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Activity Coefficients of Fission Products in Highly Salinary Solutions of Na+, K+, Mg2+, Ca2+, Cl−, and SO42−: Cs+ T. Scharge, A. G. Muñoz,* and H. C. Moog Gesellschaft für Anlagen und Reaktorsicherheit (GRS)mbH, Theodor-Heuss-Straße 4, 38122 Braunschweig, Germany S Supporting Information *

ABSTRACT: Binary and ternary interaction parameters of the Pitzer formalism for the thermodynamic modeling of the fission product Cs+ in concentrated salt solutions of the hexary oceanic system Na−K−Mg−Ca− Cl−SO4−H2O at 25 °C were calculated from experimental isopiestic, potentiometric, and solubility data available in the literature. The obtained parameters were checked by comparing measured and predicted water activities and solubilities for binary, ternary, and quaternary systems.

1. INTRODUCTION Knowledge of thermodynamic properties of heavy alkaline and earth alkaline metal ions in concentrated solutions of the hexary oceanic salt system is essential for the transport modeling of radioactive fission products in repositories for long-term disposal of radioactive waste in rock salt formations.1 Among the more common fission products from spent nuclear fuels, the radionuclides 137Cs and 90Sr with half-lives of 30.17 years and 28.2 years, respectively, are mostly critical for the design of the repository because of the intense γ radiation and the heat generated by the decay process as well as the high solubilities of their chlorides. Corrosion of steel-based spent fuel disposal containers could be caused by their contact with aqueous solution.2,3 This leads to the generation of hydrogen and corrosion products, thereby generating considerable mechanical stress that accelerates the corrosion process and the formation of fissures, through which drainage of radioactive products could occur. International concepts for repositories of nuclear waste are mainly based on geological barriers constituted by salt, argillaceous rock, or crystalline rock.4,5 Rock salt features a low permeability for gases and liquids under natural disposal conditions and high heat conductivity. The viscoplastic properties of salt rock, on the other hand, enable a seal up of cavities remaining after the final closure of the repository. The modeling of dissolution and precipitation processes as well as surface complexation phenomena in brines requires an adequate thermodynamic model for the prediction of ionic activities beyond the limited Debye−Hückel theory. This requirement is fulfilled by the model of Pitzer and co-workers,6 formulated as an analogy of virial concepts used for describing the behavior of real gases. Deviations from the limiting Debye− Hückel behavior are expressed in terms of specific interaction parameters, the so-called Pitzer parameters, among the constituting ionic species, which have to be determined experimentally. This paper presents a comprehensive evaluation of existent © XXXX American Chemical Society

experimental thermodynamic data on the system Cs−Na−K− Ca−Mg−Cl−SO4−H2O reported in the literature. Binary and ternary Pitzer interaction parameters at t = 25 °C are calculated, and the predictive power of the generated set of parameters is analyzed. In this work, Pitzer parameters were calculated from solubility, potentiometric, and isopiestic data available in the literature. Derived Pitzer parameters are consistent with those for the system of the oceanic salts developed by Voigt.7

2. PITZER FORMALISM AND METHOD The Pitzer formalism extends the Debye−Hückel description of electrolyte solutions by the introduction of a virial expansion to account for short-range interaction forces between ions in high ionic-strength media.8 This model describes electrolytes according to the following expression for the excess Gibbs energy: Gex = f (I ) + n w RT

∑ λij(I )mimj+ ∑ μijkmimjmk i,j

i ,j,k

(1)

where nw represents kilograms of water in the system, mi is the molality of aqueous species i, and f(I) is a function of the ionic strength: 1 I = ∑ mizi 2 2 i (2) λij(I) are ionic-strength dependent and represent the interaction between pairs of species i and j. μI,j,k represent the interaction between triplets of species considered independent of the ionic strength. The function f(I) accounts for the electrostatic interactions and adopts a similar form as the Received: September 8, 2011 Accepted: March 24, 2012

A

dx.doi.org/10.1021/je200970v | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Review

αij(1) = 1.4. These values, however, can be varied to yield a better representation of activity coefficient data at high concentrations, where ion association occurs to a large extent. The parameter Cij accounts for the formation of cation−anion pairs, and Φij represents the interactions between ions of likewise charge and appears only in ternary or multinary solutions. Φij and Φ′ij are given by:

Debye−Hückel equation. It was found that the function describing electrostatic interactions for high ionic-strength solutions best is obtained after introducing the Debye−Hückel radial ionic distribution in the osmotic pressure equation derived from statistical mechanics: f (I ) = −

Aγ I 4 ln(1 + b I ) 3 b

(3)

where Aγ is the Debye−Hückel parameter (considering ln γ± = Aγ|z+z−|I1/2) given by: Aγ = (2NAρw·1000/π2)1/2(e2/4ε·ε0kT)3/2 (kg1/2·mol−1/2); ρw (kg·dm−3). The parameter b accounts for effects of the distance of closest approach of atoms in the calculation of the electrostatic energy. Expressions for the activity and osmotic coefficients can be obtained by derivation of the excess energy (eq 1). After a convenient grouping of the interaction parameters λij and μij, the following general expressions for the activity and osmotic coefficients are obtained for the general case of a cation−anion pair M−X in the presence of additional cations c and anions a: ln γM = −

⎤ zM2 ⎡ 2 I + ln(1 + b I )⎥ + A γ⎢ 3 b ⎢⎣ 1 + b I ⎥⎦ Nc − 1

+

Nc

Na − 1

∑ ∑

mc mc ′Φ′cc ′+

c = 1 c ′= c + 1 Na

+

mc mc ′Φ′cc ′+

c = 1 c ′= c + 1 Nc

+

∑ ∑

⎡

I 3/2 ⎤ ⎥+ ⎣1 + b I ⎦

Nc − 1

+

Na

Nc

∑ ∑

c=1 a=1 Na

mc mc ′[(Φcc ′ + I Φ′cc ′) +

∑ maΨcc′ a] a Nc

mama ′[(Φaa ′ + I Φ′aa ′) +

a = 1 a ′= a + 1

Figure 1. Interaction octahedron for Cs+ in the ozeanic system.

∑ mc Ψaa ′ c] c=1

(6)

salts. It is constructed by 16 triangles, the edges of which represent interactions of ion pairs. Each triangle represents the interaction of ion triplets. The external facets of the octahedron correspond to the ternary interaction within the system of oceanic salts which are already available.7 Our task is to construct the internal facets by quantifying the interactions of the two binary and nine ternary systems containing Cs+. The determination of Pitzer parameters by applying eqs 4 to 6 requires methods where concentrations and activities can be measured simultaneously. In this work, electromotive force (emf) measurements, isopiestic data and solubility data were used. The required solubility constants of minerals corresponding to the system of oceanic salts were taken from a revision provided by Voigt,7 reproduced in Table 1.

