Geochimica et Cosmochimica Acta Vol. 48, pp. 723-751 0016-7037/84/$3.00 + .00 © Pergamon Press Ltd. 1984. Printed in U.S.A.

The prediction of mineral solubilities in natural waters: The Na-K-Mg-Ca-H-Cl­ S04-0H-HC03-C03-COrH20 system to high ionic strengths at 25°C

CHARLES E. HARVIEt, NANCY M.0LLER and JOHN H. WEARE* Department of Chemistry, University of California, San Diego, La Jolla, CA 92093

(Received May 4, I 983; accepted in revised form January 12, 1984)

Abstract-The mineral solubility model of HARVIE and WEARE ( 1980) is extended to the eight component system, Na-K-Mg-Ca-H-CI-S04-0H-HC03-C03-C02-H 20 at 25°C to high concentrations. The model is based on the semi-empirical equations of PITZER ( 1973) and co-workers for the thermodynamics of aqueous electrolyte solutions. The model is parameterized using many of the available isopiestic, electromotive force, and solubility data available for many of the subsystems. The predictive abilities of the model are demonstrated by comparison to experimental data in systems more complex than those used in parameterization. The essential features of a chemical model for aqueous electrolyte solutions and the relationship between pH and the equilibrium properties of a solution are discussed.

I. INTRODUCTION In Appendix A, we define the phenomenological equations used for mineral solubility prediction, and GEOCHEMICAL MODELS based on equilibrium ther­ discuss several extensions to the equations used by modynamics have been widely used to interpret field HW. In sections II and III details related to the con­ data and to provide theoretical descriptions for the struction of models for concentrated aqueous solutions origin and evolution of natural systems. GARRELS and are discussed. When necessary, ion complex species THOMPSON ( 1962) introduced general equilibrium are included (e.g. HC03, HS04) within the virial ex­ models to analyze rock-water environments. Their ap­ pansion model to describe the observed solution be­ proach has been adopted by many workers and has havior. Guidelines for incorporating these species are been successfully applied to a broad range of geo­ discussed in section II. In section III, the approxi­ chemical systems. The most comprehensive effort to mations in calculating the pH are assessed, and the model equilibrium properties has been that ofHELGE· method for utilizing pH data in the parameterization SON (1978) and co-workers. Other aqueous solution is discussed. models for a large number of components have been In section IV, we describe the parameterization of developed. These models have been described and the model. In this section, model calculations are com­ compared in a recent review (NORDSTROM eta!., 1979; pared to experimental data in numerous systems in­ KERRISK, 1981 ). Because of the inherently complicated cluding seawater. The prediction of data not utilized nature of concentrated aqueous solutions, these models in the parameterization suggests that mineral solubil­ are limited in their application primarily to the dilute ities can be calculated to within I 0% of the experi­ solution range (I < .I). Such limitations have been mental results in concentrated multicomponent sys­ discussed earlier (HARVIE and WEARE, 1980; KERRISK, tems. For some systems where a large amount of ex­ 1981). perimental data is available (e.g. gypsum) solubility Recently HARVIE and WEARE ( 1980) (cited hereafter predictions are more accurate. as HW) developed a chemical equilibrium model for calculating mineral solubilities in the Na-K-Mg-Ca­ II. THE PHENOMENOLOGICAL DESCRIPTION Cl-S04-H20 system at 25°C. This model, which was OF AQUEOUS ELECTROLYTE SOLUTIONS­ based on the PITZER (1973) equations for aqueous ION ASSOCIATION AND IONIC STRENGTH electrolyte solutions, is accurate to high ionic strengths DEPENDENT VIRIAL COEFFICIENTS (20m). A specific interaction model based on a virial expansion In this article, we extend the HW model to include with ionic strength dependent virial coefficients correctly rep­ the carbonate system and acid-base equilibria. This resents the thermodynamic behavior of many mixed electro­ generalized model accurately predicts mineral solu­ lyte solutions to high concentration. With this type of model bilities in the Na-K-Mg-Ca-H-Cl-S0 -0H-HCOrC0 - the explicit definition of ion complex species is not normally 4 3 required. However, the observed concentration dependence COrH20 system at 25°C to high concentration and of solution properties for certain electrolytes which exhibit variable C02 pressure. strong attractive interactions can only be described with the use of ion complex species (e.g. HCO)). The dilute solution behavior may indicate when complex species are required in a model. We believe that a virial expansion model which * Address all correspondence regarding this manuscript to includes strongly bound ion complex species is both con­ John H. Weare, Department of Chemistry, B-014, UCSD, venient and sufficiently general to accurately describe the La Jolla, CA 92093. observed behavior of most multicomponent electrolyte so­ t Present address: Shell Development Co., P.O. Box 481, lutions to high concentration. Houston, TX 7700 I. Many aqueous solution models have relied exclusively on 723 724 C. E. Harvie, N. M0ller and J. H. Weare ion pairing to account for the thermodynamic behavior re­ success of this approach is illustrated in the following simplified sulting from the specific interactions among the dissolved example related to Fig. I. Neglecting typically less important ions in solution. In such models ion complexes, such as terms proportional to HK. CHch CKcl and lfHKCh Eqn. (A3) NaS04 or NaHCO~, are defined explicitly and the component for "YHa and "Yib in a HCI-KCI-H20 system are simplified activities are calculated from the activity coefficients and the to give equilibrium distributions of mass among the various species. Characteristically, the activity coefficients for all solute species are defined to be universal functions of ionic strength, and therefore, do not depend explicitly on the relative concen­ + BKCJ(l)mK + BHa(/)ma (Ia) trations of the various species in solution. The dependence In "Y~o = In "YoH(l) + BHa(/)mH of the component activities on the solute composition is de­ scribed totally in terms of the association equilibria and the + BKcl(/)mK + BKcM)mo. (!b) resulting decrease in the apparent ionic strength. While this model can be accurate in dilute solutions, or over a limited In "YoH represents an extended Debye-Hiickel function com­ solute concentration range, it cannot be extended to concen­ mon to all ions. BHo and BKa are the ionic strength dependent trated electrolyte solutions of arbitrary composition. The fail­ second virial coefficients. ure of this ion pairing model stems from the use of activity The ionic strength dependent interaction functions, B»o coefficients which depend only on ionic strength. It is an and BKch may be evaluated from the data in the single elec­ experimental fact that above the dilute range, the activity trolyte solutions, HCI-H20 and KCI-H20. The following for­ coefficients depend on the relative concentrations of the major mula, which is obtained from Eqn. (I), can be used to calculate solutes present in solution. The upper two curves in Fig. I the activity of a trace amount of HCI in a KCI solution illustrate that the mean activity coefficient for HCI, "YHc1. depends strongly on whether the major solute is HCI or KCI ±t• _ In -yfi~JU) + In "Y~~(l) In "YHCI - . (2) (the "YH~ 1 or "Yfit1 curve). Similar plots of "YAo measured in 2 other electrolyte solutions (see HARNED and OWEN, 1958, Fig. 14-2-2) also reveal this compositional dependence. Under The superscript zero denotes the experimental mean activity the reasonable assumption that HCI, KCI, NaCI, etc., are coefficients in single electrolyte solutions (e.g. HCI-H20 or highly dissociated in solution, a model activity coefficient for KCI-H20). Since no ion association is assumed, I equals the HCI which depends only on ionic strength cannot explain total concentration of the electrolytes in the respective so­ this behavior. (See HARVIE, 1981 for details concerning the lutions. Equation (2) gives a relationship between the inde­ significant problems in fitting the data in Fig. I when HCI pendently observable values of "YI'I\S, "YA~, and "Y~ (at the or KCI are assumed to be strongly associating electrolytes.) same ionic strength) which is in good agreement with the Advances in electrolyte solution theory have suggested new experimental data (Fig. I, dashed line). phenomenological approaches which emphasize an excess free In the model discussed in this article, our use of ion complex energy virial expansion with ionic strength dependent virial species is dictated by their importance in representing the coefficients. This form of expansion is obtained from the experimentally determined thermodynamic properties. The statistical mechanical treatment of electrolyte solutions given virial expansion approach accurately represents the compo­ by MAYER ( 1950), and is incorporated into the semi-empirical sitional dependence of the thermodynamic properties in most approach of PITZER ( 1973), described in Appendix A. The multicomponent electrolyte solutions to high ionic strengths.

2.0 15 ! -· /YHCI ~ 1.5 1.0 ./ 15 ... 2 ./ - >-- ./ -- 10 .------_.--J=--- .-- t' ----- rKCJ 0.5 -4-·-·-·-·----·----·----4----·----·

1.0 2.0 3.0 4.0 5.0 Is

FIG. I. The mean activity coefficient of HCL in an HCI-H20 system, ("YA~I), the mean activity coefficient of HCL in a KCI-H20 system ("YI'i~ 1 ), and the mean activity coefficient for KCI in a KCI-H20 solution ("Y~~ 1 ) versus the stoichiometric ionic strength (/,). The data points are from ROBINSON and STOKES (1968) and HARNED and OWEN (1958). The dashed curve is calculated from the literature data using Eqn. (2). The solid curves are calculated using Eqn. (A.3). Mineral solubilities in natural waters 725

When an accurate description of the data is possible without Eqn. (A.3). The critical value for Kd depends on the activity the addition of ion complex species, this model is preferred coefficient expression used. When a typical extended Debye­ due to its computational simplicity. The complete dissociation Hiickel activity coefficient (fit to -yf.g02), description appears possible, when the dilute solution activity -zfA'.fi coefficients are moderately less than or exceed those given (3) by the limiting law in dilute solutions. However, for certain log-y,= I+ 1.85VI' strongly associating or even covalently bound pairs of ions (e.g., H+ and S04 or H+ and CO)), the activity coefficients is used to evaluate Kd from experimental data in dilute so­ in dilute solutions are significantly smaller than those predicted lutions, the critical value of Kd = .05 appears to be reliable by the limiting law assuming complete dissociation (i.e., In for 2-1 electrolytes. A similar analysis is possible for 2-2 elec­ "Y± ~ -lz+z-IAY/). In such cases, the observed solution be­ trolytes. Comparison of the results of PITZER and MAYORGA haviorcannot be conveniently represented by Eqn. (A.3) unless (1974) to that of PITZER (1972) suggests that the critical Kd ion complex species are assumed in the model (e.g., HS04 value is less than .002 for these electrolytes. and HCO.J). Even in these cases, it should be emphasized, Our experience in parameterizing the various subsystems the virial expansion activity coefficients are necessary for a of the complete model (section IV) supports the use of the correct representation of the thermodynamic properties at ion pair model when large negative deviations from the lim­ high concentration. iting law behavior are observed. In these cases, the dilute A hypothetical system, A +2-B--c+ -D--H20, was selected solution properties appear to be better represented by the ion for investigating the different thermodynamic behavior pre­ complex form. The additional flexibility provided by the virial dicted using a vi rial expansion model with or without an AB+ expansion of the ionic complex activity coefficients is generally ion complex. Model solutions were selected evenly spaced required to fit the high concentration behavior. For example, between solutions rich in A to solutions rich in B. The salt, the data in the single electrolyte system, H2S04-H20, cannot CD, was added to many test solutions to increase the ionic be accurately represented using Eqn. (A.3) without an strength without increasing the A or B concentration. The HS04 complex. Kd for this species is about .0 I (PITZER et AB2 activity was calculated in each of test solutions using the a!., 1977). The data in mixed electrolyte solutions containing model with the ion complex. The activities at all points were H2S04 also cannot be fit accurately without the use of this then used as data to be fit by adjusting parameters in Eqn. complex. In contrast to the H2S04-H20 system, the model (A.3) without the ion complex. A parameter in these calcu­ for Ca(OHh does not require a CaOH+ ion pair. The activity lations is the dissociation constant, Kd, for the ion complex. coefficients for Ca(OHh calculated with Eqn. (A.3) deviate As Kd is increased the agreement between the two models by less than 2% from the Kd = .05 curve depicted in Fig. 2. improves. A critical value for Kd may be defined. For any Kd These calculated activity coefficients for Ca(OHh are in good above this value the thermodynamic behavior predicted by agreement with precise emf data in dilute Ca(OH)rCaClr the model with the ion complex can be fit to within some H20 and Ca(OHh-KCI-HP solutions. Moreover, Portlandite specified tolerance by the model without the ion pair. This solubilities in various mixed electrolyte solutions are accurately feature is illustrated for dilute single electrolyte solutions in represented by the model (Fig. II). The Ca(OHh model ex­ Fig. 2. For Kd ;o,: .05, it is always possible to fit the thermo­ hibits good predictability in mixed electrolyte solutions to dynamic properties given by the model with the ion complex high ionic strengths without the CaOH+ species. (solid lines) using Eqn. (A.3) and {3~~ = {3~~ = C~ 8 = 0. For In parameterizing the model in section IV we have first Kd somewhat below this value, the two models differ signif­ evaluated virial coefficients assuming no complex species. icantly, regardless of the parameter value of {3~~ chosen in When, by this analysis. the virial coefficients, BMx(/), were

-[5

.10

FIG. 2. The calculated dilute solution behavior of the thermodynamic mean activity coefficient for a hypothetical 2-1 electrolyte, AB2. A typical ion pair model with activity coefficients given by Eqn. (3) is used to calculate the solid curves for particular values of dissociation constant, Kd. The dashed curves are calculated using Eqn. (A.3) with {3~ 8 = f3lo = C~ 8 = 0, and particular values for f3i 8 . The results are plotted versus the square root of the total AB2 concentration. 726 C. E. Harvie, N. M0ller and J. H. Weare

found to be large and negative an ion complex model was In "Yc1 = In "YR't!U) Extended Macinnes convention (7c) defined. There is a strong correlation between negative virial coefficients and the formation of ion complex species (PITZER In "YCI = -A Vi!(l + 1.5Vi) and SILVESTER, 1976). Extended Bates-Guggenheim convention. (7d)

