:3)1 bar T=K K lg 2 ¼lg 2 þbpðCO Þ=bar
bar bar 2
(14)
þcðT=KÞðpðCO Þ=barÞ: (17)
2
Note that the fitting parameters (a, b, …) in the equations in
this section are not meant to have the same meaning in each SubstitutioninEq.(14)leadstoanequationoftheform,
equation.Whenidealgasbehaviorisassumed,thefugacitycan
(cid:3) (cid:4) (cid:3) (cid:4)
be considered equal to the partial pressure. However, when s pðCO Þ pðCO Þ
lg ¼aþblg 2 þc 2
suchanequationisadopted,allthenon-idealitiesofthesystem molkg(cid:3)1 bar bar
are absorbed in parameter b (which should approximate 1=3). TpðCO Þ e (cid:3)T(cid:4)
þd 2 þ þf lg : (18)
Preliminary tests with nesquehonite (MgCO3(cid:2)3H2O) solubility K bar T=K K
data in the MgCO þH OþCO system showed that this led
3 2 2
to an unrealistically large value of b (0.38), making the equa-
Equation (18) showed a more realistic value of b (0.347) in
tionunreliableforuseinanextendedpressurerange.Makingb
thepreliminaryanalysiswithnesquehonite,andwasretained
temperaturedependentdidnotsolvetheproblembecauseitled
fortheevaluation.
to an unrealistically large temperature dependence of b with
the MgCO þH OþCO dataset. Instead, a more realistic
3 2 2 1.3.2. Thermodynamicmodelforsolubility
assumptionrelatingfugacitytopartialpressurewasused.When
asecond-ordervirialequationofstateoftheform, Thefollowingreactionsareconsideredinthemodel:
MCO (cid:2)xH OðcrÞÐM2þðaqÞþCO2(cid:3)ðaqÞþxH OðlÞ K ¼ðM2þÞðCO2(cid:3)Þaxðm(cid:4)Þ(cid:3)2; (19)
3 2 3 2 s 3 w
CO ðgÞÐCO ðaqÞ K ¼ðCO ðaqÞÞf(cid:3)1ðCO ðgÞÞðf(cid:4)Þðm(cid:4)Þ(cid:3)1; (20)
2 2 c 2 2
CO ðaqÞþH OðlÞÐHþðaqÞþHCO(cid:3)ðaqÞ K ¼ðHþÞðHCO(cid:3)ÞðCO ðaqÞÞ(cid:3)1a(cid:3)1ðm(cid:4)Þ(cid:3)1; (21)
2 2 3 1 3 2 w
HCO(cid:3)ðaqÞÐHþðaqÞþCO2(cid:3)ðaqÞ K ¼ðHþÞðCO2(cid:3)ÞðHCO(cid:3)Þ(cid:3)1ðm(cid:4)Þ(cid:3)1; (22)
3 3 2 3 3
H OðlÞÐHþðaqÞþOH(cid:3)ðaqÞ K ¼ðHþÞðOH(cid:3)Þa(cid:3)1ðm(cid:4)Þ(cid:3)2; (23)
2 w w
M2þðaqÞþOH(cid:3)ðaqÞÐMOHþðaqÞ K ¼ðMOHþÞðM2þÞ(cid:3)1ðOH(cid:3)Þ(cid:3)1ðm(cid:4)Þ; (24)
MOHþ
M2þðaqÞþCO2(cid:3)ðaqÞÐMCO0ðaqÞ K ¼ðMCO0ÞðM2þÞ(cid:3)1ðCO2(cid:3)Þ(cid:3)1ðm(cid:4)Þ; (25)
3 3 MCO0 3 3
3
M2þðaqÞþHCO(cid:3)ðaqÞÐMHCOþðaqÞ K ¼ðMHCOþÞðM2þÞ(cid:3)1ðHCO(cid:3)Þ(cid:3)1ðm(cid:4)Þ: (26)
3 3 MCOþ 3 3
3
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013105-8 DEVISSCHERETAL.