The coefficients Bij and B′ij account for the interaction of pairs of ions with opposite charge and are defined as: Bij = β(0) + β(1) g (α(1)ij I ) + β(2) g (α(2)ij I ); ij ij ij B′ij = [β(1) g ′(α(1)ij I ) + β(2) g ′(α(2)ij I )]/I ij ij

(7)

where the functions g and g′ are defined as: g (α I ) = 2[1 − (1 + α I )exp(−α I )]/α 2I ; g ′(α I ) = − 2[1 − (1 + α I + α 2I /2)exp(−α I )]/α 2I (8)

In general αij is set to zero, and αij(1) and 4:1 type salts. For 2:2 salts, αij(2) (2)

(11)

Na

c = 1 c ′= c + 1 Na − 1 Na

+

j=1

∑ ∑ mamc(Bca + IB′ca + ZCca)

Nc

∑ ∑

m

(5)

c=1 a=1

∑ mi(ϕ − 1) = − 2 A γ⎢ 3

Nc

mc mc ′Ψcc ′ X+|z X| ∑ ∑ mamc Cca

c = 1 c ′= c + 1

i

c=1 a=1

c=1 Nc

(10)

The differentiation of eq 11 with respect to each m parameter yields a system of m equations with as many unknowns. After equating to zero and making rearrangements, the system is solved by a series of matrix operations as described in ref 9. Phase diagrams were constructed by using the programs The Geochemist's Workbench and ChemApp with a self-generated parameter file.10 The octahedron shown in Figure 1 represents the interactions of the investigated cation within the system of oceanic

Na

mama ′Φ′aa ′

a=1

∑ ∑

Nc

∑ ∑ mamcB′ca

∑ ma(2ΦXa + ∑ mc ΨXac)

Nc

Yn = ln K or ϕ

∑ (∑ (AijPj) + Ci − ϕi)2 i=1

(4)

Na

a = 1 a ′= a + 1 Na

+ ∑ mc (2Bc X + ZCc X) + c=1 Nc − 1

E=

c=1 a=1

Na − 1

∑ ∑

n

Na

mama ′Ψaa ′ M+|z M| ∑ ∑ mamc Cca

Nc

∑ A n,PiPi + Cn;

where each An,Pi is the constant prefactor in the nth data set for the ith Pitzer parameter P and C is a constant. The fitting procedure is based on the minimization of error function:

Na

⎤ zX2 ⎡ I 2 A γ⎢ + ln(1 + b I )⎥ + b 3 ⎢⎣ 1 + b I ⎦⎥ Nc − 1

+

mama ′Φ′aa ′

a=1 Nc

(9) 6

E

i

∑ mc(2ΦMc + ∑ maΨMca)

a = 1 a ′= a + 1

ln γX = −

Yn =

c=1 a=1

c=1

∑ ∑

Na

∑ ∑ mamcB′ca

a = 1 a ′= a + 1 Nc

Na

Φ′ij = Eθ′ij

The definition of θij and θ′ij can be found elsewhere. The parameter Ψijk, assumed to be independent of the ionic strength, accounts for interactions between three ions of different charges (two cations and one anion or vice versa). The modeling of the solution thermodynamics is undertaken by adjustment of semiempirical Pitzer equations to experimentally accessible quantities (osmotic and activity coefficients, solubilities). The Pitzer equation is linear with respect to the unknown parameters and can be written for each individual data set as: E

Na

∑ ∑

+ ∑ ma(2BMa + ZC Ma) + a=1 Na − 1

Nc

Φij = θij + Eθij ;

= 2 for 1:1, 1:2, 2:1, 3:1, is usually set to 12, and B



Review

Table 1. Solubility Constants of Cesium Salts Consistent with the Developed Pitzer Parameters and Minerals of the Oceanic System at 25 °C Using Data from Reference 7 mineral

dissolution reaction

CsCl(cr) Cs2SO4(cr) CsCl·MgCl2· 6H2O(cr) Cs2SO4·MgSO4· 6H2O(cr) halite thenardite mirabilite

CsCl(cr) → Cs+(aq) + Cl−(aq) Cs2SO4(cr) → 2Cs+(aq) + SO42−(aq) CsCl·MgCl2·6H2O(cr) → Cs+(aq) + Mg2+(aq) + 3Cl−(aq) + 6H2O(l) Cs2SO4·MgSO4·6H2O(cr) → 2Cs+(aq) + Mg2+(aq) + 2SO42−(aq) + 6H2O(l) NaCl(cr) → Na+(aq) + Cl−(aq) Na2SO4(cr) → 2Na+(aq) + SO42−(aq) Na2SO4·10H2O(cr) → 2Na+(aq) + SO42−(aq) + 10H2O(l) K2SO4(cr) → 2K+(aq) + SO42−(aq) MgCl2·6H2O(cr) → Mg2+(aq) + 2Cl−(aq) + 6H2O(l) MgSO4·7H2O(cr) → Mg2+(aq) + SO42−(aq) + 7H2O(l)

arcanite bischofite epsomite

log K298.15K 1.53 0.66 3.61 −4.70 1.586 −0.287 −1.228 −1.776 4.455

Figure 3. Reported experimental and calculated activity coefficients of CsCl for the binary CsCl−H2O system.

−1.881

3. BINARY SYSTEMS 3.1. The CsCl−H2O System. The binary Pitzer parameters for the interactions of Cs−Cl were obtained by fitting eq 6 to the experimental isopiestic measurements performed by Kirgintsev and Luk'yanov,11,12 Frolov et al.,13,14 Robinson and Sinclair,15 Robinson,16 Bahia et al.,17 Makarov et al.,18 and Rard and Miller19 in a concentration range from (0.1 to 11.6) m (Supporting Information, Table S1). A general agreement of the various set of experimental values is observed (Figure 2).