III. THERMODYNAMIC INTERPRETATION For the extended Macinnes convention, 'YR~ is the mean OF pH activity coefficient for KCI in a KCI-H20 solution at the same ionic strength as the electrolyte solution in question. Similar The only laboratory cell measurements which We have definitions are used for the sodium-chloride and hydrochloric found for a few aqueous electrolyte systems are pH data. pH acid conventions. The BATES and GUGGENHEIM ( 1960) con­ is one of the most common chemical measurements made vention has been utilized by Bates and co-workers in defining in the field. It may also be the only practical cell measurement (by interpolation and at low /) the pH of N.B.S. standard in some natural waters due to experimental difficulties. reference solutions (BATES, 1973). In Eqn. (7d) A is the Debye­ Therefore, it is of interest for parameterization and for com­ Hiickel limiting slope. parison to field data that a method relating pH to the ther­ In order to relate pH( X) to the thermodynamic properties modynamic properties of a solution be defined if possible. of solution X, some assumption regarding the difference in The pH is a semi-quantitative indicator of the acid-base the liquid junction potentials of the cells with solution X and equilibrium properties of aqueous solutions. However, since S must be made. Substituting Eqn. (4) for the cell potentials the emf of a cell with a liquid junction depends on the ir­ of Eqn. (5) the following equation can be derived. reversible as well as the reversible properties of the system, any interpretation of pH in terms of purely reversible (equi­ M"u(X, S) pH(X) = -log10 aH(X) - RT{in IO)/F librium) properties is approximate. In this section we attempt to quantitatively assess the approximations involved in equating the operational definition of pH with an equilibrium = -log10 aH(X) - ~pH. (8) property of the system. M"u represents the difference in the liquid junction potentials Consider the following cell which may be used in a pH between a cell with solution X and a cell with solution S. In measurement: deriving Eqn. (8) the terms involving pH(S) and aH(S) exactly cancel providing that the same ion activity convention was Pt, H2lsoln XIIKCI(sat)IHg2Cl2, Hg, Pt. (A) used in Eqn. (4) as was originally used to define the pH of The cell potential, E, may be calculated by the equation (see the standard. The value of the term ~pH reflects this choice Appendix B): of convention. The usual equilibrium interpretation of pH assumes that the irreversible term, M"u, is negligible; and RT therefore, that pH(X) is approximately equal to -log10 E = E0 - FIn aH(X)- Eu(X). (4) a~(X). Consequently, the magnitude of M"u is proportional to the error in calculating the thermodynamic property In E is independent of the composition of solution X and is a 0 aHe~(X) by this assumption. constant for fixed hydrogen fugacity. Eu(X) is the liquid The magnitude of M"u or ~pH can be determined ex­ junction potential between the KCI-saturated solution and perimentally by replacing the hydrogen electrode in cell A the unknown solution, X. Since absolute single ion activities with an electrode sensitive to the ion whose activity is defined cannot be measured, aH is a conventionally defined hydrogen by convention. For the case of chloride the Ag-AgCI electrode ion activity in solution X. It is useful to define conventional may be used in place of the hydrogen electrode. The emf for single ion activities in terms of the measurable mean activities. this modified cell differs from Eqn. ( 4) in that the conventional Such a definition requires that one reference ion activity or activity for chloride appears rather than that for hydrogen ion activity coefficient is specified arbitrarily. The observable and E differs by an additive constant. Since the liquid junction emf cannot depend upon 0 the convention used to define the potential does not depend on the electrodes used, Eu(X) is ion activities. However, each of the component terms in Eqn. the same for both cells. The difference in the emf between (4) is a function of this definition. Therefore, a different choice two cells with the AgCI-Ag electrode, one with unknown of convention will alter , the relative magnitudes of E0 Eu solution X and the other with standard solution S, can be and the term involving aH, while the sum of all three terms ex pressed as: is invariant. (Appendix B). Operationally, the pH of solution X is defined by the equa­ E' _ E' = RT I ("Yci(X)mdX)) _ M (X S) (9) tion (BATES, 1973): x s F n "Ye~(S)mdS) u ' · (Ex-Es) Equation (9) can be used to calculate M"u with respect to pH(X) = pH(S) + RT(In 10)/F. (5) an assumed standard since all other terms can be measured or are defined by convention. Ex and Es are the measured emf values of the cell of type A The four curves plotted in Fig. 3 give M"u in NaCI solutions with unknown solution X or with standard solution S, re­ calculated from the data of SHATKA Y and LERMAN (1969). spectively. The pH, pH(S), of a standard containing chloride, Each curve is defined for a different ion activity convention can be defined in terms of a measurable mean activity, as (also note that the values of Ee~. calomel reported by SL equal -E' in Eqn. (9)). In principle any solution could be used as (6) a reference for calculating M"u. In obtaining Fig. 3, we have defined a .01 m NaCI solution as the standard reference so­ aHCI is the mean activity for hydrochloric acid in solution S lution. Assuming an ideal glass electrode, this choice of stan­ determined using a reversible cell (e.g. a cell without a liquid dard is comparable to the M"u one would expect with stan­ junction). "Ycl is a specified value for a conventional chloride dardization using the NBS Scale. (Note that NBS standards ion activity coefficient in solution S. The following conventions contain no chloride and therefore the equation for pH is defining chloride ion activity in a solution of a known ionic slightly more complicated than Eqn. (9). Extrapolation of strength will be discussed in this and the next section: Eqn. (9) to zero chloride in the standard solution S would provide a consistent definition for M"~os.) In Fig. 3, M"u is In "YCI = In "YH~(/) Hydrochloric acid convention (7a) about 3 mv (~pH = .05) using the Macinnes convention for .725 m NaCI solution. Also, using the Macinnes convention, In "YCI = In -y~~CI(/) Sodium chloride convention (7b) M"u is computed to be about 3 mv between the NBS standard Mineral solubilities in natural waters 727

a~ 88 , where pHNBs is determined using the NBS standard­ ization procedure. y~88 can typically be calculated using data on the acid side of a titration curve (see CULBERSON and

10 PYTKOWICZ, 1973 or HANSSON, 1972). 'Ylt is the hydrogen activity coefficient defined within the extended Macinnes convention and may be calculated using 'Yfia for the same solution. Using the equation, 'Ylt = 'YHah~. with Eqn. (7c) ('YHa can be measured by experiment or calculated .§.> using a :::J suitable model.), reported values of apparent equilibrium w

IV. PARAMETERIZATION AND DATA COMPARISON In this section, we discuss the extension of our pre­ .001 01 vious solubility model to include acid-base equilibria and mNoCI the carbonate system at 25°C. Parameters for cal­ culating mineral solubilities in the system Na-K-Ca­ FIG. 3. The value for the liquid junction potential calculated Mg-H-Cl-S04-0H-HC03-C03-COrH20 using the from the data of SHATKA Y and LERMAN (1969) using Eqn. model defined in Appendix A are provided in Tables (9). Each curve is calculated using one of the ion activity conventions given by Eqn. (7). (Curve a corresponds to con­ I, 2, 3 and 4. Since in most cases the model is pa­ vention Eqn. (7a), etc.). rameterized from the data in binary and common-ion ternary systems, the following comparisons to data in and a .725 m NaCI plus .005 m NaHC03 solution (using the data of HAWLEY and PYTKOWICZ, 197 3 ). Figure 3 emphasizes the conventional nature of the liquid Table 1: Single electrolyte solution para­ junction. While it has long been recognized that the liquid meter values. junction potential between two different solutions cannot be measured (GUGGENHEIM, 1929), once an ion activity con­ Cation Anion vention has been defined the value of the corresponding liquid Na C1 .0765 . 2644 .00127 junction is also defined and measurable by experiment. Con­ Na so 4 .01958 1.113 • 00497 ventional ion activities can similarly be Na HS04 .0454 . 398 measured. From a Na OH .0864 .253 . 0044 thermodynamic point of view all ion activity conventions are Na HC03 .0277 .0411 equivalent and no theoretical value for an ion activity can Na co 3 .039Q l. 389 .0044 be verified directly by experiment. That the liquid junction K C1 . 04835 . 2122 -.00084 K so 4 . 04995 . 7793 potential is small for a particular convention does not imply K HS04 -.0003 .1735 that the corresponding 'Yo- resembles in any way a real ion K OH .1298 .320 .0041 activity coefficient for the chloride ion. In this article we adopt K HC03 .0296 -.013 -.008 K co .1488 l. 43 -. 0015 the Macinnes convention and consistently 3 report ion activities Ca C1 . 3159 l. 614 -. 00034 and liquid junction changes with respect to this convention. Ca so 4 .20 3.1973 -54.24 With a proper choice for w, Eqn. (B.7) in Appendix B can Ca HS04 . 2145 2.53 be used to convert Eqn. (A.3) to this convention. Ca OH -.1747 -. 2303 - 5. 72 Ca HC03 . 4 2. 977 Due to the difficulties associated with the exact interpre­ Ca co 3 tation of the pH(X) in terms of the thermodynamic properties 11g C1 . 35235 l. 6815 . 00519 of a solution, we utilize reversible cell, isopiestic and solubility Mg so 4 . 2210 3. 343 -37.23 .025 data in Mg HS04 .4746 1.729 preference to pH data in the parameterization in !1g OH section IV. However, pH measurements are the only cell data llg HC0 3 . 329 • 6072 that we found in certain concentration ranges. In these cases, Mg co, it is necessary to estimate the change in the liquid junction HgOH C1 -.10 1.658 MgOH so4 potential (plus any corrections due to the glass electrode HgOH HS0 4 asymmetry potential) using the available data. MgOH OH To convert pH data into a form which is useful to ather­ l1gOH HC03 modynamic model, a constant ionic media assumption often MgOH co 3 H C1 .1775 . 2945 .0008 provides a convenient and accurate method to eliminate the H so 4 .0298 .0438 ApH term (see, for example, BATES, 1973 and references H HS04 . 2065 . 5556 therein). Under certain titration conditions, the activity coef­ H OH ficients and ApH are approximately constant over the entire concentration range resulting from the addition of titrant to For each cation-anion pair there are four model solution. Often in such cases, the conventional ApH can be parameters. Up to three ~ parameters specify evaluated from the data in a narrow concentration range of the ionic strength dependence of the second the titration curve. By assuming this D.pH value is constant, virial coefficients, Bc3 (I), via Eqs. (A.S). the remaining pH data can be corrected to the appropriate (Dashes indicate zeros.) A constant third virial coefficient is used as a fourth nara­ ion activity convention and subsequently used to evaluate meter to describe the thermodynamic behavior mean activity coefficients or apparent equilibrium constants. at high concentrations, when necessary. Hhen ApH can often be calculated using the equation, Eqs. (A. 3) are sim!llified for single electrolyte solutions, only four model parameters for the particular cation-anion pair remain. log 'Y~Bs = logw 'Ylt + D.pH. (10) Hhen 10 available, data in single electrolyte solutions are used to evaluate these parameters. (See 'Y~BS is defined by a convention equating pHNBs to -log10 Pitzer and Hayorga (1973, 1974) for details.) 728 C. E. Harvie, N. M0ller and J. H. Weare

