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Canadion MineralogistY ol. 29, pp. 909-942 (1991)

UNIFIED DESCRIPTION OF INCONGRUENT REACTIONS AND MINERAL SOLUBILITIESAS A FUNCTION OF BULK COMPOSITION AND SOLUTION pH

IN HYDROTHERMAL SYSTEMS

VITALII A. POKROVSKII ANI HAROLD C. HELGESONDepartment of Geology and Geophysics, University of Cali/ornia, Berkeley, California 94720' U.S.A.

ABSTRACT

Depiction of mineral solubilities on isobaric isothermalbulk composition - pH diagrams facilitates considerablythe conelation of the consequences of irreversiblereactions with the solubilities of incongruent reactionproducts. The reaction-progress variable (f) is related tothe bulk composition variable (r1", which has units of moles(kg HzO)-r) by the stoichiometries of the irreversiblereactions and the relative rates of reaction of the reactantminerals. To illustrate the advantages of using diagramsof this kind to describe simultaneously mineralsolubilities, phase relations, and mass transfer resultingfrom reaction of minerals with hydrothermal fluids inboth open and closed systems, equilibrium solubilities ofstable minerals in the system K2O-Na2O-AI2O3-SiO2-H2O were computed as a function of pH in NaCl-HCl-NaOH-H2O solutions in which r1?Nacl = 0.01 or 1.0 atvarious pressures and temperatures of geological interest.These solubilities were then plotted together withrepresentative reaction paths on ,?AI2Si2O5(OH)4 - pH'

4KAIlsi?orn(OH)? - PH, 4retsiron - PH' and 45*tt ' ,ot -pH dialgrdms. Considerationbf these diagrams indicatesthat kaolinite, muscovite, and K-feldspar dissolve con-gruently only over relatively narrow langes of solutionpH. Above and below the pH limits of these ranges, therninerals dissolve incongruently to form quartz, diaspore,or aluminosilicates. Albite dissolves incongruently overthe entire range of solution pH from zero to 12. Changesin solution composition and the identities and number ofmoles of minerals that precipitate and dissolve alongincongruent reaction paths can be assessed directly frombulk composition - pH diagrams, which can also be usedto interpret phase relations in terms of mineral solubilitiesover wide ranges of pressure, temperature, and fluidcomposition.

Keywords: mineral solubility, incongruent reaction, bulkcomposition, pH, kaolinite, muscovite, K-feldspar,albite.

SoruvernE

Une repr6sentation de la solubilitd des min6raux aumoyen de diagrammes de composition versas pH, conquspour pression et temperature constantes, facilite consid6-rablement la corr6lation des cons6quences des r6actionsirr6versibles avec la solubilit6 des produits des r6actions

incongruentes. La variable I qui marque le progrds d'uner6action est li6e ir la variable ?c, Qui repr6sente lacomposition globale par la stoechiom6trie des r6actionsirr6versibles et par le taux relatif d'une r6actionimpliquant les phases mindrales r6actives. Afin d'illustrerles avantages de tels diagrammes pour d6crire simultan6-ment les solubilit6s de phases mindrales, les relations dephases, et le transfert de matibre r6sultant de la r6actionde min6raux avec une phase fluide hydrothermale dansun systbme ouvert ou ferm6, la solubilit6 des min6rauxstables e l'6quilibre dans le systbme K2o-Na2O-Al2O3-SiO2-H2O a 6t6 calcul6e en fonction du pH d'une solutioncontenant NaCI-HCI-NaOH-H2O dans laquelle mpu61 estsoit 0.01 ou 1.0, et ce, i plusieurs valeurs de pression etde temp€rature d'int6r0t g6ologique. Ces solubilit€s sontensuite present6es graphiquement avec des trajectoires der6action typiques en termes de ?etzsizos(osp - FH'4KAt3si3ol0(oH)2 - pH, 4rulsirot - pH, et.lvuo15i3os - pH'A la lirmibre'?le ces diagrammes, kaolinite, muscoviteet feldspath potassique entrent en solution de fagoncongruente seulement sur un intervalle restreint de pH dela solution. A un pH plus 61ev6 ou plus faible, cesmin6raux entrent en solution de fagon incongruente pourformer quartz, diaspore ou les aluminosilicates. Parcontre, I'albite se dissout de fagon incongruente pour toutpH compris entre 0 et 12. Il est ensuite possible d'dvaluerles changements dans la composition d'une solution etdans I'identit6 et le nombre de moles de min6raux quipr€cipitent ou se dissolvent le long de la trajectoire d'uner6action incongruente d'aprbs ces diagrammes de compo-sition globale en fonction de pH. Ils servent aussi irinterpr6ter les relations de phase en fonction de solubilit6sdes phases min6rales sur un grand intervalle de pression,temp6rature, et composition de la phase fluide.

(Traduit par la Rddaction)

Mots-cl6s: solubilit6 de phases min6rales, r6action incon-gruente, composition globale, pH, kaolinite' mus-covite, feldspath potassique, albite.

INTRODUCTION

Prediction of the equilibrium solubilities ofrock-forming minerals in aqueous electrolyte solu-tions involved in geochemical processes provides aframe of reference for interpreting the composi-

909

910 THE CANADIAN MINERALOGIST

tions of these fluids and the extent to which theyreact with their mineralogical environment. Manygeochemical processes take place at constanttemperature and pressure. Under these conditions,the solubilities of minerals are controlled primarilyby the solution pH. The pH of natural aqueoussolutions ranges from < I in mine waters and areasof recent volcanic and geothermal activity to 12 insolutions involved in the weathering of ultramaficigneous rocks (Ellis & Mahon 7964, Ivanov 1975,Barnes & O'Neil 1969, Barnes 1985, Varekamp &Kreulen 1990, Nordstrom et al. 1991, and others).Comprehensive calculation of the extent to whichmineral solubilities depend on pH is fundamentalto our understanding of phase relations inhydrothermal systems. These solubilities can beportrayed on bulk composition - pH diagrams(Helgeson 1970b, Sokolova & Khodakovskiy 1927,Pokrovskii & Ivanov 1982, Nesbitt 1984, Pok-rovskii 1989), which can then be used to assess theconsequences of the chemical interaction ofhydrothermal fluids with minerals in geochemicalprocesses. The purpose of the present communica-tion is to (l) formalize the relation between mineralsolubilities and reaction paths on such diagrams,and (2) demonstrate with the aid of phase relationsin the system K2O-AI2O3-SiO2-HCI-NaCI-NaOH-H2O how they can be used to advantage in assessingmineral solubilities and predicting changes in fluidcomposition and the identities and relative amounrsof products of incongruent reaction formed anddestroyed during reaction of hydrothermal fluidswith their mineralogical environment.

REecrroN Pnocnnss AND MTNERAL SoLUBrLrry

To illustrate the relation of the conceot ofreaction progress to the solubilities of incongruentreaction products, let us consider a hypotheticalsystem consisting of three thermodynamic com-ponents designated by A-B-HrO, in which thecomponents A and B form crystalline phases withthe compositions A, B, and AB. Phase relations inthis system are depicted schematically in Figure l.Diagrams of the kind shown in this figure havebeen used extensively to describe phase relationsamong minerals and aqueous solutions (Ricci 1951,Petersen 1965, Garrels & Mackenzie 1971, Nesbitt1978, Pokrovskii & Sorokin 1983, and others) eversince Roozeboom (1894) and later Van't Hoff(1905, 1909) and Jtinecke (1906) pioneered theirapplication to the study of phase relations in saltdeposits.

The irreversible dissolution of AB(c) in water canbe described in terms of

AABBFtc. l. Schematic phase diagram for the idealized

hyporhetical system A-B-H2O at constant pressureand temperature (see text).

where the subscripts (c) and (a4) denote crystallineand aqueous states, respectively. Reaction (1)results initially in a change in solution compositionfrom the H2O apex in Figure I toward point a.This process can be described in terms of thereaction-progress variable (De Donder 1922, DeDonder & Van Rysselberghe 1936, Helgeson 1968,1970a, 1979) for reaction (l) by writing

ian1"1,0) =ry

and

, - nNG) {r)

-&t"t

Yl) - -;- (3)

zaa1"y,(D

where r4s,.,.11, stands for the number of moles ofAB,", in the system after a given extent of reactionprogress represented by the progress variable {1,,rf,s,., refers to the number of moles of AB,., inthe system at {trt : 0, and fnsrcr,(r) denotes thestoichiometric coefficient of AB(c)'in reaction (l),which is equal to -1. As f11, increases, thecomposition of the aqueous solution approachessaturation, with A,", at point a in Figure l. If thedissolution of AB1", is the rate-limiting step in theprocess, further increase of {,u along reaction path

(2)

ABt " ) * A (oq ) tB (oq \ ( l )

INCONGRUENT REACTIONS AND MINERAL SOLUBILITIES 9 l l

a, is accompanied by formation of A,"., in accordwith

A1a4y - A1c; @)

as {11., continues to increase and the composition ofthe solution changes along ac. At f,1y correspondingto point b, the composition of the solution reachesc, where it becomes saturated with AB1"1 and overallequilibrium is achieved among A1"y, AB1"y, and theaqueous phase. However, in order for reaction (l)to achieve equilibrium, the bulk composition of thesystem must lie on the line connecting b and ABin Figure 1. For example, if instead the bulkcomposition coincides with a point on the lineconnecting a and b in Figure 1, all of the AB1", inthe system would have been consumed by thereaction, and the system would then consist simplyof A,", coexisting with the aqueous phase, whichwould have a composition at the right of point aand to the left of point c along the curve cc.

The relation between {,1, and the bulk compos!tion of the system depicted in Figure I can beexpressed in terms of the number of moles in thesystem of the compositional variable correspondingin stoichiometry to the mineral represented by AB,",that have reacted (kg HzO)-t (4ou), which can beexpressed as

_ nag - IlAB,"r,r,i i en= *

- ( 5 )wHro

where nas denotes the number of moles of AB inthe system, and Wrro designates the number ofkilograms of H2O in the aqueous phase, which isgiven by

wHzO = nnzoM, (6)

where 1916 stands for the number of moles of H2Oin the aqueous solution, and Mn, refers to themolecular weight of H2O in kilograms. CombiningEqns. (3) and (5) leads to

t'hs =uas - riBt"r - iABt"r,(t) Eo)

(7\wttro

which couples reaction progress and bulk composi-tion. For example, if the system depicted in FigureI is closed with respect to component AB (whichis true for the reaction process described above),rnu in Eqn. (7) is equal to nf,s,",. Under thesecircumstances, Eqn. (7) reduces to

where

I?iBr"1 -uAt1"1,{t)r l A E - - -

wHzo

In contrast, if the system is open to component ABand no, * niy1"y it .follows from Eqn. (7) that,los may contini; to increase after equilibrium isreached if the bulk composition changes along bABtoward AB in Figure 1. Furthermore, in the absenceof irreversible chemical reactions, u AB(c),(r) : ripr"r: fiots, where nls stands for the number of molesof AB in the system before any AB is added to' orremoved from, the system. Under these circumstan-ces, both Eqns. (5) and (7) can be written as

TIAB=+#

and for noes = 0,

TIAB = #LwHro

(10)

( l l )

Equation (11) can be used to construct diagramsof mineral solubility in which one of the descriptivevariables is 46s by specifying a series of bulkcompositions and minimizing the Gibbs free energyof the system for each one. In this way, mineralsolubilities can be expressed in terms of 4as, whichcan also be used to describe the consequences ofirreversible reactions among minerals and theaqueous phase in the system.