using the set of parameters shown in Table 2 (see solid line in Figures 2 and 3). These values are different from those given by Rard and Miller.19 They approximated their experimental values by two sets of parameters: β(0) = 0.03478, β(1) = 0.03974, and Cϕ = −0.000496 and β(0) = 0.03917, β(1) = −0.002984, and Cϕ = −0.001183 for maximum concentrations of (7.3551 and 11.382) m, respectively. αCsCl(1) was set as usual to 2. We have undertaken a new parameter adjustment setting βCsCl(2) and αCsCl(1) as free variables and αCsCl(2) = 12. This procedure results in an improved reproduction of experimental activities in the whole range of concentrations up to saturation and presupposes strong ion pairing effects. Stewart and Zener29 inferred the formation of ion clusters in CsCl solutions of concentrations higher than 5.9 M which leads to deviations of the calculated osmotic coefficient from the experimental one when assuming only the formation of ion pairs, a fact which is fulfilled by NaCl, KCl, and RbCl solutions. Ion association effects are accounted for in the coefficient (BCsCl + IB′CsCl). The introduction of the coefficient βCsCl(2), which is related to the association equilibrium constant,6 intends to account for the formation of ion pairs in CsCl solutions. The negative value of αCsCl(1) accounts for the downward deviation of the term mCsCl (BCsCl + mCsClB′CsCl) of eq 7 for binary systems from a linear dependency found with αCsCl(1) = 2. This accounts for the formation of clusters. Table 2 includes a second parameter set with the conventional value αCsCl(1) = 2. Ternary interaction coefficients based on it are listed in Table 3. These parameters are limited to a maximum concentration of 7 m CsCl. For calculating activities and solubility constants (Figures 2 to 13; Supporting Information, Tables S1 to S5) the parameter set with α(1) = −1 was used. The solubility constant of CsCl(cr) was calculated from a mean value of the saturation concentration taken from 17 different sources (see Table 4): ms = 11.360 ± 0.023 m (65.66 ± 0.05 wt %) and the activity coefficients calculated with eqs 3 and 4 by using our generated set of parameters. A value of log K = 1.53 was obtained, that is, the Gibbs free energy of dissolution: ΔrGmϕ = −8.74 kJ·mol−1. 3.2. The Cs2SO4−H2O System. For the system Cs2SO4− H2O isopiestic measurements are reported by Ludlum and Warner,30 Cudd and Felsing,31 Filippov et al.,32 Palmer et al.,33 and Kirgintsev and Luk'yanov.34 Particularly, at concentrations above 1 m Cs2SO4, published data differ from each other. Osmotic

Figure 2. Reported experimental and calculated osmotic coefficients for the binary CsCl−H2O system.

Stagis and Mishchenko20 and Mikulin21 reported vapor pressure measurements for CsCl concentrations of (3.469 and 11.36) m, respectively, from which only the latter was included in the analysis. Guendouzi et al.22 determined water activities by using a special hygrometric method, which unfortunately shows a high dispersion and is not reliable enough to be included in our analysis. Reliable potentiometric experiments were reported for concentrations of 2 m down to 9·10−4 m23−28 (Figure 3). Only potentiometric data up to 1 m were found in the literature, which were included in the data set for the determination of the Pitzer parameters (Supporting Information, Table S2). A reasonable reproduction of experimental data covering the whole concentration range up to saturation was obtained by C



Review

Table 2. Set of Binary Pitzer Parametersa M

X

+

−

Cs Cs+ Cs+ Na+ Na+ K+ K+ Mg2+ Mg2+ Ca2+ Ca2+

Cl Cl− SO42− Cl− SO42− Cl− SO42− Cl− SO42− Cl− SO42−

a

β(0)

β(1)

0.03676 0.03945* 0.09849 0.07528 0.01958 0.04808 0.04995 0.35235 0.22088 0.30654 0.19974

−0.00050 -0.00875* 0.53084 0.27692 1.11299 0.21808 0.77929 1.68148 3.3429 1.70811 3.19739

Cϕ

α(1)

α(2)

0.00024 -0.00242* −0.00300 0.00141 0.00497 −0.00079

−1 2 2 2 2 2 2 2 1.4 2 1.4

12 12

β(2) 0.3259 0.33175*

0.00519 0.025 0.00222

−37.2495 −54.5673

12 12

7

The binary systems of the ozeanic salts were also included for the sake of completeness. Values marked with an asterisk (*) are calculated by setting α1 = 2 and α2 = 12, valid up to a maximum concentration of 7 m CsCl.

Table 3. Set of Ternary Pitzer Parametersa

Table 4. Solubility Data of CsCl and Cs2SO4a

M

c

X

θM‑c

ψM‑c‑X

Cs+ Cs+ Cs+ Cs+ Cs+ Cs+ Cs+ Cs+ Cs+ Cs+ Cs+ Cs+ Cs+ Cs+ Cs+

Na+ Na+ Na+ Na+ K+ K+ K+ K+ Mg2+ Mg2+ Mg2+ Mg2+ Ca2+ Cl− Cl−

Cl− Cl− SO42− SO42− Cl− Cl− SO42− SO42− Cl− Cl− SO42− SO42− Cl− SO42− SO42−

−0.01542 −0.01565* −0.01542 −0.01565* −0.00555 −0.00893* −0.00555 −0.00893* −0.35098 −0.30045* −0.35098 −0.30045* −0.35420 0.02 0.02*

−0.00485 -0.00479* −0.00040 -0.00035* 0.00020 0.00079* 0.00306 0.00420* 0.00694 -0.01090* 0.02361 0.00849* 0.01299 0.01039 0.00829*

CsCl

θCl‑SO4 is taken from ref 7. Values marked with an asterisk (*) are consistent with binary parameters of the CsCl−H2O system derived by setting α1 = 2 and α2 = 12 for their calculation. They are limited to a maximum concentration of 7 m CsCl.

a

coefficients determined by Palmer et al.33 are systematically higher than the values reported by Ludlum and Warner,30 whereas data from Cudd and Felsing31 lead to lower osmotic coefficients. Because no convincing criterion for the selection of the reported data sets could be set, all data were used for the calculation of the binary Pitzer parameters (Supporting Information, Table S1). Reported isopiestic data cover the concentration range from 0.026 to 3.65 m. An additional experimental point obtained by the measurement of vapor pressure of a saturated solution was taken from ref 21. The set of calculated Pitzer parameters is given in Table 2. Our parameter set gives an improved representation of experimental data up to concentrations close to 1 m in comparison with that obtained by using the parameters determined by Filippov et al.32 Palmer et al.33 have fitted their experimental data with Archer's extension of the Pitzer equation, which includes additional parameters in the Cacϕ constant: Cacϕ = Cac0 + Cac1 exp(−ωacI1/2). The fitting curve with the reported parameters β0 = 0.09104, β1 = 0.5659, Cac0 = 3.683·10−5, Cac1 = 0.07669, α = 2, and ωac = 2.5 is reproduced for the sake of comparison in Figure 4. It shows a good representation of data at concentrations lower than 1.5 m. At higher concentrations the reliability of the parameter set

ms

ref

11.031 11.336 11.277 11.282 11.309 11.327 11.327 11.332 11.360 11.362 11.377 11.382 11.397 11.398 11.400 11.413 11.413 11.428 11.588 11.860

68 69 70 71 72 49 73 74 75 76 77 19 35 48 18 78 56 79 80 81 Cs2SO4

a

solubility/mol·kg−1

ref

4.990 5.008 5.027 5.029 5.030 5.105 5.132

55 69 82 83 84 56 85

Values in italic were excluded from the averaging.

cannot be verified due to the inconsistence of published experimental data. A value of the solubility of Cs2SO4 ms = 5.046 ± 0.039 m (64.60 ± 0.18 wt %) was calculated by averaging seven values taken from different sources (see Table 4). The activity coefficients calculated with our set of Pitzer parameters were used for calculating a solubility constant log K = 0.66 and ΔrGmϕ = −3.75 kJ·mol−1. In spite of the lack of experimental data near the saturation point, the reliability of the calculated parameters is supported by their high predictive power in ternary systems, as will be shown later. D



Review

Figure 4. Reported experimental and calculated osmotic coefficients for the binary Cs2SO4−H2O system.