Table 2: Common-ion two electrolyte parameter values. Table 4: Values for the standard chemical potentials of the aque-

c' ecc' !Pee 'Cl tllcc'S0 lj.lcc'HS0 I)Jcc'OH l.jlcc'HC0 l.j;cc' CO 0 4 4 3 3 Species or Nineral Chemical Formula p /RT Na -.012 -. 0018 -.010 -.003 .003 Water H,o Y5. 6635 Na+ - 105.651 Na Ca .07 -.007 -.055 Sodium Ion K+ Na Mg .07 -.012 -.015 Potasium Ion - 113.957 ca+ 1 r:a MgOH Calcium Ion - 223. 30 Ng+2 Na H .036 -.004 -. 0129 llagnesium Ion - 183.468 M OH+ K Ca .032 -.025 Nagnesium Hydroxide Ion - 251.94 K Mg 0. -.022 -.048 Hydrogen Ion H~ 0. Chloride Ion Cl­ - 52.955 MgOH 2 H . 005 -.011 .197 -. 0265 Sulfate lon S04 - 300.386 Ca Mg .007 -.012 .024 Bisulfate Ion \ISO~ - 304.942 ou- Ca MgOH Hydroxide Ion - 63.435 Ca H .092 -.015 Bicarbonate Ion HCOJ - 216.751 Carbonate Ion co- 1 - 212.944 Mg MgOH .028 3 0 Mg H .10 -.011 -.0178 Aq. Calcium Carbonate CaCO 3 - 443.5 MgOH H Aq, Hagnesium Carbonate ~lgCO ~ - 403.155 Aq, Carbon Dioxide cog - 155.68 Carbon Dioxide Cas C07 (~as) - 159.092 a' eaa' \j!aa 'Na lj.laa'K tj.laa' Ca lj.l aa'Mg tpaa'MgOH lj.laa 'H Anhydrite casu, - 5'll. 7J Aphthitalite (Glaserite) NaK 1(S0,,) 2 -1057.05 Antarcticite CaC1 2 •6H 1 0 - 893.65 .02 .0014 -.018 -. 004 C1 so, Aragonite CaCO 3 - 455.17 C1 HSO,. -.006 -.006 .013 Arcanite K2SO, - 532. 'l9 C1 OH -.050 -.006 -.006 -.025 Bischof i te ~IgCl2•6H?O - 853. I C1 HC03 .03 -.015 -.096 Bloedite Na;>H~(S0,)2•4H 0 -I 383.6 C1 co, -.02 .0085 .004 Brucite Ilg~OH) 2 - J ]5. 4 -.0425 so, Hso .. -.0094 -. 0677 Burkeite Na~C03(S0,)2 -1449.4 so, OH -.013 -.009 -.050 C.1lcite CaC03 - 455.6 -.005 so, HC03 .01 -.161 Calcium Chloride Tl>tr<~hydrate C.1Ch•4H?0 - 698.7 .02 -.005 -.009 so, co, Calcium Oxychloride A Ca,Clz (Oil) t. •lJH;>O -2658.45 HSO., OH C.:llcium Oxychloride B Ca 2Cl 7 (Oil) 2 •H 70 - 778.41 HSO., HCO 3 Carnallite K!1)o;Cl,•6H20 -1020.) HSO~+ co, Do lomite Ca1'1g(COl) 2 -871.99 OH HC03 Epsomi te NgSO,, • 7H;o0 -1157.83 OH .10 -.017 -.01 co, Caylussite CaNa 2 (CO 1) 2 • SH20 -1360.5 HC03 -. 04 .002 .012 co, Clauberite Nct 2 Ca(SO,)? -1047.45 For each cation-cation and each anion-anion pair, a single e para­ Gypsum CaSO~t • 2H;o0 - 725.56 meter is specified, if necessary. (Dashes indicate zeros,) For lla lite NaCI - 154.99 •6H;>O -1061.60 each anion-anion-cation and each cation-cation-anion triplet a Hexahydri te i'lgS0 4 Kaini te KHgClSO" • JH20 - 918.2 single IJ! parameter is used to describe the high concentration be­ KHC0 - 350.06 havior, when necessary. When Eqs. (A. 3) are simplified for common­ Kalicinite 3 i'lgS04 •H20 - 579.80 ion ternary solutions (e.g., NaCl-KC1-H20), only one 8 and one 'i-' Kieserite Salt Na 4 Ca(S0 4 ) 1 •2H 2 0 -1751.45 parameter (in addition to some single electrolyte parameters) re­ Labile K;>~1g(S04)2•4H20 -140). 97 main. Thee parameter must be chosen uniquely for all solutions con- Leonite :!agnes ite }lgCO, - 414.45 taining the anion-anion or cation-cation pair. When available, Hagnesium Oxychloride ~·1g?Cl(OH)3•4H;>O -1029.0 these parameters are evaluated from data in common-ion ternary KHS0 - 417.57 solutions. Hercallite 4 Hirabil ite Na 2S0 4 •lOH 20 -1471.15 t-lisenite KsH 5 (S0,,) 7 -3039.24 Nahcolite :-JaHC0 1 - 343.]] Nat ron Na 2C0 3•10H20 -1382. 7B more complex systems generally represent predictions Nesquehonite MgC0 3 • JH 10 - 695.3 the model with the Picromerite (Schoenite) K 2 Hg(S04 ) 2 •6H2 0 -1596.1 by the model. The agreement of P irssoni te Na;>Ca(C01)2•2H20 -1073.1 data is good, the model exhibiting good predictability Po lyha lite KzHgCa,(S04),.•2H 2 0 -2282.5 Port landi te Ca(OH) 7 - 362.12 even in complex, mixed electrolyte solutions. While Potassium Carbonate K?C0 3•3/2 H20 - 577.37 Potassium Sesquicarhon.lte KeH 4 (C0 3 )&•3H 2 0 -2555.4 some important qualifications are discussed in this Potassium Sodium Carbonate KNaC0 3 •6H 2 0 -1006.& Potassium Trona K2NaH(C0 3 ) 7 •2H 2 0 - 971.74 section, we believe that the model defined here is suf­ Scsquipotassium Sulfate K3H(S04) 2 - 950.8 ficiently accurate for most geological applications. It Sesquisodium Sulfate Na 3H(S0,) 2 - 919.6 Sodium Carbonate Heptahydrate Ni1 7 C0,·7H20 -1094.95 will calculate accurately mineral solubilities over broad Sylvite KCI - 164.84 Syngenlte K2Ca(S04)2"\!20 -1164.8 ranges of relative composition and to high ionic 'I'<:Ichyhydri te Hg 7 C.'1Cl~·121!20 -2015.9 'lhenardite ~a 2 S0 4 - 512.15 strength. Thcrmonatri te Na,co,·H/o - 518.8 In the following discussion, the model is compared 1 rona Na]ll(COJ)2"2lb0 - 960.18 to the experimental data for each of the subsystems. A single (unitless) parameter is specified for each model species and mineral. Hany salt chemical potentials had to be evalu<1ted The agreement with isopiestic and electromotive force in systems more complex than common-ion ternary (e.g. polyhal it e). However • the compos it ion dependence of such a salt's soluhi 1 i ty data is designated by citing standard deviations. For dC'pends on the trends predicted by the solution model which is parameterized in simple systems (i.e .• one parameter, \-1° /RT, must isopiestic data the standard deviation is given in terms constants may be fit many solubility data points). Equilibrium 0 calculated from thPse data using the equation £n 1Z =- I:viC•i/RT), of the osmotic coefficient (e.g., action. 1

Table 3: Neutral-ion parameter values. data, unless otherwise indicated, the standard deviation 0.0 is given in terms of the natural logarithm of the activity Na .100 K . 051 coefficient for the cell. For example, the standard de­ Ca .183 viation for the data determined from a cell utilizing Mg .183 MgOH a hydrogen electrode and a silver-silver chloride elec­ C1 -.005 so, . 097 trode is reported in terms of In 'Yfict' - In 'Yfi~Ic. The Hso, -. oo3 OH comparison to the solubility data is made graphically. The parameter values for each system are deter­ standard deviation For each neutral-ion pair, one model mined by minimizing a weighted parameter is used in Eqs. (A. 3), when of all the data for the system. In general, low weights necessary, to describe the experi­ mental data. are assigned to solubility data in comparison to the Mineral solubilities in natural waters 729 typically more accurate isopiestic and cell data. This agreement (I 0%) with the observed trends in solubility approach represents an improvement over the methods at high concentrations. This is probably related to the used by HW where parameter values were determined rapidly increasing activity coefficient for CaCI2 , in using various graphical methods. The parameter values which case small changes in concentration produce given in Tables 1-4, are usually cited to higher accuracy pronounced changes in the activity. than is warranted by the data fit. The choice of different PITZER et a!. ( 1977) have accurately fit the data for weights can change parameter values significantly. We the sulfuric acid-water system, incorporating the species have attempted to select weights which give the sol­ HS04. We found that it is not possible to accurately ubilities within 5% of their observed values. A brief fit the data for the H2S04-H20 system, without a discussion of the numerical method used to evaluate HS04 ion pair, using Eqn. (A.3). Since we are using parameters is given by HARVIE (1981). Many param­ the unsymmetrical electrolyte theory the parameters eters in the tables are set equal to zero (denoted by given by Pitzer et a!. are re-evaluated. This is accom­ dashes). For some cases, these parameters are ap­ plished by fitting the unsymmetrical mixing equations proximately redundant with other parameters (see fol­ to the interpolated activity and osmotic coefficients lowing discussion of H2S04-H20 and PITZER et a!., given by Pitzer et a!. In agreement with Pitzer et a!. 1977). In other cases, no data are available to evaluate an approximate redundancy among the parameters is a parameter. noted. For example, the standard deviation of a least In light of new data, the CaS04 parameters of the squares fit when adjusting the parameters, fJI'l~s04 , original Harvie-Weare model have been revised to im­ c~.so •• Mi!Hso. and fJWHso., is essentially independent prove the calculated dilute solution solubility of gyp­ of the value of fJWs04 • Within a broad range of sum. Recently, ROGERS ( 1981) fit the CaS04 system fJU!so. values the optimal value for any of the adjustable using the Pitzer model. We utilize her parameters when parameters changes but the standard deviation of the they are internally consistent with our model. The fit remains the same. Thus, the parameters for the revised CaS04 model has been discussed in HARVIE H2S04-H20 system could not be uniquely determined. et a/. (1982) and HARVIE (1981). Nevertheless, the thermodynamic properties of the In Fig. 4a the calculated solubilities of halite, sylvite, system are accurately described by any set of these bischofite, antarcticite and CaCh · 4H20 in aqueous four parameter values corresponding to a given

HCI solutions are plotted together with the experi­ fJU!s04 . We have adopted Pitzer's convention of setting mental data. The experimental data usually are those the redundant parameters, fJWso •• c~.Hso •• OHso •. so., summarized in LINKE (1965). The data for bischofite and 1/lso•. Hso •. H. equal to zero. As should be expected, in hydrochloric acid solutions are given by BERECZ we agree with the tabulated activity and osmotic coef­ and BADER (1973). The parameters values for Mib, ficients of Pitzer et a!. The standard deviation of the fJWo, and C~.c1 are given by PITZER and MAYORGA overall fit to 4> and In y± is u == .0007. (1973). The values for OKH, ONa.H, and 1/!Na,H.CJ are taken The agreement of the model with the data for the from PITZER and KIM (1974). The value for 1/IK,H.CI is HCI-H 2S04-H20 system is good. The data for this sys­ adjusted slightly from the Pitzer value to improve the tem are the emf data of NAIR and NANCOLLAS (1958), agreement of the model with the solubility data in DAVIES et a/. (1952) and STORONKIN et a/. ( 1967). the KCI-HCI-H 20 system. The first two sets of experiments are confined to low The values for OMg.H and 1/;Mg.H.cJ are obtained by concentrations, I ~ I. The data of Storonkin apply to refitting the emf results of KHoo et a!. (1977b) together systems up to ionic strengths of almost 4. The standard with the solubility data for the MgCh-HCI-H20 system. deviation of the Nair and the Davies data is rr == .0008 Unlike the model used by Khoo eta!. the equations In y±. For the Storonkin data, the standard deviation we use contain terms to account for electrostatic forces is rr = .0 15. All of the data are insensitive to reasonable in unsymmetrical mixtures (PITZER, 197 5 ). Hence, it variations in the parameter 1/IH.so4 ,0 . Consequently, was necessary to reevaluate the parameters given by this parameter is set equal to zero.

Khoo et a!. The standard deviation of our fit to the The parameters, fJ~l.Hso4 , f3m.Hso4 , 1/;H,Na,Hso., and

Khoo et a!. data is u == .0021 in In y±. When the emf 1/!Na.Hso4,so4 , and the standard chemical potential for results are fit without the solubility data, u = .00 16. Na3H(S04)z are evaluated simultaneously by a least In evaluating Oc •. H and 1/lca,H,CJ, a similar analysis was squares fit of the emf data of HARNED and STURGIS carried out using the emf results of KHoo eta!. ( 1977a) (HS) ( 1925), RANDALL and LANGFORD ( 1927), and and the solubility data in the CaCI-HCI-H20 system. COVINGTON et a/. (COW) ( 1965), together with the

The standard chemical potential of CaCh · 4H20 is solubility data (LINKE, 1965). The parameters, treated as an adjustable parameter in the fit. Our stan­ 1/!Na,H.so4 and C~a.Hso4 , are approximately redundant dard deviation to the emf data in the CaCh-HCl-H20 with the above parameters; therefore, they are set equal 0 system is u = .0027. The activity coefficients for CaCI2 to zero. The standard emf, E , values of Randall and at high CaCh concentrations are not in good agreement Covington are also treated as adjustable parameters, with experiment. To fit the solubility data we have while the standard emf for the HS data is fixed so that made small changes in the chemical potentials for salts the activity coefficient in 0.1 m H2S04 solution agrees like antarcticite. When third virial coefficients are with PITZER et a!. ( 1977). As noted by Pitzer et a!. treated as adjustable parameters, it is possible to obtain the interpolated E 0 value for the Randall data does 730 C. E. Harvie, N. M01ler and J. H. Weare

6 b

4 g ~"' 3 E E

1.0

3 4 5 6 7 8 0 3 6 8 mHCI

c d

'~ .0 C?_o F···-O· I?

Epsomite Kieserile

en~., :::E ·-o E

6 8 0 2 6 8

.032

.028 •

.024 e

g., g <..> 8 E gypsum E .012

008

004

0 .8 1.6 2.4 3.2 40 4.8 5.6 6.4 6 8 mH2S04

FIG. 4. The calculated and experimental solubilities of salts in acidic solutions. The model is also in agreement with various emf and isopiestic measurements (see text). Curves a-e were used in parameterization. Curve f was predicted using fully parameterized model for acidic solutions.

not agree well with the accepted value for similar cells. these data is obtained. This procedure tends to min­ As usual in fitting the parameters, the weights on the imize the standard deviation of the emf data while solubility data are increased until good agreement with insuring good agreement with the solubility measure- Mineral solubilities in natural waters 731

ments. The resulting standard deviations are u = .0 18, rameters for the system. Hence, Jfea,H,so4 , lfca,H,Hso., u = .0 13, u = .006 for the Harned, Randall and Cov­ Oso •. Hso., Jfso.,Hso •. ca and c&,Hso. are all set equal to ington data, respectively. Additional emf measure­ zero. In Fig. 4f the calculated solubility of gypsum in ments at concentrations which will define the Na-HS04 hydrochloric acid solutions is in good agreement with interaction are desirable for this system. The resulting the experimental data summarized in LINKE (1965). solubility curve is given in Fig. 4b. The data defined In Figs. 5a and 5b the calculated solubility of C02 by the closed circles are that of FOOTE (1919) and in different aqueous electrolyte solutions is compared LuK'YANOVA (1953). The open circles and dashed line to experiment. Each curve is labelled with the salt denote the data of KORF and SHCHA TROVSKA YA present in the solution. As previously discussed, the ( 1940). The Korf experiments observed an additional parameterization includes the evaluation of a single monohydrite salt separating the thenardite, and parameter, Xco,,;, for each ion i present in the system.

