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Weare, 1987, and Pitzer, 1991, for reviews). Using this formalism, Holmes & Mesmer (1983) have proposed an aqueous solution model for CsCl(aq) that allows ...
Eur. J. Mineral. 1999,11, 477-482

Thermodynamics of the CsCl-H20 system at low temperatures CHRISTOPHE MONNINU and MICHEL DUBOIS 2 *

iLaboratoire de Géochimie, CNRS/UPS, 38 rue des Trente-Six Ponts, 31400 Toulouse, France 2

Université des Sciences et Technologies de Lille, Laboratoire de Sédimentologie et Géodynamique, UMR CNRS 719, 59655 Villeneuve d'Ascq Cedex, France

Abstract: The interpretation offluid-inclusiondata requires knowledge of phase diagrams at low (subfreezing) tem­ peratures. From the example of the CsCl-H20 system, we here investigate the possibility to build such diagrams from thermodynamic models of aqueous solutions parameterized at higher temperatures. Holmes & Mesmer (1983) have built a model for the thermodynamic properties of CsCl(aq) based on Pitzer's equation fit to thermodynamic data mainly at temperatures above Ö°C along with a few freezing-point-depression data down to -8°C. We show how this model can be used along with the published water-ice equilibrium constant and thermodynamic data at 25 °C for Cs+(aq), Cl-(aq) and CsCl(s), to predict with confidence the ice-liquid-vapor (ILV) and the salt-liquid-vapor (SLV) curves down to the eutectic temperature for the CsCl-H2O system. Key-words: aqueous solutions, cesium chloride, solubility, freezing-point, phase diagram.

Introduction Phase diagrams of aqueous systems at low temperature are essential in the interpretation of fluid-inclusion data. Using the example of the CsCl-H2O system, Dubois et al (1993) have shown how a constrained least-squares method can be used to reconstruct binary phase diagrams from scarce data. We here use recent advances in the thermodynamics of aqueous solutions at high concentrations and available thermodynamic data to show how such a diagram can be built through simple equilibrium calculations at high concentra­ tions and at low temperatures. A detailed descrip­ tion of the topology of such a simple diagram is

given by Dubois et al (1993). We focus on the prediction of the liquid water-ice equilibrium curve (commonly reported as freezing point depression data), labelled as the ILV curve (IceLiquid-Vapor), i.e.: H 2 O(l) = H 2 O(s) (1) and the salt-aqueous solution equilibrium (SLV: Solid-Liquid-Vapor curve), i.e.: GsCl(s) = Cs+(aq) + Cl-(aq) (2) The equilibrium constant of Eq. (1) is simply the activity of water of the aqueous solution while that for Eq. (2) is the solubility product of solid cesium chloride, Ksp: Ksp = m Cs+(aq) . m cl - (aq) • Tcsci(aq) (3) In Eq. (3), γ is the mean activity coefficient of

a

) email: [email protected] ) email: [email protected] 1 .fr

b

0935-1221/99/0011-0477 $ 1.50 @ 1999 E. Schweizerbart'sche Verlagsbuchhandlung. D-70176 Stuttgart

478

C. Monnin, M. Dubois

aqueous cesium chloride and m the molality of the designated species. Pitzer's ion interaction approach has recently allowed the calculation of the thermodynamic properties of aqueous solu­ tions up to high concentrations and has hence fos­ tered the development of accurate solubility models of great interest for the earth sciences (see Weare, 1987, and Pitzer, 1991, for reviews). Using this formalism, Holmes & Mesmer (1983) have proposed an aqueous solution model for CsCl(aq) that allows the calculation of the activity of water and the CsCl(aq) activity coefficient. In the pre­ sent work, we investigate the reliablity of the cal­ culations carried out with this aqueous solution model outside the temperature-pressure-concen­ tration ranges within which it has been parameter­ ized. Besides its capacity in predicting the properties of binary systems, one of the obvious advantages of the present methods over the purely empirical (polynomial) representation of the data lies in the fact that phase diagrams for multicomponent solutions can be predicted once the proper­ ties of simple systems have been investigated (Spencer et al, 1990).