4. TERNARY SYSTEMS 4.1. The CsCl−NaCl−H2O System. Solubility experiments in this ternary system were reported by Balarew et al.,35 Chou et al.,36 Arkhipov et al.,37 Plyushchev et al.38 and Chou and Lee39 (see Figure 5). According to published data, there is a general agreement that halite is formed up to CsCl concentrations of 6 m. From this concentration to the saturation limit of CsCl at 11.36 m a solid solution, [Cs1−x(Na·H2O)x]Cl appears as precipitate,36 the composition of which can be expressed as: x = 0.330 + 0.05006 mCsCl − 0.0067 mCsCl2 after interpolation of the experimental data in ref 36 with a secondorder polynomial. According to Chou et al.,36 the double salt CsCl·2NaCl·2H2O becomes stable between (6 and 6.5) m. No solution data are available for this system with CsCl(cr) as a stable phase. Isopiestic data were reported by Kirgintsev and Luk'yanov,12 Robinson,16 and Rard and Miller19 (Supporting Information, Table S3). Guendouzi et al.40 determined water activities by a special hygrometric method. Like the reported data for CsCl they were excluded from parameter development. Figure 5b shows the water activities as a function of the solution composition obtained from the reported experimental data. The parameter θCs−Na was calculated by fitting simultaneously the data of the ternary system Na2SO4−Cs2SO4−H2O to gain consistency. The obtained parameters are shown in Table 3. Only solubility data in the concentration range where halite appears as precipitate (Supporting Information, Table S5) were considered for the evaluation of the predictive character of the calculated set of Pitzer parameters. The values reported by Chou et al.36 and an obvious deviating point reported by Plyushchev et al.38 were excluded. Solubility data in the concentration range for which a solid solution precipitates were also not considered, since there is no appropriate model for the calculation of the activity of solids. The calculated set of parameters yields an excellent prediction of the solubility data with halite (solid line in Figure 5a). The isoactivity lines also show a good agreement with experimental values. They show a large degree of linearity for water activities between 0.9 and 1. For lower activities linearity is only observed for CsCl concentrations lower than 3 m. Linear isoactivity lines are predicted by the Zdanovskii−Stokes−Robinson model, 41−43 according to

Figure 5. (a) Solubility diagram of the ternary CsCl−NaCl−H2O system at 25 °C. The reported water activity measurements and calculated isoactivity lines are also plotted. (b) Reported and calculated water activities as a function of the concentration of salt components. Inset: Absolute relative deviations of calculated activities from experimental data.

which the activity of a mixture of two salt solutions can be expressed in terms of the properties of individual salts as: m m 1 = 10 + 20 m1 m2 (12) where m10 and m20 are the molalities of the pure solutions of the solutes 1 and 2 at the water activity of the mixture. Equation 12 implies that the osmotic coefficient can be expressed as: ϕ=

(m1ν1ϕ10 + m2 ν2ϕ2 0) ∑i mi

(13)

where ν1 and ν2 are the number of particles produced by dissociation of salts 1 and 2, respectively. A deviation from this behavior can be interpreted as caused by formation of ion pairs at high CsCl concentrations. E



Review

4.2. The Cs2SO4−Na2SO4−H2O System. This system was thoroughly investigated by Filippov et al.32 by means of isopiestic and solubility experiments. According to their published results (Supporting Information, Table S5), three solid phases are formed by increasing the Cs2SO4 concentration in saturated sodium sulfate solutions (Figure 6). Up to 1.7 m mirabilite

introducing the calculated parameter set. The isoactivity lines are quite linear in the sulfate system, suggesting in principle a low degree of ion pairing. 4.3. The CsCl−KCl−H2O System. According to solubility data reported by Merbach and Gonella,48 Kirgintsev and Trushnikova,49 and Arkhipov and Kashina,50 solid solution crystals are formed in saturated CsCl−KCl ternary solutions. Depending on the relative concentrations of both salt components in the liquid phase, different solid phase structures are formed, one K-rich phase at CsCl concentrations up to 10.5 m and a Cs-rich phase upon higher concentration increments. Isopiestic data were reported by Robinson,51 Kirgintsev and Luk'yanov,11 and Bahia et al.17 with CsCl concentrations in the electrolyte up to 4.27 m (Supporting Information, Table S3). Pitzer parameters obtained by fitting these data are shown in Table 3. Since the activity of end-members CsCl(cr) and KCl(cr) in the solid solutions introduces an additional variable not experimentally measured, solubility data were not considered for the evaluation of the ternary Pitzer interaction parameters. Figure 7

Figure 7. Solubility diagram of the ternary CsCl−KCl−H2O system at 25 °C. The reported water activity measurements and calculated isoactivity lines are also plotted. Inset: Absolute relative deviations of calculated activities from experimental data.

Figure 6. (a) Solubility diagram of the ternary Cs2SO4−Na2SO4−H2O system at 25 °C. The reported water activity measurements and calculated isoactivity lines are also plotted. (b) Reported and calculated water activities as a function of the concentration of salt components. Inset: Absolute relative deviations of calculated activities from experimental data.

shows the calculated isoactivity lines, which are in good agreement with the reported experimental data. As in the CsCl− NaCl−H2O system, the system CsCl−KCl−H2O follows the Zdanovskii−Stokes−Robinson model for water activities larger than 0.85. 4.4. The Cs2SO4−K2SO4−H2O System. For this system, solubility investigations reported by Nosova et al.,52 Filippov et al.,32 Konik and Storozhenko,53 Nalivaiko et al.,54 and Kripin55 were found. Also, isopiestic data were reported in ref 32 (Supporting Information, Table S3). According to the reported data, two minerals appear as the solid phase in the solubility diagrams: arcanite (K2SO4) up to a Cs2SO4 concentration of m = 4.88 mol·kg−1 and Cs2SO4(cr) at higher sulfate concentrations (Figure 8). There is a relative large data dispersion concerning the triple-point arcanite−Cs2SO4−solution and

(Na2SO4·10H2O) appears. Between (1.7 and 4.4) m, the formation of thenardite (Na2SO4) is thermodynamically favored. Beyond this concentration, Cs2SO4(cr) is formed. Both transition points were experimentally investigated by Poletaev et al.,44 Shevchuk and Ushakov,45 Foote,46 and Poletaev and Krasnenkova.47 Calculated θCs−Na and ψCs−Na−SO4 parameters are shown in Table 3. θCs−Na was determined together with data of the homologous CsCl−NaCl−H2O ternary system. Figure 6 shows that solubility and isopiestic data can be well-reproduced by F



Figure 8. system at calculated deviations

Review

Solubility diagram of the ternary Cs2SO4−K2SO4−H2O 25 °C. The reported water activity measurements and isoactivity lines are also plotted. Insert: Absolute relative of calculated activities from experimental data.