Na3H(S04h fields. We have parameterized the Since measurements can only be made in neutral so­ equations to the Foote and Luk'yanova data since lutions, one of the parameters must be assigned ar­ these authors are in good agreement, and the bitrarily. We use the convention of setting Aco,,H equal

Na3H(S04)2 • H20 salt has not been observed above to zero. The remaining parameters, evaluated directly 0°C by other authors (see LINKE, 1965). from the solubility data, are given in Table 3. The

The data for the system, K2S04-H2S04-H20, are fit standard chemical potential for C02 (gas), given in in much the same way as the corresponding sodium Table 4, is that of ROBIE et a!. (1978). ~~o2(aq) is eval­ system, except that the parameter, JfK,H,so., is allowed uated, together with the ;\'s, from the solubility data. to vary. The cell data of HAI~NED and STURGIS ( 1925) The calculated C02 solubility in pure water is about are fit with a standard deviation of .0 18. The calculated 3% low. This is probably the result of a deficiency of solubilities are compared in Fig. 4c to the data of the linear theory. However, since deviations in the D'ANS (1913) (solid circles) and of STOROZHENKO entire concentration range are usually within 5%, the and SHEVCHUK (1971) (open circles). The difference increased complication of higher order terms for neu­ between these two sets of data is sizeable. The major tral species does not seem warranted. (This is partic­ difference in the parameters fit with either set of data ularly true in the context of the geochemical appli­ is in the chemical potentials of the acid salts. We have cations for which the model is intended.) The solubility parameterized the model to the D'Ans data. data given in Fig. 5 are primarily those of Y ASUNISKI

A similar analysis for the MgS04-H2S04-H20 system and YOSHIDA ( 1979) and MARKHAM and KOBE ( 1941 ). yields a standard deviation of u = .02 to the emf data The data ofGEFFCHEN (1904) are given for the COT of HARNED and STURGIS ( 1925). The solubility data HC1-H20 system. The HARNED and DAVIS ( 1943) data predicted in Fig. 4d are that offiLIPOV and ANTONOVA are included in the figure for the NaCl-HCI-H20 sys­ ( 1978). tem. The parameter, Xco,,o, is determined from the The parameters, ~!:9l,Hso4 and ~g~.Hso4 , are evaluated data in the HCI-C02-H20 system. Using this param­ directly from the solubility data of MARSHALL and eter, the value of ;x for each of the cations (except H+) JONES (1966) depicted in Fig. 4e. These data are in­ is obtained by fitting the data in the chloride systems. sensitive to reasonable adjustments in all other pa- The parameter, Aso •. co,, is then evaluated from the

03

"' 03 0 8"' ft E ,_ 02 02 • ~,. 01 01

16 2.4 32 40 48 56 m m

FIG. 5. The solubility of carbon dioxide in single electrolyte solutions. The curves in MgS04 and K2S04 solutions were predicted using the model fully parameterized from the other data. 732 C. E. Harvie, N. M0ller and J. H. Weare data in the Na2S04-COrH20 system. Lastly, and SCHREINER (1910) for the Na-OH-S04 system are

XHso.,co2 is evaluated from the H2S04-COrH20 sys­ not in good agreement with that of Windmaisser tem. The data in the K2S04 and MgS04 systems in (LiNKE, 1965)). Fig. 5b test the specific interaction model, since all The parameters representing the Na-HC03 inter­ the parameters for these systems are evaluated from action and 8Hco,,c1are from PITZER and PE!PER ( 1980). other data. (At the time of publication improved parameter values The Na-OH and K-OH interaction parameters are have been evaluated by PEIPER and PITZER, 1982.) obtained from PITZER and MAYORGA ( 1973). The val­ The chemical potential for bicarbonate is evaluated ues for OoH,CI and lfoH,CI,Na of PiTZER and KIM (1974) from the equilibrium constant given by PITZER and are retained, while lfoH,CI,K is slightly adjusted to im­ PEIPER ( 1980). The Na-C03 interaction parameters, prove the fit with the solubility data. The calculated together with JL~o,, are evaluated from the isopiestic solubility curves for these hydroxide systems are plotted results of ROBINSON and MACASKILL ( 1979) and the together with the solubility data of AKERLOF and emf results of HARNED and SCHOLES ( 1941 ). Param­

SHORT (1937) in Fig. 6a. The parameters, OoH.so4 , eters for Na, C03 listed in Table 2 differ from those lfoH,so4Na and lfoH,so4 ,K, are evaluated solely from the given by Robinson and Macaskill because we account solubility data in these systems. For the Na-OH-S04 for the hydrolysis of carbonate to bicarbonate. The system the data of WINDMAISSER and STOCKL (1950) standard deviation of the isopiestic data remains are used exclusively (Fig. 6b). For the K-OH-S04 sys­ at u = .002 in the osmotic coefficient. The standard tem the data of D'ANS and SCHREINER ( 191 0) were deviation of the Harned and Scholes emf data used (Fig. 6d). (It is noteworthy that the data ofD'ANS equals .004.

0 b

4.8 24

~ 32 fl"" 1.6 :z :'i. E E Thenordile

1.6 .8

2 4 6 1.0 2.0 3.0 4.0 50 6.0 mNaOH mNaOH c .8I d r 4.8~

~ 3.2 fl E "" E"" • Sylvite

16 .2 ·~ • Arconile ·- 0 2 3 4 5 6 7 8 0 4 6 8 10

mKOH mKOH

Flo. 6. The solubilities of sodium and potassium salts in hydroxide solutions. The model is also in agreement with emf data at lower concentrations. Mineral solubilities in natural waters 733

The remainder of the Na-C03-HC03-CJ-S04-0H­ burkeite type are known to occur (see JONES, 1963). H20 system is parameterized exclusively from solu­ In Fig. Sf, the model activity of Na2C03 in aqueous bility data in common ion systems. The chemical po­ solution is plotted versus the model activity for NazS04 tentials of nacholite and natron are obtained from the in aqueous solution. Each point represents the Na2C03 solubility data of HILL and BACON ( 1927) and and Na2S04 activities calculated for each solution ROBINSON and MACASKILL ( 1979), respectively. The composition reported by ITKINA and KOKHOVA (1953) parameters, llco,,Hco, and !fco,,Hco,,Na and the standard to be in equilibrium with a burkeite phase. A curve chemical potential for trona are based on the solubility resembling that of a Na2C03 • 2Na2S04 mineral (solid data of HILL and BACON ( 1927) and FREETH (1922) curve) is suggested. In contrast, an ideal solid solution (Fig. 7a). Several of the Freeth points are in poor agree­ would satisfy linear behavior (e.g. dashed curve). The ment with the Hill data and the model. The parameter, mineral approximation for the burkeite phase gives lfCI.Hco 3 ,Na, is evaluated from the data of BOGOYA v­ relatively good results. The Na2C03-Na2S04 diagram LENSKII and MANANNIKOVA (1955) and FREETH indicates that burkeite is only slightly unstable at 25°C ( 1922). 8Hco,,so and lfHco,,so ,Na are evaluated pri­ 4 4 in this system. This is consistent with the 25.5°C in­ marily from the data of MAKAROV and JAKIMOV variant point for burkeite-natron-mirabilite-solution ( 1933). In the Na-S04-HC03 system Oso4 .Hco, and coexistence in Na C0 -Na S04-H 0 solution (MAK­ !fso•. Hco,,Na are nearly redundant, hence these param­ 2 3 2 2 AROV and 8LEIDEN, J93S). eters cannot be determined uniquely. Acceptable values Further comparisons of the model with experiment which are in good agreement with the majority of the are given for the Na-COrCI-OH-H 0, Na-COrCI-S0 - data in the more complex systems are given in Table 2 4 2. (See Fig. 7b.) Additional experiments are required H20, Na-COJ-HCOrCI-H20 and Na-COrHCOrS04- to refine these values. H20 systems (Fig. S). With the exception of the Na­ The solubility data of FREETH ( 1922) are used in COrS04-CI-H20 data of MAKAROV and BLEIDEN evaluating the parameters, OCJ.co, and lfnco,.Na, as well ( 193S), all of the calculated diagrams are in good as the standard chemical potential for sodium car­ agreement with the experiments. In the Na-COrS04- bonate hepahydrate (Fig. 7d). The parameters, CJ system (Fig. 8e) the experimental natron-mirabilite­ burkeite invariant llso •. co3 and !fso •. co,,Na• are evaluated primarily from point (triangle) is not in good agree­ the data of MAKAROV and KRASNIKOV ( 1956) and ment with the model or the experimental 25.5°C in­ CASPAR! ( 1924 ). Given the data available there is re­ variant point on the COrS04 edge. dundancy between these parameters. The values cho­ In Table 5, the calculated activities of water and sen are consistent with the data (Figs. 7 and S). the equilibrium carbon dioxide partial pressures are

The parameters, OoH.Hco, and !foH,Hco3 .Na• are un­ compared to the experimental determinations of necessary since the concentrations of OH and HC03 HATCH (1972) and EUGSTER (1966) in the Na-C03- cannot simultaneously be large. The small effects of HC03-CI-H20 system. These experiments were these parameters are redundant with the more im­ performed by saturating aqueous solutions with the portant parameters, llco,,oH and !fco,,oH.Na. The pa­ various minerals listed in Table 5 and measuring the rameter, OoH.Hco,, and all If's for OH, HC03 and a activity of water andjor carbon dioxide pressure. cation are set equal to zero. Oco,.oH and !fco3 .oH.Na are Agreement with the activity of water measurements evaluated from the data of FREETH ( 1922) and Hos­ is within 3% and often better. The calculated C02 TALEK ( 1956). The chemical potential of thermonatrite pressures are within the scatter of the data for the is also determined from these data. Eugster measurements, and within about 10% of the Data from more complex systems are used to test Hatch measurements. the model. The Na-C03-S04-0H-H20 system was The data available for the K-COrHCOrOH-Cl-S04- studied by ITKINA and KOKHOVA ( 1953). From their H20 system are more sparse than for the corresponding data the burkeite chemical potential is evaluated. sodium system. In particular, emf data in the moderate Comparison of our solubility calculations with these concentration appear to be absent. Consequently, a experimental data is given in Fig. Sa. In general the parameterization procedure using more complicated agreement is quite good. With the exception of bur­ data is used. The value for {J~~Hco 3 is estimated by keite, 70% of the calculated activity products for each PITZER and PEIPER ( 1980). {JQ~co, is estimated from salt at each of the points (Fig. Sb) are within 5% of the data of MACINNES and BELCHER ( 1933). The ex­ the corresponding equilibrium constant. 90% of the tensive solubility data in the Na-K-COrHC0rH20 activity products are within 10% of the equilibrium system are used in a nonlinear least square evaluation constant. An exception is the natron-Na2C0 • 7H 0- 3 2 of the parameters: {J~!Hco,, f3~!co 3 , C(Hco3 , C(co3 , burkeite point which appears from calculation to be lfNa.K.Hco,, lfNa.K.co 3 • and lfHco,,co 3K· The standard undersaturated by about 12% in the calculated equi­ chemical potentials for the carbonate salts with po­ librium constant for natron. In Fig. S, the burkeite tassium are also adjusted in an eleven parameter fit. fields are assumed to be in equilibrium with the mineral The data used are those of HILL and HILL ( 1927) for having a sulfate to carbonate ratio of 2 to I. The the KHCOrK2C03-H20 system; HILL and MILLER agreement of the data with this model is somewhat ( 1927) for the K2C03-Na2COrH20 system; HILL and surprising, since Na2C03-Na2S04 solid solutions of the SMITH (1929) and OGLESBY (1929) for the KHCOr 734 C. E. Harvie, N. Meller and J. H. Weare

32 a b ''f 2.8 24

2.0t-~-o=---· 8 g Mirobilite .._\ .g" 16 ~ .8 z E E 12 Nahcolite

.4 8 4 ·~

1.0 2.0 3.0 4.0 50 '------:c------'4,----:'.6------L8- 1.0 1.2'----:1'-:-.4 __-,JI.6 mNoCI

c d 1.6f 32~ 1.4 28 Notron ~ 1.2 2.4 ·- 1.0 2.0 "' "' 8::c 8.,_. Cl 8 ~ 16 z E E Halite .6 1.2

4 8

.2 .4 Not ron

L____ ILQ--~2~0--~3~.0----4~0~--~5.0~--6~0- 0 .8 1.2 t.6 2.0 2.4 2.8 3.2 \ mNa co mNaCI 3.2 2 3 e 3.21 28 28~

2.4 2.4 ~ Notron •

2.0 2.0 'il Burkeite Cl ~ 1.6 z "" Thermonatrite E E 1.2 12 •

.8 .8

4 .4

L---L---~---L---L---L--~--~·~ .4 8 1.2 1.6 2.0 2.4 2.8 3.2 1.0 20 3.0 4.0 5.0 6.0 mNoOH mNa2co3

FIG. 7. Salt solubilities in the Na-Cl-SO.-HC03-C03-0H-H20 system. Closed systems.