The Pitzer-Holmes-Mesmer aqueous solution model for CsCl(aq) Holmes & Mesmer (1983) have constructed an aqueous solution model for CsCl(aq) from a regression of a large experimental data base using expressions for the molality dependency of the thermodynamic properties of the aqueous solution given by Pitzer's ion-interaction formalism (Pitzer, 1973). The data base used by Holmes & Mesmer (1983) includes isopiestic, emf, calorimetric (heat capacity and enthalpies of dilution and dissolu­ tion) and freezing point depression data. The data used in the model parameterization range up to 6 mol.kg-1 below 100°C at 1 bar pressure, and to 8.3 mol.kg-i from 100 to 250°C at water-vaporsaturation pressures (Holmes & Mesmer, 1983). The osmotic coefficient of an aqueous solution of a 1-1 salt is:

where fΨ is the Debye-Hiickel term and is given by:

AΨ is the Debye-Hiickel slope. It depends only on temperature, pressure and solvent characteristics (density and dielectric constant). Holmes & Mesmer (1983) have used A^ values calculated for temperatures above 0°C. In their low-temperature model of the Na-K-Ca-Mg-Cl-SO4-H2O system, Spencer et al (1990) have treated AΨ as an ajustable parameter and determined the following expression that allows its calculation down to -55°C: AΨ = a! + a2T + a3T2 + a^P + (a5 / T) + a^n T (7) The 3L{ parameters are given in Table 1. We have checked that the discrepancy in the calculated osmotic coefficient using the two sets of values for A(^ does not exceed 0.002 between 0 and 100°C. We therefore have retained the AΨ expres­ sion given by Spencer et al. (1990) which is more convenient for calculations at subfreezing temper­ atures. In Eq. (5), B is the second Virial coefficient for the osmotic coefficient. It depends on concen­ tration (as well as on T and P) and incorporates two empirical parameters ß(°) and ß(*) specific of a given solute:

BΨ = ß(0)+ß(,)exp(-2Vm)

The third Virial coefficient CΨ is a constant at T and P. So the construction of an aqueous solution model within Pitzer's formalism mainly consists in determining the temperature and pressure varia­ tions of Pitzer's parameters ß(°), ß(D and CΨ through a regression of experimental data. Holmes & Mesmer have also determined the standard enthalpy and heat capacity of CsCl(aq). Pitzer's parameters for aqueous cesium chloride can be calculated as a function of temperature using the Table 1. Parameters of Eq. 8 for the Debye-Hiickel slopes and the water-ice equilibrium constant (Spencer etal, 1990). InKw-ice 7.875060393 10+3

A*

expression in which Mw is the water molecular weight (in g/mol), m the salt molality and aw the water activity. In Pitzer's ion-interaction formal­ ism, the osmotic coefficient of an aqueous solution of a 1-1 salt can be expressed as a function of the salt molality as: Ψ= 1 +f+mB + m20) (5)

(8)

ai

86.6836498

a2 a3 a4 a5 a6

8.48795942 10"2

11.6911849

-8878515 10"5

-1.1783789 10"2

4.88096393 10"8 -1.32731477 10 -17.6460172

3

1.24395542 10"5 -9.331479 10"4 1.7287461 10+3

1

479

Thermodynamics of the CsCl-H2O system at low temperatures Table 2. Parameters for the temperature-dependent expression (Eq. 9) of Pitzer's parameters for CsCl(aq) (Holmes & Mesmer, 1983). ß(0)

ß(D



Pi P2

0.03352

0.0429

-1290.0

-38.0

-2.62 × 10-4 157.13

P3

-8.4279

0

1.0860

P4

0.018502

0.001306

-0.0025242

P5

-6.7942 × 10 6

0

9.840 × 10'7

1

1

T0 is 298.15 K. The pj parameters are given in Table 2. The Gibbs-Duhem relationship applied to Eq. (5) leads to the expression for the activity coeffi­ cient of the aqueous solute: lnγ=fY+mBY + m2CY (10) Now fY is the Debye-Hiickel term, and BY and CY the Virial coefficients for the activity coefficient: fγ=-A,

l + 1.2Vrn

—lnfL1 + 1.2 Vml J (11) 1.2

BY is defined as: following empirical expression (Holmes & Mesmer, 1983): f(T) = P l + p 2

1__L T

[l - [l + 2Vm - 2m)]exp(-2Vm)]/2m

A

(12)

Tπ (9)

■p 4 [T-T 0 ] + p 5 [T 2 -T 0 2 ]

+ p3ln

B γ =2ß ( 0 ) +ß ( 1 )

oj

So Eqs. (4) to (11) along with the parameters given in Tables 1 and 2 allow the calculation of the thermodynamic properties of aqueous CsCl solutions.

Table 3. Standard (25 °C, 1 bar) thermodynamic properties of aqueous cesium and chloride ions, of solid cesium chloride and of the dissolution reaction of CsCl(s). The underlined values have been retained in this study.

