Solubility Model for Ferrous Iron Hydroxide, Hibbingite, Siderite, and

Article http://pubs.acs.org/journal/aesccq

Solubility Model for Ferrous Iron Hydroxide, Hibbingite, Siderite, and Chukanovite in High Saline Solutions of Sodium Chloride, Sodium Sulfate, and Sodium Carbonate Sungtae Kim, Cassandra Marrs, Martin Nemer, and Jay Je-Hun Jang* Sandia National Laboratories, 4100 National Parks Highway, Carlsbad, New Mexico 88220, United States S Supporting Information *

ABSTRACT: A solubility model is presented for ferrous iron hydroxide (Fe(OH)2(s)), hibbingite (Fe2Cl(OH)3(s)), siderite (FeCO3(s)), and chukanovite (Fe2CO3(OH)2(s)). The Pitzer activity coefficient equation was utilized in developing the model to account for the excess free energies of aqueous species in the background solutions of high ionic strength. Solubility limiting minerals were analyzed before and after experiments using X-ray diffraction. Formation of Fe(OH)2(s) was observed in the experiments that were initiated with Fe2Cl(OH)3(s) in Na2SO4 solution. Coexistence of siderite and chukanovite was observed in the experiments in Na2CO3 + NaCl solutions. Two equilibrium constants that had been reported by us for the dissolution of Fe(OH)2(s) and Fe2Cl(OH)3(s) (Nemer et al.) were rederived in this paper, using newer thermodynamic data selected from the literature to maintain internal consistency of the series of our data analyses in preparation, including this paper. Three additional equilibrium constants for the following reactions were determined in this paper: dissolution of siderite and chukanovite and dissociation of the aqueous species Fe(CO3)2−2. Five Pitzer interaction parameters were derived in this paper: β(0), β(1), and Cφ parameters for the species pair Fe+2/SO4−2; β(0) and β(1) parameters for the species pair Na+/Fe(CO3)2−2. Our model predicts that, among the four inorganic ferrous iron minerals, siderite is the stable mineral in two WIPP-related brines (WIPP: Waste Isolation Pilot Plant), i.e., GWB and ERDA6 (Brush and Domski), and the electrochemical equilibrium between elemental iron and siderite provides a low oxygen fugacity (10−91.2 atm) that can keep the actinides at their lowest oxidation states. (Nemer et al., Brush and Domski; references numbered 1 and 2 in the main text). KEYWORDS: ferrous iron hydroxide, hibbingite, siderite, chukanovite, speciation, Pitzer activity coefficient equation, internal consistency of thermodynamic database

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INTRODUCTION Groundwater of high salinity (brine, hereafter) that could infiltrate the WIPP (Waste Isolation Pilot Plant) after closure poses unique experimental and analytical challenges, one of them being a greater extent of nonideal behavior of the aqueous species. WIPP is a deep underground repository developed by the U.S. Department of Energy (DOE), and the purpose of the WIPP is to permanently isolate defense-related transuranic (TRU) radioactive wastes by taking advantages of the properties of rock salts, e.g., low porosity, self-sealing, and high heat conductivity. WIPP is located within the bedded salts of the Permian Salado Formation, which consists of interbedded halite (NaCl) and anhydrite (CaSO4) layers overlaying the Castile Formation. To calculate the concentrations of aqueous species in brines, the current WIPP geochemical thermodynamic database was built upon multiple brine models.3−6 These models3−6 employed the Pitzer activity coefficient equation.7−9 Pitzer’s equation is applicable from zero to high ionic strength.10 There is a general consensus that the other activity coefficient models, such as Debye−Huckel, Davies, B-dot, and SIT, are useful when the ionic strength is less than 3.5 molal.11 © 2017 American Chemical Society

Detailed information on iron (Fe) chemistry is required for the WIPP Performance Assessment because of the chemical linkage to the oxidation states and mobility of actinides. A significant amount of Fe will be emplaced in the WIPP by the time the repository closes, in great excess with respect to the mass of the waste.12 Iron is a part of the waste and the repository infrastructure, and it is the main component of steel drums that are used to contain the waste. The WIPP geochemistry model postulates that anoxic corrosion of Fe will produce aqueous ferrous iron, Fe+2, after closure of the repository. The anoxic corrosion of Fe will dominate the electrochemical condition of the WIPP, which is expected to keep the actinides at their lowest oxidation states of lower mobility. Aqueous ferrous iron, along with other dissolved metals such as calcium and magnesium, is expected to decrease the activities of anionic ligands (both inorganic and organic), such as OH−, CO3−2, SO4−2, EDTA−4, citrate−3, oxalate−2, and acetate−, by complexing with them or by Received: Revised: Accepted: Published: 647

June 5, 2017 September 11, 2017 September 18, 2017 November 20, 2017 DOI: 10.1021/acsearthspacechem.7b00065 ACS Earth Space Chem. 2017, 1, 647−663

Article

ACS Earth and Space Chemistry

Table 1. Solubility Data for Fe2Cl(OH)3(s) and Fe(OH)2(s) Experiments by Nemer et al.1 (Fe+2−Na+−H+−Cl−−H2O System)a Σ[Fe+2]

pmHc

Hibbingite (Fe2Cl(OH)3(s)) experiments 7.66 × 10−04, 1.35 × 10−03, 1.47 × 10−03, 1.52 × 10−03, 1.90 × 10−03 1.40 × 10−03 4.11 × 10−04 (29%) 2.76 × 10−04, 2.13 × 10−04, 2.50 × 10−04, 2.51 × 10−04, 3.45 × 10−04, 3.93 × 10−04, 4.26 × 10−04, 4.96 × 10−04, 2.59 × 10−04 3.23 × 10−04 9.66 × 10−05 (30%) 1.56 × 10−04, 1.72 × 10−04, 1.73 × 10−04, 1.72 × 10−04, 3.24 × 10−04, 3.52 × 10−04, 4.05 × 10−04, 4.11 × 10−04 2.71 × 10−04 1.13 × 10−04 (42%) 1.27 × 10−04, 1.70 × 10−04, 1.24 × 10−04, 1.51 × 10−04, 2.16 × 10−04, 2.60 × 10−04, 2.90 × 10−04, 3.29 × 10−04 2.08 × 10−04 7.80 × 10−05 (37%) 1.00 × 10−04, 9.00 × 10−05, 1.03 × 10−04, 1.19 × 10−04, 1.42 × 10−04, 2.33 × 10−04, 1.88 × 10−04, 3.15 × 10−04 1.61 × 10−04 7.92 × 10−05 (49%) 8.57 × 10−05, 9.99 × 10−05, 1.10 × 10−04, 9.52 × 10−05, 2.54 × 10−04, 1.46 × 10−04, 3.21 × 10−04, 1.97 × 10−04 1.63 × 10−04 8.62 × 10−05 (53%) NaCl Σ[Fe+2]

8.33, 8.19, 8.17, 8.22, 8.14 8.21 0.07 (1%) 8.58, 8.63, 8.63, 8.61, 8.36, 8.38, 8.42, 8.39, 8.68 8.52 0.13 (2%) 8.74, 8.81, 8.73, 8.73, 8.37, 8.43, 8.35, 8.40 8.57 0.20 (2%) 8.81, 8.91, 8.79, 8.70, 8.51, 8.49, 8.45, 8.46 8.64 0.18 (2%) 8.89, 8.99, 8.86, 8.80, 8.49, 8.44, 8.69, 8.55 8.71 0.20 (2%) 8.98, 8.96, 8.83, 8.84, 8.42, 8.61, 8.56, 8.55 8.72 0.21 (2%) pmHc

NaCl 0.1 average SDb (% SD) 1.0 average SDb (% SD) 2.0 average SDb (% SD) 3.0 average SDb (% SD) 4.0 average SDb (% SD) 5.0 average SDb (% SD)

Ferrous iron hydroxide (Fe(OH)2(s)) experimentsd 1.41 × 10−03, 1.52 × 10−03, 1.53 × 10−03 1.49 × 10−03 6.66 × 10−05 (4%) 1.12 × 10−03, 1.23 × 10−03, 1.23 × 10−03 1.19 × 10−03 6.35 × 10−05 (5%) 1.00 × 10−03, 1.12 × 10−03, 1.13 × 10−03 1.08 × 10−03 7.23 × 10−05 (7%) 8.77 × 10−04, 9.32 × 10−04, 9.34 × 10−04 9.14 × 10−04 3.23 × 10−05 (4%) 6.83 × 10−04, 6.98 × 10−04, 6.66 × 10−04 6.82 × 10−04 1.60 × 10−05 (2%)

0.04 average SDb (% SD) 0.15 average SDb (% SD) 0.50 average SDb (% SD) 1.22 average SDb (% SD) 3.03 average SDb (% SD)

7.93, 7.95, 7.95 7.94 0.01 (0%) 8.04, 8.05, 8.04 8.04 0.01 (0%) 8.12, 8.17, 8.15 8.15 0.03 (0%) 8.26, 8.32, 8.30 8.29 0.03 (0%) 8.44, 8.51, 8.50 8.48 0.04 (0%)

a

Concentrations are in molal units (moles of solute in kg of water). Averaged data were used in model calculations. bStandard deviation. cNegative 10-based logarithm of H+ concentration in molal scale. dThe samples representing NaCl = 6 molal in Nemer et al.1 are being investigated separately due to the need for further solid phase characterization.