In Eqs. (19)–(26), round brackets denote activities, f denotes By substitution of Eq. (29), the following equations can be
fugacity,a referstowateractivity,m(cid:4) isthestandardactivity derived:
w
(1molkg(cid:3)1),andf(cid:4) isthestandardfugacity(1atmwasused
aass danataopwtieorneacloemqupailteiodnininatthme).eTvahleualatisotne,qausattihoenewxiasstetnrecaeteodf (cid:6)HCO(cid:3)(cid:7)¼rKffiffiffiffisffiKffiffifficffiffiKffiffiffi1ffiffif1=2ðCO2Þawð1(cid:3)xÞ=2ðm(cid:4)Þ3=2; (36)
this ion pair has been subject to continuing debatefor almost 3 K2 ðf(cid:4)Þ(cid:6)M2þ(cid:7)1=2
50 years. The CO dissolution reaction (Eq. (20)) was only
2
consideredintheso-calledopensystem(seeSec.1.3.2.1). (cid:6)CO2(cid:3)(cid:7)¼K ðm(cid:4)Þ2 ; (37)
3 sax(cid:6)M2þ(cid:7)
1.3.2.1. Model equations for open system. By open w
system,wemeantheMCO þH OþCO systemcontaining
3 2 2
asolidMCO3phase, agas phase containing aknown partial ðOH(cid:3)Þ¼K rffiffiffiffiffiffiKffiffiffisffiffiffiffiffiffiffi ðf(cid:4)Þaðw1(cid:3)xÞ=2 ðm(cid:4)Þ3=2; (38)
pressure of CO2, and an aqueous phase in equilibrium with w KcK1K2f1=2ðCO Þ(cid:6)M2þ(cid:7)1=2
thetwootherphases. 2
The condition of charge neutrality in the aqueous phase
leadstothefollowingequation: ðMOHþÞ
2½M2þ(cid:6)þ½MOHþ(cid:6)þ½MHCOþ3(cid:6)þ½Hþ(cid:6) ¼KMOHþKwrffiKffiffiffiffiKffiKffiffiffisffiffiKffiffiffiffiffi(cid:6)M2fþ1=(cid:7)21ð=C2aOwð1(cid:3)ÞxÞ=2ðf(cid:4)Þ1=2ðm(cid:4)Þ1=2;
¼½HCO(cid:3)(cid:6)þ2½CO2(cid:3)(cid:6)þ½OH(cid:3)(cid:6) (27) c 1 2 2
3 3
(39)
Thisequationiswrittenintermsofactivities:
K K
2(cid:6)M2þ(cid:7) ðMOHþÞ (cid:6)MHCOþ(cid:7) ðHþÞ (cid:6)MCO0(cid:7)¼ MCO03 sðm(cid:4)Þ; (40)
þ þ 3 þ 3 ax
c c c c w
M2þ MOHþ MHCOþ Hþ
3
¼(cid:6)HCO(cid:3)3(cid:7)þ2(cid:6)CO23(cid:3)(cid:7)þðOH(cid:3)Þ: (28) (cid:6)MHCOþ3(cid:7)
cHCO(cid:3)3 cCO23(cid:3) cOH(cid:3) ¼K rffiKffiffiffisffiKffiffifficffiffiKffiffiffi1ffiffif1=2ðCO2Það1(cid:3)xÞ=2(cid:6)M2þ(cid:7)1=2ðm(cid:4)Þ1=2:
Tocalculatesolubility,eachterminthisequationwillbecal- MHCOþ3 K2 ðf(cid:4)Þ w
culated in terms of the free metal ion activity (M2þ). First a (41)
relationship between free metal ion activity and hydrogen
ionactivityisderivedfromEqs.(19)–(22), SubstitutionintoEq.(28)leadstothefollowing:
ðHþÞ¼rKffiffiffifficffiKffiffiffiffi1ffiffiKffiffiffi2ffiffif1=2ðCO2Það1þxÞ=2(cid:6)M2þ(cid:7)1=2ðm(cid:4)Þ1=2: 2(cid:6)M2þ(cid:7) K K rffiffiffiffiffiffiKffiffiffiffiffiffiffiffiffiffiað1(cid:3)xÞ=2(cid:6)M2þ(cid:7)1=2
Ks ðf(cid:4)Þ1=2 w c þ McOHþ w K KsK w f1=2ðCO Þ ðf(cid:4)Þ1=2
M2þ MOHþ c 1 2 2
(29)
The following relations can be derived from the reaction (cid:5)ðm(cid:4)Þ1=2þKMHCOþ3 rffiKffiffiffisffiKffiffifficffiffiKffiffiffi1ffiffif1=2ðCO Það1(cid:3)xÞ=2
c K 2 w
equilibria: MHCOþ 2
3
(cid:6)HCO(cid:3)(cid:7)¼K K fðCO2Þawðm(cid:4)Þ2; (30) (cid:5)(cid:6)M2þ(cid:7)1=2ðm(cid:4)Þ1=2þ 1 rffiKffiffifficffiKffiffiffiffi1ffiffiKffiffiffi2ffiffif1=2ðCO2Þ
3 c 1 ðf(cid:4)ÞðHþÞ cHþ Ks ðf(cid:4)Þ1=2
(cid:6)CO23(cid:3)(cid:7)¼KcK1K2ðffð(cid:4)CÞOðH2ÞþaÞw2ðm(cid:4)Þ3; (31) (cid:5)awð1þxÞ=2(cid:6)M2þ(cid:7)1=2ðm(cid:4)Þ1=2
1 rffiKffiffiffiffiKffiffiffiffiffiKffiffiffiffiffif1=2ðCO Það1(cid:3)xÞ=2
K a ¼ s c 1 2 w ðm(cid:4)Þ3=2
ðOH(cid:3)Þ¼ ðHwþwÞðm(cid:4)Þ2; (32) cHCO(cid:3)3 K2 ðf(cid:4)Þ1=2(cid:6)M2þ(cid:7)1=2
a (cid:6)M2þ(cid:7) 2Ks ðm(cid:4)Þ2
ðMOHþÞ¼KMOHþKw wðHþÞ ðm(cid:4)Þ; (33) þcCO2(cid:3)axw(cid:6)M2þ(cid:7)
3
(cid:6)MCO0(cid:7)¼K K K K fðCO2Þaw(cid:6)M2þ(cid:7)ðm(cid:4)Þ2; (34) þ Kw rffiffiffiffiffiffiKffiffiffisffiffiffiffiffiffiffi ðf(cid:4)Þaðw1(cid:3)xÞ=2 ðm(cid:4)Þ3=2: (42)
3 MCO03 c 1 2 ðf(cid:4)ÞðHþÞ2 cOH(cid:3) KcK1K2f1=2ðCO2Þ(cid:6)M2þ(cid:7)1=2
(cid:6)MHCOþ(cid:7)¼K K K fðCO2Þaw(cid:6)M2þ(cid:7)ðm(cid:4)Þ: (35) This is a fourth-order polynomial in (M2þ)1=2. After rear-
3 MHCOþ3 c 1 ðf(cid:4)ÞðHþÞ rangement,oneobtains
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IUPAC-NISTSOLUBILITYDATASERIES.95-1 013105-9
0KMOHKwrffiffiffiffiffiffiKffiffiffisffiffiffiffiffiffiffiðf(cid:4)Þ1=2aðw1(cid:3)xÞ=2þKMHCOþ3 rffiKffiffiffisffiKffiffifficffiffiKffiffiffi1ffiffif1=2ðCO2Það1(cid:3)xÞ=21
(cid:6)M2þ(cid:7)2 2 (cid:6)M2þ(cid:7)3=2BB cMOHþ KcK1K2 f1=2ðCO2Þ cMHCOþ K2 ðf(cid:4)Þ1=2 w CC
þ B 3 C
ðm(cid:4)Þ2 cM2þ ðm(cid:4)Þ3=2 B@þ 1 rffiKffiffifficffiKffiffiffiffi1ffiffiKffiffiffi2ffiffif1=2ðCO2Það1þxÞ=2 CA
cHþ Ks ðf(cid:4)Þ1=2 w
: (43)
(cid:6)M2þ(cid:7)1=2 1 rffiKffiffiffiffiKffiffiffiffiffiKffiffiffiffiffif1=2ðCO Þ K rffiffiffiffiffiffiKffiffiffiffiffiffiffiffiffiffiðf(cid:4)Þ1=2að1(cid:3)xÞ=2!