reported solubilities. Therefore ternary parameters (Table 3) were calculated by using only isopiestic data. The parameter θK−Cs was calculated by including data of both ternary systems CsCl−KCl and Cs2SO4−K2SO4. Solubility and isoactivity lines calculated by using the obtained ternary parameters shows a good agreement with reported experimental data. 4.5. The CsCl−MgCl2−H2O System. This ternary system was investigated by Shevchuk and Vaisfel'd,56 D'Ans and Busch,57 and Skripin et al.,58 who reported solubility data (Supporting Information, Table S5). According to these data, bischofite (MgCl2·6H2O) forms as solid phase up to a CsCl concentration m = 0.089 mol·kg−1. At higher CsCl concentrations, the double salt CsCl·MgCl2·6H2O is found up to concentrations of about 7.35 mol·kg−1. From this point on, CsCl(cr) appears as the solid phase on increasing the CsCl concentration (Figure 9a). Unfortunately, isopiestic data reported by Skripin et al.58 (Supporting Information, Table S3) are only available in graphical form. Hence, they are difficult to be evaluated. Digitalized data were taken to calculate ternary Pitzer parameters together with solubility data reported by those authors and some obtained by D'Ans and Busch.57 Following ref 59, values of Shevchuk and Vaisfel'd56 were disregarded. A comparison of the calculated water activities (using our Pitzer parameters) with experimental values is visualized in the tridimensional diagram presented in Figure 9b. The water activities as well as the solubility of bischofite and the double salt can be well-described in spite of the uncertainty contained in the isopiestic data. The calculated solubility of CsCl(cr) is to some extent questionable. Some inconsistency between isopiestic and solubility data with CsCl(cr) as solid phase was noted. Isopiestic experiments on this system are in progress and will be published elsewhere. From calculated ion and water activities, the solubility constant of CsCl·MgCl2·6H2O, log K = 3.61, could be calculated. This value differs from that reported by Balarew et al.59 (log K = 4.52) which was calculated by taking only solubility data from ref 57. A value of log K = 3.604 was reported by

Figure 9. (a) Solubility diagram of the ternary CsCl−MgCl2−H2O system at 25 °C. The reported water activity measurements and calculated isoactivity lines are also plotted. (b) Reported and calculated water activities as a function of the concentration of salt components.

Neck et al.60 after having calculated Pitzer parameters from solubility data of CsTcO4, MgCl2, and MgSO4. The bending of the isoactivity lines indicates a deviation from the ideal Zdanovskii−Stokes−Robinson behavior. This can be explained in terms of the formation of the species MgCl+,61,62 which leads to an overestimation of the ionic strength. 4.6. The Cs2SO4−MgSO4−H2O System. For this system only solubility data reported by Kovalev et al.63 and Shevchuk and Vaisfel'd56 can be found in the literature. According to these publications, epsomite (MgSO4·7H2O) is formed up to a Cs2SO4 concentration of 0.58 mol·kg−1 (Figure 10). Upon further increase of the cesium sulfate concentration, the double salt CsSO4·MgSO4·6H2O appears as an equilibrium phase. The solubility of Cs2SO4·MgSO4·6H2O decreases exponentially with the Cs2SO4 concentration until it reaches a value of about 0.1 mol·kg−1 near the saturation point of Cs2SO4. Ternary parameters were obtained in this case by using solubility data with epsomite as an equilibrium phase (Supporting Information, Table S5). The parameter θMg−Cs was calculated by G



Review

the experimental determined value. Further experimental work is then necessary to improve and verify the predictive precision of Pitzer parameters. Isopiestic experiments are presently in work and will be published elsewhere. 4.8. The CsCl−Cs2SO4−H2O System. For this system potentiometric measurements of activity coefficients of CsCl− Cs2SO4 solutions, up to maximal concentrations of 0.25 mol·kg−1 for Cs2SO4 and 1.04 mol·kg−1 for CsCl, were reported by Hu et al.24 (Supporting Information, Table S4). Vaisfel'd and Shevchuk66 reported solubility data, according to which only two minerals appear as precipitated phases: CsCl(cr) and Cs2SO4(cr) (Supporting Information). Both publications were used to calculate the parameter ΨCs−Cl−SO4 (Table 3). Figure 12 shows that the Figure 10. Solubility diagram of the ternary Cs2SO4−MgSO4−H2O system at 25 °C.

including data of both ternary systems CsCl−MgCl2 and Cs2SO4−MgSO4. An acceptable reproduction of the experimental reported data calculated with the obtained parameter is observed. From the calculated activity coefficients and the solubility data, a solubility constant of the double salt CsSO4·MgSO4·6H2O log K = −4.70 could be calculated. A value of log K = −4.503 was reported by Neck et al.60 based only on solubility data reported in ref 56. Isopiestic experiments are presently being performed and will be published elsewhere. 4.7. The CsCl−CaCl2−H2O. Ternary solution systems including Ca-salts, with the exception of one publication for the CsCl−CaCl2−H2O system by Plyushchev et al.,64 were not explored at all. According to this work, which reports only solubility values, three double salts are formed by continuous addition of CsCl to a saturated CaCl2 solution: CsCl·CaCl2 from 1·10−3 m to 0.53 m, 2CsCl·CaCl2·2H2O from (0.53 to 8.06) m, and 5CsCl·CaCl2 up to 9.59 m (Figure 11). Single salts are formed

Figure 12. Solubility diagram of the ternary CsCl−Cs2SO4−H2O system at 25 °C.

Figure 11. Solubility diagram of the ternary CsCl−CaCl2−H2O system at 25 °C.

Figure 13. Solubility diagram of the quaternary system CsCl− Cs2SO4−NaCl−Na2SO4−H2O. Experimental values taken from ref 67. , calculated by using binary and ternary Pitzer parameters given in Tables 2 and 3. Concentrations are expressed as a fraction of the total cation molality: x = mNa(100/mNa + mCs); y = 2 mSO4(100/mNa + mCs).

only by CsCl concentrations lower than 0.001 m (antarcticite: CaCl2·6H2O) or higher than 9.59 m (CsCl(cr)). Ternary parameters (Table 3) were calculated by using the solubility data of CsCl(cr). Concentration values are still within the range for which binary Pitzer parameters for the systems CaCl2−H2O were obtained.65 Taking calculated ternary Pitzer parameters, the solubility constants for 5CsCl·CaCl2 and 2 CsCl·CaCl2·2H2O were calculated: log K = 9.92 and log K = 5.73, respectively. It is notable that the calculated solubility curve can reproduce experimental data reported in ref 64 well. The triple-point 5CsCl·CaCl2−2CsCl·CaCl2·2H2O solution appears shifted from

solubility diagram constructed by using the already calculated set of binary Pitzer parameters (Table 2) and the ternary parameter reproduces the experimental data very well.