Table 2. Solubility Data of Fe(OH)2(s) and Fe2Cl(OH)3(s) in Na2SO4 ± NaCl Solutions (Fe+2−Na+−H+−Cl−−“SO4−2”−H2O System)a Cl−

SO4−2

Na+ 0.17

0.01

0.35

0.10

1.15

0.5

2.15

1

3.15

1.5

3.75

1.8

0.15 average SDb (% 0.15 average SDb (% 0.15 average SDb (% 0.15 average SDb (% 0.15 average SDb (% 0.15

SD)

SD)

SD)

SD)

SD)

Σ[Fe+2] Ferrous iron hydroxide (Fe(OH)2(s)) experiments 1.67 × 10−03, 1.86 × 10−03, 1.88 × 10−03 2.28 × 10−04 (12%) 1.30 × 10−03, 1.54 × 10−03, 1.51 × 10−03 1.97 × 10−04 (13%) 1.19 × 10−03, 1.30 × 10−03, 1.34 × 10−03 1.75 × 10−04 (13%) 9.70 × 10−04, 1.07 × 10−03, 1.15 × 10−03 2.22 × 10−04 (19%) 7.68 × 10−04, 1.12 × 10−03, 1.04 × 10−03 2.47 × 10−04 (24%) 7.68 × 10−04, 8.53 × 10−04, 648

2.12 × 10−03

1.69 × 10−03

1.53 × 10−03

1.40 × 10−03

1.24 × 10−03

1.21 × 10−03

pmHc 8.06, 7.89, 7.95 0.09 (1%) 8.25, 8.27, 8.23 0.05 (1%) 8.34, 8.37, 8.30 0.09 (1%) 8.39, 8.43, 8.34 0.12 (1%) 8.53, 8.56, 8.47 0.12 (1%) 8.54, 8.58,

7.90

8.17

8.20

8.20

8.33

8.39

DOI: 10.1021/acsearthspacechem.7b00065 ACS Earth Space Chem. 2017, 1, 647−663

Article

ACS Earth and Space Chemistry Table 2. continued Na+

0.1

0.76 1.52

2.28

3.04

3.8

Cl−

SO4−2

0.05 average SDb (% 0.38 0.76 average SDb (% 1.14 average SDb (% 1.52 average SDb (% 1.9 average SDb (%

SD)

SD)

SD)

SD)

SD)

Σ[Fe+2]

pmHc

Ferrous iron hydroxide (Fe(OH)2(s)) experiments 9.44 × 10−04 2.35 × 10−04 (25%) Hibbingite (Fe2Cl(OH)3(s)) experiments 10−03, 9.48 × 10−03 1.40 × 10−02, 1.90 × 10−02 −03 10 1.65 × 10−02 −03 10 (21%) 3.51 × 10−03 (21%) 10−03d 1.58 × 10−02d 10−03, 7.34 × 10−03, 8.41 × 10−03 1.69 × 10−02, 1.47 × 10−02, 1.68 × 10−02 −03 10 1.61 × 10−02 −04 10 (8%) 1.27 × 10−03 (8%) 10−03, 7.31 × 10−03, 6.60 × 10−03, 7.08 × 10−03 1.32 × 10−02, 1.46 × 10−02, 1.32 × 10−02, 1.42 × 10−02 10−03 1.38 × 10−02 −04 10 (5%) 7.03 × 10−04 (5%) −02 −02 −02 10 , 1.33 × 10 , 1.37 × 10 2.25 × 10−02, 2.65 × 10−02, 2.74 × 10−02 10−02 2.55 × 10−02 10−03 (10%) 2.64 × 10−03 (10%) 10−02, 1.87 × 10−02, 1.52 × 10−02, 2.05 × 10−02 2.40 × 10−02, 3.75 × 10−02, 3.03 × 10−02, 4.11 × 10−02 10−02 3.32 × 10−02 10−03 (23%) 7.61 × 10−03 (23%)

average SDb (% SD)

8.51 0.10 (1%)

× × × × × × × × × × × × × × × ×

7.75, 7.69 7.72 0.04 (1%) 7.85d 7.64, 7.68, 7.69 0.06 (1%) 7.65, 7.73, 7.76 0.10 (1%) 7.62, 7.77, 7.73 0.10 (1%) 7.76, 7.64, 7.74 0.08 (1%)

7.00 8.24 1.76 7.88 8.47 8.07 6.35 6.62 6.90 3.51 1.12 1.27 1.32 1.20 1.66 3.81

7.76

7.89, 7.78

7.80

7.72, 7.83

a

Concentrations are in molal units (moles of solute in kg of water). Averaged data were used in model calculations. bStandard deviation. cNegative 10-based logarithm of H+ concentration in molal scale. dAverage and standard deviation cannot be calculated because only one measurement was available.

Table 3. Reactions Selected To Update the Thermodynamic Data in Nemer et al.1 (Reactions Selected for the Sulfate System Are Also Listed) Reactions aqueous reactions H+ + OH− = H2O HSO4− = SO4−2 + H+ FeOH+ + H+ = Fe+2 + H2O Fe(OH)2(aq) + 2H+ = Fe+2 + 2H2O Fe(OH)3− + 3H+ = Fe+2 + 3H2O Fe(OH)4−2 + 4H+ = Fe+2 + 4H2O dissolution NaCl(s) = Na+ + Cl− Na2SO4·10H2O(s) = 2Na+ + SO4−2 + 10H2O Na3H(SO4)2(s) = 3Na+ + 2SO4−2 + H+ Na2SO4(s) = 2Na+ + SO4−2 Fe(OH)2(s) + 2H+ = Fe+2 + 2H2O

log K 4 4 27 25 28 28

1.57 −1.22 −0.81 −0.28 12.95 12.83 13.27 13.14 12.89b

4 4 4 4 1 Figure S1 Figure S6 Figure 3 updated in this paper, Figure 5 1 updated in this paper, Figure S1, Figure 5 29,30 11 11 11 32

17.12 17.08

FeSO4(s) = Fe+2 + SO4−2 FeSO4·H2O(s) = Fe+2 + SO4−2 + H2O FeSO4·4H2O(s) = Fe+2 + SO4−2 + 4H2O FeSO4·7H2O(s) = Fe+2 + SO4−2 + 7H2O

1.93c −0.99c −1.65c −2.27c −2.34c

are subject to change under the Pitzer formulation once experimental data (e.g., concentration versus pH) becomes available for high ionic strength systems. bTo be maintained in our database until reliable isopiestic data for the species pair Fe+2/SO4−2 are available. cKept in the database to check if our experimental conditions indicate any precipitation of these solids.

refs

13.99 −1.97 9.31a 20.82a 31.00a 46.00a

Fe2Cl(OH)3(s) + 3H+ = 2Fe+2 + Cl− + 3H2O

Table 3. continued

forming solids of low solubility, such as Fe(OH)2(s), Fe2Cl(OH)3(s), FeCO3(s), Fe2CO3(OH)2(s), and FeOxalate·2H2O(s) (Humboldtine). The net result of Fe+2−anionic ligand interaction is that there are fewer ligands available for complexing with actinides. The Geochemistry team at Sandia National Laboratories in Carlsbad, New Mexico, U.S.A. has worked on expanding their thermodynamic database to include the aqueous chemistry of ferrous iron. This paper is the second in a series continuing from Nemer et al.1 and presents a solubility model that is internally consistent for the four inorganic ferrous iron minerals, i.e., Fe(OH)2(s), Fe2Cl(OH)3(s), FeCO3(s), and Fe2CO3(OH)2(s), in high saline solutions of NaCl, Na2SO4, and Na2CO3. The equilibrium constants for the dissolution of Fe(OH)2(s) and Fe2Cl(OH)3(s) in Nemer et al.1 were reparameterized using newer thermodynamic data that cover a wider ionic strength range. In developing the model, the thermodynamic data (i.e., equilibrium constants of reactions and the related Pitzer interaction parameters) common to multiple systems were kept the same to maintain the internal consistency of the final database.

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MATERIALS AND METHODS Experiments that contain the ferrous iron (Fe+2) were performed in anoxic gloveboxes made by LABCONCO and VAC (OmniLab) to minimize the oxidation of Fe+2 by oxygen. Inert gas filling the gloveboxes is argon or nitrogen, and the gas inside the gloveboxes was continuously treated by oxygen scrubbers. Oxygen concentration inside the gloveboxes routinely reads 0 (LABCONCO)

a These Fe+2 hydrolysis constants were selected after critically reviewing values from multiple references. For example, log K(FeOH+) are 9.10 in Lemire et al.11 and 9.5 in Stumm and Morgan.25 Log K(Fe(OH)3−) is 31.9 in Langmuir.31 However, the selected values

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Table 4. Pitzer Interaction Parameters Related to the Fe+2−Na+−H+−SO4−2−Cl−−H2O System (Those Used to Update the Thermodynamic Data in Nemer et al.1 Are Also Listed)

α1 and α2 are preset constants used in the Pitzer activity coefficient equation. α1 and α2 apply for only cation−anion binary pairs. α2 is not applied when β(2) is zero or not used. Unit for α1 and α2 is kg1/2·mol−1/2. BTo be maintained in our database until reliable isopiestic data are available.