Equation (7) can be generalized for any open orclosed system by writing

n-=n" -n i - f i "Ee)* Wtro

where 4" stands for the number of moles in thesystem of the compositional variable correspondingin stoichiometry to the mineral or mineral as-semblage represented by the subscript c that havereacted or been added to, or removed from, thesystem (kg H2O)-1, r" refers to the number of molesof the subscripted compositional variable in thesystem, ri denotes the number of moles of c in thesystem before any reactions have taken place orany c has been added to or removed from thesystem, t designates the overall progress variablefor the reaction process (Helgeson 1970a, 1979),and rt, represents the overall stoichiometricreaction-coefficient defined by

(r2)

, WH,oTIABq l )=_- " ,a

(8)

9t2 THE CANADIAN MINERALOGIST

(13) andi "=I0

Io,q,"r

n,," = Z Zoq,,Qr

where n$,, and n6,, denote the number of moles ofthe @th reactant mineral in the system prior to therth reaction and the corresponding number ofmoles at any subsequent stage of reaction progress,respectively. It follows from these definitions thatf" in Eqn. (13) can also be expressed as

The bulk composition of a system of icomponentscan be expressed in terms of the mole fractions ofthe components, which are given by

v - n iA i = - Q l )n

where a; and X; stand for the number of moles andmole fraction of the rth thermodynamic component(i : 1,2,...,f) in the system, and

where ie;., refers to the number of moles of the rthcomponent in the @th reactant mineral, and r,.,represents the number of moles of the rthcomponent in the aqueous solution.

Although i... in Eqn. (13) is a constant equal to-1, ft, is constant only if o, is independent ofreaction progress for all values of r. Under thesecircumstances, fi" car be set to -1, and Eqn. (13)reduces to

t-!

LC, = ' (rt)r

If in addition the rates of all the irreversibledissolution reactions are equivalent,

o r=X i , "=XQ, ,

where

( te)where ft*., refers to the stoichiometric reaction-coefficient of the dth reactant mineral (d =1,2,..., 6) in the nh independent reaction (r =1,2,..., f) representing irreversible dissolution of onemole of the subscripted mineral, and o" denotes therelative rate of reaction given by (Helgeson 1987)

*=k=ffi=ffi (,4)where {, stands for the progress variable for therth reaction, and / refers to time. It follows fromthese definitions rhat dt / dt =

Fdt, / dt, 1$ : V,fi0,, = -1, and ft" = -2.

In many instances, dt,/dt in Eqn. (14) can beexpressed as a function of the activitv of thehydrogen ion. For example, ifthe subscriit r refers10 the hydrolysis ofK-feldspar in acid solutions farfrom equilibrium, d{,/dt is given by (Helgeson e/al. 19841

*=k.rarr 6

where k stands for the rate constant. s refers to theeffective surface area of the reactant feldspar, andaH* denotes the activity of the hydrogen ion.

If the general system considered above is closedto the compositional variable represented by thesubscript c, it follows tha't- nc : n? , a\d Eqn. (12)reduces to

6 = -wHaolLnc

where

1 1 - = d , " - t b , = - f i r E , , - \4' w"ro wHro

(r/''

where z!," and nr.r. represent the total number ofmoles in the system of the reactant mineral ormineral assemblage represented by the subscript cat f = 0 and {, respectively, which are given by

I,'i,"r

^ d n'"=fi

' = ?[*". ?'**J

" i"=*

(20)

(15)

(22)

(16)

0

(24)

d," ( t 8 ) (2s)

INCONCRUENT REACTIONS AND MINERAL SOLUBILITIES 9t3

and

*qn =Y

Although 4" is discussed above in the context ofchemical reactions among minerals and an aqueousphase in systems closed to the compositionalvariable represented by the subscript c, it can alsobe used in the absence of irreversible reactions todescribe the consequences of varying the bulkcompositions of open systems. For example, in theabsence of irreversible reactions, Eqn. (12) reducesto

interpreting the record of reaclion paths preservedin metamorphic rocks and planning experimentalinvestigations of metamorphic phase-relations inthe laboratory. A number of diagrams of this kindare described below.

IsoTHERMAL-IsoBARIc tt" - pH DIAGRAMSFOR THE SYSTEM

K2O-Al2O3-SiO2-HCl-NaCl-NaO H-I{2O

Depending on the composition and pH of theaqueous phase, various charged and neutralaqueous species may contribute significantly to thesolubilities of minerals in hydrothermal solutions.Of these, calculations based on thermodynamicanalysis of experimental solubility data taken fromsources cited in Table I indicate that the speciesshown in Table 2 predominate in aqueouselectrolyte solutions coexisting with minerals in thesystem K2O-Na2O-AI2O3-SiO2-H2O at pressuresand temperatures corresponding to those along thevapor-liquid equilibrium curve for the system H2O.Thermodynamic calculations also indicate that theaqueous species listed in Table 2 account for thebulk of the solute in these solutions over the entirepH range from I to 12. The calculations werecarried out using the revised HKF (Helgeson et al.1981) equations of state (Tanger & Helgeson 1988,Shock & Helgeson 1988, 1990, Shock e/ ql, 1989,1992), together with the Hiickel (1925) andSetch6now (1892) equations for the activity coeffi-cients of aqueous species (Helgeson et al. 1981).Polynuclear complexes of aluminum and siliconform to appreciable degrees only in solutions thatare highly supersaturated with respect to stableminerals, and the degrees of formation ofmononuclear species such as H2SiO?- and HSiOI-become appreciable only at values of solution pHgreater than 12 at the pressures and temperaturesconsidered in the present study (Baes & Mesmer1976, Busey & Mesmer 1977). Accordingly, onlythe species shown in Table2 were considered in thesolubility calculations described below. Thedielectric constant, density, and thermodynamicproperties of H2O used in the calculations weregenerated using equations and parameters takenfrom Johnson & Norton (1991). The apparentstandard partial molal Gibbs free energies offormation of the aqueous species shown in Table2 were calculated as a function of temperature andpressure with the aid of the revised HKF (Helgesonet al. 1981) equations of state (Tanger & Helgeson1988, Shock & Helgeson 1988, Shock et al. 1989,1992), summarized in Appendix A, using equationsof state parameters and standard partial molalproperties at25"C and I bar taken from Tanger &Helgeson (1988), Shock & Helgeson (1988), Shock

(26)

r=ffi;L (27)

and for n? : 0,

llct I - - -* WHro (28)

If phase relations are depicted for any system ondiagrams in terms of 4" and any other descriptivevariable of interest, the diagrams can be usedtogether with Eqn. (17) to describe the consequen-ces of chemical reactions among minerals andaqueous solutions in either open or closed systemsin terms of the solubilities of products of theincongruent reactions (see below). Expressing thesesolubilities as functions of q" makes it possible tocalculate the total molalities of the elements in theaqueous phase that correspond to those in thereactants from the stoichiometry of the composi-tional variable represented by c, which maycorrespond to that of a single mineral or anassemblage of minerals. In addition, it followsfrom Eqn. (16) that the number of moles of anygiven reaction product precipitated or dissolvedalong the reaction path can be computed from thedifference between 4" and the value of 4" cor-responding to the first appearance of the reactionproduct along the patb. Hence, the destiptivevariable qc serves a multiple purpose. It simul-toneously represents I) the equilibrium solubilitiesof minerals in units consistent with the molalityscale of concentrotion, and 2) the consequences ofthe irreversible reaction of a minerol or minerolassembloge with the aqueous phase in terms ofmineral solubilities and the overoll progress vuri-able for the process (kg HtOfI .

Combining the descriptive variable 4" withsolution pH results in isothermal-isobaric 4" - pHdiagrams that can be used to advantage in both


TABLE 1. ST'I{MARY OF P(PR,IMENTAL SruDIES OF THE EQI'IIIBRIUM SOLUBILMES GSTABLBMINBRAIS REFORIEDINTIIELIIERATUREFORTIIESYSIEMKzGn{q2GAl2O3=Stqi{I2O

Mnmlolvfinsal Tempmrre,PlxmAss@blage

Initislsolnion Referloc€

ardtzAEtzAtatz

astzau0tz

alatzauatzAlatz

arEEAlatz

arstz

audtzatdEaoutzausrz

alau

aEaqlrtz

250-350PgPsAT Hp+NaOH250-450Pg0.(}H.8kbsr H2O+NaOHt6G.373'C,Psar lW256-6100q 0. 15-1.75 khr

llrle &Rtedman 19218&ledran 1949Itennedy 1950

lhdey & Hesslg6r€r l95laIt{sey & Hessoleesser 1951b

Ittocy & I{esselgesser 1952Federiclam&Cox 1954WyEt&Sabatier 1954

W)'ct& Sabalia1955aw!'st & Sabali€r 1955b

Khitcqv 1956

Khitarw 1957l[dey l9tr au,li.e 1959V&Lb6al.lW

Kitobrn t9fr

Kitahra 1960bKitahgra l9d)c

Iaulise & Ballman 1961Fyft & I\{cKay l1b2Mg3y etaI.1962

Siev6 1962\rdl&Fyfe 1%4Yendlandt & Glemser 1964

Andersm & Butrbrm 1!X5L.arcd 1964Lcg'fdad.L96lAndeno&Buntrm 1967

Smfeld196/

OsopoloeraL 1969

Seomva&Tsiklis 190MacK€ozi. & G€€s l9llAtrr&Anderson 191Oseapeneo&Arryoa l91aSh€el lt3Sh€@l1Yt4Ssssd 194

Nwgmdov 1975Nwgcodo 197

ltffiIgy et al.lg8,)

Fqmierat4L 1982Ragnrsd6cir & Walher 1983Wallhfr & Orville 1983

Sitritsyn & Ivrnd t9E4Rimsidr 1984Pascal 1984Sinitsyn 1986Schwurtzeambs et ar. 19&7Redtin & Chevychelovo 1988Pascal & Anderson 1989Samia&Sey&ied 1990

reQ0.2-2kbsr3u)-5flrc'0.64-1.034 kbar40[pC, O.U-2sttuZX)-355'C,0.3 kbonzl{noC' 0.ul8kbd;4l0C' 0185kh;47fC' 0.38tbarz|qfc' 05-2kbd;5moC' 0.5 kbor

4trq 1.47-3.92kb@

2m-60fc' 0.1{.9 kbtr50'g lkbd3@-4trq 0.7-2.1kh60-lffiC,Psar

1rl0-37trGPsl.r,;3E0-5q),q 0.4q.91 kbsr1&-4zfc' 0.flX-O.4kbor4fl).C'0372 llor

3G.4009C'0.7-3.3kbar33fC,Pser2t24{FQPs,lrl45-3mog lLbo12$-1815'C, Pslr4n-55(rc' l-4kboi4{r}-5qrg0.m}{J2 kbarsm-qxfc' 1-10kbsr1m-25(PC' 0.1-l.8kbar;

6{XHfl).g3-4lbg

4q)-sfffC' I LbG

260Pq 0.06 kbs

6qH'mg0.7-3kbot2rg I b@125-329oGPser2850C' 0.45 kbtr7trq5kbm50-9trq2-5kbal3{1.35fC, Psnr