NaHC03-H20 system; and HILL and SMITH (1929) except for the nacholite data of OGLESBY (1929) at and HILL ( 1930) for the reciprocal system (Fig. 10). Pco, = I atm. (Fig. 9a). However in Fig. 9a, calculation The agreement between the model and the above ex­ does agree well with the experimental value for the perimental data is generally good (see Figs. 9 and I 0), nacholite-KHC03 invariant point of HILL and SMITH Mineral solubilities in natural waters 735

a b

Halite

c d

e .5

.4

4

FIG. 8. Predicted Jiinecke projections for ternary systems in the Na-CI-SO.-HCOrC03-0H-H20 system. Closed systems. See text for discussion of (f). Figures predicted from fully parameterized model using solubility data in Fig. 7, emf and isopiestic data.

( 1929) (square point in Fig. 9a), and the KHC03 sol­ between the Hill and Oglesby data must be resolved ubility data of Oglesby. We suspect that the Hill and experimentally. Smith invariant point is probably correct, since the The "mineral," KNaC03 • 6H20, is an approxi­ nacholite-KHC03 coexistence data of Hill plotted in mation for the solid solution (K,Na)C03 • 6H20 (HILL, Fig. I 0 extrapolate to this value. The 13% discrepancy 1930) (Fig. 9e). As was the case with the burkeite phase, 736 C. E. Harvie, N. Meller and J. H. Weare

Table 5: Comparison of the calculated and experimental water activities and equilibrium Pco2 pressures for solutions in equilibrium with the specified phase assembl­ ages in the Na-Cl-IIC0rC0rC0z-Hz0 system at 250C.

aH20 P COzx 103 calc Hatch calc Eugster Hatch

Na-HC03-C03-H20 + Nahcolite + Trona . 906 . 899-. 903 1.87 1.80-1.95 2.02 Ha-HCOrC03-H20 + Natron + Trona . 888 . 868-.872 .37 . 30-.34 Na-HCOJ-C03-Cl-H20 +Nahcolite+ Trona+ Halite .746 .765-.771 1.54 1. 45-l. 60 1. 72-1. 77 Solution+ Natron + NazCOJ•7H2o . 756 . 756* Solution+ Thermonatrite+ NazCOJ•7HzO . 697 . 705* *Extrapolated to 25 C by Hatch The data cited are those of Hatch (1972) and Eugster (1966), data giving the solid phase composition in equilibrium aqueous solution concentrations in equilibrium with with an aqueous solution are required to model the the solid solution are adequately calculated using the solid solution behavior. Nevertheless, the experimental mineral approximation. (See Figs. 9 and 10.) The data

4 "f a b 1.2"

KHC03 ...... 0 8 <...> X X ~ E E ""

.4 KHC03

--' 0 2 4 1.6 3.2 mKHC03 mKCI d 4.8

.... 8 1iii N E E"" Sylvite

16

3 lK2C03;! H20 0 4 0 4 6 8 10 mKOH m~co3

B 4 ,cNazC~·7H 20 g

.6

g :.::"" .4 E "'""7""'"" ~ •c~l•• J ~--~--~4--~6---~---To 0 mK2C03

Fla. 9. Salt solubilities in potassium carbonate systems. Closed systems. Mineral solubilities in natural waters 737

2K2CO~ · 4KHC03 ·3H20

'.-.-!t--.-----.---.----,----,,--,----,---.---,----,K2(HC03l2/

Trona Nahcolite

FIG. 10. The reciprocal Na-K-HC03-C03 closed system.

for this solid solution are not used in the fit of the phase diagram where a NaKC03 · 6H20-aphthitalite­ potassium carbonate parameters. arcanite invariant point is stable. Also, a stable zone The data for the chloride system of potassium car­ for burkeite between the aphthitalite-mirabilite and bonate and bicarbonate are sparse. The parameters, natron fields may be present. lfci.co 3 ,K and lfci,Hco 3K, are evaluated from the solu­ The KOH-K2C03 data (Fig. 9c) used to fit bility data ofBLASDALE (1923) and BAYLISS and KOCH lfoH.co,,K are that of LANG and SUKA VA (1958) (circles) ( 1952). The agreement of the model with the emf data and KLEBANOV and PINCHUK (1967) (squares). These of MACINNES and BELCHER (1933) is good. The stan­ two sets of data are not in good agreement with each dard deviation of the fit to these authors' potassium other and an average of the two sets is taken. bicarbonate data is u = .006 in In (/'cii'YHco,) and the A CaOH+ ion pair is not explicitly included in our standard deviation to their potassium carbonate-bi­ model (see section II). The aqueous solution parameters carbonate data is u = .014 in In /'~CI· The conditions for the Ca(0Hh-H20 system have been evaluated from of the Macinnes and Belcher experiments are analo­ the emf data of BATES et a/. ( 1959) and the solubility gous to the Hamed emf experiments in the sodium data of MILLIKAN (1918) in the Ca(OHh-CaCh-H20 system. The fit to the BLASDALE ( 1923) solubility data system. In Fig. 11 the calculated solubilities for is good, with the exception of several natron points Ca(OHh and other oxychloride salts are plotted vs. which correlated quite well with the sodium carbonate experiment. Since the parameterization is based only heptahydrate salt. Blasdale also does not observe the on the Bates and Millikan data the calculated solu­ heptahydrate in the NaC03-NaCI-H20 ternary system. bilities in the Ca(OHh-NaCI, Ca(OHh-KCI, Ca(OHh­ The single point in the K2C03-KCI diagram (Fig. 9d) NaOH and Ca(OH)rKOH aqueous solutions are 3 is the K2C03 · f2H 20-KCI coexistence point of BLAS­ checks on the model (Figs. llc-llf). The agreement DALE ( 1923). The data for the KHC03-KCI system is for the most part excellent. The data denoted by are those of BAYLISS and KOCH ( 1952) for sylvite­ squares in Fig. lie and lld are those ofFRATINI (1949) KHC03 coexistence. at 20°C. The analytical values of Fratini are consis­

The value of the parameter, !fso4 ,co,,K, is based on tently higher than the model and higher than the data the data of HILL and MOSKOWITZ ( 1929) in the K2C0r of other authors in Ca(OH)rH20 solutions (circles in K2S04-H 20 system (Fig. 9f). No data are found which the same figures). An increased chemical potential for are sensitive to the parameter, !fso4Hco3K. Conse­ portlandite brings all of the Fratini data in good agree­ quently, this parameter is set equal to zero until data ment with the model. The data in the NaCI and KCI become available. In disagreement with the data of solutions are those of JOHNSTON and GROVE (1931)

BLASDALE (1923) the calculated reciprocal diagram and YEATTS and MARSHALL (1957). The CaS04- Na-K-S04-C03 displays different, perhaps more stable, Ca(0Hh data are those of CAMERON and BELL ( 1906) mineral coexistences than those reported. In particular, and JONES ( 1939). The Bates data are for dilute aphthitalite appears to occupy a large portion of the Ca(OHh-KCI and Ca(OHh-CaC12 solutions. The 738 C. E. Harvie, N. M01ler and J. H. Weare

b 0 • .06 • • • CoC" ·""{OHI,·131¥l~ ~·f • Ca(OH~ N s: N • Q .04 % .016 0 0 '-' E 8 E

008

~

_J 0 3 4 5 6 7 8 004 008 .016 mcoCI2 meoso4 .0241 c .024i d t

-""::1: g ! 8 8 E E

008

.20 0 .04 .08 .12 .16 .20 0 .04 .08 .12 .16 mKOH mNooH e

Ca(.OHl2 ·~

... .-£"a .016 8 .016 E

008 .008

1.0 20 3.0 4.0 .8 2.4 mNoCI

FIG. II. Ca(OHh salt solubilities in various salt solutions. In (a) and (b) solubility and emf data are used in parameterization. (c)-(f) are predicted using fully parameterized model.

measurements are at concentrations where significant CaC03-H20-C02 system (Fig. 12a) are those sum­ ion association should be present, yet we did not need marized by JACOBSON and LANGMUIR (1974) to l to include a CaOH+ species to obtain good agreement atm. and those of MILLER (1952) (below the curve) with the data. The standard deviation of the model to and MITCHELL (1923) (above the curve) at higher the data is u = .003. pressure. For C02 pressures somewhat greater than I In Fig. l2a-f the calculated solubilities of calite (solid atm. the fugacity was calculated from the C02 pressure curves) in water and NaCJ solutions are compared to using the real gas virial coefficient summarized in AN­ experiment. The solubilities of aragonite (dashed GUS eta/. (1976). Figure l2a compares the calculated curves) are also plotted. The experimental data in the and measured solubilities of calcite in pure water as Mineral solubilities in natural waters 739

l\:a1 • 06 aim 008 •

-6 8 e 004

Halite 002 (d)

·7 -6 -3 -2 10 20 40 50 60

--- Pco,' 0013

002 ------~:~nile -.. ______

Calcite 8 e .01 8 e Halite 001 Halite

(b) (e)

10 2.0 3.0 4.0 5.0 60 1.0 2.0 4.0 50 60 mNoCI Pco, •. 00033

8 e 8 e Halite Halite (c) (f)

10 2.0 3.0 40 50 6.0 1.0 20 3.0 40 50 60 mNoCI mNoCI

FIG. 12. The solubility of calcite in water (a) and the predicted solubilities of calcite in NaCI solutions (b)-(f).

a function of the fugacity of C02 in the vapor phase. plex is the better model for this system. This is con­ (The lowest and right hand scales depict the lower sistent with the conclusions drawn in section II for pressure range, whereas the upper and left hand scales 2-1 electrolytes. This conclusion is admittedly based are for higher C02 fugacities.) The calcium carbonate on a relatively sparse set of pH data. With or without interaction parameters and the chemical potentials for cacog' the resulting model is found to be consistent 0 calcite and argonite are evaluated from these data. p. with the CaCOrH20-C02 solubility data when the for argonite is evaluated from the data of BACKSTROM Ca-HC03 second virial coefficient parameters are ad­ (1921). justed to fit the data. A neutral ion complex, Cacog, was defined for this JACOBSON and LANGMUIR (1974) showed that the system, since the parameter, ~g~c03 , was extremely C02 pressure dependence of the solubility of calcite large and negative (- - 200) when the pH data of in water is not consistent with strong Ca(HC03)+ ion REARDON and LANGMUIR (1974) are fit without this pair formation. Our calculations agree with this result complex. We suspect that the model with the ion com- Since these solubility data, plotted in Fig. 12, are re- 740 C. E. Harvie, N. Meller and J. H. Weare producible an ion pair is not assumed. Positive coef­ Since the solubility of calcite is not negligible, Eqn. ficients, which are inconsistent with strong association, ( 13) is approximate due to the neglect of the Ca-HC03 are obtained when these data are fit without the ion interaction. From other data we have an independent pair, CaHCOj. The value for 1'1~Hco, is selected within determination of 'Y~~Hco 3 )2 and we can, therefore, cal­ a range of possible values consistent with the data. culate the effects due to this interaction. When theCa­ 1'1g~Hco 3 is fit to the data given this choice of HC03 interaction is positive the observed solubility 1'1~~Hco,. More recent data taken by PLUMMER and will be less than that predicted by Eqn. (13) as is the BUSENBERG ( 1982) suggest that ion association is im­ case below I m NaCI and for calcite in pure water. portant. When the interaction is negative (e.g. ion association) In Figs. 12b-f, the predicted solubility of calcite in the opposite behavior should be observed. This is con­ NaCl solutions is plotted together with the available sistently the case above I m NaCI. data. At 0.97 atm. the data are those of SHTERNINA However, there exists an inconsistency between a and FROLOV A (1952, 1962), FREAR and JOHNSTON strong negative interaction and a 113 power law in the ( 1929) and CAMERON eta!. ( 1907). At lower pressures, solubility. At 2 m NaCl and Pco, = .97 atm. the cal­ the data are primarily those of SHTERNINA and FRO­ culated solubility is about 85% of the experimental LOY A (1952). In Fig. 12f, the results of CAMERON and value. A Ca(HC03)+ ion pair might be introduced to SEIDELL ( 1902) are plotted. The Shternina data are improve the agreement at this pressure and NaCl con­ consistently designated by circles. All of the data are centration. However, such a model is inconsistent with reported for calcite solubility. other data at lower NaCI concentrations. Furthermore, The calculated behavior for the solubility of calcite calculations verify that while agreement can be im­ is constrained by the data in other systems. For proved at any given pressure with a CaHCOj ion pair, 2 Pc0 , ~ .06 atm. the concentrations of C03 and it is not possible to fit the observed pressure dependence cacog are negligible compared to the solubility of ofSHTERNINA and FROLOV A (1952) with such a model. calcite. Consequently, the dominant reaction deter­ As the pressure is reduced, the concentration and the mining the calcite solubility is: degree of association are also reduced. Further data 2 are needed to understand these discrepancies. = ca+ 2HC03, CaC03 + H20 + COigas) + The pH data of STOCK and DAVIES ( 1948) are used and the solubility may be calculated to good approx­ to evaluate the chemical potential for the MgOH+ ion imation by the following equation: pair which is found to have a pKd value of 2.19. A liquid junction plus asymmetry potential of .23 pH 2 3 3 K = ac.(aHco,) ~ ('Y~a(Hco,),) m 4 (II) units is obtained from the acidic region of the titration aH,oPco2 aH,oPco, curve reported by these authors (Table II ofSD). While In the above equation m is the solubility of calcite. this value is large, our Kd is also in good agreement Since the solubility is small, the thermodynamic mean with that determined by McGEE and HosTETLER (1975) from pH data. With the McGee and Hostetler activity coefficient for Ca(HC03h may be approxi­ data, however, the model deviations trend from -.029 mated by the trace activity coefficient for Ca(HC03h = = in in NaCI solutions. This activity coefficient is related at pH 10.03 to .005 at pH 10.39. The change the solution composition for this range is small. If this to the trace activity coefficients in the CaCI2-NaCI­ trend is significant there may be a problem with an H20 and NaHC03-H20 systems by the equation, MgOH+ model. A detailed reversible cell study of the 13 'Y~~Hco,>, = 'Y~~'C"bl'ico,/'Yai • (12) Mg(OH)z-MgC}z-H20 system would be useful in pre­ cisely characterizing the interactions in this system. 'Y~~c" may be determined from the isopiestic data of Higher concentrations of MgCI should be possible ROBINSON and BOWER ( 1966) or from the solubility 2 owing to the increasing solubility of brucite. This study data of gypsum or portlandite in NaCI solutions. The would also be useful due to the importance of the Mg­ activity coefficient ratio ('Yl'ico /'Yc ) is measured di­ 3 1 OH interaction in determiningpKw in seawater. There rectly by the emf experiments of HARNED and BoNNER is also some evidence that the precipitation of a mag­ (1945) (see also BONNER, 1944) to 1.0 molal NaCI. nesium oxychloride buffers highly concentrated MgC}z Our model is in good agreement with all the above evaporite solutions (BODINE, 1976). Our preliminary data. Substituting Eqn. (12) into Eqn. (II), the fol­ calculations support this result. lowing equation is obtained: The solubility data for brucite and magnesium plotted in Fig. 13. _ n.aH20v )1/3 1/3 oxychloride in MgC}z solutions are m - ±tr 3 ±tr 2 Pco, . (13) ( 4( 'Ycao,) ('YHco,/'Yo) Brucite is denoted by the circles and the oxychloride is denoted by squares. Closed points correspond to the For relatively large NaCI concentrations the ionic data of ROBINSON and WAGGAMAN (1909). Open strength, aH,o and the trace activity coefficients are points are those of D'ANS and KATZ ( 1941) and D'ANS fixed and the solubility of calcite should depend roughly et al. ( 1955) at 20°C. It is difficult to obtain any de­ on the C02 pressure to the 113 power. As noted by finitive information from these data. We, therefore, SHTERNINA and FROLOVA ( 1952), this behavior is sat­ estimate the intermediate concentration behavior of isfied by the data. MgOH+ from the CULBERSON and PYTKOWICZ (1973) Mineral solubilities in natural waters 741