A

A UV−visible spectrophotometer (CARY 300 Conc) was used to measure the absorbance of Fe+2−ferrozine complex at the wavelength of 562 nm. The total dissolved concentration of Fe+2, Σ[Fe+2]meas, measured using the ferrozine method, did not show significant difference from the concentration of total dissolved Fe, Σ[Fe]meas, by ICP-AES. The concentrations of SO4−2 and Cl− were measured using an ion chromatograph (IC, DIONEX 3000). The CO3−2 concentrations were measured using a CO2 coulometer (UIC, Inc., CM5015). Details on the conversion from mol/L or mg/L to molal (mole solute in kg water) scale are in Nemer et al.1 and Jang and Kim.13 All experiments were performed at ambient room temperature and pressure. Syntheses of Fe(OH)2 and Fe2Cl(OH)3(s) were described in Nemer et al.1 Briefly, Fe(OH)2(s) (ferrous iron hydroxide) was synthesized by mixing 24.992 g of FeCl2·4H2O (Fisher) and 10.059 g of NaOH (Fisher) in 500 mL of DDI water. Precipitation was observed immediately, and the suspension was shaken periodically for at least a week. The precipitated solid was washed by volumetrically replacing the supernatant with DDI water until the calculated concentration of the dissolved NaCl concentration decreased to 0.036 mol/L. Fe2Cl(OH)3(s) (hibbingite) was synthesized by mixing FeCl2·4H2O (Fisher) and KOH (Fisher) in molar ratio of 1:1.86 in 700 mL total volume with net chloride concentration of 3.2 mol/L. The solids were analyzed using an X-ray diffractometer (XRD, Bruker, D8) before and after the experiments (Nemer et al.1). In these experiments, the identities of the phases did not change from start to finish. FeCO3(s) (siderite) was synthesized by mixing 150 mL of 4.0 m NaHCO3

or 0.30 ppm (VAC, Omni-Lab), occasionally reaching up to 10 ppm when the transfer chamber doors were opened to move supplies and samples into or out of the gloveboxes. Whenever the transfer door was opened, experimentation inside the gloveboxes began after at least 1 h to ensure the oxygen concentration was well below the detection limit. For the LABCONCO glovebox, the oxygen meter was periodically calibrated by the manufacturer, and sensors were replaced to avoid erroneous readings that come from the use of nitrogen or argon as inert gas inside the gloveboxes and the aging of the sensors. For the VAC (OmniLab) glovebox, the oxygen scrubber was periodically regenerated, and the sensor was replaced when we noticed that the routine reading steadily increased. All experiments were prepared inside the gloveboxes using serum bottles that use rubber seals and aluminum crimps. Deionized (DI) water was purged by circulating the inert gas of the gloveboxes through the DI water for at least 3 h (deoxygenated deionized, DDI, water). Filtration (PALL nylon membrane syringe filters with pore size of 0.2 μm) followed by acidification and dilution was also performed inside the gloveboxes. Membrane filters with nitrate functional groups were not used due to immediate oxidation of the ferrous iron upon contact. The concentration for the acidification was either 5% nitric acid (final concentration in the diluted samples) for the measurement of the total dissolved metal cations by inductively coupled plasma atomic emission spectrophotometry (ICP-AES, PerkinElmer, OPTIMA 3000 Dual View). For the ferrozine assay, hydrochloric acid was used at the final concentrations of 0.1− 1 M in the diluted samples for the total dissolved ferrous iron. 650


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siderite above was aged in carbonate solutions spiked with NaCl. The Fe+2-containing solids were packed into an anoxic holder for the XRD inside the gloveboxes prior to XRD scans. An aqueous speciation code, EQ3NR packaged in EQ3/6, version 8.0a,14 was used for model calculations. Initial model calculations for each system were performed to calculate the Σ[Fe+2]calc using a set of thermodynamic data (i.e., the equilibrium constants of chemical species and the related Pitzer interaction parameters) selected from the literature. When the Σ[Fe+2]calc did not match satisfactorily with the Σ[Fe+2]meas, thermodynamic data were adjusted as fitting variable(s) until a better match was obtained between Σ[Fe+2]calc and Σ[Fe+2]meas. Adjustment of fitting variables and execution of EQ3NR using the adjusted fitting variables were iterated until a minimized residual was obtained. The residual is defined in equation e1. The iteration was driven by a script written in the Python computer language. Definition of the residual. residual =

∑ (log∑ [Fe+2]calc

− log∑ [Fe+2]meas )2 (e1)

where Σ[Fe ]calc and Σ[Fe ]meas mean calculated and measured aqueous Σ[Fe+2], respectively. Data analysis began with the simplest system and progressed to other systems that have additional components. Thermodynamic data common to multiple systems were kept the same to maintain the internal consistency of the final database. +2

Figure 1. XRD of solids used for the experiments in the Na2SO4 ± NaCl solutions. (A) Solid collected from an experiment in solution made of Na2SO4 and NaCl, where Fe(OH)2(s) was added at the beginning of experiments. Major peaks match with Fe(OH)2(s) and minor peaks with Na2SO4 and NaCl that precipitated from background solution trapped in the pore of collected solid. (B) Solid collected from an experiment in solution made of Na2SO4 without added NaCl, where Fe2Cl(OH)3(s) was added to initiate the solubility experiments. Major peaks match with Fe2Cl(OH)3(s) and Fe(OH)2(s), indicating that the Fe(OH)2(s) formed at the expense of Fe2Cl(OH)3(s). Minor peaks match with Na2SO4. Solids after reactions were not washed to not create abrupt undersaturation of newly formed mineral.

+2

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RESULTS AND DISCUSSION Solubility data, their averages, and standard deviations, as well as the experimental conditions for the Fe2Cl(OH)3(s) and Fe(OH)2(s) experiments in NaCl solutions (Fe+2−Na+−H+− Cl−−H2O system) are listed in Table 1. These data are from Nemer et al.1 Solubility data, their averages, and standard deviations, as well as the experimental conditions for the Fe2Cl(OH)3(s) and Fe(OH)2(s) experiments in Na2SO4 ± NaCl solutions (Fe+2−Na+−H+−SO4−2−Cl−−H2O system) are listed in Table 2. Averaged data were used to fit the model described below. Table 3 and Table 4 list the thermodynamic data, i.e., equilibrium constants for the reactions and the related Pitzer interaction parameters, selected to describe the Fe+2−Na+−H+−SO4−2−Cl−−H2O

(Fisher) and 200 mL of 2.95 m FeCl2·4H2O (Fisher), where m represents molality (moles solute in kg water). An XRD scan positively identified the formation of siderite. Chukanovite was identified by XRD from the experiments where the synthesized

Figure 2. Stability diagrams of Fe(OH)2(s) and Fe2Cl(OH)3(s) in the Na2SO4 ± NaCl solutions. Our experiments reached the stability field of Fe(OH)2(s). (A) Na2SO4 solutions spiked with NaCl = 0.15 molal. (B) Na2SO4 solutions without added NaCl. No Pitzer interaction parameters related to species Fe+2 and SO4−2 were used at all in constructing these diagrams. Interim updated log K values for Fe(OH)2(s) and Fe2Cl(OH)3(s) were used (12.83 and 17.08, Figure S1). 651


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Figure 3. Concentrations of the relevant Fe+2 species in equilibrium with (A) Fe2Cl(OH)3(s) in NaCl, (B) Fe(OH)2(s) in NaCl, (C) Fe(OH)2(s) in Na2SO4 + NaCl (0.15 m), and (D) Fe(OH)2(s) in Na2SO4 solutions. Experiments for (D) were initiated with Fe2Cl(OH)3(s), but they reached the stability of Fe(OH)2(s) (Figure 1 and Figure 2). The calculated and measured Σ[Fe+2] are plotted together. The log K values for hibbingite and ferrous iron hydroxide were adjusted as fitting variables, which were determined to be 17.08 and 13.14. The Pitzer interaction parameters for the pair Fe+2/SO4−2 were selected from Reardon and Beckie17 for this fit. The activity coefficients are illustrated in Figure 4. Fit in (B) became worse than that in Figure S1 for Fe(OH)2(s) experiments, where the Na2SO4 experiments were not fitted simultaneously. The residuals are 0.001 (A) + 0.495 (B) + 0.304 (C) + 0.294 (D) = 1.098.