7moC'3-5Lb6?mC, l.5kbd

2fl)-350G Psl:i2m-50q 1-2kbo350oC, 0.18{.5 kbor25f90.25-1kh3g)-55fC' lrkbd:6mog2kh{n-6lEog 1-2 kbor4m_450eq 1kh5G96.C, Ps616moC'2kba3il)-475oc' 1 khr9GC' I btr30C' lkb@6m-7m"C'2kbc3q)-4trC,05kb6

H2O+N8OHH&Hp

HpH2O+ NaC1, H2O+NaOII,HzO+ KCIH2O, H2O + NaCLH2O+NaOHII'/oH2O,H2O+CqHp+N8OHH2O,H2O +Naq,H2O + NaOItH2O+Na2BaO7Hp

H2O+NaClH2O,H2O+HCl,H2O+NaOHH2O+NaOHHpHp

H2O,H2O+ KOHrl,orwrwH2O +NaOH, H2O +Na2S

H2O,H2O+Naq,HzO+ KO, H2O + Naoll,ll2O+KOHHp+Ar

H2O+NaotlH2O +Na2SrwHpH2O,H2O+NaOHHzO+HClH2O,H2O+CQI''o'WA+COzHP+Na2BaO;,H2O+ B(OI03 +KOHHP+CO2H2O,H2O +Naq,Hp+CQH2O,H2O + NaCt,H2O+KClH2O+NaClrt,oH',/OH2O+CO2H2O +ArH2O+ NooHrwH2O+KOHH2O+NaOHH2O+ NaOHH2O+NaCl +AlO3 +HClH2O+KOHH2O+NaCl +MgCl2

HpH2o

Al6E

algflz

qrEEAlarE

arfi

Al8EaErtzauEtz

aEtzaldaAIEE

algEArstz

alau

atrstza:utzalrua$uarEEamtzq$tz

AtrEat8tzAtalu

aEtzaumzaustanraAraizaudEausEamz

INCONGRUENT REACTIONS AND MINERAL SOLUBILITIES

TABLEl(@NTINUD)

915

It/rn€ml6lffffmlAss€mblagp

Temperarre,Pn$$re Inttialsoluim Refetlnae

ausuDiaspq€Diaspq€Diasporc,Diaspw +OmmdmDbspdBDdaryo€DianpqrDiafpo€Diaspdr

DaspdeOorundm

CcundrmConndmC.onmdum

CorundmCoundun

C.qundumCmdmCorunfuoCorundmConmdmCorundm

CrundumCsundunCuundumKaolinieI(adinirKsolinie,DichE,PyqhyllitcAndalusite,KyeiEKymiFKyantqAndaluibKaolinitePyrophyliE +IkoliniteKaolinitc +Dirspq€

ryrcphyUiE+DiaspqeAndrlusie +rynphyllirAndabsiE+DaryqrAndalusib +Cqundum

Krolidte+Atarq/tophylib+alal?Andalosi@+auEEKaolirirKyanibKroliDite +DaspdsKoolidlcKaolinite +Diaspqe

296'q I kb@Z[eCPsr250-3flFCPsar250-350CPs,lr

2YC' l bdr25G-325'CPslr25'q I b63trc'rlh2t-35fC,Psar

46oq 1kb6strC, l.O}4kbar

ECq lbo250-3moC' r kbd

H2O,H2O+HClH2O+NaOHH2O+NaOHH2O+NaOH

HpHp+NaOHH2O+HClH2O+NaCl+Aq3 +HClHzO +NaO,H2O +NaOItH2O +N8CX +NaOHH2O,H2o+HClHp

380-420o90.25-O.491$ar H2O,H2O+NaOH Yalffi€'dlmrm-450'q0.51-1.52kbar H2O+NgOH Yamguchtaalllr62zm-{trq 0.31-a8 kbar HzO +NaOII, H2O + KOH, Bsm€ra/. 1963

HzO+NsC],H2O+KCl,H20+HCl

150-29fc' 0.9E kbqr H2O +AlCl3 +HCl

3mrmfC'0.98kbd H2O+AlCl3+HCl

430-5(fc'0.98lbd H2O+AlCl3+HCl

2f,C' I ba H2O+HCIrm-sofq 13kh H2o+HCl3moc' lkbr HP+NaO+AlCl3+HCl

Redtin & Chsvychelwa l99lDruzhinina 1955B€mshEin & Matsemoe 1965Wsf€rs 1967

Reesman&Keller 1968Avagad.1979Peryes&Kimick 1988Redtin& @vphslova 1988Apps ar 4r. 1989

R€dIdtr & Ch€vychelova 1991Itds€y 1957

'.eifdo[ad.1965Ande(roaaL l9&7

Osapenko& Ar4oval9laBurnhamaaL l93Ganew & Rtmpntsev 194Bf'l<saal.l%3Rngnssddoh & Walther 1985Krzhinskiy 19e7

Bomgartofr&Eug@ 1988Fay€6& KiEickl9EEhscal€t4r. 1989Folz€r&I&m l%5KiEick 1966Reesoan& Kell€r196E

Brcm&Fyfe 191

O*qenlo& Arapwalg/laOslapen&o & Arapova l9lb

Huang & Kelkr f93IleolcyacL l9&)

It€tllbyeraL 1980

[email protected]

If€rol€yadr. 1980

llaleyad.19&

IlmbyaaL 1980

Rrdldn & Ivarcv 1980

R€dtin & Ivanov 1980

R€dtin & Ivanov 1980

Kitick 1980Orrapenkoaal. l9&/Redldn& Chwphelm1988

Nary&ksaga 1990Redtin & Chwychel,ova 1991

3?J-515'C' 0.34-1.% kbar H2O +NaaB4O/7qH(ryC'2-6.751&6 HzO,U2O+NoO.

H2O+K(], H2O +NaoH,

285'q 0.45 kbor5fl1-8moC, 6kbar350-500e9 0.2-1.% kbor670-7trC' 2.5- 6tbarrm-7mql-3kbor450.7trC, ljkbar

6{npci 2kb825"q I bd6trc'2kh25'q I bar2f,c' 1b@2trc' I bd

(n-550o9 l-3 kbd

285'C'0.45kbd4z)-strq l3kb6

25'C' 1 bsr2m-325o9 1-2kb6

ZI)-3(fc' 1-2kb6

3m-325'c' l-2kbd

340-45().C' l-2kba

350-390.c'll(ho

4{I}-5flfC' 1-2kbd

H2O+KOHH2O +HCtHpHprwHpH2O +HO,H2O + NaCLH2O+KC'1"IIzO +AICX:Hp+HClH2O+HClH2O +NaCl. H2O +KClHp+HClH2O+HClHp

H2o

H2O+HClwoHpH2o

rwrwHp

rwrw

H2O+HClH2O, H2o+Itcl

9t6 THE CANADIAN MINERALOGIST

TABLEl(COMINUD)

MneralqMftralA$sernblrye

Temp€ratuqft€s$r€ ldtidsohsim Refeoco

Kaolinite +audtztr(aolinite +Pyr{phyllitePyrqhyllite+Dia&qePyrc'phylliE+AdaluiEAndalusir +Diaspq€Andalurie +ConmdnmAdduib+a8rtzAl&K{eldspdK-feldryo,AlbK-feldspar,Al&MuscovieK{el&pr+M[scovite +arrtzMuscovite +KaoliniteMoscovic +Brcphylite+BchtrMEcovib+Andalusib+a|leAlh+Paragodb +aurtzPragmiE+h/FphyltE +

25fC' lkbd

250-280eq I kb@

2fi-375oq 1 kb6

336-{0299 I kbar

336-433"C' I kbtr

n2433"glletu

,r{I2'C' lrbr

5moC' 0.4-2 kbarsmoC' lrkbarlu)-35rc'0.m3{.34 kbar5(nc' lkbd

2m-{moq03Lb62m-50fC' 0.34-2.4 kbtr550-5E0eg 1 kbar

An-3trQ 0.14-2.4 kbor

3m-450oq m4-2.4kbar

4{IF580PC, I kb6

3m-strc' 1.(B1$e

350-5fl).C' 1.08 kbst

H2O,H2O+HCl

H2O,H2O+HO

H2o,H2O+HCl

H2O,H2O+HCl

H2O,It2O +HCl

H2O,H2O+HCl

H2O,H2O+HCl

HpHprwHp

HpH2O+KCl+HCl

H2O+KCl+HCl

H2o+KCl+HCl

H2o

Hpup

H2O+ KCI

HpH2O +KCl+HCl

H2O+Kq+Hq

H2O+KCl+HCl

Redlin & Chevychelova 1991

R€dtin & Chsvychelova 1991

R€dtin & Chwychelova 1991

Redtdn & Chw,'chelova 1991

R€dtin & Chcr''chelova 1991

Redtin & Gcvycbelova l9l

Redtin & Chwychelova 1991

Morcy & Ilesselgesser 1951aIt'lory & I{xselgesser 1951aMony&Gen 1955

lvld€y 1957

Khitalov 1957H@ley 195qHemley & Jms 1964;Motoya&Hemley lt5Heml€y 1959;Il€oby & Iones l96tIlelnl€y 1959

Itrdl€y l95qIlemlcy & Jm 1964;Mmoya& HEdley 19/5Elfrtst aal.l5liH€mlelr& Jqes 1964;Ir[6to]a& H@bylnsHnLcy a al.196l;II@ky& I@6 1964

Ildcy&Futrier196l

Fyfe & McKay 1962

Schfo@ 1962

Reesman & Keller 19i5

Adrms 1968Gnbl%8Reesman& Kelb1968Altnarrs & Johrnn€s 1969

Srr0bel ly'l

Dstisl9/2I{ung & Kcller 1912

Usdowski & Bsnes 192

Ituang& Kellcr 193Shade 1974

Shrdc 1y/4

Shadc 1974

Hp+N8Cl+HCl

H2O+NaCX +HCl

Hp

H2o

rw

Hp

rwrr,oHpIt2O+NaCl

K-feldspar, 295og0.l7kbqAlbie, NqhelireAlbq 33(rCPsarAlbiF+ QErzK-f€ldspar, 3d)-6dfC,0.2-2-5kbarKleldspq+Al8EMuscovie, 25oq lborK{eldspr,NephelfuAl& ruoq2kb@AI& /m-60fq 0.75-3.5 kbqrI\[nscwir 2fC. I bdAIbiE+ 450'q l LberMo@irs+arrdt4Albb+PEagooiE,Plirg@ite+$rophyllitcMuscwir l0-350PCPslr:l

4ff}-6(X)oC'0.3-3.1kbqrAltfu 5fr!-7trq2-{.4kbeK-felftpd, 2fC, lbqM|rwiEK-feldspa+ 30-3trCPsarMuscwie+AIEEAIhe 25"C' l barK-feldrpo+ l(n-7trQl-tkbdMuecqir+a'ratKleldspn+ 650-7trq1-tkbsrAndaluiE+asutzMusc@fte+ 6m-7mq ljkboAndalusiE +al8o


TABLEI (@NTINT,ID)