the .97 atm result is in agreement with these deter­

0056 minations as well as the smoothed temperature de­ pendence (See LINKE, 1965, and LANGMUIR, 1965). In fitting the high pressure results the fugacity-pressure

004 ,; correction is m(!.de as in the CaC03 system. ~ In Table 7, reported pK'1 and pK2 values are com­ pared to those calculated. The total hydrogen activity E"' 0024 coefficients (in NBS convention), determined by MEHRBACH et a!. ( 1973) may be used with the cal­

D culated activity coefficients in the Macinnes convention 0008 o 08 ___..~·•°<.... ~ to evaluate the liquid junction potential contribution,

O~ 1 I I I I L___j ~pH, using Eqn. (10) (section III). The resulting values 8 16 24 32 40 48 56 64 differ from those calculated with the CULBERSON and mMgCI 2 PYTKOWICZ ( 1973) data by about .02 pH units (see FIG. 13. The predicted solubility of brucite and magnesium Table 6). Since the differences in the concentration oxychloride in Mg-OH-Cl-H 20 solutions versus the available are small (as comparison of the calculated 'Y~ suggests), data. this would appear to reflect a changing liquid junction potential. (MEHRBACH eta!., 1973, observe a .Oil pH change between "identical" reference electrodes.) measurements of pKw in artificial seawater. Adjust­ There appear to be some problems with the lower ments in the third virial coefficients, fMg.MgOH.cl, are pressure results of KLINE ( 1929). A solubility product then made so the DBF data are fit at high concentra­ for nesquehonite of 3.5 X 10-5 is consistent with the tion. We select these over the other data in Fig. 13 Kline brucite-nesquehonite equilibrium Pco2 (.00038 since the model fit to the dilute solution and seawater atm.) and the MCGEE and HOSTETLER (1973) brucite system approximately without the third virial coeffi­ solubility product. Using the 3.5 X 10-5 value and the

cient predicts these data. We also require that the bru­ analytic concentrations of Mg and HC03 cited by cite-oxychloride invariant point is Jess than 2 M MgCh Kline, 'Y~s

calculations, except that NaF is replaced by NaCI. The quehonite at Pco2 ~ I atm. presence ofF in solution should cause a decrease in Assuming that the Kline nesquehonite data are ac­ the total (stoichiometric) activity coefficient for H due curate, a K,P = 1.2 X I o- 4 may be determined from to HF association. The experimentally determined ap­ the Mg and HC03 concentrations at low pressures parent equilibrium constant, K'w = m~m[JH, should assuming limiting law activity coefficients. To explain therefore be larger in solutions with traces of fluorine the high carbonate concentrations at low pressures a than in solutions without fluorine. However, HANSSON MgCO~ ion pair (or large negative MgC03 interaction ( 1972) has determined Kw in the absence of F, and parameters) may be defined. This model, however, his values are larger than those in the fluorine con­ cannot account for the rapidly decreasing total co3 taining solutions when corrected to the same units as concentration observed by Kline at high pressure. (The CP. Our calculations indicate that the difference cannot MgCO~ concentration is fixed when in equilibrium be explained by the concentration differences of the with nesquehonite, neglecting small changes in

artificial seawater used in the different studies. For the aH 2o, and the concentration determined from the low above reasons, we make no corrections for this effect. The fitted results are compared to the data in Table 6. Values for ~pH (Eqn. 10) calculated from these Tnh 1 e h: pKw i ·"- s_c_il"-'<1 t_e~ _a_t _v_a_~ in_us_~-;~ l_i ~l_i_t_ie:<;, - S_;'!_l)n_i_ty 19.90 26.87 ____ l4.82 44.0_ data and the activity coefficient for H (in molality pKt(('Xp) 11-.-J-1-1 i.cl2- 1-J~-24-lJ.-is 11.19 1 I. 12 units) are also given. rKw(calc) ll. 12 1 I. 25 II. 19 ll. 12 ~~BS(exp) . n95-. 698 . 694-. 696 . 702-. 704 . 719-723 The Mg-HC03 and Mg-C03 interaction parameters (~ (cllc) . nJo . h2 3 . 624 . 6'32 are estimated from the HANSSON ( 1973) data for K'1 r,_pH . 04 ]-. 044 .047-.048 _.0_51-_. 05_2 . 056-.058 .. ~ ~------and K2 in seawater together with the high pressure *Kw = 111H mOll (-m-~)-1-al_i_t_y_)_:' nesquehonite solubility data of MITCHELL ( 1923) and 'I he data for p~ and y NHS are those cited by Culberson and l'~tl~(lwicz (1973) (converted from molarity tn molality units). the Pco - I atll\ result of KLINE ( 1929). The high f BS is tlll' tn~al hydrog~n ion activity co~f:icient definPd 2 11 pressure (1-10 atm) trend for the solubility has been by thl' conventwn, p!l(NBS) = -logloaH· YjJ lS the hydrogen ion rtctivitv coefficient defined using the extended Macinnes reproduced at a number of different temperatures and convent ion, Eq. (7c). pH is calculated using Eq. (10). 742 C. E. Harvie, N. Meller and J. H. Weare

Table 7: pKi and PK2 calculated from a fit of Hansson's data (1973).

Salinity M pKi pKl pKi pK~ pK2 pK; (%,) YH ~calc2 {Hehrbach~ ~Hansson~ {calc) (Mehrbach~ ~Hansson~ 20 .631 5.893 5.920 5.921 9.133 9.130 9.117 25 .625 5.865 5.882 5.892 9.064 9.060 9.052 30 .624 5.842 5.860 5.866 9.006 9.000 8.987 35 . 625 5.823 5.833 5.842 8.956 8.949 8.932 40 .629 5.808 5.810 5.831 8.911 8.896 8.883

pressure data is significantly larger than the total co3 centrations are derived from the Appendix Table 2 in observed at high pressure.) RILEY and SKIRROW (1975). To explain the Kline data, we must assume that Starting with natural seawater, in contact with calcite enormous changes in the interactions occur over a crystals, calcite will precipitate from solution under very small concentration range. We could not fit the atmospheric conditions. Specification of one additional

Kline data, using a number of conventional electrolyte variable, such as pH, Pco2 or Ac is sufficient to com­ solution models including those with and without pletely define chemical equilibrium. For a given value

MgHCOj, etc. type ion pairs. Kline points to some of Ac, the pH and Pco2 can be calculated from equi­ problems with his HC03 determination. Also, his so­ librium conditions using a model. The data and cal­ lutions may not have equilibrated with the low Pco2 culated curve in Fig. 15 represent the dependence of atmospheres in 3 to 5 days. As nesquehonite dissolves, the equilibrium pH as a function of A0 • The apparent

C02 is depleted from solution. If C02 were not suf­ Pco 2 also varies along the curve. By virtue of electrical ficiently replenished from the atmosphere, the apparent

C02 pressure could be significantly reduced and brucite would precipitate. This might explain Kline's obser­ 040,------, vation of the nesquehonite to brucite conversion at a 036- A seemingly high Pco2 • Using our model derived from data other than Kline's we calculate the total Mg con­ 032- centration at nesquehonite-brucite equilibrium to be 028- .0140. This is in agreement with the value of .0136 which Kline extrapolated from his alkalinity mea­ 024 surements, but our calculated transition pressure is ~ 020 ::::-.-- .. 7.6 X atm. as compared to Kline's value of 3.8 ,. 0~0------w-s 0 16 ° 0 X w- 4 atm. Further data for this system are needed. After establishing the parameters {3° and (3°> for the 012

MgHC03 and MgC03 systems, the parameters oo8r- ,PMs.Hco,,so. and ,PMg,Hco,,o were obtained from the 0041-- nesquehonite solubility data of TRENDAFELOV et a/. 0 ( 1981 ). The low concentration end of these data places o 04 08 12 16 20 24 28 a rather strong constraint on the acceptable values of MgS04 (3< 0 and (3< 0>. The predicted solubilities of the model for these systems are compared to experimental data 0 B in Fig. 14. In Fig. 15, the pH for 35o/oo salinity seawater in equilibrium with calcite is plotted versus the carbonate alkalinity. The data are those of MORSE et at. ( 1980). 014 These authors determine the calcium concentration, pH, and carbonate alkalinity, Ac. Calcite equilibrium 8 012 is approached from supersaturation and undersatu­ ,."" 010 ration in a closed apparatus. The supersaturation ex­ 008 periments are performed by adding calcite to natural 006 seawater. For these experiments the relationship, 2mca 004 - Ac = Q, (where Q is a constant for seawater), is approximately satisfied by their data. The curve cor­ 002 responding to the data from supersaturation is cal­ 0 o~~~-~~~~~~2~8~3~2~3~6-4~0~ culated using seawater with composition given in Table 8. In Table 8, the molal concentration of 35o/oo salinity MgCI2 seawater are given together with the calculated total Fla. 14. Predicted solubility ofnesquehonite in MgS04 (a) Macinnes ion activity coefficients. The seawater con- and MgCI2 (b) solutions. Mineral solubilities in natural waters 743

pH

undersaturation supersaturation

2mc0-Ac '.0198 ( eq /kgswl 2mc0-Ac '.0184 (eq/kgsw)

.5 2.5

Ac (eq /kgsw)

FIG. 15. The predicted relationship between pH and carbonate alkalinity (Ac = (HCO))T + 2(C03-)T) for seawater at 35%o and 25°C in equilibrium with calcite. Closed circles represent the raw data of MORSE et a!. ( 1980).

neutrality constants, the function is independent of The solid curves in Fig. 15 correspond to the cal­ the equilibrium values of Pco,, pH or Ac. For un­ culated "pH" using the conventional hydrogen activity modified seawater Q = .018 eq/kg SW. for the Macinnes convention. The two dashed curves To approach calcite equilibrium from undersatu­ are calculated assuming that ApH for the Morse et a/. ration, Morse et a!. add a small amount of HCl to apparatus equals .03 (Table 6) or .05 (Table 7). The undersaturate the natural seawater with respect to cal­ .05 curve is generally above the undersaturated data cite. From the average value of Q calculated for the points and below the supersaturation points. There data from undersaturation, the quantity ofHCl added appears to be little trend in the data with equilibration has been estimated and added to the synthetic seawater times or the small variations in Q. Morse et a/. also in Table 8. This modified seawater solution was then report no statistically significant variation in the sol­ used to calculate the curve corresponding to the un­ ubility with the solid calcite to solution ratio. dersaturation approach to equilibrium (leftmost curve The increased solubility due to the precipitation of in Fig. 15). magnesium-calcite surface layers has recently received careful consideration (WOLLAST eta/., 1980; SCHOON­

Table 8: The composition of artificial 35/.,., salinity MAKER, 1981 ). The measurements from supersatu­ seawater used in the calculations for this article and the total ion activity coeffi­ ration of Morse et a/. should presumably be sensitive cients calculated with the extended ~1aclnnes to this effect although undersaturated experiments ion activity cnefficil:'nt convention (Eqs. (7c)).