5. QUATERNARY SYSTEM The predictive power of calculated binary and ternary parameters was tested in a quaternary system. Solubility data for the H



Review

system CsCl−NaCl−Cs2SO4−Na2SO4−H2O were reported by Poletaev et al.67 According to them, halite, mirabilite, thenardite, Cs2SO4(cr), and the solid solution Cs(Na)Cl appear as solid phases. The different solid domains as a function of the solution concentration are visualized in the form of a Jänecke diagram in Figure 13. Experimental and calculated data agree adequately.

2004; Erikson, C. ChemApp; GTT Technologies: Herzogenrath, Germany, 1996−2003. (11) Kirgintsev, A. N.; Luk'yanov, A. V. Isopiestic Investigations of Ternary Solutions, VII. Russ. J. Phys. Chem. 1966, 40, 686. (12) Kirgintsev, A. N.; Luk'yanov, A. V. Isopiestic Investigations of Ternary Solutions. Russ. J. Phys. Chem. 1963, 31, 1501. (13) Frolov, J. G.; Nikolaev, V. P.; Jabov, V. P.; Ageev, A. A. Isopiestic study of mixed solutions of electrolytes containing Co2+, Ni2+, Cu2+. Termodin. Stroen. Rastv. 1974, 2, 55. ̀ (14) Frolov, Y. G.; Nikolaev, V. P.; Karapetyants, M. K.; lasenko, K. K. Excess Thermodynamic Functions of Mixing of Aqueous Isopiestic Electrolyte Solutions without Common Ions. Russ. J. Phys. Chem. 1971, 45, 1054. (15) Robinson, R. A.; Sinclair, D. A. The Activity Coefficients of the Alkali Chlorides and of Lithium Iodide in Aqueous Solution from Vapor Pressure Measurements. J. Am. Chem. Soc. 1934, 56, 1830. (16) Robinson, R. A. The Osmotic Properties of Aqueous Sodium Chloride−Cesium Chloride Mixtures at 25°. J. Am. Chem. Soc. 1952, 74, 6035. (17) Bahia, A. M.; Lilley, T. H.; Tasker, I. R. The osmotic coefficients of aqueous CsCl and CsCl + KCl mixtures at 298.15 K. J. Chem. Thermodyn. 1978, 10, 683. (18) Makarov, L. L.; Evstrop’ev, K. K.; Vlasov, Y. G. The Osmotic and Activity Coefficients of RbCl, CsCl and KI in Aqueous Solutions of High Concentrations. Zurn. Fiz. Chim. 1958, 32, 1618. (19) Rard, J. A.; Miller, D. G. Isopiestic determination of the osmotic and activity coefficients of aqueous cesium chloride, strontium chloride, and mixtures of sodium chloride and cesium chloride at 25 °C. J. Chem. Eng. Data 1982, 27, 169. (20) Stagis, A.; Mishchenko, K. P. Thermodynamic Characteristics of Aqueous Salt Solutions at the Total Hydration Limit in the −10 to +50 deg. Zurn. Obsc. Chim. 1970, 40, 2141. (21) Mikulin, G. I. Voprosy fiziceskoj chimii rastvorov elektrolitov (Issues in Physical Chemistry of Electrolyte Solutions); Izd. Khimiya: St. Petersburg, 1968. (22) Guendouzi, M.; El Dinane, A.; Mounir, A. Water activities, osmotic and activity coefficients in aqueous chloride solutions at T = 298.15 K by the hygrometric method. J. Chem. Thermodyn. 2001, 33, 1059. (23) Hu, M.-C.; Cui, R.-F.; Li, S.-N.; Jiang, Y.-C.; Xia, S. P. Determination of Activity Coefficients for Cesium Chloride in Methanol−Water and Ethanol−Water Mixed Solvents by Electromotive Force Measurements at 298.15 K. J. Chem. Eng. Data 2007, 52, 357. (24) Hu, M.-C.; Tang, J.; Li, S.-N.; Xia, S.-P.; Cui, R.-F. Activity Coefficients of Cesium Chloride and Cesium Sulfate in Aqueous Mixtures Using an Electromotive Force Method at 298.15 K. J. Chem. Eng. Data 2007, 52, 2224. (25) Harned, H. S.; Schupp, O. E., Jr. The Activity Coefficients of Cesium Chloride and Hydroxide in Aqueous Solution. J. Am. Chem. Soc. 1930, 52, 3886. (26) Caramazza, R. Coefficienti di Attività di Elettroliti Forti in Soluzioni Acquose Concentrate. Nota I. Cloruro di Cesio. Ann. Chim. 1963, 53, 472. (27) Lebed', V. I.; Aleksandrov, V. V. Electromotive Forces and Normal Potentials of Cells without Transport at Various Temperatures. Russ. J. Phys. Chem. 1964, 38, 1414. (28) Cui, R.-F.; Hu, M.-C.; Jin, L.-H.; Li, S.-N.; Jiang, Y.-C.; Xia, S.-P. Activity coefficients of rubidium chloride and cesium chloride in methanol−water mixtures and a comparative study of Pitzer and Pitzer−Simonson−Clegg models (298.15 K). Fluid Phase Equilib. 2007, 251, 137. (29) Stewart, R. F.; Zener, C. Cluster formation in aqueous solutions of strong electrolytes. J. Phys. Chem. 1988, 92, 1981. (30) Ludlum, D. B.; Warner, R. C. Equilibrium Centrifugation in Cesium Sulfate Solutions. J. Biol. Chem. 1965, 240, 2961. (31) Cudd, H. H.; Felsing, W. A. Activity Coefficients of Rubidium and Cesium Sulfates in Aqueous Solution at 25°. J. Am. Chem. Soc. 1942, 64, 550.

6. CONCLUSIONS A consistent set of binary and ternary Pitzer parameters was generated from a comprehensive compendium of reported experimental isopiestic, solubility, and potentiometric data at 25 °C. Solubility constants of cesium minerals formed in the ozeanic salt system were calculated. Pitzer parameters were tested satisfactorily on a quaternary system. Isopiestic experiments for improving ternary interaction parameters for systems containing Ca and Mg are in work.