log K for the Fe(OH)2(s) in Figure S1, i.e., 12.83, was determined without considering the experimental data in Table 2 (Figures 3 and 5), where the Fe(OH)2(s), common to the experimental data in Table 1, was assigned to be the solubility limiting phase. Detailed discussion follows below. Ferrous iron hydroxide, Fe(OH)2(s), was the solubility limiting solid for the experiments in solutions made of mixtures of Na2SO4 and NaCl (Table 2, upper part). Hibbingite, Fe2Cl(OH)3(s), was the initial solid for the experiments in solutions made of Na2SO4 only (Table 2, lower part). Analysis by XRD indicated no mineralogical changes in Na2SO4 + NaCl experiments in which Fe(OH)2(s) was the starting phase (Figure 1A). However, from the Na2SO4 experiments conducted without added NaCl, Fe(OH)2(s) formed at the expense of Fe2Cl(OH)3(s) that was added as the initial solid phase (Figure 1B). Application of the thermodynamic data in Table 3 and Table 4 indicates that our experiments were performed within the stability field of Fe(OH)2(s) (Figure 2), meaning that the log K values for ferrous iron hydroxide and hibbingite derived in the fit shown in Figure S1 support our observation. Up to this point, any Pitzer parameters for pairs and triplets of species related to Fe+2 and SO4−2 were not employed in the model calculation (those bound solid and dashed vertical red lines in Table 4), and the neutral aqueous species FeSO4(aq) will not be considered in further discussions as the ionic interaction between Fe+2 and SO4−2, major dissolved species of interest, will be accounted for. Fe(OH)2(s) is the solid closer to equilibrium than Fe2Cl(OH)3(s), and Fe2Cl(OH)3(s) showed undersaturation consistently. Other solids in Table 3 also showed undersaturation. The deficiency of Cl− would make the Fe2Cl(OH)3(s)

system, and these thermodynamic data in Table 3 and Table 4 are inclusive for the experimental data in Table 1 and Table 2. Nemer et al.1 have derived the following thermodynamic data using the solubility data in Table 1 only: log K of dissolution of Fe(OH)2(s), log K of dissolution of Fe2Cl(OH)3(s), and a Pitzer interaction parameter (θ) for the species pair Na+/Fe+2. The values were 12.95, 17.12, and 0.08, respectively.1 For the derivation of the values in Nemer et al.,1 a set of binary Pitzer interaction parameters, i.e., β(0), β(1), β(2), and Cφ for the species pair Fe+2/ Cl−, selected from Pitzer,9 had been used. The values are 0.3359, 1.5322, 0.0, and −0.00861, respectively. This set of parameters presented in Pitzer9 are valid up to 2 molal ionic strength. Moog et al.15 reported a set of Pitzer interaction parameters for the same pair, Fe+2/Cl−, as well as the θ parameters for the species pair Na+/Fe+2 and the ψ parameter for the species triplet Fe+2/Na+/Cl− from isopiestic measurements (Table 4). The values in Moog et al.15 are valid for ionic strength up to 6 molal. Our experiments covered ionic strength up to 5 molal; therefore, it is appropriate to rederive those thermodynamic data that had been derived in Nemer et al.1 using the Pitzer interaction parameters for the pair of Fe+2/Cl− and the triplet of Fe+2/Na+/ Cl− reported in Moog et al.15 Rederivations are illustrated in Figure S1. The newly derived thermodynamic data in Figure S1, i.e., two log K values for Fe(OH)2(s) and Fe2Cl(OH)3(s), do not differ considerably from those originally derived in Nemer et al.1 (Table 3 and Figure S1). This process of rederivation, however, is necessary to maintain the internal consistency of our final database because the values by Moog et al.15 will be used for the series of our data analyses, including this paper. Note that the content of Figure S1 is not yet the conclusion of this paper because the 652


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Figure 4. Activity coefficients of aqueous species in Figure 3. (A) Fe2Cl(OH)3(s) in NaCl, (B) Fe(OH)2(s) in NaCl, (C) Fe(OH)2(s) in Na2SO4 + NaCl (0.15 m), and (D) Fe(OH)2(s) in Na2SO4 solutions. Experiments for (D) were initiated with Fe2Cl(OH)3(s), but they reached the stability of Fe(OH)2(s) (Figure 1 and Figure 2). The Pitzer interaction parameters for the pair Fe+2/SO4−2 were selected from Reardon and Beckie17 for this calculation.

Reardon and Beckie.17 Use of the parameters for the same pair calculated using equations in Kobylin et al.16 and the parameters in Moog and Hagemann18 resulted in similar quality of fit (model fits not shown). Kobylin et al.16 presented equations for temperature dependencies of the Pitzer parameters for the pair Fe+2/SO4−2 by critically reviewing multiple references cited therein.17,19 Close examination of Figure 3 reveals that the only option left to improve the model fit is to adjust the Pitzer parameters for the species pair Fe+2/SO4−2 as fitting variables. If any Pitzer parameters of pairs and/or triplets of species are to be adjusted to improve the fit, the pairs and/or triplets should be those of species Fe+2 because it is the major aqueous species of dissolved Fe+2. Since the ionic interaction of Fe+2 with other ions in the background electrolytes, such as Na+ and Cl−, are already accounted for by use of the corresponding Pitzer interaction parameters selected from literature (those bound by vertical blue lines in Table 4), the Pitzer interaction parameters for the species pairs Fe+2/Cl− and Na+/Fe+2 should not be adjusted further to maintain the internal consistency of the final database. We were reluctant to adjust the Pitzer parameters for species pair Fe+2/SO4−2 knowing that the parameters for such pair would better be obtained from other experimental techniques, such as isopiestic experiments. At the same time, however, we were motivated to do so because one of the authors of Moog et al.15 also addressed difficulties in obtaining reproducible results in his recent isopiestic experiments for the species pair Fe+2/SO4−2 for reasons that need to be analyzed in near future.20 Adjustment of β(0), β(1), and Cφ for the pair Fe+2/SO4−2 as fitting variables resulted in a significant improvement of the fit

unstable and forced the formation of Fe(OH)2(s) at the expense of Fe2Cl(OH)3(s). Full conversion of Fe2Cl(OH)3(s) to Fe(OH)2(s), however, would not be expected due to limitation of reactants for the conversion, i.e., OH−. The log K for Fe(OH)2(s) determined in Figure S1, i.e., 12.83, did not result in a satisfactory fit of data in Table 2 (Figure S2). Use of other Pitzer parameters related to the species Fe+2 and SO4−2 (those bound with dashed red vertical lines in Table 4) has insignificant impact on the overall fit (Figure S3), and they will be kept in further fittings for the completeness of reference citation. Use of two sets of published Pitzer parameters16,17 for the species pair Fe+2/SO4−2 (major aqueous species of interest, those bound within solid red vertical lines in Table 4) resulted in poorer fits when they are combined with log K(Fe(OH)2(s)) = 12.83 (Figure S4 and Figure S5). When the model fitting was performed solely for the experimental data in Table 2 with the log K(Fe(OH)2(s)) as a fitting variable, the value for the log K was determined to be 13.27 (Figure S6). Observations made in Figures S4−S6 indicate that the log K(Fe(OH)2(s)) = 12.83 is biased to the NaCl experiments data in Table 1. When the log K(Fe(OH)2(s)) was adjusted as a fitting variable over the experimental data in Table 1 and Table 2, a significant reduction of the residual was achieved for the data in Table 2, while the model obviously loses accuracy for the data in Table 1 to some extent as the log K becomes more positive (Figure 3, compared with Figure S1). The log K(Fe(OH)2(s)) was determined to be 13.14. For the fits in Figure 3 (activity coefficients of species therein are shown in Figure 4), the Pitzer interaction parameters for the pair Fe+2/SO4−2 was selected from 653


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Figure 5. Concentrations of the relevant Fe+2 species in equilibrium with (A) Fe2Cl(OH)3(s) in NaCl, (B) Fe(OH)2(s) in NaCl, (C) Fe(OH)2(s) in Na2SO4 + NaCl (0.15 m), and (D) Fe(OH)2(s) in Na2SO4 solutions. Experiments for (D) were initiated with Fe2Cl(OH)3(s), but they reached the stability field of Fe(OH)2(s) (Figure 1 and Figure 2). The calculated and measured Σ[Fe+2] are plotted together. The log K values for hibbingite and ferrous iron hydroxide were adjusted as fitting variables, which were determined to be 17.08 and 12.89. The Pitzer interaction parameters, i.e., β(0), β(1), and Cφ, for the pair Fe+2/SO4−2 were adjusted as fitting variables, which were determined to be 0.354, 0.375, and 0.00189. The β(2) for the pair was kept the same (−42.0) as prescribed in Reardon and Beckie17 for this fit. The activity coefficients are illustrated in Figure 6. The residuals are 0.001 (A) + 0.024 (B) + 0.047 (C) + 0.206 (D) = 0.281.

XRD scans showed the copresence of chukanovite and siderite in the entire range of added Na2CO3 concentrations (0.5, 1.0, 1.5, and 2.0 m with NaCl = 1.5 m) after more than 4 years of aging (Figure 8). This observation is consistent with pH decreases that occurred at the earlier stage of the experiments, indicating that the following reaction proceeded to the right. Reaction of siderite to form chukanovite. Note that H+ is produced.