Cs+(aq)

CΓ(aq)

CsCl(aq)

CsCl(s)

Reference

ΔfH° kJ.mol'1 -258.28

S° (J.molΛK 1 )

(J.molΛlC 1 )

133.05

-10.5

Wagman era/., 1982

-258.11

132.63

-5.86

Naumov et al,

-167.159

56.5

-136.4

Wagman era/., 1982

-167.159

56.5

-136.40

Naumov etal.,

1971

-425.87 (a)

189.55 (a)

-146.90(a)

Wagman etal,

1982

-425.70 (a)

189.13(a)

-142.25 (a)

Naumov etal,

1971

-427.67 / -425.64 (b)

-

-145.04

-443.04

101.17

52.47

Wagman etal,

1982

-442.83

101.17

52.47

Naumov etal,

1971

-

-

52.44

ΔrH° kJ.mol 1 17.601

Δ r S° J.mol'.K 1

17.130

1971

Holmes & Mesmer, 1983

Holmes & Mesmer, 1983

Δ r C°

88.38

J.moΓ'.K'1 -199.37

Wagman etal,

1982

87.96

-194.93

Naumov etal,

1971

17.366

-

-197.48

-

89.1

•-

Holmes & Mesmer, 1983 This work

1(a) Val.ies for CsCl(aq) from Wagman et al (1982) and from Naumov et al (1971) are calculated from thel thermodynamic properties of the aqueous ions reported by these authors while Holmes & Mesmer (1983) directly report values for the aqueous salt, (b) Calculated for comparison purposes from the experimentally determined enthalpy of solution (17.366 kJ/mol; Holmes & Mesmer, 1983) and the two alternate values (Wagman et al., 1982; Naumov et al, 1971) for the standard enthalpy of formation of CsCl(s). j

480

C. Monnin, M. Dubois

Thermodynamic data for the water-ice and the salt-solution equilibria The parameters of Eq. (7) for the equilibrium constant of the liquid water-ice reaction (Eq. 1) are given by Spencer et al (1990) and are reported in Table 1. The solubility product of solid cesium chloride can be calculated from the standard enthalpies, entropies and heat capacities of Cs+(aq), Ch(aq) and CsCl(s). We used two main sources of infor­ mation: the NBS Tables (Wagman et al, 1982) and the compilation of Naumov et al (1971). It is not possible to check the data sources in the NBS Tables as no reference is given. So the perfect agreement between these two data bases for sever­ al properties reported in Table 3 is certainly due to the fact that they use the same original data. First one can see in Table 3 that the CsCl(s) heat capacity value of Naumov et al (1971) (same as the NBS value) is confirmed by the recent data of Holmes & Mesmer (1983). The latter authors have directly determined the CsCl(aq) standard heat capacity as well as the enthalpy of solution of CsCl(s) from their analysis of calorimetric data (enthalpies of dilution and enthalpies of solution). Naumov et al (1971) also report a temperaturedependent expression for the CsCl(aq) heat capac­ ity. The value calculated for 25 °C from this expression is in good agreement with other values (Table 3). To calculate the CsCl(s) solubility prod­ uct, this expression for the CsCl(aq) heat capacity must be used with a corresponding temperaturedependent heat capacity function for CsCl(s) which is also given in Naumov et al (1971) in the classi­ cal Maier-Kelley format. Unfortunately the CsCl(s) heat capacity at 25 °C obtained with this expression (44.81 J/moH.K"1) is not consistent with the value from other sources (Table 3) or with the 25°C value reported by Naumov et al (1971) themselves. The CsCl(s) heat capacity function given by Naumov et al (1971) has not been given further consideration. Therefore we calculated the CsCl(s) solubility product (Ksp) at all temperatures from the values of the standard enthalpy, entropy and heat capacity of the CsCl(s) dissolution reaction at 25 °C, assuming that they do not vary with temperature, which is quite justified in the narrow temperature range con­ sidered here. The discrepancy between ln(Ksp) val­ ues calculated for temperatures below 25 °C down to the eutectic using Naumov et al data at 25 °C, and those obtained with the NBS thermodynamic data is between 0.1 and 0.2. This discrepancy is reduced to about 0.05 in ln(Ksp) when the standard enthalpy and heat capacity of reaction of Holmes &

Mesmer (1983) are used along with the standard entropy of reaction of Wagman et al (1982). We also found that a slight modification of the standard entropy of reaction from the NBS value of 88.38 J/moH.K-i to 89.1 J/mol^.K-i brought into per­ fect agreement the CsCl(s) solubility product val­ ues calculated from the standard enthalpy, entropy and heat capacity of reaction and those calculated from the solubility data for temperatures between that of the eutectic and 20°C. This amounts to a slight modification of the standard entropy of solid CsCl. To summarize, we here used the enthalpy and heat capacity of reaction given by Holmes & Mesmer (1983) and an entropy of reaction value of 89.1J/moH.K-i to calculate the CsCl(s) solubility product at the desired temperatures.