------~------T should not. With the uncertainty due to the liquid mi y i Na- ---.-4869-5 -- -. 706 -- junction and the potential formation of magnesium­ K .01063 .651 Ca .01073 . 229 calcite surface layers, it is not possible to make an Mg .05516 .251 exact comparison to the data of Morse et al. Pessi­ H • 622 Cl . 56817 . 623 mistically, the calculation is within 10% of the true 504 . 02939 . 0864 OH • 243 solubility. If ApH = .05 and the data represent true Hco 3 .00185 .547 co, .000276 .0346 calcite equilibrium the agreement is much better. Using C02 9.63x 10~ 1.13 7 the model, a value of K~alcite = mt.mto 3 = 4.98 X 10- - p CO'l =3. 3~·17f4:--- 2 7 2 (molal) is obtained (4.65 X 10- (moles/kg SW) ). -log10 a~ = 8. 31, aH = .981 • 20 The solution given is in equilibrium with a CO? pressure V. DISCUSSION of 3. 3 x 10- 4 atm. Units are in moles/kg H20. Neutral activity coefficients can be calculated+ using the 1 formula Eq. (R.S) in Appendix B, i.e. YCaco3=[(.23)(.035)J':l, In the previous section, we have utilized, for the The concentrations and activity coefficients are cited to high accuracy to facilitate program verification. See most part, data in binary and ternary systems to pa­ Harvie et al. (1982) for tables which are also useful in this regard. rameterize the solution model. We have tested the ......

t

~

::r:

0 !"T1

~ I» ~

3: <> ..., ~ :z c:>. I» ?= = til ... I»

ji"

Kz

and

closed

Teeple

of equilibria

35°C

the

for

the

data

phase

50°C

between

equilibria

and

Predicted

(b)

phase

35°C

504

the

interpolated

circles.

Predicted

was

from

HC03i

(a)

closed

Nahcolite

(No

the

estimated

(NaCI).

with

2

l

3

were

halite

level.

+(HC0

3

2

(Aph-Bur-Hai-Then)

with

agreement

co

Pco

triangles

circle

K2

good

open

in

saturated

open

are

The

also

atmospheric

The

data

are

the

l

Teeple.

2

l

4

b.

(1938). of

Teeple (S0

3

times

K

solutions

Aphthitolite

the 10

data

(No

All

or

,

BLEIDEN

using

50°C

02

s~

Pc

25°C.

and

INo2S~l

Thenordite

3

and

·2H20)

at

3

10-

C0

2

estimates

X

35°C

No

Trono

•

3

system

l

3.3

the

MAKAROV

0

HC0

2

at

·KCI

Similar

3

(No

and

C0

from

2

2

l

3

Honksite

•2No

-COrH

3

4

(1933)

S0 +lHC0

equilibria

2

3

-C0

3

co

I9Na

thermonatrite.

extrapolated

phase

D'ANS

K2

-HC0

4

of

was

replaces

those

0

Predicted

2

square

(c)

are

7H

•

Na-K-Cl-S0

3

open

a.

atm.

the

C0

2

circles

The

in

Na

w-•

X

closed

1929).

(

where

3.3

by

s~

of

solubilities

20°C

TEEPLE

at

level 0l

2

denoted

of

·H

mineral

3

Pco,

C0

l

2

data

points

data

Thermonatrite

1Na

·KCI

3

The

C0

2

0

20°C

Predicted

2

Honksite

I

·2Na

·7H

invariant

4

16.

3

atmospheric

S0

C0

2

system:

2

the

2

No

the

FIG.

19No

metastable C0 and at

co3 Mineral solubilities in natural waters 745 model by calculating mineral solubilities in different, rameters, some of which have more recently been im­ more complex systems. For example, in Fig. 15, the proved (see DOWNES and PITZER, 1976; PEIPER and predicted relationship between the pH and carbonate PITZER, 1981 ). In the future, as refinements of the alkalinity of 35%o salinity seawater in equilibrium with model are made, we will attempt to incorporate the calcite is shown to be in good agreement with exper­ currently accepted parameter values into the solubility iment. model. The reader is cautioned, however, from mod­ The chemistry of seawater has been well measured. ifying parameters in the present model without ex­ While this system provides an excellent test of the tensive checking of the calculated solubilities, since model, there are other models which can accurately the parameters are quite interdependent. The param­ produce these data over a limited range of composition eter values in Tables 1-4 are a function of the model and concentration. The model, used in calculating Fig. chosen. The parameters in Table 4 may differ slightly 15, also accurately predicts thermodynamic properties from those of other authors. However in order to obtain to very high concentration for systems with compo­ consistent solubilities these values must be used. sition very different from seawater. This capability is The most important limitation of the application unique. To illustrate this flexibility, the predicted halite­ of this and similar models to natural systems is the saturated Janecke projection for the Na-K-CI-S04-C03- inherent equilibrium nature of the predictions. Re­ H20 quinary system is compared to experimental data cently, we have used this model to compare the evo­ in Fig. 16a. lution of seawater in natural evaporation processes The calculations and data depicted in Fig. 16a are with the prediction of chemical equilibrium. The confined to a closed system, where co3 bearing min­ agreement between the results of the equilibrium erals are dissolved in water and C02 transfer between models and the measured field results is remarkable, the atmosphere and solution is prevented. For many emphasizing the value of equilibrium evaporation natural waters, the aqueous C02 activity or the effective paths as guidelines for understanding evaporite evo­ equilibrium Pc02 is controlled by reaction with the lution (MeiLLER et al., in preparation). atmosphere, photosynthesis, water-rock reactions, etc. Fig. 16b and 16c depict the change in the phase equi­ Acknowledgements-We gratefully acknowledge many fruitful libria from that shown in Fig. 16a when the solutions discussions with Hans P. Eugster and the help of J.P. Green­ are allowed to equilibrate with a gas phase of constant berg with the parameterization in the MgC03 system. The 4 3 manuscript was improved through comments of Andrew Pco2 (3.3 X 10- and 3.3 X 10- atm., respectively). Comparison of Figs. 16a, 16b and 16c illustrates Dickson and the reviewers: Mark Bodine, Frank Millero and Niel Plummer. Work was supported by the Petroleum Re­ the strong Pco2 dependence of the stable mineral equi­ search Fund, PRF # 12992-AC5, Department ofEnergy, AT03- libria. It is known that the aqueous C02 activity is an 81SF-11563 and 4X29-935M-l and the National Science important indicator of the chemical processes leading Foundation, OCE 82-08482. to the formation and subsequent diagenetic evolution of carbonate sediments. However, quantitative inter­ REFERENCES pretation of carbonate sediments in terms of this C02 variable has not generally been possible due to the AKERLOF G. and SHORT 0. (1937) Solubility of sodium and lack of data or of a sufficiently accurate model. The potassium chlorides in corresponding hydroxide solutions model described here enables accurate prediction of at 25°C. J. Amer. Chern. Soc. 59, 1912-1915. ANGUS S., ARMSTRONG B. and REACH K. M. 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for the system CaC03-COrH20. Geochim. Cosmochim. YEATTS L. B. and MARSHALL W. L. (1957) Aqueous systems Acta 46, 1011-1037. at high temperatures, XVIII. Activity coefficient behavior RANDALL M. and LANGFORD C. T. ( 1927) The activity coef­ of calcium hydroxide in aqueous sodium nitrate to the ficient of sulfuric acid in aqueous solutions with sodium critical temperature of water. J. Phys. Chern. 71, 2641- sulfate at 25°C. J. Amer. Chern. Soc. 49, 1445-1450. 2650. REARDON E. J. and LANGMUIR D. (1974) Thermodynamic properties of the ion pairs MgCO~ and CaCO~ from 10°C to 50°C. Amer. J. Sci. 274, 599-612. APPENDIX A RILEY J.P. and SKIRROW G. (1975) Chemical Oceanography, PHENOMENOLOGICAL EQUATIONS Academic Press (2nd Edition). ROBIE R. A., HEMINGWAY B.S. and FISCHER J. R. (1978) The theory of calculating multiphase equilibria at fixed Thermodynamic properties of minerals and related sub­ temperature and pressure is based on the Gibbs free energy stances at 298.15 K and I bar pressure and at high tem­ minimization principle (CALLEN, 1960). The solution to the peratures. U.S.G.S. Bulletin 1452. following minimization problem is required. ROBINSON R. A. and BOWER V. E. (1966) Properties of aqueous mixtures of pure salts. Thermodynamics Minimize of the N ternary system: Water-sodium chloride-calcium chloride G = 2: n;!L;, (A. Ia) at 25°C. J. Res. U.S. Nat. Bureau of Stand. Sect. A70, i=l 313. ROBINSON R. A. and STOKES R. H. (1968) Electrolyte So­ subject to

lutions, Butterworths. N ROBINSON R. A. and MACASKILL J. B. ( 1979) Osmotic coef­ 2: n;c;1 = b, j = I, M + PE. (A.lb) ficients of aqueous sodium carbonate solutions at 25°C. i=l J. So/n. Chern. 8, 35-40. ROBINSON W. 0. and WAGGAMAN W. H. (1909) Basic Mag­ n; ;o: 0 i = I, N nesium Chlorides. J. Phys. Chern. 13, 673-678. In Eqn. (A.l), G is the Gibbs free energy for the system; n; ROGERS P. S. K. (1981) Thermodynamics of Geothermal is the number of moles of species i; IL; is the chemical potential Fluids. Ph.D. Thesis, Univ. of California, Berkeley. for species i; b is the number of moles of component j; c; ScHOONMAKER J. E. ( 1981) Magnesian Calcite-Seawater Re­ 1 1 are the coefficients in the linear mass and charge balance actions, Solubility and Recrystallization Behavior. Ph.D. equations; N is the total number of species; PE is the number Thesis, Northwestern University, Evanston, Illinois. of possible electrolyte aqueous and solid solution phases; and SHATKA Y A. and LERMAN A. ( 1969) Individual Activities of M is the total number of components. All the variables in Sodium and Chloride Ions in Aqueous Solutions of Sodium Eqn. (A. I) are adequately defined except the chemical po­ Chloride. Anal. Chern. 41, 514-517. tentials, which depend upon the macroscopic chemical prop­ SHTERNINA E. B. and FROLOVA E. V. (1952) The solubility erties of the system. Since it is currently impossible to calculate of calcite in the presence of C02 and NaCI. lz. Sek. Fiz. these properties ab initio, a phenomenological description of Khim. Anal. Inst. Ob. Neorg. Khim. Akad. Nauk SSSR these functions must be provided. 21, 271-287. (English translation: Associated Tech. Services, It is conventional to define the activities of the species, a;, New Jersey, USA). in electrolyte solutions by the following equation: SHTERNINA E. B. and FROLOVA E. V. (1962) Extraction of Ballast Carbonates from Kara-Tau Phosphorite Ore. Zh. aG) o Prikl. Khim. 35, 751-756. (Tr. J. Chern. USSR 35, 1962, - = IL; = lli + RTln a;, (A.2a) (an; T,P,n 729-733). 1 STOCK D. I. and DAVIES C. W. ( 1948) The second dissociation where ,..? is the standard chemical potential for species i. The constant of Magnesium hydroxide. Trans. Faraday Soc. activity and osmotic coefficients are defined by 44, 856-859. STORONKIN A. V., SHUL'TS M. M., LANGUNOV M. D. and In a; = In 'Y;m; (A.2b) OKA TOY M. A. ( 1967) Aqueous solutions of strong elec­ for each trolytes IV. Activity of hydrogen chloride in the hydrochloric solute species i and, acid-sulfuric acid-water system and of sodium chloride in the sodium chloride-sodium sulfate-water system. Russ. J. (A.2c) Phys. Chern. 41, 541-543. STOROZHENKO V. A. and SHEVCHUK V. G. (1971) The for the solvent, 'Y; and m; are the activity coefficient and K S0 -H S0 -H 0 system at 25°C. Russ. J. lnorg. Chern. 2 4 2 4 2 molality of the solute species. The osmotic coefficient, ¢, is 16(1), 121-124. related to the activity of the solvent by Eqn. (A.2c) where W TAYLOR B. ( 1927) Electromotive P. force with transference is the molecular weight of water (18.016). (The sum over i and theory of interdiffusion of electrolytes. J. Phys. Chern. in Eqn. (A.2c) represents the sum over all solutes: cations, 31, 1478-1500. anions and neutrals.) TEEPLE J. E. ( 1929) The industrial development of Searles The chemical potentials for pure phases, such as minerals, Lake brines with equilibrium data. A mer. Chern. Soc. Mono. are constants at fixed temperature and pressure. For gases, Ser., Mono. 49. the fugacity of a gas phase species,;;, is defined by the equation, TRENDAFELOV D., MARKOV L. and BALAREV KH. ( !981) 0 Phase equilibria in the MgCOrMgS04-H20 and MgC03- ..!!:.!.. =.!:!....+In/; (A.2d) MgCh-H20 systems at 25°C in a C02 atmosphere. Russ. RT RT ,. J. lnorg. Chern. 26(6), 907-909. WINDMAISSER F. and STOCKL F. (1950) Basic alkali sulfate. For many gases below one atm., the fugacity nearly equals Monatsb. 81, 543-550. the partial pressure, P;. WOLLAST R., GARRELS R. M. and MACKENZIE F. T. ( 1980) The remaining variables lacking explicit definition in the Calcite-Seawater Reactions in Ocean Surface Waters. A mer. theory are the excess functions, 'Y; and (¢ - 1). We use the J. Sci. 280, 831-848. semiempirical equations of PITZER (1973) and co-workers to Y ASUNISKI A. and YOSHIDA F. (1979) Solubility of carbon model these functions. These functions have been rewritten dioxide in aqueous electrolyte solutions. J. Chern. Eng. in Eqn. (A.3), and resemble those of HW except for the ad­ Data 24, 11-14. dition of terms for neutral species. The neutral species terms Mineral solubilities in natural waters 749 include new parameters, A, which account for the interactions Eqn. (A.3) should not be interpreted as having special physical between neutral species and ionic species in the solution (see significance as written. Equations (A.3b) and (A.3c) are sym­ PITZER and SILVESTER, 1976). In the carbonate system, the metric for anions and cations, and satisfy Maxwell relation­ inclusion of neutral species (e.g. C02(aq)) is required to de­ ships among all the species in solution. When these equations scribe observed solution behavior. are used to calculate mean activity coefficients, or any linear combination, 2: v,ln ai, for which 2: vizi = 0, (e.g. solubilities), L: mi(t/>- I) they are equivalent to the equations given by Pitzer and co­ workers. Nc Na The second virial coefficients, B, in Eqn. (A.3) are given 0 312 112 = 2(-A / j(l + 1.2/ ) + L; L: mcm.(Bt, + ZCca) the following ionic strength dependence. (See PITZER, 1973). c=l a=l (A.5a) Nc-1 Nc No BMx = ~x + ~xg(aMxv']) + 13Wxg(12V]) (A.5b) c=l c'=c+l a= I