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ASSOCIATED CONTENT

S Supporting Information *

Isopiestic and potentiometric data for the determination of binary parameters (Tables 1 and 2) and isopiestic, vapor pressure, potentiometric, and solubility data for ternary systems (Tables 3 to 5). This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Funding

This work has been funded by the German Federal Office for Radiation Protection (BfS), contract number 8584-6. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Committee on Separations Technology and Transmutation Systems, National Research Council. Nuclear Wastes: Technologies for Separations and Transmutation; The National Academies Press: Washington, DC, 1996. (2) Loida, A.; Metz, V.; Kienzler, B.; Geckeis, H. Radionuclide release from high burnup spent fuel during corrosion in salt brine in the presence of hydrogen overpressure. J. Nucl. Mater. 2005, 346, 24. (3) Bonin, B.; Colin, A.; Dutfoy, A. Pressure building during the early stages of gas production in a radioactive waste repository. J. Nucl. Mater. 2000, 281, 1. (4) Wanner, H. Solubility data in radioactive waste disposal. Pure Appl. Chem. 2007, 79, 875. (5) IAEA. The Principles of Radioactive Waste Management, Safety Series No. 111-F; International Atomic Energy Agency: Vienna, 1995. (6) Pitzer, K. S. Activity coefficients in electrolyte solutions; CRC Press: Boca Raton, FL, 1991; Chapter 3. (7) Altmaier, M.; Brendler, V.; Bube, C.; Neck, V.; Marquardt, C.; Moog, H. C.; Richter, A.; Scharge, T.; Voigt, W.; Wilhelm, S.; Wilms, T.; Wollmann, G. THEREDA-Thermodynamische Referenzdatenbasis. Report GRS 265 (German), 2011; ISBN 978-3-939355-41-0. (8) Pitzer, K. S. Thermodynamics of electrolytes. I. Theoretical basis and general equations. J. Phys. Chem. 1973, 77, 268. (9) Moog, H. C.; Herbert, H. J. Modeling of Hg(II)-Solubility in Binary and Ternary Solutions Containing Na+, K+, Mg2+, Ca2+, H+ and Cl−. Z. Phys. Chem. 2000, 214, 313. (10) Bethke, C. M. The Board of Trustees of the University of Illinois. The Geochemist’s Workbench; University of Illinois: Urbana, IL, I



Review

(54) Nalivaiko, E. M.; Storozhenko, V. A.; Prikhod’ko, M. K. The K2SO4-Cs2SO4-H2SO4-H2O System at 25 °C. Russ. J. Inorg. Chem. 1988, 33, 1233. (55) Kripin, L. A. Russ. J. Inorg. Chem. 1960, 5, 86. (56) Shevchuk, V. G.; Vaisfel'd, M. I. The 2CsCl + MgSO4 = Cs2SO4 + MgCl2-H2O System at 25 °C. Russ. J. Inorg. Chem. 1967, 12, 1481. (57) D'Ans, J.; Busch, W. Ü ber die Fraktionierung inkongruent löslicher isomorpher Doppelsalze-Die quaternären Systeme KCl-RbCl(CsCl)-MgCl2-H2O bei 25 °C. Z. Anorg. Allg. Chem. 1937, 232, 337. (58) Skripin, M. Y.; Rumyantsev, A. V.; Solechnik, N. D. Thermodynamic Study of Rb+, Mg2+//Cl−-H2O and Cs+, Mg2+// Cl−-H2O Ternary Systems at 25 °C. Russ. J. Appl. Chem. 1993, 66, 807. (59) Balarev, C.; Christov, C.; Valyashko, V.; Petrenko, S. Thermodynamics of formation of carnallite type double salts. J. Solution Chem. 1993, 22, 173. (60) Neck, V.; Könnecke, T.; Fanghänel, T.; Kim, J. I. Activity coefficients and Pitzer Parameters for the Fission Product Ions Cs+ and TcO−4 in the system Cs+/Na+/K+/Mg2+/Cl−/SO42−/TcO−4/ H2O at 25 °C. Radiochim. Acta 1998, 83, 75. (61) Elguist, B.; Wedborg, M. Stability constants of NaSO4−, MgSO4, MgF+, MgCl+ ion pairs at the ionic strength of seawater by potentiometry. Marine Chem. 1978, 6, 243. (62) Larentzos, J. P.; Criscenti, L. J. A Molecular Dynamics Study of Alkaline Earth Metal−Chloride Complexation in Aqueous Solution. J. Phys. Chem. B 2008, 112, 14243. (63) Kovalev, A. E.; Shevchuk, A. V.; Shevchuk, V. G. Phase Equilibria in the System (NH4)SO4-Cs2SO4-MgSO4-H2O at 25 °C. Ukr. Chim. Zurn. 1991, 57, 356. (64) Plyushchev, V. E.; Tulinova, V. B.; Kuznetsova, G. P.; Korovin, S. S.; Petrova, R. G. Investigation of the Ternary System NaCl-CsClH2O. Zurn. Neorg. Chim. 1957, 2, 2212. (65) Phutela, R. C.; Pitzer, K. S. Thermodynamics of aqueous calcium chloride. J. Solution Chem. 1983, 12, 201. (66) Vaisfel'd, M. I.; Shevchuk, V. G. Equilibrium in the CsCl-MgCl2H2O and CsCl-Cs2SO4-H2O Systems at 25 °C. Russ. J. Inorg. Chem. 1967, 12, 1317. (67) Poletaev, I. F.; Plyushchev, V. E.; Lyudomirskaya, A. P. Russ. J. Inorg. Chem. 1974, 19, 926. (68) Belyaev, I. N.; Lobas, L. M. The CsCl-ZrOCl2-H2O and RbClZrOCl2-H2O Systems at 25 °C. Russ. J. Inorg. Chem. 1968, 13, 601. (69) Berkeley, E. On Some Physical Constants of Saturated Solutions. Philos. Trans. R. Soc. London, Ser. A 1904, 203, 189. (70) Arkhipov, S. M.; Kashina, N. I. Solubility in the Cs+, Na+//Cl−, ClO3−-H2O System at 25 °C. Russ. J. Inorg. Chem. 1970, 15, 391. (71) Blidin, V. P. Zurn. Obsc. Chim. 1956, 62, 1281. (72) Zhao, W.-X.; Hu, M.-C.; Jiang, Y.-C.; Li, S.-N. Solubilities, Densities and Refractive Indices of Rubidium Chloride or Cesium Chloride in Ethanol Aqueous Solutions at Different Temperatures. Chin. J. Chem. 2007, 25, 478. (73) Fedorova, O. N.; Serebrennikova, G. M.; Stepin, B. D. Solubility in the RbCl-TeCl4-H2O and CsCl-TeCl4-H2O System at 25 °C. Russ. J. Inorg. Chem. 1971, 16, 1495. (74) Foote, H. W. Equilibrium in the systems; alkali chloride-cobalt chloride-water. Am. J. Sci. 1927, 5, 158. (75) Clynne, M. A.; Potter, I. R. W. Solubility of some alkali and alkaline earth chlorides in water at moderate temperatures. J. Chem. Eng. Data 1979, 24, 338. (76) Kartzmark, E. M. Double salts of indium trichloride with the alkali chlorides, with ammonium chloride, and with indium sulfate. Can. J. Chem. 1977, 55, 2792. (77) Lilieev, A. S.; Tepavicharova, S.; Lyashenko, A. K.; Balarev, K. Dielectric Properties of Saturated Solutions and the Solubility Diagram of the CsCl-NiCl2-H2O System. Russ. J. Inorg. Chem. 1989, 34, 281. (78) Bykova, I. N.; Kuznetsova, G. P.; Kolotilova, V. Y.; Stepin, B. D. The RbCl-RbH2PO4 and CsCl-CsH2PO4-H2O Systems at 25 °C. Russ. J. Inorg. Chem. 1968, 13, 282. (79) Mironenko, A. P.; Stepina, S. B.; Plyushchev, V. E.; Zotova, L. A. The CsCl-Br2-H2O System at 25 °C. Russ. J. Inorg. Chem. 1968, 13, 1460.