(Figure 5, compared with Figure 3). The values were determined 0.354, 0.375, and 0.00189. The β(2) value for the pair was kept the same (−42.0) as prescribed in Reardon and Beckie17 for this fit due to lack of measurement at lower ionic strengths. The log K for Fe(OH)2(s) was simultaneously adjusted to be 12.89, which is pretty close to the calculation in Figure S1. The newly derived values for β(0), β(1), and Cφ for the pair Fe+2/SO4−2 make the activity coefficient of Fe+2 behave more like double-charged species, for example, SO4−2, indicating less ionic interaction between Fe+2 and SO4−2 (compare Figure 4C,D and Figure 6C,D). When the newly derived set of the Pitzer interaction parameters for the species pair Fe+2/SO4−2 were used to calculate the properties of FeSO4 solutions, such as activity of water, activity coefficients of Fe+2 and SO4−2, and the osmotic coefficient of FeSO4−H2O system, deviations were noticed from the calculations using the values selected from Kobylin et al.16 and Reardon and Beckie;17 our values assign activity coefficients to the species Fe+2 and SO4−2 that are closer to those Debye−Huckel limiting law would calculate (Figure 7). We will have the newly derived set of parameters in our database until newer experimental data at ambient temperature and pressure is available to give us a clearer picture of FeSO4−H2O system. Solubility data, their averages, and standard deviations are listed in Table 5 for the experiments where siderite, FeCO3(s), was used as the initial solubility limiting solid (Fe+2−Na+−H+−CO3−2− Cl−−H2O system). XRD scan of the initial siderite is in Figure 8.

2FeCO3(s) (siderite) + 2H 2O = Fe2CO3(OH)2 (s) (chukanovite) + HCO3− + H+ (r1)

The dissolution of chukanovite can be described by the following reaction: Dissolution of chukanovite. Fe2CO3(OH)2 (s) (chukanovite) + 3H+ = 2Fe+2 + HCO3− + 2H 2O; log K chu

(r2)

The Gibbs free energies of formation for the species in reaction r2 are listed in Table 6. Using equation e2 below, the 10-based logarithm of the equilibrium constant for the dissolution of chukanovite is calculated to be log Kchu = 12.42 ± 0.10. The uncertainty was estimated by methods in Harris.21 654


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Figure 6. Activity coefficients of aqueous species in Figure 5. (A) Fe2Cl(OH)3(s) in NaCl, (B) Fe(OH)2(s) in NaCl, (C) Fe(OH)2(s) in Na2SO4 + NaCl (0.15 m), and (D) Fe(OH)2(s) in Na2SO4 solutions. Experiments for (D) were initiated with Fe2Cl(OH)3(s), but they reached the stability field of Fe(OH)2(s) (Figure 1 and Figure 2).

Figure 7. (A) Activity of water, (B) activity coefficients of Fe+2 and SO4−2, and (C) osmotic coefficient in the FeSO4−H2O system. They were calculated using the Pitzer interaction parameters for the species pair Fe+2/SO4−2 selected from Kobylin et al.,16 Reardon and Beckie,17 and those derived in this paper. Oykova and Balarew (1974) are cited in Reardon and Beckie.17

Dissolution reaction of siderite

Calculation of the equilibrium constant using the Gibbs free energies of formation (ΔGf0) of products and reactants. 0

K = exp( −ΔGr /RT ) ΔGr0

FeCO3(s) (siderite) + H+ = Fe+2 + HCO3− ; log K sid

(e2)

(r3)

where = ΣΔGf ,products − The dissolution of siderite can be expressed by the following reaction: 0

ΣΔGf0,reactants.

Since we observed coexistence of siderite and chukanovite in the XRD after more than 4 years of aging (Figure 8), we assumed that the aqueous species are in equilibrium with both siderite and 655


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ACS Earth and Space Chemistry Table 5. Solubility Data for Siderite (FeCO3(s)) Experiments (Fe+2−Na+−H+−Cl−−“CO3−2”−H2O System)a NaCl

Σ[Fe+2]

Na2CO3 −05

−05

pmHc −05

1.80 × 10 , 1.89 × 10 , 2.00 × 10 , 1.94 × 10−05 1.91 × 10−05 8.41 × 10−07 (4%) 2.20 × 10−05, 6.49 × 10−05, 6.44 × 10−05, 2.09 × 10−05, 6.34 × 10−05, 6.31 × 10−05

1.5

0.5

1.5

average SDb (% SD) 1.0

1.5


4.98 × 10−05 2.20 × 10−05 (44%) 9.57 × 10−05, 1.14 × 10−04, 1.18 × 10−04, 9.94 × 10−05, 1.04 × 10−04, 1.06 × 10−04

1.5


1.06 × 10−04 8.62 × 10−06 (8%) 2.06 × 10−04, 1.73 × 10−04, 1.80 × 10−04, 2.03 × 10−04, 2.15 × 10−04, 2.10 × 10−04

0.15


0.15


0.15


0.15


1.98 × 10−04 1.72 × 10−05 (9%) 1.33 × 10−05, 1.28 × 10−05, 1.48 × 10−05, 1.40 × 10−05 1.37 × 10−05 8.67 × 10−07 (6%) 5.69 × 10−05, 5.56 × 10−05, 6.08 × 10−05, 6.09 × 10−05 5.86 × 10−05 2.72 × 10−06 (5%) 1.33 × 10−04, 1.33 × 10−04, 1.30 × 10−04, 1.29 × 10−04 1.31 × 10−04 2.25 × 10−06 (1%) 2.53 × 10−04, 2.51 × 10−04, 2.55 × 10−04, 2.54 × 10−04 2.53 × 10−04 1.82 × 10−06 (1%)

average SDb (% SD)

10.43, 10.40 10.41 0.02 (0%) 10.39, 10.42, 10.48, 10.41 10.42 0.04 (0%) 10.65, 10.59, 10.74, 10.61 10.65 0.07 (1%) 10.65, 10.62, 10.60, 10.67 10.64 0.03 (0%) 10.35, 10.40 10.38 0.04 (0%) 10.29, 10.35 10.32 0.04 (0%) 10.36, 10.39 10.38 0.03 (0%) 10.55, 10.56

Figure 8. XRD scans indicating that chukanovite has formed at the expense of siderite through reaction r1. The solids collected after aging were not rinsed with water due to possible loss of newly formed chukanovite by creating abrupt undersaturation; thus, the existence of NaCl peaks can be explained by the NaCl precipitated from the residual background solutions trapped in pores of the collected solids. For identification of siderite and chukanovite, two reference PDFs (powder diffraction files) were plotted for each mineral.

10.56 0.01 (0%)

a

Concentrations are in in molal units (moles of solute in kg of water). Averaged data were used in model calculations. bStandard deviation. c Negative 10-based logarithm of H+ concentration in molal scale.

Table 6. Gibbs Free Energies of Formation of the Components (ΔGf0) To Calculate the log K of Reaction r2 for Chukanovite

chukanovite under the experimental conditions of this study with the uncertainties of log Ksid and log Kchu. Thus, it is necessary to check if the log Kchu and log Ksid selected from the literature are consistent with each other to support our assumption. The following is the thermodynamic constraint for our assumption. A thermodynamic constraint for the activity of Fe+2, {Fe+2}, in equilibrium with both siderite and chukanovite. {Fe+2}sid = {Fe+2}chu = {Fe+2}mix

component

ΔGf0 (kJ/mol)

refsb

Fe2CO3(OH)2(s), chukanovite

−1171.5 ± 3.0 −1174.4 ± 6.0 −1169.3 ± 6.0a −1171.7 ± 9.0 −90.719 0 −586.903 −237.149

36 37 38

average Fe+2 H+ HCO3− H2O

(e3)

where “mix” means mixture of siderite and chukanovite. One way to evaluate the activity of Fe+2 in equilibrium simultaneously with siderite and chukanovite, i.e., {Fe+2}mix, is to examine reaction r4 below.

11 4 4 4

a

Uncertainty not given in the reference and assumed to be the larger one (6.0 kJ/mol) among the published uncertainties. bThe ΔGf0 value reported in Chen et al.39 (−1151.1 ± 5.3 kJ/mol) was considered as an outlier and excluded in this calculation.

Equilibrium between Fe+2, siderite, and chukanovite. FeCO3(s) (siderite) + Fe+2 + 2H 2O

chukanovite are present and in equilibrium, and the value of which can be calculated as in the following:

= Fe2CO3(OH)2 (s) (chukanovite) + 2H+; log K mix (r4)

Calculation of the log Kmix.