9t7

It/frner3ltrMFafAss€mt{ago

Topcrame"Prewre Idtidsoldm Rc&@

Pragodtc+ {I}-5moq lkbar H2O+NsCl+HCl Mmbys& Il€d€yfy/5Andalusite +al6uK-{eldspc+ 3m-strq0.9tkbor H2O+KO+HCI lvan&6al.lyl9MwitE+aigtzK{eldspor+ 2fr}-5mc'0.98kba H2O+NaO+KO+HO lvamt,'al.lngAlbb+MuscoviE +audtzK-feldspd+ 6(D-67(fC,1-2kbdIvllls@ib+agizK-feldspd+ l8l}{23oC'2kbd;Muscovire+ 205'CPSlrawtzAlbb+ 5m-70cc. l kbarAndalude+AlatzKjeldspor+ ffifc' 1-2kbmIJuciE,N€phelirAlbib+ 3m-5mq I kborMuscwito +au0tzAIffiE 125-350eC, PslrMuscdite 3ffiC,PsarMuscdile+ 5m-6trc'2kbdAndrluiE+aldtzMuscoviB+ 7trc'2kbarAnalalusiE +CorundumK-fsldspor+ 7m"q'2kbarAndahsite+affizK{eldspd+ 65fC'2kb@Iftuscovile +tudaluieKleldspd+ ?trc'2kbtrAndrlusib+CorundmK-feldspa+ 5@C'2kb@IsdE +tvluscovileK-feldspc+ 7trg2kbdIsrhB+CorundunMwirc+ 5m-{ffic'2kb6Le|lciB +CorundumKl€ldlpd+ 5fr)-700oq2.-2.38kbarMuscovite +al8tzAlbib+ 60oq2tbaK-feldspr+MuscoviE +aarzAlbfts+ 350-5trC.rrjkborkagofte+anrrzK-feldspe + 3flF55fc, 0.5-2 kborMwite+aEaMuscovirc+ 4{n-55fc.l-2kbfiAndaluite +anraMuscovite+ 3m-35fc. I kborPfophyliF +AlrEMuscorrite+ 3nq I kb6KoliniE+Al8zK-{eldrpr+ 6trC'lrlt6Andalusit6 +audtzAlbib+ 590'qHkb6hragmite+aiartz

H2O+KCl+HCl

H2O+KCl

H2O+NaCl+HCl

rw

H2O+Nacl+KCl+HO

HzO+NaClH2O+NaOEH2O+KCl+HCt

H2O +KCl+HCl

H2O,H2O+KCl+HCl

Hp

Hp

Hp

H2o

H2O,H2O+CO2,H2O+KCl

H2O,H2O+ KCI +HCl,HP+CO2

H2O+Naq

wo

H2O+KCl+HCl

H2O+KCl+HCl

H2O+KCl+HCl

H2O+KCl+HCl

H2O+KCl+HCl

H2O+NaCl+ HCI

Guter& Eug$s 1980

wlntschet4L 1980

PAp & Frantz 1980

Adcock&Macbzis l9El

Pohovskii 1982

Apps & Neil 1983Mukhanet{abrsv aat 1984Pasel l9E4;Andersoaaf. 1987

hscal 1984;Andgsonaa/. 1987

hscal 1984;Andssonaal, 19E7

kscal 1984;Anderson er aL l9fi

hscal 1984;Ardersmeral l9&7

hscal l9E4;ArdersmaaL l9&7

escal1984;AndersoaaL l9ST

escal f984;And€$m€tat l9E7

Pbcal 1984;And€rsoaat l9E7

AdersonaaL l9&/

V@dlard A Walher l9f,

Sverinr&yaal 199l

Svrrjms&yaaL l99l

Svtr!:nskyaaL t9l

SverlnrkyaaL l9l

SverjenrkyaaL l9l

Yolfnger&Rou 191

9 1 8 THE CANADIAN MINERALOGIST

At3'. Hrg '4g19x)zl n'

A FRINK AND PEECH (1963)

O rooxxov ETAL (rgzt. MAT TELMKE, AiD

JACKSON fl979)

TEMPERATURE. C

Al(oH)z"* Fl2o " Al(oH[ + H+

TEI4PERATUREt

rffiF'bl*tBO LUKASHoV ETAL 09?5)

O'loelrens anoaJHELGESoN (eB8)

O poKRovsK[ ET AL (rgst )

StJquNDUM . t5 Flro :-- /rr(oH€

!fl BEcKER, cemtd, aro

LANGER (98:t). 670.rorcI nlenlmo6rrn AM)

WALTHER (985), 685.C

PRESSURE. KB

TABLE 2. ACI'EOUS SPBCIES CONSIDBRD IN THB PRESBNTSTUDY AND TIIE SGJRCES OF THERMODYNAMIC DATA AND

EQUATIONS OF STATB PARAMSIERS USD TO CAI{I,]I.A'IE THEIRRSA.-TTVE SIABILITIES AT EI.,EVATBD TEMPERATURES AND

PRESSIjRES

So|Ece ofThemodyn{micDara

mlrq"atims d Star fuameters

Ht, oH-, Nsi, K+, o-

NaCl"

Kclo, HCt"

sioi 4

H:sioo , xanrsioi, KH:sioi 5

ar3', Allon;2', A(oH)t, er1onl!, a4on;,

NrAr(oH[, KAI(oH[, NaoHo, Korf 6

400 500 600

IEMPEMTURE. "C

Frc. 2. Logarithm of equilibrium constants for hydrother-mal reactions as a function of temperature at constantpressure (labeled in kilobars) or P561 or pressure atconstant temperature (labeled in 'C). The symbolsrepresent experimental data taken from the literature,but the curves were generated by regression of thedata using equations given in Appendix A, togetherwith equations of state parameters and values of thethermodynamic properties of the aqueous species at25oC and I bar taken from Pokrovskii & Helgeson(1989) and Pokrovskii et al. (1991).

et al. (1989,1992), Pokrovskii & Helgeson (1989),Pokrovskii et al. (1991), and V.A. Pokrovskii &H.C. Helgeson (in prep.). Calculations of this kindwere used together with Eqn. (Al0) in AppendixA to generate the curves depicted in Figure 2. Itcan be seen in this figure that all of the curvesrepresenting the logarithms of the equilibriumconstants for the reactions shown in the figure arein close agreement with their experimental counter-

I

2

3

tTanger & Ilclgeson (19881. zg1o"1 ",

,. (192). 3Pohovsfii er ar.(191). 4shock ?, 4L (1989). 5V. A pokrovskii & Il c. Itelgoson (inprreprarior). 6Pokovskii & Hetg€son (1989).

QTJARTZ300 tI K B

I snrsvn toael

parts. Similar agreement is apparent in Figure 3,where the solubilities of corundum, diaspore, andquartz in NaOH solutions are plotted as a functionof the molality of NaOH at various high tempera-tures and pressures. These observations, togetherwith the fact that the curves in Figure 3 weregenerated independently of the experimental datarepresented by the symbols, strongly support thevalidity and generality of the equations and

9t9

LOG mroo,

thermodynamic data used to calculate the mineralsolubilities depicted in the bulk composition - pHdiagrams discussed below.

The apparent standard partial molal Gibbs freeenergies of formation of minerals used in thesolubility calculations described in the present studywere calculated as functions of temperature andpressure from Eqns. (Al) and (A2) in Appendix Ausing values of the standard partial molal ther-


6E(9q -2 f

(9

9-3 2

LOG m**

f(9oJ

(9oJ

-40 -3.o -20 1.O OO

LOG m."NoOHLOG m*oo,

Ftc. 3. Solubilities of corundum, diaspore, and quartz in NaOH solutions at various elevated pressures andtemperatures. The symbols represent experimental data taken from the literature, but the curves were generatedindependently assuming b",y6oH" = br,Nacl. using equations given in Appendixes A and B, together with equationsof state parameters, activity coefficiehts, and thermodynamic properties of the minerals and aqueous species at25'C and I bar taken from Pokrovskii & Helgeson (1989), Oelkers & Helgeson (l99la), Pokrovskii et al. (1991),and V.A. Pokrovskii & H.C. Helgeson (in prep.).

Opascal aruo- ANDERSON (1989)

ABER{SI{TEIN ANDV MATSENOK (1965),Qwerm rrseztAg1g95rx' llto

OeARNrs. LAUDTsE.- AND STiIELDSF63)


modynamic properties of the minerals at 25oC andI bar generated by V.A. Pokrovskii & H.C.Helgeson (in prep.). Taking account of thedifference in the reference standard partial molalenthalpy of formation from the elements ofcorundum adopted in the two studies, the valuesof these properties are closely consistent with thoseat 25"C and I bar retrieved by Helgeson et a/.(1978). Values of the activity of HrO werecomputed from osmotic coefficients of NaClsolutions generated from equations and parameterstaken from Helgeson et ul. (1981), Oelkers &Helgeson (1990), and Pokrovskii et ql. (1991),which yield values that are closely consistent withthose generated by Pitzer et al, (1984). The activitycoefficients of aqueous species used to calculate themineral solubilities summarized in the followingpages were computed in the manner described inAppendix B. The dependence of these solubilitieson bulk composition and solution pH are discussedin subsequent pages in the context of reactionsamong minerals and aqueous solutions ingeochemical processes.

The bulk composition - pH diagrams describedbelow were generated by computing the solubilitiesof minerals in either 0.01 m or l.0m NaCl solutionscontaining either HCI or NaOH concentrationsconsistent with values of solution pH ranging from0 to 12 at 25",200o, and 300"C at P5a1, whichrepresents pressures corresponding to liquid-vaporequilibrium for the system H2O, except at tempera-tures less than l00oC, where it refers to thereference pressure of I bar. Accordingly, theeffective ionic strength of the aqueous phase is adependent variable, as is the activity of H2O. Thecalculations were carried out with the aid ofcomputer code PHX (Molchanov 1988), which wasused to locate the boundaries of the stability fieldsas a function of 4" and solution pH by solvingsimultaneously statements of the law of mass actionand material-balance equations for specified valuesof 4" and pH. The reaction paths represented bythe dashed lines with arrows in the 4" - pH diagramswere generated using the Gibbs free energyminimization code named GIBBS (Shvarov 1981).For the sake of simplicity and clarity in demonstrat-ing the application of these diagrams to hydrother-mal systems, only equilibrium solubilities ofstoichiometric minerals that are thermodynamicallystable were considered in the calculations. Meta-stable phase-relations, solid solutions such as illiteand smectite, multiple reactants, and the effect ofthe pH dependence of reaction rates and activationenergies on reaction paths and nonequilibriummineral solubilities will be considered in subsequentcommunications. The abbreviations of mineralnames used in the present communication to

designate the stability fields of stoichiometricminerals in the bulk composition - pH diagramsdescribed below were taken from Kretz (1983).These are: Ab albite, Anl analcite, Dsp diaspore,Kln kaolinite, Kfs K-feldspar, Kls kalsilite, Msmuscovite, Ne nepheline, Prl pyrophyllite, and Qtzqvartz. The terms albite and K-feldspor refer to thestoichiometric minerals in their stable states oforder-disorder at any pressure and temperature(Helgeson et al. 1978).