(cid:3) s c 1 2 að1(cid:3)xÞ=2þ w s w
ðm(cid:4)Þ1=2 cHCO(cid:3) K2 ðf(cid:4)Þ1=2 w cOH(cid:3) KcK1K2 f1=2ðCO2Þ
3
2K 1
(cid:3) s ¼0
c ax
CO2(cid:3) w
3
This equation has one positive real root, (M2þ)1=2(m(cid:4))(cid:3)1=2, low, equilibration can take weeks or months. Also, due to
which can be obtained by iteration. The solubility of the thelowsolubilityofmostMCO þH Osystems,recrystalli-
3 2
metalcarbonate,s,canbecalculatedas zation is extremely slow, which increases the risk of crystal
size effects. For these reasons, the evaluation of the open
s¼½M2þ(cid:6)þ½MOHþ(cid:6)þ½MHCOþ(cid:6)þ½MCO0(cid:6): (44) systemwasconductedfirst,andclosedsystemmeasurements
3 3
were evaluated by comparison with model predictions using
Substitutionoftheappropriateequationsleadsto K valuesobtainedintheopensystemevaluation.
s
Again the charge balance was used as a starting point
(cid:6)M2þ(cid:7) K K rffiffiffiffiffiffiKffiffiffiffiffiffiffiffiffiffiað1(cid:3)xÞ=2(cid:6)M2þ(cid:7)1=2 (Eq. (28)). This time a second balance is needed, as the
s¼ þ MOH w s w amountofalkalineearthmetalinthesolutionmustequalthe
c c K K K f1=2ðCO Þ
M2þ MOHþ c 1 2 2 amountoftotalcarbonate,
(cid:5)ðf(cid:4)Þ1=2ðm(cid:4)Þ1=2
þKMHCOþ3 rffiKffiffiffisffiKffiffifficffiffiKffiffiffi1ffiffif1=2ðCO2Það1(cid:3)xÞ=2(cid:6)M2þ(cid:7)1=2ðm(cid:4)Þ1=2 ½M2þ(cid:6)þ½MOHþ(cid:6)þ½MHCOþ3(cid:6)þ½MCO03(cid:6)
cMHCOþ3 K2 ðf(cid:4)Þ1=2 w ¼½CO2ðaqÞ(cid:6)þ½HCO(cid:3)3(cid:6)þ½CO23(cid:3)(cid:6)
þKMCO03Ksðm(cid:4)Þ: (45) þ½MHCOþ3(cid:6)þ½MCO03(cid:6): (46)
ax
w
Twospecies contain bothametalatomandacarbonatespe-
Equations(43)and(45)calculatethesolubilityofanalkaline
cies,andcanbeleftoutofthebalance.Theequationiswrit-
earthcarbonate for agiven setof equilibrium constants(and
tenintermsofactivities,
hence the temperature), including K, and the fugacity of
s
CO2. In practice, our intention was to derive a value of Ks (cid:6)M2þ(cid:7) ðMOHþÞ ðCO ðaqÞÞ (cid:6)HCO(cid:3)(cid:7) (cid:6)CO2(cid:3)(cid:7)
for each solubility measurement. For that purpose, the value þ ¼ 2 þ 3 þ 3 :
c c c c c
of s was determined for different values of Ks, and Ks was M2þ MOHþ CO2 HCO(cid:3)3 CO23(cid:3)
determinedfromsbyiteration.Withineachiteration,theac- (47)
tivity coefficients and the water activity need to be known.
They were calculated with the Pitzer formalism, but for that AlltheactivitiesinEqs.(28)and(47)arewrittenintermsof
theconcentrationofallthespeciesneedtobeknown.Hence, the M2þ activity and the Hþ activity, in order to obtain two
an iteration within the iteration was needed where Eq. (43) equationswithtwounknowns,
was solved with provisional values of the activity coeffi-
cients, and the resulting concentrations were entered in the (cid:6)HCO(cid:3)(cid:7)¼ Ks ðHþÞ ðm(cid:4)Þ; (48)
Pitzer equations to obtain activity coefficients for the next 3 K ax(cid:6)M2þ(cid:7)
2 w
iteration,untilconvergencewasreached.