The activity of Fe+2 of the reaction r4 represents the {Fe+2}mix of the equation e3. The log Kmix is the 10-based logarithm of equilibrium constant for reaction r4 where both siderite and

log K mix = log K sid − log K chu 656

(e4) DOI: 10.1021/acsearthspacechem.7b00065 ACS Earth Space Chem. 2017, 1, 647−663

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Table 7. Reactions Used To Calculate the Values for Log{H+}, Log{HCO3−}, and Log{H2O} in Table 9 and Table 10 (Reactions Describing the Dissolution of Siderite and Chukanovite Are Listed Together) log K

reactions aqueous reactions H+ + OH− = H2O CO3−2 + H+ = HCO3− CO2(aq) + H2O = H+ + HCO3− dissolution CO2(g) + H2O = H+ + HCO3− FeCO3(s) + H+ = Fe+2 + HCO3−

Fe2(OH)2CO3(s) + 3H+ = 2Fe+2 + HCO3− + 2H2O

refs

13.99 10.33 −6.33

4 4 4

−7.81 −0.19 −0.47 −0.12 12.42 ± 0.10 12.32

40 23,24 22 25, this paper Table 6 and equation e2 This paper

Table 8. Pitzer Interaction Parameters Used To Calculate the Values for Log{H+}, Log{HCO3−}, and Log{H2O} in Table 9 and Table 10 i

j −

+

Cl OH− Cl− HCO3− CO3−2

α1/α2a

β(0)

β(1)

β(2)

Cφ

2.0/12.0 2.0/12.0 2.0/12.0 2.0/12.0 2.0/12.0

0.0765 0.0864 0.1775 0.0277 0.0399

0.2664 0.253 0.2945 0.0411 1.389

0.0 0.0 0.0 0.0 0.0

0.00127 0.0044 0.0008 0.0 0.0044

refs

i

j

θij

refs

k

ψijk

4 4 4 4 4 refs

Na+ ClCl− Cl− OH− HCO3−

H+ OH− HCO3− CO3−2 CO3−2 CO3−2

0.036 −0.05 0.03 −0.02 0.1 −0.04 j

4 4 4 4 4 4

Cl− Na+ Na+ Na+ Na+ Na+ λij

−0.004 −0.006 −0.015 0.0085 −0.017 0.002

4 4 4 4 4 4

Na Na+ H+ Na+ Na+

i CO2(aq) CO2(aq) CO2(aq)

H+ Na+ Cl−

refs

0.0 0.1 −0.005

4 4 4

α1 and α2 are preset constants used in the Pitzer activity coefficient equation. α1 and α2 apply for only cation−anion binary pairs. α2 is not applied when β(2) is zero or not used. Unit for α1 and α2 is kg1/2·mol−1/2. a

Table 9. Calculation of Log{Fe+2} in the Presence of Both Siderite and Chukanovite Using Equation 5a experimental constraints

model calculations

NaCl, m

Na2CO3, m

log{H2O}

log{H+}

log{HCO3−}

log{Fe+2}chu

log{Fe+2}sid

log{Fe+2}mix

SIb

1.5 1.5 1.5 1.5 0.15 0.15 0.15 0.15

0.5 1.0 1.5 2.0 0.5 1.0 1.5 2.0

−0.031 −0.041 −0.051 −0.063 −0.011 −0.018 −0.026 −0.035

−10.500 −10.550 −10.797 −10.791 −10.689 −10.685 −10.768 −10.954

−1.891 −1.778 −1.932 −1.855 −1.859 −1.787 −1.831 −1.979

−8.56 −8.68 −8.97 −8.99 −8.88 −8.91 −9.00 −9.20

−8.80 −8.96 −9.06 −9.13 −9.02 −9.09 −9.13 −9.17

−8.33 −8.41 −8.88 −8.84 −8.75 −8.72 −8.87 −9.23 Σ(SI)2

0.48 0.56 0.18 0.28 0.28 0.37 0.26 −0.06 0.933

The log Kmix = −12.61 with log Ksid = −0.1923,24 and log Kchu = 12.42. bSaturation index = log(ion activity product/equilibrium constant). They are the same for both siderite and chukanovite due to difference in the stoichiometry of Fe+2. a

Table 10. Calculation of {Fe+2} in the Presence of Both Siderite and Chukanovite Using Equation 5a experimental constraints

model calculations

NaCl, m

Na2CO3, m

log{H2O}

log{H+}

log{HCO3−}

log{Fe+2}chu

log{Fe+2}sid

log{Fe+2}mix

SIb

1.5 1.5 1.5 1.5 0.15 0.15

0.5 1.0 1.5 2.0 0.5 1.0

−0.031 −0.041 −0.051 −0.063 −0.011 −0.018

−10.500 −10.550 −10.797 −10.791 −10.689 −10.685

−1.891 −1.778 −1.932 −1.855 −1.859 −1.787

−8.61 −8.73 −9.02 −9.04 −8.93 −8.96

−8.73 −8.89 −8.99 −9.06 −8.95 −9.02

−8.50 −8.58 −9.05 −9.02 −8.92 −8.89

0.23 0.31 −0.07 0.04 0.03 0.12

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ACS Earth and Space Chemistry Table 10. continued experimental constraints

model calculations

NaCl, m

Na2CO3, m

log{H2O}

log{H+}

log{HCO3−}

log{Fe+2}chu

log{Fe+2}sid

log{Fe+2}mix

SIb

0.15 0.15

1.5 2.0

−0.026 −0.035

−10.768 −10.954

−1.831 −1.979

−9.05 −9.25

−9.06 −9.09

−9.04 −9.40 Σ(SI)2

0.01 −0.30 0.267

Refined log K values were applied, i.e., logKmix = −12.44 with logKsid = −0.1225 and logKchu = 12.32. bSaturation Index = Log (Ion Activity Product/Equilibrium Constant). Calculated to be the same for both siderite and chukanovite due to difference in the stoichiometry of Fe+2.

a

Thus, the 10-based logarithm of activity of Fe+2 in the mixed solid system, log{Fe+2}mix, can be expressed as the following:

Table 11. Reactions for the Complexation of Fe+2 with CO3−2a reactions aqueous reactions FeHCO3+ = Fe+2 + HCO3− FeCO3(aq) + H+ = Fe+2 + HCO3− Fe(CO3)2−2 + 2H+ = Fe+2 + 2HCO3−

log K −1.47 4.87 4.83 13.49 13.56

refs

Log activity of species Fe+2, {Fe+2}, in r4.

26, not selected as recommended in Lemire et al.11 26 22 26 22

log{Fe+2}mix = 2 log{H+} − 2 log{H 2O} − log K mix (e5)

where {i} stands for the activity of species i. Two terms in the right-hand side of equation e5, i.e., log{H+} and log{H2O}, can be readily calculated by the experimental constraints with aid of the aqueous speciation code, EQ3NR packaged in EQ3/6, version 8.0a.14 Thermodynamic data for the

a Good agreement for Fe+2−CO3−2 complexation constants among references was observed.

Figure 9. Measured data (blue squares) compared to the prediction with siderite (solid lines in A and B) and chukanovite (dashed lines in A and B). Fe(CO3)2−2 is the major species. Each data point represents an average of two or more measurements. (A,C) Concentrations and log activity coefficients of relevant species in the experiments in background NaCl concentration = 1.5 molal. (B,D) Concentrations and log activity coefficients of relevant species in the experiments in background NaCl concentration = 0.15 molal. Residuals are 8.502 (A) + 6.817 (B) = 15.320. “E-xx” means “× 10−xx”. 658


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Figure 10. Concentrations (A,B) and activity coefficients (C,D) of relevant Fe+2 species in equilibrium with siderite. The calculated and measured Σ[Fe+2] are plotted together. Fitting variables are the β(0) and β(1) of the species pair Na+/Fe(CO3)2−2, which are determined to be −0.252 and 7.66, respectively. The β(2) and Cφ were set to zero. The log K(Fe(CO3)2−2) was fixed at 13.56 as in Bruno et al.22 (A,C) Background NaCl concentration = 1.5 molal with residual = 0.026. (B,D) Background NaCl concentration = 0.15 molal with residual = 0.146. Residuals are 0.026 (A) + 0.146 (B) = 0.172. (Not a conclusion of this paper yet).