Hydrolysis of kaolinite at 25oC qnd I bar

To illustrate the advanlages of simultaneouslydescribing mineral solubilities and the consequencesof reactions among minerals and aqueous solutionsin terms of 4,., an 4Al2si2os(oH)4 - pH diagram isdepicted in Figure 4 for the system Al2O3-SiO2-HCI-NCI-NaOH-H2O al 25oC, I bar, and ra*u.,: 0.01. As indicated above, the components HCIand NaOH are included in this system (as well asthose considered below) in order to independentlyvary solution pH. The boundaries of the stabilityfields, other than those that are vertical in Figure4, represent mineral solubilities. The reactionsrepresented by the stability-field boundaries in thisfigure are listed in Table 3. The dashed reaction-paths labeled abcd, efg, and hijk in Figure 4represent the consequences of the reaction ofkaolinite with 0.01 m NaCl solutions in opensystems in which the values of pH are buffered byflowing fluids and equal to those at a, e, and h.These reaction paths are discussed in later pages.

It can be deduced from Figure 4 that kaolinitedissolves congruently at 25oC and I bar at valuesof pH between 3.73 and 4.27 in accord withreaction (3-3). [In the two-digit reaction numberscited in the text, the first digit refers to the tablein which the reaction occurs, and the second, tothe numerical sequence of the reaction in the table.lIn more acid solutions, kaolinite dissolves incon-gruently to form qlJaftz. At values of pH greaterthan4.27, diaspore is the first mineral to precipitatefrom solution, which occurs over a wide range ofsolution pH from 4.27 to 12.

The values of log 4a1rs;r65(ofl;a represgnted by thestability-field boundaries in Figure 4 can be usedto compute the total molalities of Al and Si byadding the logarithm of the number of moles ofAl and Si, respectively, in one mole of kaolinite (2)to the values of 11" on the ordinate. Although thetotal molality of silica in the aqueous phasecoexisting with kaolinite and quartz at values ofpH less than 3.73 is controlled by the solubility ofquartz, the total molality of Al is controlled by theequilibrium constant for reaction (3-2). In solu-


TABII3. REACTIONSREPRESENIINGTTIESTABIUTYFIELDBOI,'NDARIESDEPICIEDINFIG.4.

921

-s:Eoo'-oa_s\Js

(9

9

-2

-3

-4

-5

-6

-7

-8

-9

-to

pHFtc. 4. 44r5ir6\(oH)a - pH diagram for the system AI2O3-SiO2-HCI-NaC1-NaOH-H2O at 25oC, and zNacl :

0.01 (se6 t?xi). The annotated reaction-paths represented by the dashed lines with arrows at pH 3.65, 4.00, and4.35, correspond to those shown in Figure 5. These reaction paths are a consequence of the irreversible reactionof kaolinite in an open system with 0.01 raNusl solutions in which the values of pH are buffered by flowing fluids.

REACTIONNT'MBER REACTIOIv pERANGE,

ffi-(9r+sIlL)

Kln + Dsp+591

UNSATURATED SOLUTION

(l-r) sta " (fi:k)

(3-2) 2SiO2 +2Al*+5HrOCAl2Si2Or(OH)4+6H'(quo) (hdffi)

(3-3) 2Alk + 2SiOi + fi2o e A2Si2O5(OH)4 + 6Hr(telidb)

(H) A(oH)L, + (z-1)H2o C AlqoH) + nHt; (a=-!...,3)(dluFoi!)

(3-5a) 2AlqoH) + 2sioi + H2o p Al2Si2O5(OH)a(dt|!pd6) (6ir#.)

(3-5b) 2AlqOH) + 2H3SiOa + 2H' C Al2St2O5(OH)a + 3H2O(dilseqe) (rdini6)

2-35

2 -35

3.73 - 4.n

4n -12

4.n -E.5

8.5 - t2

alte aqueous alminm andsilica spocies shom in thesetaacfioos dE thce thatpaedodnaain thepH-rangeshownontherightsideofthetable htepH-*angercfers!othepHliminoftheslabilityfieldboondcieedepictedin tbfigue.


tions saturated with both kaolinite and diaspore,the total molality of aluminum is fixed by thesolubility of diaspore in accord with reaction (3-4),but the total molality of Si is controlled by theequilibrium constants for reactions (3-5a) and(3-5b).

The slopes of the srability-field boundariesdepicted in Figure 4 are determined by thedependence of the mineral solubilities on pH in thevarious ranges of pH in which the minerals arestable. For example, the slope of the quartzsolubility curve is zero because H3SiO; and itsdissociation products form to negligible degrees inacid solutions. Hence, reaction (3-l) determines thesolubility of quartz shown in the diagram. For the

same reason, the solubility of kaolinite in thepresence of diaspore is controlled by reaction (3-5a)until the pH increases sufficiently for HrSiOl toform to appreciable degrees, and reaction (3-5b)then controls the pH dependence of the solubilityof kaolinite. Accordingly, the solubility curveshown for kaolinite in the presence of diaspore inFigure 4 is essentially horizontal below a pH ofapproximately 9, and then increases with increasingpH. The minimum in the solubility curve fordiaspore occurs in response to the successivepredominance of aluminum hydroxide complexeswith increasing pH as n increases in reaction (3-4).

The phase relations depicted in Figure 4 can becompared with those in the solubility diagrams

/ , r . \z'uilsafuMfED

HCo{tfdo+Hq | 2 3

X**' 106--

Ftc. 5. Mineral solubilities and phase relations in the system AI2O3-SiO2-HCI-NaCI-NaOH-H2O as a function ofthe mole fractions of SiO2 and Al2O3 in the system at 25oC, I bar, rn51u61 : 0.01, and constant values of thesolution pH of 3.65 (diagram A), 4.00 (diagram B), and 4.35 (diagram C); see text. The annorared reaction-pathsshown as dashed lines with arrows correspond to those depicted in Figure 4 (see caption of Fig. 4).

Xqq'lo6-

shown in Figure 5, where the mole fraction of SiO2(Xs1er) in the system is plotted against the molefraction of AlrO, (Xe,rzor) at 25"C, I bar, andconstant values of solution pH of 3.65 (Fig. 5A),4.00 (Fig. 5B), and 4.35 (Fig. 5C). The dashedreaction-paths with arrows labeled abcd, efg, andhijk in Figure 4 are similarly labeled in Figure 5.It can be deduced from Figures 4 and 5A thatkaolinite dissolves congruently along reaction pathaD. However, with continued dissolution along bc,a small amount of quartz is precipitated as aproduct of the incongruent reaction. The numberof moles of quartz precipitated (kg HzO)-tcorresponds to twice the value of 4er2si2o51o11g atpoint c minus twice that at point b. At point c, theaqueous phase reaches equilibrium with bothquartz and kaolinite. Addition of more kaoliniteto the system then causes the bulk composition tochange toward point d, in accord with Eqn. (28).

In contrast to reaction path obcd in Figures 4and 5A, kaolinite dissolves congruently until itreaches equilibrium with the aqueous phase alongreaction path efg in Figures 4 and 5B. Note that

923

the scale of the solubility diagram in Figure 5B ismuch larger than that of the diagram in Figure 5,A.,which is a consequence of the dramalic decrease inthe total molality of Al in solutions that equilibratewith kaolinite as the solution pH increases from3.65 to 4.00. At pH : 4.35 along reaction pathhijk in Figures 4 and 5C, kaolinite dissolvesincongruently to form diaspore along y. At 7, theaqueous phase reaches saturation with bothdiaspore and kaolinite. If kaolinite is subsequentlyadded to the system, the bulk composition thenchanges along jk in accord with Eqn. (28). Thedashed reaction-paths in Figures 5A, 58, and 5Ccoincide with the position of the tie line betweenH2O and kaolinite, which is not shown in thefigures.

Hydrolysis of muscovite at 300"C and Ps67

Phase relations in the system K2O-AI2O3-SiO2-HCI-NaCI-NaOH-I{2O are shown in Figure 6 asa function of 4rerrsi:or0t611,, and pH in a 0.01 mNaCl solution at 300oC and Pso1. The reactions


(\l

-9,oq6

rq

:<r(9q-l

pH

(Prl^+.Qtz '\. Ms +prl.\*rh, .r +D!P.

!l ',. * 5-or-

Pr l+Dsp+SOL

flMs+ Kfs + SOL)

I$'L/,#"Ms + Dsp+SOL

Ftc. 6. 4xa1r513ol0(oH)2 - pH diagram for the system K2O-AI2O3-SiO2-HCI-NaCI-NaOH-H2O at 300'C, PsAr,and rnNacl= 0.01 (see text).


TABLE4. RBACTIONSRBPRBSENTINGTIIESTABILXTYFIELDBOI,JNDARIESDEPICIDINFIG.6.

REACIIONNT'MBER REACTIOI\4 PHRAIW4

sioi c

4siq + 2Al$ + 4H2o C Al2si4oro(oH)2 + 6Ha(q@c) (pyrc,F$yltB)

2Al3+ + zlsioj + 4H2O e AlzSlOro(OH), + Ott+

AI(OH)L, + (r-l)H2O e AlqoH) + nH+; (n=-!-.3)(didp@)

2AlqoH) +4sioi C At2si4qo(oH)2(dt!rpq!) (!tedy[tro)

-

3Ar2Si4Or0(OH)2 + 6AtqOH) + 4K+ e 4KAl2(AtSi3)qo(OH0'ytphyltb) (dirspor.) (wire)

3llgol) + 3sio: + K* a KA2(Atsi3)oro(oH)2+ If(du+of!J (@)

K+ + 3Al(oH); + 3sioi + 2H+ e KAlr(mkl(oH)2 + 61120

K' + AI(OH); + 3StOi a KAsi3q + 2H2o(K-fcldspo)

ffi# + 2A{oH); + 2Hr C *r(ffiP;i(orh + 4H2o 8.84-e.r

K' + AI(OH); + SiOl e KASiO4 + 2H2O(r!&iltE)

KAlSiO4 + 2SrOi C KAlSi3Or(rddi@) (K-rouspd)

)2+ 4ff

sio2(qao)

0-0.9

0.E4 - 0.9

0.9 - 0.98

0.98 - 8.0

0.98 - 4.5

t.8 - 4.5

4.5 - E.0

8.0 - 8.84

8.8/437

<+-z)

(H)

(6)

(4-7)

(H)

(4.9')

(4-10)

(4-ll)

(4-r2'

9.37 - tl

9.37 -rr

(4-r3) o.5KAtSiO4+0.5XAISi3O8+2AI(OH);+2Ht+SiOi e KAl2(Arii3)O'0(OH)2+4H2O 9.1 - 1r(r!mn6) (K-fddspd) (*q;rib)

6€e footndes a and b otTa!/c-2.

represented by the stability-field boundaries shownin this figure are listed in Table 4. lt can be deducedfrom the curves depicted in Figure 6 that muscovitedissolves congruently in alkaline solutions with apH between 8.0 and 8.84, which is consistent withexperimental observations reported by Mukhamet-Galeyev et al. (1984). At a pH grearer than 8.84,muscovite dissolves incongruently to form K-feldspar or kalsilite and K-feldspar.