1.3.2.2. Model equations for closed system. By (cid:6)CO23(cid:3)(cid:7)¼Ksax(cid:6)M12þ(cid:7)ðm(cid:4)Þ2; (49)
closedsystem,wemeantheMCO þH Osystemcontaining w
3 2
a solid MCO phase and an aqueous phase. Experimentally
3 K a
this system is much more challenging than the open system ðOH(cid:3)Þ¼ w wðm(cid:4)Þ2; (50)
ðHþÞ
because contamination of CO from the surroundings can
2
influencethesolubilitymarkedly.Somestudiesattemptedto a (cid:6)M2þ(cid:7)
minimize this effect by stripping the solution with a CO2- ðMOHþÞ¼KMOHþKw wðHþÞ ðm(cid:4)Þ; (51)
free gas after addition of MCO . However, this leads to a
3
system that cannot be described as MCO3þH2O. Such sys- K ðHþÞ2
temswereevaluatedwithgreatcaution,orrejected.Because ðCO ðaqÞÞ¼ s ; (52)
2 K K a1þx(cid:6)M2þ(cid:7)
thedissolution rateoftheMCO3þH2Osystemisextremely 1 2 w
J.Phys.Chem.Ref.Data,Vol.41,No.1,2012
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013105-10 DEVISSCHERETAL.
(cid:6)MCO0(cid:7)¼K K 1 ðm(cid:4)Þ; (53) with
3 MCO03 saxw (cid:3) pffiIffi 2 (cid:9) pffiffi(cid:10)(cid:4) XX
(cid:6)MHCOþ(cid:7)¼KMHCOþ3KsðHþÞ: (54) F¼(cid:3)A/ 1þbpffiIffiþbln 1þb I þ mcmaB0ca
3 K ax c a
2 w X X X X
þ m m /0 þ m m /0 : (59)
c>c0 c c0 cc0 a>a0 a a0 aa0
SubstitutionoftheaboveequationsintoEq.(47),andsolving
forthemetalionactivity,leadsto
Intheaboveequations,thesubscriptsaandcrefertoanions
vuuuffiffiffiffiffiffiKffiffiffisffiffiðffiHffiffiffiffiþffiffiffiÞffi2ffiffiffiffiffiffiffiffiffiþffiffiffiffiKffiffiffiffisffiðffiffiHffiffiffiþffiffiffiÞffiffiðffiffimffiffiffi(cid:4)ffiffiÞffiffiffiþffiffiffiffiffiKffiffiffisffiffiðffiffimffiffiffi(cid:4)ffiffiÞffiffi2ffiffi aanndd cZat(i¼onPs,aremspazeactþivPelyc;mzcizics)tihseachmaergaseunreumofbetrheofchioanrgie,
(cid:6)M2þ(cid:7)¼uuuK1K2cCO21aw1þx K K2cHKCO(cid:3)3aaxw cCO23(cid:3)axw: (55) bminoalarlyitiyo.nBiinjtaenrdacCtiiojnarpeasrianmgleet-eerlefocrtrioolnystewpiathraamcehtearrsg,e/oijfitshea
t þ MOHþ w wðm(cid:4)Þ samesign,w isaternaryioninteractionparameter,andk
c c ðHþÞ ijk ni
M2þ MOHþ isanion-neutralspeciesinteractionparameter.
Substitution of the same equations in the charge balance Bij and B0ij are functions of ionic strength and depend on
Eq.(28)leadsto two input parameters, bðij0Þ and bðij1Þ. Parameters Cij are writ-
ten in terms of input parameters C/. The parameters / are
2(cid:6)M2þ(cid:7) K K a (cid:6)M2þ(cid:7) written in terms of input parameteirjs h . Details, as weiljl as
þ MOHþ w w ðm(cid:4)Þ ij
c c ðHþÞ comprehensive tables of ion interaction parameters, are
M2þ MOHþ givenbyPitzer.23Anabridgedversionofthemodeldescrip-
þKMHCOþ3KsðHþÞþðHþÞ tion is given in Pitzer.24 The Pitzer parameters used in this
c K ax c
MHCOþ 2 w Hþ volumearegivenbelow(Secs.1.3.3.6and1.3.3.7).