−0.1225 (Table 7). The combination of log Kchu = 12.32 (the lowest of the range) and log Ksid = −0.1225 (Table 7) gave a minimized value of Σ(SI)2 = 0.267 with log Kmix = −12.44 (Table 10). To calculate the total dissolved Fe+2, Σ[Fe+2], it is required to consider the complexation of Fe+2 with CO3−2 in addition to the reactions in Table 3 and Table 7. Without considering the Fe+2−CO3−2 complexation, very large Pitzer interaction parameters for the pairs Fe+2/CO3−2 and FeOH+/CO3−2, which usually is a strong indication of ion pairings, as well as larger deviation of log Kchu from the literature values, were required.13 Thus, the reactions selected from the literature (Table 11) are added to the thermodynamic database. Figure 9 shows the calculated total dissolved Fe+2, Σ[Fe+2]calc, calculated using the Fe+2−CO3−2 complexation model in Bruno et al.22 in addition to the aqueous reactions in Table 3 and Table 7. The log K values for Fe+2−CO3−2 complexation showed great agreement between Bruno et al.22 and Millero et al.26 (Table 11), so they can be used interchangeably in the following discussion. The species FeHCO3+ (Millero et al.26) was not used in this paper as recommended by Lemire et al.11 When it was used in one of our preliminary calculations, it was not a major species in the experiments performed in this paper. The calculated Σ[Fe+2] and concentrations of individual species were virtually the same whether siderite or chukanovite is designated as the solubility limiting solid (Figure 9). Therefore, in the following discussion, siderite will be used as the solubility limiting solid because the shape and slope of the Σ[Fe+2]calc matches better with experimental data when siderite is the solubility limiting solid.

calculation of log{H+} and log{H2O} can be found in Table 7 and Table 8. In the carbonate system of this paper, we have a new component, HCO3−, in addition to Fe+2−Na+−H+−Cl−−H2O. Accordingly, the reactions in Table 7 are required to address the system Fe+2−Na+−H+−HCO3−−Cl−−H2O in addition to the reactions in Table 3. Likewise, the Pitzer interaction parameters related to the carbonate system are in Table 4 and Table 8. Thermodynamic data for Fe+2−CO3−2 complexation and the related Pitzer interaction parameters will be discussed in sections below where Table 11 is mentioned. Published log K values for siderite and chukanovite support our observation made using the XRD scans presented in Figure 8. The log{Fe+2}mix indicates slight deviations from equilibrium with both siderite and chukanovite (Table 9). The extent of nonequilibrium can be represented by the summation of squared saturation indices (SI), Σ(SI)2, which is 0.933 with log Kmix = −12.61. Theoretically, the activity of Fe+2 in equilibrium with mixture of siderite and chukanovite, {Fe+2}mix, should be very close to {Fe+2}sid and {Fe+2}chu, if not the same as dictated by equation e3. Solid-solution formation is not to be considered for the simplicity of model. Σ(SI)2 = 0.933 with log Kmix = −12.61 may be simply regarded as a model uncertainty, but it is evident that this uncertainty would propagate into larger uncertainties in the thermodynamic data that will be derived through model fittings. Therefore, the values of log Kchu and log Ksid were adjusted within the uncertainty of log Kchu and within the range of log Ksid to give a minimized Σ(SI)2. In the literature, it is clear that there is no consensus regarding the value of log Ksid; −0.47,22 −0.19,23,34 and 659


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Figure 11. Concentrations (A,B) and activity coefficients (C,D) of relevant Fe+2 species in equilibrium with siderite. The calculated and measured Σ[Fe+2] are plotted together. Fitting variables are the log K of Fe(CO3)2−2 and the β(0) and β(1) of the species pair Na+/Fe(CO3)2−2, which are determined to be 13.89, −0.230, and 6.26, respectively. The β(2) and Cφ were set to zero. Note that the log K(Fe(CO3)2−2) in Figure 10 was fixed at 13.56 as in Bruno et al.22 (A,C) Background NaCl concentration = 1.5 molal with residual = 0.027. (B,D) Background NaCl concentration = 0.15 molal with residual = 0.142. Residuals are 0.027 (A) + 0.142 (B) = 0.169.

With Fe(CO3)2−2 in the speciation model, the calculated Σ[Fe+2] is higher than the measured Σ[Fe+2] by about 1.5 orders of magnitude, which is not uncommon considering the charge of Fe(CO3)2−2 and the ionic strengths of the experiments (Figure 9A,B). The residuals defined by equation e1 are 8.502 (for the NaCl = 1.5 m experiments) and 6.817 (for the NaCl = 0.15 m experiments), with the total residual being 15.320. The 10-based logarithm of activity coefficient of the major species Fe(CO3)2−2, log γ(Fe(CO3)2−2), ranges from −1.91 to −2.36 in NaCl = 1.5 m experiments and from −1.52 to −2.21 in NaCl = 0.15 m experiments (Figure 9C,D). The values of γ(Fe(CO3)2−2) were calculated using the Pitzer activity coefficient equation like those of other species, but at this stage, the interaction of Fe(CO3)2−2 with background electrolytes was not taken into consideration yet. Only the charge of the species (−2) and the interaction of background electrolytes with species other than Fe(CO3)2−2 were considered to calculate the values of γ(Fe(CO3)2−2). The log γ of species with charges of +1 or −1 are clustered within +0.5 to −1. The log γ of neutral species are clustered within 0 to +0.5. The log γ of species with charges of +2 or −2, whose activity coefficients are corrected using the Pitzer interaction parameters of their own, such as Fe+2 and CO3−2, are clustered within −1 to −1.5. Assuming the log K of Fe(CO3)2−2, which is 13.56 by Bruno et al.,22 is accurate, the log activity coefficients of the Fe(CO3)2−2 need to be less negative for the calculated Σ[Fe+2], which is virtually equal to

[Fe(CO3)2−2], to match the measured Σ[Fe+2] according to the following relationship: Activity, concentration, and activity coefficient. {Fe(CO3)2−2 } = γ(Fe(CO3)2−2 ) × [Fe(CO3)2−2 ] or log{Fe(CO3)2−2 } = log γ(Fe(CO3)2−2 ) + log[Fe(CO3)2−2 ] (e6)

where {i}, γ(i), and [i] mean activity, activity coefficient, and concentration of species i. In spite of the deviation between the calculated and measured Σ[Fe+2] (Figure 9A,B), the species Fe(CO3)2−2 is required to keep the slope of the calculated Σ[Fe+2] as defined by the experimentally measured Σ[Fe+2]. In other words, when the species FeCO3(aq) is designated as the major species without Fe(CO3)2−2 in the speciation model, better fit can be obtained only by assigning nonacceptably large activity coefficient to the neutral species, i.e., large value to λ for the pairs FeCO3(aq)/Na+ and/or FeCO3(aq)/Cl−, to address the slope of the calculated Σ[Fe+2] (Figure S7). To assign less negative log γ values to the species Fe(CO3)2−2, the Pitzer interaction parameters for the species pair Na+/ Fe(CO3)2−2 was adjusted so that the residuals become less than 8.502 (NaCl = 1.5m) and 6.817 (NaCl = 0.15m) as in Figure 9. The species pair Na+/Fe(CO3)2−2 was selected because Fe(CO3)2−2 is the major Fe+2 species in both experiments. 660


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ACS Earth and Space Chemistry Table 12. Summary of Fittings for the Carbonate System Variables of interest log K Fe(CO3)2−2 β(0) Na+/Fe(CO3)2−2 β(1) Na+/Fe(CO3)2−2 residual in NaCl = 1.5 m NaCl = 0.15 m total residual range log γ(Fe(CO3)2−2) remarks a

Figure 9

Figure 10

Figure 11

13.56a 0.0 0.0

13.56a −0.252 7.66

13.89 −0.230 6.26

8.502 6.817 15.320 −1.52 to −2.36 initial model calculation with thermodynamic data selected from literature; no ion interaction of Fe(CO3)2−2 considered

0.026 0.146 0.172 −0.05 to −1.17 fitting of β(0) and β(1) with log K kept as selected from Bruno et al.22

0.027 0.142 0.169 −0.34 to −1.49 fitting of β(0), β(1), and log K; conclusion of this paper; see text for rationales

Bruno et al.22

A major cation, Na+, was selected because the stronger interaction is expected for the background cation than anion, for example, Cl−, for the anionic species Fe(CO3)2−2. The results are illustrated in Figure 10, where β(0) and β(1) are determined to be −0.252 and 7.66, respectively. The residuals are 0.026 (NaCl = 1.5m) and 0.146 (NaCl = 0.15m), with the total being 0.172. Another numerically equivalent fitting can be performed using the logK of Fe(CO3)2−2 as one of the fitting variables. The log K of Fe(CO3)2−2 used in Figure 10, the value of which is 13.56, was quantified in Bruno et al.,22 where the experimental conditions were significantly different from this study; 1.0 M NaClO4 solutions, pH 6.0−8.9 under the partial pressure of CO2(g) at 0.01 and 0.05 atm, and the equilibration time was less than 3 days. Under the experimental conditions described in Bruno et al.,22 the total dissolved carbonate concentration would be expected to range from 0.0005 to 0.9 molal when the carbonation reaches equilibrium, which is significantly lower than the experimental conditions of this paper. The specific ion interaction theory (SIT) was used for the extrapolation to infinite dilution to determine the log K of Fe(CO3)2−2 in Bruno et al.22 Thus, it is worth re-evaluating the log K using the Pitzer activity coefficient equation for the experimental conditions of this study and calculate/compare the Gibbs free energy of formation of the species Fe(CO3)2−2 with literature values. In the fitting illustrated in Figure 11, the log K of Fe(CO3)2−2 was one of the fitting variables, and the fitted value is 13.89 accompanied by minor changes in the β(0) and β(1) of the species pair Na+/Fe(CO3)2−2 (−0.230 and 6.26, respectively). The Gibbs free energy of formation for Fe(CO3)2−2 that matches log K of 13.89 is −1185.24 kJ/mol referring to the values in Table 6, which shows an excellent agreement with the value in Lemire et al.:11 −1186.67 kJ/mol. The log K of Fe(CO3)2−2 in Lemire et al.11 is 13.62. Model calculations for the carbonate systems above are summarized in Table 12. Two calculations illustrated in Figure 10 and Figure 11 are numerically equivalent; no significant difference in the residual values. If log K of Bruno et al.22 is considered applicable for the experimental conditions of this paper, larger interaction between Fe(CO3)2−2 and Na+ reduces the excess free energy of Fe(CO3)2−2 from what was assigned solely by background electrolytes and its charge, making Fe(CO3)2−2 behave more like those species charged +1 or −1 (Figure 10C,D). If the change in the excess free energy, i.e., the activity coefficient, is due to uncertainties associated with log K of Bruno et al.,22 which was quantified under significantly different experimental conditions, then the newly derived log K of Fe(CO3)2−2 = 13.89 in combination with β(0) and β(1) (−0.230 and 6.26,