The total molalities of potassium, aluminum,and silicon (mx, mx, 6\d ft15i, respectively) at anypoint in the bulk composition - pH diagram inFigure 6 can be computed from 4KAhsirornroH)r, Forexample, at a solution pH of 4, 211

-at'foir11 c is

equal to l0-2', but mAt arrdmsi at point c are equalto 3 X 4rat3si3o16(oH)2 at point a and 3 X4KAr3si3ot0(oH)2 at point b, respectively,

The order of precipitation of reaction productswith increasing tixar3si3olo(oH)2 in Figure 6 isdetermined by the equiiibriirm-constants fer thereactions in Table 4 and the extent to which themineral solubilities shown in the figure depend onpH. At a pH less than'8.00 and and greater than0.98, muscovite dissolves incongruently to form

diaspore. As diaspore continues to precipitate atthe expense of muscovite, the solution becomessaturated with respect to pyrophyllite if the solutionpH is greater than 0.98 and less than 4.50.Continued dissolution of muscovite in this pHrange finally results in equilibrium among mus-covite, diaspore, pyrophyllite, and the aqueousphase. In highly acid solutions, quartz (at a pH0.90) and pyrophyllite (at a pH between 0.90 and0.98) are the first minerals to precipitate fromsolution &S 4rar:st:oto(ouy, increases.

Hydrolysis of K-feldspar at 200"C and Ps^r

The solubilities of minerals in the systemK2O-AI2O3-SiO2-HCI-NaCI-NaOH-I{'O at200'C and P5o, in a 0.01 m NaCl solution aredepicted in terms of 4rari:or and pH in Figure 7.The reactions represented by the stability-fieldboundaries shown in this figure are listed in Table5. It can be seen in Figure 7 that K-feldspardissolves congruently over a short range of pHfrom 9.03 to 9.80. In more alkaline solutions.K-feldspar dissolves incongruently to form kalsilite.

@or -26)< -?

s(9

: - 4

INCONGRUENT REACTIONS AND MINERAL SOLUBILITIES 925

pH

Ftc. 7. 21x6151r6, - FH diagram for the system K2O-AI2O3-SiO2-HCI-NaCI-NaOH-H2O ar 200'C, P541, and rzsu61= 0.01 (see text). The annotated reaction-paths corresponding to the dashed lines with arrows represent theconseqences of the irreversible dissolution in a closed system of K-feldspar in 0.01 lrlNusl solutions with differentinitial values of oH.

t lto9Bo4o

In less alkaline solutions, the identities and relativeamounts of the minerals that form as intermediatereaction-products during the dissolution of K-feldspar are primarily determined by the initial pHof the aqueous phase. For example, it can bededuced from Figure 7 that reaction of K-feldsparwith an acid aqueous solution with an initial pHof 2.08 in a closed system causes precipitation ofdiaspore along reaction path ab. The number ofmoles of diaspore precipitated (kg H2O)-1 cor-responds to the value of 4xe,rsiros at point b minusthat at point a. At the stage of reaction progressrepresented by b in Figure 7, kaolinite begins toprecipitate at the expense of diaspore in accord withreaction (5-5), which continues until the solutionreaches composition c, where no diaspore remainsin the system. The number of moles of kaolinite(kg HuO)-t precipitated along reaction path ,c is

equal to one half ?resi:os at point c minus one halfthat at point D. As K-feid-spar continues to dissolve,kaolinite precipitates along cd until the solutionbecomes saturated with quartz at d. Kaolinite andquartz then coprecipitate along segment de as thesolution pH increases and reaches e, wheremuscovite becomes a stable phase. The number ofmoles of kaolinite (kg HzO)-r precipitated alongreaction path de is equal to one half 4Kr,ls136* atpoint e minus one half that at point d. In contrast,the number of moles of quartz (kg Hz.O)-tprecipitated along reaction path de is equal to onethird the difference between 4xersi3os at point eminus the sum of one half of the number of molesof kaolinite (log H2O)-t precipitated and theequilibrium solubility of quartz. Along reaction-path segment e/ in Figure 7, kaolinite reacts withthe aqueous phase to form muscovite until all of

(Kfs +SOL)-.--+

K fs *Ms+SOL

Kfs+

Kls+

soLI (Ms + Klnl+Qtz + SOL)I

. e > _ -

/ rnn+ soL)-

* (Ms+erz+SOL)

(Kln*Dsp*SOL

| (K tn+Ms* Dsp*SOLi (nas + DsP + SOL)-| (rcn + Ms + soL)-


TABLE 5. RBACTIONS REPRESENTING TIIB STABILXTY FIELD BOI,'NDARIES DEPISTD IN FIG. 7.

NTJMBER RBACTION4 PHRANGB4

(5-l)

(5-2)

('-3)

(5-4)

(!t

(x)

(t7)

(H)

(H)

(5-l0)

(5-1 1)

(5-12)

(5-13)

sioi c sio2(q'@)

2SiO2 + 2Al3+ + 5H2O e Al2Si2O5(OH)a + 6H+(qrc) (Lold.)

2Al3i + 2sioi + 5H2o !1 Al2si2o5(oH)a + 6H+(bolidb)

Al(oH)L, + (n-l)H2o e AlqoH) + zHt; (u =-1,...,3)(dtuF@)

2AlqoD + 2SiO; + H2O C AI2Si2O5(OH)4(dir+do) &ohn6)

3Al2si2or(oH)4 + 2Kr C 2KAl2(Alst3)olo(oH)2 + 2t + 3H2Q 2.13 - 5J(rrdid6)

KAl2(Atsi3)oro(oH)2 + 6siq + 2Kt e 3KAlsi3os + 2rr1(q!@) (K-fet&F)

3ArqOH) + 3SiOi + K+ C KAt2(ASi3no(OH)2+ H*(dhq@) (@iE)

KAl2(Alsit)or0(oHh + ZK+ + 6SiOi C 3KAlSi3Os + 2H+(,ttl'sdiE) (K-fold!Fd)

K' + A|(OH); + 3SiO;? KAlSi3O8 + 2H2O(K-foHqr)

K' + Al(oH); + Sio;C KAlSio4 + 2H2O(krldlib)

KAlSiO4 + 2SiO;e KA$i3q(btdn6) (x-fdd4d)

Kt + 3Al(OH)l + 3SiOi + 2Ha e KAI2(AISi3)O10(OH)2 + 6H2O

0-6.6

l.t - t.3

t.3 - t.4

1.4 - 8.0

t.4 - 5J

3.35 -6:6

5.7- t

6.6-9.O3

8.0 - 9.03

9.03 - 9.8

9.8 - 11.0

9.8 - 11.0

asee footn@s a ard b of Tabb 2^

the kaolinite is consumed at point/. Muscovite andquartz then coprecipitate along/g until point g isreached, where the aqueous phase achieves equ!librium with K-feldspar.

The logarithm of the number of moles ofminerals produced and destroyed (kg H2O)-' (nr)along reaction path abcdefg in Figure 7 is depictedas a function of 4rasiro. in Figure 8. The curve forK-feldspar shown in ihis figure represents theconsequences of adding K-feldspar to the systemin accord with Eqn. (28) along the path above g inFigure 7. It can be seen in Figure 8 that the reactionprocess described above leads to precipitation (kgHzO)-t of 0.005 moles of muscovire and 0.025moles of quaftz at the expense of 0.016 moles ofK-feldspar.

The sequence of events along reaction pathabcdefg in Figure 7 is quite different from thosealong paths e'b'c'd' arrd a"b". As K-feldspardissolves in a closed system along reaction patho'b'c'd', kaolinite and quartz fail to appear asintermediate reaction-products because theirstability fields are restricted to more acid solutions.In highly alkaline solutions along path a"b",

kalsilite appears as a product of incongruentreaction at point o" and continues to precipitatealong reaction-path segment a"b" until the solutionreaches equilibrium with K-feldspar.

The release of K2O into the aqueous phase duringthe dissolution of K-feldspar displaces thehydrolysis reaction represented by

K2O + 2H* e 2K+ + IJ2O es)

to the right, which favors increasing pH. However,the reaction paths are affected dramatically by thisreaction only if -log qre6tsor > pH. Precipitationof products of incongruent reactions, such asmuscovite at the expense of kaolinite in accord withreaction (5-6), is accompanied by the release ofhydrogen ions. The two opposing processes thatfavor increasing and decreasing pH, respectively(i.e., release of K2O into solution as a result of thedissolution of K-feldspar and release of H+ duringprecipitation of reaction products), compete witheach other during the dissolution process, whichmay lead to complex changes in pH along thereaction path.


Lm ?rasgo.

927

-I

\iz

(9

:

N

(9aJ

Ftc. 8. Moles of minerals precipitated and dissolved (kgH2Ofl (tJ as a function of bulk composition duringthe incongruent reaction of K-feldspar with theaqueous phase along reaction path abcdefg in Figure7 (see text and caption of Fig. 7).

The reaction paths shown in Figure 7 are alsoplotted on the activity diagram depicted in Figure9, where it can be seen that ey, / os* in the aqueousphase increases to a greater degree along reactionpath o'b' than it does along ab, which results inthe large increase in pH along a'b' in Figure 7.Because the solution pH is low along path ab,

LOG oo.^.,"2

Frc. 9. Activity diagram for the system K2O-AI2O3-SiO2-HCI-H2O at 200'C and P5a1 (see text). The annotatedreaction-paths represented by the dashed lines witharrows correspond to those shown in Figure 7.

precipitation of diaspore along this path has littleinfluence on solution pH. Taken together,diagrams like rhose shown in Figures 7-9 affordcomprehensive and quantitative description ofphase relations in hydrothermal systems before,

*6:<s"

(9

I

K-TLDSPAR

I

lz-ffit'ot

,/

o,../ KAoLlNlrE

DIASPORE

Kfs +Qfz +SOL

.+Qtz +SOL1gs + Kln+Qtz+SOL)

Kln + Qfz +SOL

FIc. 10. 4KAtsi3o8- pH diagram for the system K2O-Al2O3-SiO2-HCl-NaCl-NaOH-H2O at 200oC, Ps41, and &Nacl = 0.01 in an aqueous solution co-existing with quartz (see text).

928 THE CANADIAN MINERALOCIST

during, and after irreversible reaction of a givenmineral or mineral assemblage with the aqueousphase.

Reaction paths obcdefg, e'b'c'd' , and o"b" inFigures 7 and 9 represent the evolution of solutionpH in a closed system with a given bulk-composi-tion. However, if the system is open, the pH of theaqueous solution may change independently ofchemical processes that occur in the system.Changes in solution pH in open systems can becaused by dilution of hydrothermal fluids withgroundwater or mixing of fluids of differentcomposition due to reopening of fissures and otherprocesses. In the laboratory, similar changes canbe imposed by the "pH-stat" technique to changepH over a wide range at any given value of 4".Under these circumstances, the mineralogical con-sequences may be quite different than thoseresulting from the hydrolysis of K-feldspar in aclosed system. For example, if the solution pH isindependently increased from point g in Figure 7at constant 4ralsi3o6, the mass of K-feldsparincreases in accord with reaction (5-7), whichproceeds until all of the quartz in the system isconsumed. Further increase in pH then leads toconsumption of muscovite in accord with reaction(5-9) until it completely disappears at pH : 9.03,where equilibrium is achieved between K-feldsparand the aqueous phase.

The consequences of the dissolution of K-feldspar in an aqueous phase that is saturated with

qtJartz at 200'C and P5a1 c&n be assessed in Figure10. Because equilibrium with quartz reducesconsiderably the number of mineral stability-fieldsin the system, kaolinite is the first mineral toprecipitate from solution during the dissolution ofK-feldspar in solutions saturated with quartz at pHless than 7.2 in Figure 10. Kaolinite is followed bymuscovite and, finally, by equilibrium with K-feldspar, which dissolves congruently in thepresence of quartz only if the solution pH shownin Figure l0 is greater than 8.