(32) Filippov, V. K.; Kalinkin, A. M.; Vasin, S. K. Thermodynamics of phase equilibria of aqueous (lithium sulfate + cesium sulfate), (sodium sulfate + cesium sulfate), and (potassium sulfate + cesium sulfate) at 298.15 K using Pitzer's model. J. Chem. Thermodyn. 1987, 19, 185. (33) Palmer, D. A.; Rard, J. A.; Clegg, S. L. Isopiestic determination of the osmotic and activity coefficients of Rb2SO4 (aq) and Cs2SO4(aq) at T = (298.15 and 323.15) K, and representation with an extended ion-interaction (Pitzer) model. J. Chem. Thermodyn. 2002, 34, 63. (34) Kirgintsev, A. N.; Luk'yanov, A. V. Investigations of Ternary Solutions by the Isopiestic Method. X. The Solutions H2SO4-M2SO4H2O. Sov. Radiochem. 1967, 8, 64. (35) Balarew, C.; Ketenev, D. N. Study of the Systems NaCl-RbClH2O and NaCl-CsCl-H2O at 25 °C. Dokl. Bolgar. Akad. Nauk 1975, 28, 221. (36) Chou, I.-M.; Romankiw, L. A.; Evans, H. T.; Konnert, J. A. Solubility relations in the ternary system sodium chloride-cesium chloride-water at 1 atm. 2. Solubility relations at 25 °C. J. Chem. Eng. Data 1983, 28, 393. (37) Arkhipov, S. M.; Kashina, N. I.; Kuzina, V. A. Phases of Variable Composition in the CsCl-NaCl-H2O System. Russ. J. Inorg. Chem. 1970, 15, 556. (38) Plyushchev, V. E.; Tulinova, V. B.; Kuznetsova, G. P.; Korovin, S. S.; Shipetina, N. S. Investigation of the Ternary System Sodium Chloride-Cesium Chloride-Water. Zurn. Neorg. Chim. 1957, 2, 2654. (39) Chou, I.-M.; Lee, R. D. Solubility relations in the ternary system sodium chloride-cesium chloride-water at 1 atm. 1. Solubilities of halite from 20 to 100 °C. J. Chem. Eng. Data 1983, 28, 390. (40) Guendouzi, M.; El Benbiyi, A.; Azougen, R.; Dinane, A. Thermodynamic properties of two ternary systems {yCsCl+(1− y)LiCl}(aq) and {yCsCl+(1−y)NaCl}(aq) at temperature 298.15 K. CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 2004, 28, 435. (41) Zdanovskii, A. B.; Solyanoi, T. Lab. Akad. Nauk. SSSR 1936, 6. (42) Stokes, R. H.; Robinson, R. A. Interactions in Aqueous Nonelectrolyte Solutions. I. Solute-Solvent Equilibria. J. Phys. Chem. 1966, 70, 2126. (43) Clegg, S. L.; Seinfeld, J. H. Improvement of the Zdanovskii− Stokes−Robinson Model for Mixtures Containing Solutes of Different Charge Types. J. Phys. Chem. A 2004, 108, 1008. (44) Poletaev, I. F.; Plyushchev, V. E.; Lyudomirskaya, A. P. The Cs+,Na+//Cl−, SO42−-Water System at 25 and 75 °C. Russ. J. Inorg. Chem. 1974, 19, 926. (45) Shevchuk, V. G.; Ushakov, Y. V. The Cs2SO4-(NH4)2SO4Na2SO4-H2O System at 25 °C. Russ. J. Inorg. Chem. 1969, 14, 1329. (46) Foote, H. W. On the Formation of Double Salts. [Third Paper] The Question of Double Salt Formation between the Alkali Sulfates. J. Am. Chem. Soc. 1911, 33, 463. (47) Poletaev, I. F.; Krasnenkova, L. V. The Na+, Rb+// NO3−,SO42H2O and Cs+, Na+// NO3−,SO42-H2O at 25 and 75°C. Russ. J. Inorg. Chem. 1975, 20, 1250. (48) Merbach, A.; Gonella, J. Contribution á l'étude du systéme quaternaire KCI-RbCI-H2O: I. Les isothermes de 25° des systémes ternaires limites. Helv. Chim. Acta 1969, 52, 69. (49) Kirgintsev, A. N.; Trushnikova, L. N. Solubility in the KNO3CsNO3-H2O, KCl-CsCl-H2O and KI-CsI-H2O Systems at 25 °C. Russ. J. Inorg. Chem. 1968, 13, 1462. (50) Arkhipov, S. M.; Kashina, N. I. The NaCl-KCl-CsCl-H2O System at 25 °C. Russ. J. Inorg. Chem. 1984, 29, 1550. (51) Robinson, R. A. The osmotic properties of aqueous caesium chloride + potassium chloride and caesium chloride + lithium chloride mixtures at 25° C. Trans. Faraday Soc. 1953, 49, 1147. (52) Nosova, L. A.; Voskoboinikov, N. B.; Timofeev, G. S. Solubility studies in ternary aqueous systems. K2SO4-Cs2SO4-H2O and K2SO4Rb2SO4-H2O at 25, 50 and 75 °C. VINITI 2328−80 1980, 26. (53) Konik, L. P.; Storozhenko, V. A. Physicochemical Investigations of the Cs2SO4-K2SO4-Li2SO4-H2O System at 25 °C. Russ. J. Inorg. Chem. 1981, 26, 623. J



Review

(80) Benrath, A. Ü ber die Systeme CoCl2-MeCl oder MeCl2-H2O. Z. Anorg. Chem. 1927, 163, 396. (81) Lazorenko, N. M.; Shevchuk, V. G. Solubility Polytherm of the CsCl-GdCl3-H2O System. Russ. J. Inorg. Chem. 1983, 28, 1517. (82) von Dohlen, W. C.; Simons, E. L. The Systems Ag2SO4− Rb2SO4−H2O and Ag2SO4−Cs2SO4−H2O at 25°. J. Am. Chem. Soc. 1951, 73, 461. (83) Filippov, V. K.; Jakovleva, S. I. Use of the Pitzer Method for the Calculation of Thermodynamic Functions in the System M2SO4CoSO4-H2O (M-Li, Na, K, Rb, Cs) at 25 °C. Chim. Termodin. Rastvor. 1985, 5, 3. (84) Calvo, C.; Simons, E. L. The Ternary Aqueous Systems of Ammonium Sulfate with Cesium, Potassium and Rubidium Sulfates. J. Am. Chem. Soc. 1952, 74, 1202. (85) Archipov, S. M.; Kasina, N. I.; Archipov, G. I.; Kuzina, V. A. Zurn. Neorg. Chim. 1976, 21, 237.

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