Na-1 Na Nc BMx = ~d(aMxYi)/1 + i3Wd(12Yi)//. (A.5c) m.m.. (t· + mc1/laa•c) + L: L: L: The functions, g and g', are defined by the equations, a=l a'=a+l c=l

2 Nn Na No Nc g(x) = 2(1 - (I + x)e~~fx (A.5d) + L; L; mnmaAna + L; L; mnmcAnc) (A.3a) n=l a=l n=l c=l 2 g'(x) = - 2( I - (I + x + ~)e~x) / x (A.5e) N, In 'YM = z~F m.(2BMa + zcM.) + L: with x = aMx Vi or 12 Yi. When either cation M or anion X a= I is univalent aMx = 2.0. For 2-2 or higher valence pairs aMx Na Nc = 1.4. In most cases {3 121 equals zero for univalent type pairs. + L: mc(24>Mc + L: ma>/IMca) For 2-2 electrolytes a non-zero {3(2) is more common. The a= I c=l addition of a {3 121 term for univalent electrolytes represents a Na-1 Na Nc Na minor modification of the original Pitzer approach. This term + L; L; m.m.·faa'M + lzMI L; L; mcmaCca has primarily been utilized to describe small negative devia­ a=l a'=a+l c=l a=l tions from the limiting law which are observed for certain No pairs of ions. A more detailed discussion is given in + L; mn(2AnM) (A.3b) Section II. n""-1 The second virial coefficients, 4>, which depend on ionic

N, strength, are given the following form (see PITZER, 1975). In 'Yx = zW mc(2Bcx + ZCcx) + L: 4>~ = (Jij + E!Jij(l) + JEIJW) (A.6a) c=l

Na Nc Nc-l Nc ij = (JiJ + E!Jij(l) (A.6b) + L: m.(24>xa + L: mcfxac) + L: L: mcmcfcc'x a= I c=l c=l c'=c+l jj = E(JW) (A.6c) Nc Na No The functions, E!JiJ(l) and t:o;p) are functions only of ionic strength and the electrolyte pair type. Integrals defining these n=l c=J a=l terms are given by PITZER ( 1975) and are summarized in the Nc Na Appendix ofHW. The interested reader is referred to HARVIE In 'YN = L: mc(2Ancl + L: m.(2Anal (A. 3d) ( 1981) for a useful numerical method for calculating these c=l a= I functions. The constant, IJiJ• is a parameter of the model. The second virial coefficients, Ani• representing the inter­ In Eqn. (A.3) me and Zc are the molality and charge of actions between ions and neutral species are assumed to be cation c. Nc is the total number of cations. Similar definitions constant. The form of Eqn. (A.3) for neutral species follows apply for anions, a, and neutrals, n. The subscripts M, X and very closely the treatment of PITZER and SILVESTER (1976). N refer to cations, anions, and neutrals, respectively. For use We refer the reader to this article for details concerning the in Eqn. (A.3), the following terms are defined. derivation of these equations. The third virial coefficients, Ctx and >/; iJk, are also assumed Jl/2 2 112 ) F = -A" +-In (I + 1.2/ ) to be independent of ionic strength. Ctx is a single electrolyte ( I + 1.2/112 1.2 parameter which is related to CMx in Eqn. (A.3) by Eqn. Nc Na Nc-1 Nc (A.4b). 1/liJk are mixed electrolyte parameters which are defined + L: L: mcm.B:,. + L: L: mcmc'I•:X,. when the indices i, j, and k do not all correspond to ions of c=l a= I c=l c'=c+l the same sign. By convention, the first two subscripts are Na-1 Na chosen as the like charged ions and the last subscript is chosen + L: L: m.m.. ct>;..., (A.4a) as the oppositely charged ion. a= I a'=a+l The complete set of parameters defining the model for the nonideal behavior of electrolyte solutions are: ~x. ~x, (A.4b) 13Wx and Ctx for each cation-anion pair, MX; IJiJ for each and cation-cation and anion-anion pair; fiJk for each cation-cation­ (A.4c) anion and anion-anion-cation triplet; and Ani for ion-neutral pairs. Given a set of mole numbers which satisfy charge balance A" is one third the Debye-Hiickel limiting slope and equal (Eqn. A.! b), the molalities and, consequently, the functions to .39 at 25°C (BRADLEY and PITZER, 1979). I, Z, g, g', Eo, and E!J' can be calculated. The functions Equations (A.2b) and (A.3c) are ion activity coefficients Btx(l), BMx(l), BMx(l), t(I), iJ(/), ct>;p) and then F may which have been defined by convention. In general, the ther­ be calculated using their defining equations. Given these pa­ modynamic properties of a system do not depend upon the rameters the free energy may be calculated from Eqns. (A.l )­ value of any single ion activity (GUGGENHEIM, 1929, 1930a). (A.2). Equilibrium conditions are defined when the assumed Consequently, single ion activity cannot be measured, and set of ni, minimizes the free energy, Eqn. (A. I). Mathematical 750 C. E. Harvie, N. M01ler and J. H. Weare

procedures for adjusting the values for the n; so that the free The activity coefficient for ion k is defined by the familiar energy is minimized are discussed elsewhere (HW). The pa­ equation, rameters which completely define the model for the Na-K­ Mg-Ca-H-Cl-S04-HC03-C03-0H-COrH20 system are given (8.6) in Tables I, 2, 3 and 4. The process of determining these Consider the conventional definition for the ion activity coef­ parameters is discussed in some detail in section IV. ficients given by the equation,

APPENDIX 8 (B.7) As has been discussed in detail by GUGGENHEIM ( 1929, where w is chosen common to all ions in a particular solution. 1930a) an ion activity or ion chemical potential cannot be The conventional ion activity coefficients so defined are con­ measured by experiment; e.g., emf, phase equilibria, diffusion sistent with the measurable mean activity coefficients since, rates or reaction rates. However, ion activities may be defined by convention. In the following discussion, we demonstrate that the emf for a cell with a liquid junction can be calculated using any convention for the ion activities. Similar analyses implying the following results are discussed elsewhere (BATES, 1973; GUGGENHEIM, 1960; and MACINNES, !961). In obtaining Eqn. (B.8), the identities zMvM + zxvx = 0 and Consider the electrochemical cell, discussed in section III, vM + vx = v have been used. Using the definition for ion activity coefficients in Eqn. (B.6), conventional ion activities Pt,H2Isoln XIIKCI(sat)IHg2Cl2,Hg,Pt. (A) are calculated by the equation, The emf of the cell is not an equilibrium property of the af = 'Yf mk = 'YkmkWz• = akWz•. (B.9) system. In addition to the reversible electrode potential, the electromotive force, E, of the cell depends on the electro­ Substituting the natural logarithms of Eqn. (B.9) for terms potential difference between solution, X, and the KCI-satur­ like In ak + zk In w in Eqn. (B.5), the following equation for atedsolution. This liquid junction potential develops because the cell emf in terms of the conventional ion activities is of ionic diffusion between the two solution phases, and there­ obtained: fore, depends upon the relative mobilities of the various ionic species in solution. Using the principles of irreversible ther­ RT[ modynamics (see HAASE, 1963, for a general derivation), the E = E* - F In a~(X) + In a~ 1 (KCI) following equation is obtained for the emf of cell A: KCI 1 J E = E* - R: (In aH(X) +In ao(KCI) + 2.:...!;, din af . (B.IO) L k Zk KCI 1 ) Comparison ofEqns. (B. I) and (B.IO) indicates that any con­ + 2.: ..!;,din ak . (B. I) L k zk ventional ion activities defined by Eqn. (B.9) may be sub­ stituted for the theoretical ion activities in calculating the E* is given by, emf by Eqn. (B. I) without making any approximation. Therefore, it is impossible to distinguish between the various ._1 0 fi 0 E - F (1·% + RT In H, + ILH.,c, conventional or the theoretical ion activities using the mea­ 2 sured values of the emf. Consequently, it is not possible to utilize such data to unambiguously obtain any information - 2~tjl.g - 2~tjl. - 2~t~l). (B.2) regarding real ion activities. This is a general result (TAYLOR, In Eqn. (B. I), tk is the reduced Hittorf transference number 1927; GUGGENHEIM, 1929, 1930a,b, 1960). of ion k, and zk is the charge on ion k. By definition, the For convenience, Eqn. (8.10) may be written as: transference numbers satisfy the relationship, RT (8.3) E = £8 - - In a~(X) - Ef,(X). (B. II) F The sum in Eqns. (B. I) and (B.3) includes all ionic species £8 and EL are defined by the equations, in the solution. The integration in Eqn. (B. I) extends over the transition region from solution X to the KCI saturated RT £8 = E* - - In a~ 1 (KCI) (B.I2) solution. The ionic activities in Eqn. (B. I) are theoretically F defined by a derivative in the free energy (i.e., Eqn. A.2a Appendix A). and Any arbitrary function of composition, w(x), satisfies the equation, RTLKCI I EL(X) = - 2.: ...!;, dIn af rKCI F k zk In w(KCI) - In w(X) = Jx dIn w RT [lKCI "' lk d I w(KCI)J KCI tk = - L..- In ak + n --- . (B.I3) = 2.:- d(zk In w), (B.4) F x k zk w(X) L k zk where Eqn. (B.3) has been used to obtain the last identity. In Eqns. (B. II) and (B.13), nomenclature representing the Adding this equality to Eqn. (B.!) and collecting similar terms, liquid junction potential explicitly denotes the dependence the following equation, identical to Eqn. (B. I) is obtained of this term on the composition of solution X. EL also depends on the KCI reference solution and the nature RT[ of the liquid E = E* - F In aH(X) + ZH In w(X) + In ao(KCI) junction. The last equality in Eqn. (B.l3) illustrates that the liquid junction potential depends on the ion activity coefficient conventions chosen in solution X and the reference solution. + z0 In w(KCI) + fKa 2.: !.!:_ d(ln ak + zk In w)J. (B.5) While the observed emf of the cell is not dependent upon Jx k zk the conventional definition of the ion activities, each of the fhe cell emf is independent of the arbitrary function, w. separate terms in Eqn. (B. II) is a function of the convention. Mineral solubilities in natural waters 751

In particular, it is demonstrated in Fig. 3 (section III), that activity (e.g. In aH+) requires the specification of a convention. the magnitude of the conventional liquid junction term is a Once a convention is specified (e.g., 'Y8 is designated by an strong function of the convention specified for solution X. arbitrary value), the conventional ion activities are unam­ The general definition of an ion activity coefficient con­ biguously defined in terms of the mean activities of the solution vention is given by Eqn. (B.7). These equations are defined by Eqn. (B.8). Therefore, since mean activities can be obtained in terms of absolute ion activity coefficients which cannot be using equilibrium measurements (i.e. cells without liquid measured and consequently are not known. It is, therefore, junctions), it is, in principle, unnecessary to utilize cells with necessary to specify an alternate procedure for calculating the liquid junctions to obtain conventional ion activities. Of conventional ion activities. The arbitrary nature of w in Eqn. course, this fact does not preclude the use of cells with liquid (B.9) permits specifying the conventional value of any ion junctions when experimental difficulties exclude the equilib­ activity coefficient in a given solution. Defining the value of rium approach. However, the interpretation of such data in 'Yf for a particular ion k implicitly defines the value for w by terms of the equilibrium properties of the system without the Eqn. (B. 7). It is common practice to define the ion activity use of the cumbersome theory of irreversible thermodynamics coefficient for Cl- by convention when interpreting the data is approximate. Figure 3 illustrates that such an approach from cell A (BATES and GUGGENHEIM, 1960). It has been may lead to non-negligible errors in the reported values of demonstrated in this appendix that the interpretation of the the thermodynamic properties for a system when these values data from a cell utilizing a liquid junction in terms of an ion are derived from pH data.