Ifydrolysis of albite at 200oC and PssT

The analog of Figure 7 depicting mineralsolubilities in a 0.01 rn NaCl solution for thesystem K2O-AI2O3-SiO2-HCI-NaOH-HrO at200"C and Prot is shown in Figure 1l for thesystem Na2O-A12O3-SiO2-HCl-NaCl-NaOH-HrO. The chemical reactions represented by thestability-field boundaries in Figure ll are listed inTable 6. Comparison of Figures 7 and I I indicatesthat the configurations of the stability fields on theleft sides of the diagrams are almost identical, butthose on the right sides are somewhat different.These differences arise primarily from the ap-pearance of a stability field for analcite at valuesof pH in excess of 8.10 in Figure ll. It can bededuced from Figure 1l that analcite forms as aproduct of incongruent reaction during hydrolysisof albite in alkaline solutions. which is consistent

o t z 5 4 5 6 7 8 9 t o n t z

pH

Ftc. ll. ?Narsi:os- pH diagram for the system Na2O-Al2O3-SiO2-HCl-NaCl-NaOH-H2O at 200'c, P341, and zNacl = 0.01 (see text).

(P rg+K ln+Q iz+SOL

Kln+Qlz+SOL

Ab+Anl + , r \n l+Ab

Prq

cnl

lKll.Dsp | (erg+111n+soL) I *soLt

(Prg + Kln+ Dsp+SoL)


TABLE6. REACTIONSRSPRESENTINGTI{ESTABILITYFIBLDBOUNDARIESDEPICTEDINFIC. 11

929

REACTTONNT'MBER REACTIOM PHRANGE4

3Al2si2O5(OH)4 + 2Na+ p 2NaAt2(AlSi3no(oH)2 + 2H+ + 3H2o(k!o|bno) (p{ssod6)

sio; c sio,(qoo)

2SiO2 + 2Al3+ + 5H2O C Al2Si2O5(OH)a + 6Hr(q!e) (rdndF)

2Al3a + 2sioi + fi2o a At2si2o5(oH)a + 6Ht(rdidn!)

Al(oH)L, + (n-l)H2o C AlqoH) + nH+; (z=-1....,3)(dbqco)

2AIO(OH) + 2sioi + H2O C AI2Si2O5(OH)4

NaAl2(ArSi3)Ot0(OH)2 + 6SiO2 + 2Na+ P 3NaAlSi3O8 + 2H*(p6as@iE) (qm) (olbib)

3AlqoH) + 3Sioi + Na+ e NaAl2(asi3)oro(oH)2 + H*(diteqo) (p&sod!o)

NaAr2(ArSi3pro(OH)2 + 2Na+ + 6SiOi e 3NaAlIii3Os + 2H*bdrsodb) (rlbib)

Nat + 3Al(oH)f + 3sio, + 2H+P NaAl2(AlSi3)Or0(oH)2 + 6H2o

(6-1)

(G2)

(6-3)

(s)

(G5)

(ffi)

(6-7)

(H)

(6-e)

(Gl0)

(6-11)

(Gr2'

(Gl3)

(6-14)

(6-15)

0 -7.32

1.1 - 1.3

1.3 - r.4

1.2 - 8.0

1.4 - 6:78

3J -6:78

4J -7.32

6.78 - 6.0

7.32 - 8.1

8.0 - 8.52

N8Al2(Alrii3)qo(oH)2 + 5H2o c NaAtsi2o6.H2o + 2At(oH); + sio: + 2Hr 8.1 -8.52(peasoie) (@bn )

NaAlSi2O6.H2O + SiOi C NaAlSi3Ch + H2O(&dci@) (6eho)

Nar + At(OH)n + 2SiOi C NaAlSi2O6.H2O + H2O(Mlcib)

Ne+ + AI(OH); + SiOi e NaAlSrO4 + 2rr2o(i?t th.)

NaAlSiO4 + SiO: + H2O C NadSi2O6.II2O

8.12 - 11.0

8J2 - 10.06

10.06 - 11.0

10.06 - 11.0

4S€c f@md€s 4 and, of Table Z

with experimental observations reported by Apps& Neil (1983). As a consequence, no monomineralicsaturation-curve for albite appears in the diagram.Albite thus dissolves incongruently over the wholerange of pH shown in Figure ll. Note that thestability field of nepheline is restricted to values ofpH >" 10.06. As 4Nuast.o" increases at these highvalues of pH, nephelin6 ieacts with the aqueousphase to form analcite in accord with reaction(6-1 5). It can also be seen by comparison of Figures7 and 1l that the stability fields of paragonite andalbite occur at higher values of 4Naersiron than thevalues of TKarsiron corresponding to ihe stabilityfields of muscovite and K-feldspar. For example,at pH : 5, the molality of K required to precipitatemuscovite in the presence of kaolinite and quartzis > 10-2'4, but the molality of Na required forprecipitation of paragonite ir t 1g-t'r0. At any pH,albite is a more soluble mineral than K-feldspar.

The effect of increasing the total molality ofNaCl on the phase relations shown for a 0.01 mNaCl solution in Figure I I can be assessed bycomparing this figure with Figure 12, which wasgenerated for a I rn NaCl solution at 200'C andPsAr. It can be deduced from comparison of thesetwo figures that increasing mNacr expands thestability fields ofparagonite, albite, nepheline, andanalcite, which are then stable at lower values of4NaAlsi3os and pH. Note that the values of 4Nua*irrecorresponding to the lower limits of quartz stabilityin Figure 12 are slightly lower than they are inFigure ll, which is a consequence of the increasein isioz. in the more concentrated NaCl solutionconsidered in Figure 12. Comparison of Figures 1land 12 also reveals that the stability fieldsrepresenting paragonite + kaolinite + quartz,albite + paragonite + quartz, and albite -rparagonite + analcite at log 411r,,13116, less than -l


so€z,

F-(9

9

t lpH

Ftc. 12. ?NaAlsiror - pH diagram for the system Na2O-Al2O3-SiO2-HCl-NaCl-NaOH-H2O ai200'C, P5a1, and ,?N1us1 = l. The shaded area of the diagramis enlarged in Figure 13.

to986o

\r - r--. r (Ab+Prg + Q'lz+ SOL)\ l - - , - faU+Prg+SOL)

+Anl + Prg+391-1

Ab+Anl +SOL

+Dsp+sol.)

Kln r 912;591 Prg+ Qtz+

+--O-->-

Ab+Ad +SOLAb+Prg+

t' ,It

II,

, l

III

/i r '

I t. t ID C, t, t, t, ,t ,r{ ," 'n;:;-

Frc. 13. Enlargement of the shaded area in Figure 12 with annotated reaction-paths represented by the dashed lineswith arrows. The reaction paths are a consequence of the irreversible dissolution in a closed system of albite in I,zNacl solutions with different initial values of solution pH (see tex|, The shaded areas labeled I, II, and III areenlarged in Figure 14.

+Khr Qfz)---+=---

ftgtQlz


Ftc. 14. Schematic enlargements of the shaded areas labeled l, Il, and III in Figure 13 (see text). The reaction pathsrepresented by the dashed lines with arrows correspond to those shown in Figure 13 (see caption of Fig. l3).

931

shrink with increasing z?yu+ &nd become indistin-guishable from stability-field boundaries at thescale of the phase diagram depicted in Figure 11.

The shaded area in Figure 12 is enlarged inFigure 13, where a series of dashed reaction-pathslabeled e, b, c, d, e, and/are shown to illustratethe consequences of the reaction of albite in aclosed system with aqueous solutions with differentinitial values of pH on the identities and order ofappearance of reaction products that appear inresponse to albite dissolution in a I molal NaClsolution. Reaction paths a, b, c, arrd d in Figure13 were generated for molalities of HCI of 0.002,0.001, 0.0007, and 0.0001, respectively. Path eresults from reaction of albite with a I la NaClsolution (no acid or base added), but path / is aconsequence of reaction with an initial solution inwhich the molality of NaOH is 0.0001. Ir can beseen in Figure 13 that all but one of the reactionpaths result in final values of pH that are withinthe range 4.8-5.6, despite the much larger differen-ces among the initial values of pH of the solutions,which range from 3.05 for path a to 6.25 for pathe. The shaded insets labeled I, II, and III in Figure13 are enlarged in Figure 14. The phase relationsshown in the diagrams depicted in Figure 14 areschematic because they all fall within a pH rangeof 0.001. Hence, the mineral assemblages repre-sented by the stability fields in Figure 14 areessentially pH buffers in concentrated solutions ofsodium chloride.

CoNcI-uuNc REMARKS

The calculations summarized above indicate thataluminosilicates such as kaolinite, muscovite, andK-feldspar dissolve congruently at the pressures andtemperatures considered in the present study onlyin aqueous solutions with a pH that falls inrelatively narrow ranges. Beyond these limits, andover the whole pH range in the case of albite,aluminosilicates dissolve incongruently to formother minerals. The relative amounts andstoichiometries of the reaction products depend onthe solution pH. Adopting an approach similar tothat used by Frisch & Helgeson (1984), composi-tional data can be used together with fieldobservations of phase relations and 4" - pHdiagrams like those discussed above to assessreaction paths and the pH of the aqueous phaseinvolved in metasomatic processes. Although reac-tions involving only one reactant mineral wereconsidered in the present study, plans call forgenerating comprehensive ?" - pH diagrams forsystems involving solid solutions and two or morereactant minerals with and without kineticallycontrolled rates of reaction for a variety ofcompositions of aqueous solutions, at pressuresand temperatures ranging from 25oC and I bar to1000'C and 5 kbar.

Although the solubility diagrams discussed in thepreceding pages were generated for relatively lowtemperatures ( < 300qC) at PsAr, the same approach

(Ab+Prc'Anl):

Ab+FgIII

cIIII

Ab+

Arf

Arf + Prg

Ab+Prg


can be applied to prediction and interpretation ofphase relations at much higher temperatures andpressures. However, provision must be included inthe calculations for many aqueous species that donot form to appreciable degrees at lower tempera-tures and pressures. For example, conductancedata, electrostatic theory, and statistical mechanicalcalculations all indicate that triple ions such asK2Cl+, KClt, K2(OH)+, and K(OH);, as well ashigher-order polyatomic ion clusters and mixed-ligand complexes, may predominate over singleions and neutral ion pairs in concentratedelectrolyte solutions at supercritical temperaturesand pressures where the dielectric constant of H2Ois < 15 (Oelkers & Helgeson 1990, 1997a, b,1992a, b).

AcrNowlEncEMENTs

Acknowledgement is made with thanks to thedonors of the Petroleum Research Fund, ad-ministered by the American Chemical Society, forsupport of this research (ACS-PRF Grant 23026-AC2). The research also was supported in part bythe National Science Foundation (NSF Grant EAR8606052), the Department of Energy (DOE GrantDE-FG03-85ER-13419), and The Committee onResearch at the University of California, Berkeley.We are indebted to Eric Oelkers, Barbara Ransom,and Jan Amend for stimulating discussions andhelplul suggestions during the course of this study.Thanks also are due Joan Bossart for wordprocessing, Lillian Mitchell, Rebecca Arington, andKevin Kwong for drafting figures, Joachim Hampeland Peggy Gennaro for photographic assistance,and Mary Connolly for help in plotting the figures.We are grateful to Yurii Molchanov (Institute ofExperimental Mineralogy, USSR Academy ofScience) and Yurii Shvarov (Moscow State Univer-sity) for making available the computer progr€rmsPHX and GIBBS, which we used to generate thephase relations discussed above. Finally, we wouldlike to express our gratitude to J.V. Walther, G.M.Anderson, R.F. Martin and an anonymous refereefor insightful and helpful reviews of themanuscript.