3
¼ KsðHþÞ ðm(cid:4)Þþ 2Ks ðm(cid:4)Þ2 Intheequations,A/istheDebye-Hu¨ckelparameter,andb
K2cHCO(cid:3)3axw(cid:6)M2þ(cid:7) cCO23(cid:3)axw(cid:6)M2þ(cid:7) gisivaencobnystBanrta,dtlaekyeanntdoPbietze1r.,22.5ManedthboydsAtrochcearlcaunladteWAa/nga.r2e6
K a
þ w w ðm(cid:4)Þ2: (56) Thelatterschemewasusedhere.Thedifferencebetweenthe
c ðHþÞ
OH(cid:3) two schemes is negligible for the conditions considered in
thisreview.
BysubstitutingEq.(55)intoEq.(56),anequationin(Hþ)is
obtained, which can be solved iteratively. Once (Hþ) is
known,(M2þ)canbecalculated,aswellastheconcentration 1.3.2.4. Some thoughts on the calcium bicarbonate
ion pair. The existence of the calcium bicarbonate
ofallthespecies.Again,anadditionaliterationisrequiredto
(CaHCOþ)ionpair(andotheralkalineearthbicarbonateion
calculate the activitycoefficientsandthe water activity. The 3
pairs) has been subject to controversy for several decades.
solubility predicted with the model is compared with meas-
Asdiscussedbelow(Sec.1.3.3.6),moststudiesconductedat
uredvaluesforevaluation.
low ionic strength point at the existence of these ion pairs
(e.g.,PlummerandBusenberg27),whereasstudiesconducted
1.3.2.3. The Pitzer ion interaction formalism. Ac-
cording to the Pitzer framework,19–22 the activity coefficient at higher ionic strength do not point at any ion pairing (e.g.,
Pitzeretal.,28HeandMorse29).DeVisscherandVanderdee-
ofacationMandananionXcanbedescribedasfollows:
len30showedthatsomecalciumcarbonatesolubilitydataare
lnc ¼z2FþXm ð2B þZC Þ consistent with the existence of the calcium bicarbonate ion
X X c cX cX pair,whereasothersolubilitydataareinconsistentwithsuch
c
! anionpair.Theirassumptionisthatcrystaldefects(e.g.,sur-
X X
þ m 2/ þ m w face charge) could explain why some solubility data are
a Xa c cXa
a c seemingly inconsistent with the existence of the calcium bi-
X X carbonateionpair.
þ m m w
c>c0 c c0 cc0X Whatmayresolvetheinconsistencyinthedataistoassume
XX X
þjzXj mcmaCcaþ2 mnknX; (57) that the ion pair exists, but is so weak that it disintegrates at
c a n elevated ionic strength. This could be described mathemati-
X callybymeansofspecificioninteractioncoefficientsbetween
lnc ¼z2Fþ m ð2B þZC Þ
M M a Ma Ma CaHCOþ and the dominant counter ion (e.g., Cl(cid:3)). Harvie
a ! etal.31f3ollowedthisapproachforMgOHþ.Giventhe specu-
X X lativenatureofthisapproach,itwasnotadoptedhere,butthe
þ m 2/ þ m w
c Mc a Mca MHCOþ ion pair was included in the above thermodynamic
c a 3
X X models as an optional species in this volume with a stability
þ m m w
a>a0 a a0 Maa0 constant, as opposed to using Pitzer parameters for the
XX X
þz m m C þ2 m k ; (58) M2þ(cid:3)HCO(cid:3) interaction. The model variant with a MHCOþ
M c a ca n nM 3 3
c a n ion pair (no M(HCO ) Pitzer parameters) will be denoted
3 2
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