respectively) makes the species exhibit similar behavior compared to other divalent species, such as Fe+2 and CO3−2, whose interactions with other major ions are accounted for using their own Pitzer interaction parameters (Figure 11C,D). We want the log γ(Fe(CO3)2−2) to be bound between the clusters of ±1 and ±2 charged species whose activity coefficients are corrected by their own Pitzer interaction parameters as in Figure 11C,D.

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CONCLUSION The stability fields of the four ferrous iron minerals are illustrated in Figure 12 as functions of the activities of HCO3− and Cl−.

Figure 12. Stability field diagram for the four ferrous iron minerals. Elemental and ferric iron are not considered. The pH and activity of water, {H2O}, are set at 8.9 and 0.75, respectively. The equations for the construction of this stability field diagram are in Table S1.

When we constructed the diagram, the activity of water was set to 0.75 and the pH was set to 8.9 to closely mimic the WIPP condition. The equations used to construct the stability field diagram are listed in Table S1. The chemical information for the anticipated WIPP conditions (Figure 12) are from GWB and ERDA6, which are the WIPP-relevant brines,2 and plotted with exaggerated uncertainties. Under the anticipated WIPP condition, the most stable inorganic ferrous iron mineral is siderite, FeCO3(s), among those investigated in this paper. When anoxic corrosion of iron, Fe(s), reaches equilibrium with siderite, the fugacity of oxygen, f O2(g), can be calculated from the following reaction: Reaction of elemental iron, Fe(s), and siderite, FeCO3(s). Fe(s) + HCO3− + 1 2 O2 (g) + H+ = FeCO3(s) + H 2O 661

(r5)


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(7) Pitzer, K. S. Thermodynamics of electrolytes. I. Theoretical basis and general equations. J. Phys. Chem. 1973, 77 (2), 268−277. (8) Pitzer, K. S.; Mayorga, G. Thermodynamics of Electrolytes. II. Activity and Osmotic Coefficients for Strong Electrolytes with One or Both Ions Univalent. J. Phys. Chem. 1973, 77 (19), 2300−2308. (9) Pitzer, K. S. Ion interaction approach: theory and data correlation. In Activity Coefficients in Electrolyte Solutions, 2nd ed.; Pitzer, K. S., Ed.; CRC Press: Boca Raton, FL, 1991; Chapter 3, pp 75−153. (10) Qafoku, O.; Felmy, A. R. Development of accurate chemical equilibrium models for oxalate species to high ionic strength in the system: Na - Ba - Ca - Mn - Sr - Cl - NO3 - PO4 - SO4 - H2O at 25 °C. J. Solution Chem. 2007, 36, 81−95. (11) Lemire, R. J.; Berner, U.; Musikas, C.; Palmer, D. A.; Taylor, P.; Tochiyama, O. Chemical Thermodynamics of Iron, Part 1. In Organisation for Economic Co-operation and Development; Perrone, J., Ed.; Nuclear Energy Agency, 2013; Vol. 13a, Chemical Thermodynamics. (12) Lucchini, J.-F.; Borkowski, M.; Richmann, M. K.; Ballard, S.; Reed, D. T. Solubility of Nd3+ and UO2+2 in WIPP brine as oxidation-state invariant analogs for plutonium. J. Alloys Compd. 2007, 444−445, 506− 511. (13) Jang, J.-H.; Kim, S. Derivation of Pitzer Interaction Parameters and Thermodynamic Properties for the Aqueous Species of Ferrous Iron and Their Pairs, revision 2; Sandia National Laboratories: Carlsbad, NM, 2016. (14) Wolery, T. J.; Jarek, R. L. Software User’s Manual, EQ3/6, version 8.0., 10813-UM-8.0-00; Sandia National Laboratories: Albuquerque, NM, 2003. (15) Moog, H. C.; Hagemann, S.; Rumyantsev, A. V. Z. Phys. Chem. 2004, 218, 1063−1087. (16) Kobylin, P. M.; Sippola, H.; Taskinen, P. A. CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 2011, 35, 499−511. (17) Reardon, E. J.; Beckie, R. D. Modelling chemical equilibria of acid mine-drainage: The FeSO4 - H2SO4 - H2O system. Geochim. Cosmochim. Acta 1987, 51, 2355−2368. (18) Moog, H. C.; Hagemann, S. Thermodynamic modeling in highsaline solutions: Data for Fe(II), Fe(III), and S(-II) and development of a program for the modelling of reactive transport within the near field of a repository, volume number: GRS-195, final report for a project funded by the federal ministry for economy and technology (BMWA), funding number 02 E 9138, ISBN 3-931995-63-1, 224 pages. 2004. (19) Kobylin, P.; Kaskiala, T.; Salminen, J. Modeling of H2SO4-FeSO4H2O and H2SO4-Fe2(SO4)3-H2O systems for metallurgical applications. Ind. Eng. Chem. Res. 2007, 46 (8), 2601−2608. (20) Moog, H. C.; Jang, J. J. Personal communication during SNL’s visit to KIT/INE and GRS. Karlsruhe, Germany, 2017. (21) Harris, D. C. Quantitative Chemical Analysis, 2nd ed.; W.H. Freeman and Company: New York, 1987. (22) Bruno, J.; Wersin, P.; Stumm, W. Stumm, W. On the Influence of Carbonate in Mineral Dissolution: II. The Solubility of FeCO3(s) at 25 °C and 1 atm total pressure. Geochim. Cosmochim. Acta 1992, 56, 1149− 1155. (23) Helgeson, H. C.; Delany, J. M.; Nesbitt, H. W.; Bird, D. K. Summary and Critique of the Thermodynamic Properties of Rock Forming Minerals. Am. J. Sci. 1978, 278A, 1. (24) Helgeson, H. C. Errata II. Thermodynamics of Minerals, Reactions, and Aqueous Solutions at High Pressures and Temperatures. Am. J. Sci. 1985, 285 (9), 845−855. (25) Stumm, W.; Morgan, J. J. Aquatic Chemistry, 3rd ed.; John Wiley and Sons, 1996. (26) Millero, F. J.; Yao, W.; Aicher, J. The Speciation of Fe(II) and Fe(III) in Natural Waters. Mar. Chem. 1995, 50, 21−39. (27) Shock, E. L.; Sassani, D. C.; Willis, M. Sverjensky, D.A. Inorganic Species in Geologic Fluids: Correlations Among Standard Molal Thermodynamic Properties of Aqueous Ions and Hydroxide Complexes. Geochim. Cosmochim. Acta 1997, 61 (5), 907−950. (28) Baes, C. F.; Mesmer, R. E. The Hydrolysis of Cations. WileyInterscience: New York, 1976.

The log K of reaction r5, which is 57.77, was calculated using equation e2 in combination with the numbers in Table 6 and the Gibbs free energy of formation for siderite (−679.557 kJ/mol, Lemire et al.11). Thus, under anticipated WIPP conditions where the pH = 8.9 and log{HCO3−} = −3.3, the log f O2(g) = −91.2, slightly lower than the value calculated using the assemblage of Fe(s)/hibbingite in Nemer et al.1

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsearthspacechem.7b00065. Figures S1−S7 and Table S1 are cited in text (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Telephone: 1-505-284-2770. E-mail: [email protected]. ORCID

Jay Je-Hun Jang: 0000-0003-0175-6515 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are grateful to Dr. Jonathan Icenhower for his technical review on this manuscript under Sandia National Laboratories’ WIPP QA program. The authors are also grateful to Justin Dean, Leslie Kirkes, Jandi Knox, and Heather Burton for their laboratory support. The authors also thank two anonymous reviewers for valuable comments to significantly improve the initial version of this manuscript. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA-0003525. This research is funded by WIPP programs administered by the Office of Environmental Management (EM) of the U.S. Department of Energy.

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REFERENCES

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NOTE ADDED AFTER ASAP PUBLICATION This paper published ASAP on 11/20/2017. Table 4 was replaced and the revised version was reposted on 11/30/2017.

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Solubility Model for Ferrous Iron Hydroxide, Hibbingite, Siderite, and

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