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939

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Received April 22, j,99j,, revised manuscript acceptedNovember 29, 1991.


940

Appslotx A.CALcULATToN oF THE Appannnr Sre,NoannPenrral Molal Grsss FRgr ENsncEs orFoRMATToN or MrNrnals aNo Aqurous

Spscrrs nr HrcH TrptpnnerunEs AND pngssunrs

The apparent glandard partial molal Gibbs free energyof formation (AG') of a given species at a specifiedpressure (P) and temperature (T) is defined by

a6'.4C1+(9"-69,,1,) (A l )

where AG-'y refers to the standard partial molal Gibbsfree energy ol formation of the species from the elementsin their stable form at a reference pressure (p") andtemperature (T,) of I bar and 298.15K, and GBr -Gf..1" stands for the dilference in the standard paiiialmolal Cibbs free energy of the species at the pressure andtemperature of interest, and that at Pf and T". Thestandard state adopted for minerals and water in thepresent study is one of unit activity of the thermodynamiccomponents of sroichiometric minerals and pure H2O atany pressure and temperature. The standard state foraqueous species other than HzO calls for unit activity ofthe species in a hypothetical one molal solution referencedto infinite dilution at any pressure and remperature.

The last term on the righr side of Eqn. (l) can beexpressed for minerals in the crust of the Earth as(Helgeson et al. 1978)

THE CANADIAN MINERALOGIST

(A2)

IogK= -

where

aC;=:a/a6i

q = n@ V,, t,v,r. + P',lef | - z,1t'wz + uf)

wher€ r",i,pr.T, refers to the effective electrostatic radiusof the species at the reference pressure and temperature,which for monatomic ions is given by (Helgeson &Kirkham 1976)

r,;A,r,=r'; +PilQ (A5)

and for other charged aqueous species by (Shock &Helgeson 1988)

z?{nY' ' -tm)r.J&,r,=':X:!2-:J (A6)

'JI|,|T'-vz

where Z; represents the charge on thelh aqueous species,rn refeis to the crystallographic radius of the species,n": 1.66027 x 105 A cal mol-r, kz designates a constantequal to 0.94 A for cations and 0.0 A for anions, g standsfor a solvent function of temperature and density givenby Shock et al. (1992), Soj,rr.r, denotes the standardpartial molal entropy of the jth aqueous species at thereference pressure (Pr) and temperature (Tr), and e2 isdefined by

azBTr.s\Jl

(A4)

(A7)

(Al0)

(Ail)

where a, b and c stand for Maier-Kelley (1932)temperature-pressure-independent coefficients characteris-tic of the mineral, and So",r, and V.".r, represenlthe standard partial molal eri'rrbpy and vij[rime of rhemineral at 25"C and I bar, respectively.

The parenthetical lerm in Eqn. (Al) for chargedaqueous species can be written as (Tanger & Helgeson1988)

6i,r -6i,.a = - -$,.r,(r-a) - c, ft" fSl- t. t l\ \ " , / l

/w . r ' l+q lp_p, )+a2r lv* r ,7

- ( ( r r t ( t ) ) r e - r t r . / r - r r - e r ) ' )-alllr-€J-lr.-eJ)l e J-c" liffiJJ rerr/ I \ ( . / v + p ) )+ l'-"Jl+{r-r'l. " " lifilj

r r r f t )+o l : - l l -a r " - l ' - t

l+or r , , ryn , , r (T-T , ) ,\e / ""'l."r,,r, )where at, 02, 03, a4, ct, and c2 represent temperature-pressure-independent coefficients characteristic of thespecies, O and V stand for solvent parameters equal to228 K and 2600 bars, respectively, e refers to the dielectricconstant o{ fI2O, Yr,r, denotes a constairt equal to -5.80x 10-) K-t, S'p,1, dbsignates the standard partial molalentropy of the slbiies at 25 "C and I bar, and <,r designatesthe conventional Born coefficient of the species, whichcan be expressed for the jth such species as

Gi3 - di,,1, = - $,,r,1r- ) + {r-

r, - * e)

_( .b.

oH-r,l'J + $,,r. (r _r,)

The analog of Eqn. (A3) for neutral aqueous species canbe written as (Shock et al. 1989, Shock & Helgeson 1990)

c-i,r -di,,r =-8.r,(r-r,)- " ft

rpl- r.1l\ \ " , , / l

+ct(n-P,l+e2 hfJ+)\Y+Pr , /

- ( f t r t ( r ) ) f c - r t r ,_ f r , r r -e t ) ' ) . .-o ((r-e,J-lr.-ejjl e,/-e-,"liffi.; taarr t ;(

"l'-yrr')']+ lt-"Jf:(r-+) + e I qv+r,7./( | r )+ o.l Yp,,x(r-T,) + = -:-- | ,\

' ' eP,T 8P,:t. )

where c,.re denotes the effecrive Born coefficient of thespecies, which is independent of pressure and temperatureand consistent with

$r"=8+65i,:r, (A9)

where d and 6 stand for correlation parameters for variousgroups of neutral aqueous species given by Shock el a/.(1989) and Shock & Helgeson (1990).

Equations (Al) - (A9) permit calcularion of rheapparent standard partial molal Gibbs free energies offormation of minerals and aqueous species at elevatedtemperatures and pressures, which can be used tocalculate equilibrium constants for reactions among themfrom

a6;z303RT

INCONCRUENT REACTIONS AND MINERAL SOLUBILITIES 941

where AC? stands for the apparent standard partial molalGibbs free energy of formation of the /th species in thereaction given by an appropriate statement of Eqn. (Al),and fi1., denotes the reaction coelficient for the species inthe nh reaction, which is positive for products andnegative for reactants.

AppsNorx B.CALCULATION oF ACTIVITY COEFFICIENTS oF

AeuEous Sprcrss nrHIGH TEMPERATURES AND PnEssunTs

Close approximation of the activity coefficients ofcharged aqueous species (designated by the subscriprT) inaqueous solutions in which the electrollte MXpredominates over other solutes by an order of magnitudeor more can be calculated over a wide range ofconcentration from the Hiickel (1925) equation, whichcan be expressed as (Helgeson et al, l98l)

o2

0.o-o2

O l0O 2oO 3OO ,f@

TEMPERATURE. "CFrc. Bl. Serch6now coefficients for KClo in KCI solutions

and NaClo in NaCl solutions as a function oftemperature at P541 (see text). The curve representsa smooth interpolation of the experimental values ofbr,, rePresented by the symbols.

can be seen in this figure that b,.n for both speciesdecreases with increasing temperature from 0o to - l25oc,where it minimizes. With further increase in temperalure,Dr,r in Figure Bl increases to an increasing degree. Notein Figure Bl that the Setch6now coefficients for KCl" inKCl solutions and NaClo in NaCl solutions are nearlyidentical. It thus appears that in a first approximation,bt,n,MX. can be taken to be the same in KCI and NaClsolutions. Accordingly, the activity coefficients of HCI',NaOHo, KOH', NaAl(OH)a", KAI(OH)a., NaH:SiOao,and KH:SiOa' in NaCl solutions were assumed in thepresent study to be equal to those of NaClo in NaClsolutions shown in Figure B1.

The Setch6now coefficients for aqueous silica used inthe solubility calculations described in the text werecalculated by V.A. Pokrovskii & H.C. Helgeson (in prep.)from experimental solubilities of amorphous silica inaqueous solutions of NaCl reported by Marshall &Warakomski (1980) and Chen & Marshall (1982). Thiswas done by first computing values of the differencefunction represented by

Pi. . logt,-fr (B4)

t.8

t.6

I

5rcoEoa(9Y

- 0.6c

f o.o

( B I )

where A, and B, stand for Debye-Hilckel solvenrparameters, &y1 and ba.Mx denote the ion size andextended term parameters for the subscripted electrolyte,Zj stands for the charge on thejth species, 1., designatesthe conversion factor of mole fraction to molalitv. eivenby f, = - log (1 + 0.0180153 ia*;, *h.re z-.. i .-r , tothe sum of molalities of all of the solute species, and Istands for the effective ionic strength of the solution onthe molal scale of concentration, which is given by

7 = +Zz1^t @z)2 i ' r

where m; represents the molality of the lh species. Thevalues of ,\ and B, for H2O, and ty1 and b,.y1 forNaCl used in the

'present study were compiited as

functions of temperature and pressure using equationsand parameters taken from Helgeson & Kirkham (1974),Shock er ol. (1992), and Oelkers & Helgeson (1990),respectively.

The activity coefficients for neutral aqueous species inthe electrolyte solution discussed above can be calculatedat high temperatures and pressures from the Setch6now(1892) equation (Oelkers & Helgeson l99la), which canbe expressed for the molality scale of concentration as(Helgeson et ol. l98l)

tog?. = h*uxl+fr (83)

where b",r,Mx stands for the Setch6now coefficient forthe rth neutral aqueous species in an electrolyte solutionin which the electrolyte represented by MX predominatesover other solute species by an order of magnitude ormore. The Setch6now coefficients for NaClo and KCI'used in the solubility calculations described in the textwere generated by Helgeson et al, (1981) and Pokrovskiiet al. (1991) from osmotic and stoichiometric meanactivity coefficients reported in the literature. Computedvalues of the Setch6now coefficients for NaClo and KCI'in NaCl and KCI solutions, respectively, are shown inFigure Bl for temperatures from 0o to 350oC at PSAT. It

,*7, = --\4!!-+ rr + E!D(Il+tuy4Jl/2

'

Values of pf, computed from Eqn. (B4) using values of"y, retrieved{ibm experimental data can be plotted as afunction of I to generate values of &r., from

P.SAT

l'^\ KCt? POKROVSKTIv ETAL ( t 991 )

O nocrtclcasor- ET AL.Og8D

6. = 4"r (85)


rt'

Ftc. 82. Plot of Eqn. (B5) for SiOi in NaCl solurions ar200'C and P5a1 (see texr).

An example of such a plot is shown in Figure 82, wherevalue of pf, computed from the experimental solubilitiesof amorphoirs silica in NaCl solutions at 200oC and PsArreported by Chen & Marshall (1982) are plotted againsrthe effective ionic strength, which was computed usingthe logarithm of the dissociation constant for NaClo ar200oC and Psar given by Shock et al. (1992). It can beseen in Figure B2 that all but one of the experimentalvalue of pi" fall on a srraight line consistent with Eqn.(B5). Owiri! to the paucity of experimental data onsolubility of aluminum hydroxides in aqueous alkali metalchloride solutions, the Setch6now coefficient forAl(OH)r" was assumed in the present study to be equalto that of SiOz', which introduces negligible uncertaintyin the calculations (Pokrovskii & Helgeson 1989).

FROM SOLTJBILITY DA'AREPORTED BY CHEN ANDMARSHALL (1982)

unified description of incongruent …rruff.info/doclib/cm/vol29/cm29_909.pdf · canadion...

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