The calculated CsCl-H20 phase diagram at low temperatures In Fig. 1 we have plotted in a temperature-com­ position diagram the calculated SLV and ILV curves as well as the literature experimental data (freezing point depression and CsCl solubility data) down to the eutectic temperature. In this fig­ ure, the shaded area corresponds to the tempera­ ture-composition domains of the data used by Holmes & Mesmer (1983) to construct their aque­ ous solution model for CsCl(aq). The eutectic tem­ perature was measured at -23.7 ± 0.1 °C by Dubois et al (1993) using synthetic fluid inclusions. These authors calculated the eutectic composition (56.87 wt% or 7.83 M) using a constrained least square method (Dubois et al, 1993). First the calculation of the phase diagram down to the eutectic point requires the extrapolation of the Holmes-Mesmer aqueous solution model in temperature and in con­ centration at the same time. The lowest tempera­ ture considered by Holmes & Mesmer is that of the freezing-point-depression measurements of Momicchioli et al (1970) at -9.3°C and 3.1 M. The agreement between the predicted ILV curve and that given by Dubois et al (1993) is very good down to about -20°C. In Fig. 2 the SLV curve is reported to about 120°C. It is also apparent that the polynomial regression of the experimental data given by Dubois et al (1993) and the SLV curve predicted from the thermodynamic data are in very good agreement from the eutectic up to about 20°C. Again it must be emphasized that the calculations are carried out for concentrations well beyond the reported validity of the Holmes-Mesmer aqueous solution model. The largest concentration considered by Holmes & Mesmer (1983) for temperatures below 100°C is

481

Thermodynamics of the CsCl-H2O system at low temperatures 120

100+

80 4-10460 4-

o o

3

«

2 E

40 4-

20 4-20 ■

Mariani and Di Giacomo Dejak (1950) Washburnβtal.(1928) Lilley and Scott (1974) Momicchioliβtal.(1970) Duboisβtal. (1993) this work Duboisβtal. (1993) Eutectic point (Dubois et al., 1993)

D ♦ O O — . --E

-30



0

■ » *

1

|

*

* » ■

2

|





3





|



4







|

5









6

|





7



*

|

*

8



*



o+ -20 +

' *

|





9

*



.

|



*

1



*

|

*







0

mCsCI (mol/kg H20) Fig. 1. The CsCl-H2O phase diagram at temperatures below 0°C. Comparison between experimental data for the ice-water and the CsCl solubility equilibria, the curves predicted in this work and the regression of Dubois et al (1993). The shaded area corresponds to the temperature-composition domain of the data used by Holmes & Mesmer (1983) in their regression.

6 M. One can see in Fig. 2 that the CsCl(s) solubil­ ity increases with temperature and that the discrep­ ancy between the calculated SLV curve and the experimental data also increases with T. At 25 °C the measured CsCl(s) solubility is 11.302 M (Foote, 1903) and our calculated value is 11.45 M. Finally the calculated locus of the eutectic is T = -24.83°C, m = 7.6715 M (or 56.36 wt%) which is in acceptable agreement with the value given by Dubois etal (1993): -23.7°C, 56.87 wt%.

Discussion: thermodynamic models of aqueous solutions at very high concentrations It thus appears that the Holmes-Mesmer aque­ ous solution model for CsCl(aq) can be extrapolat-

■ j i it i j i i ■■ j i i i i j i

-40 6

8

10

Earl of Berkeley (1904) Hinrichsen and Sachsel (1905) Blidin (1953) Foote (1903) Lannung (1934) Dubois etal. (1993) this work Dubois etal. (1993) Eutectic point (Dubois et al., 1993 ■l""l""l""l""l""l""l""l'"

12

14

16

18

20

mCsCI (mol/kg H20) Fig. 2. The solubility of CsCl(s) as a function of tem­ perature.

ed with some confidence to low temperatures. The ILV curve deviates from experimental values only in the vicinity of the eutectic point. This good behavior of the aqueous solution model is certain­ ly due to the fact that it is consistent with heat capacity data at and above 25 °C that constrain the second derivative of the free energy (activity coef­ ficient and activity of water) at 25 °C and hence guides the extrapolation to low temperatures. As such, extrapolations of this type of aqueous solu­ tion models should prove more reliable than that of aqueous solution model obtained from free energy data alone. The performance of the aque­ ous solution model can certainly be improved by including very low temperature data in the fitted data base (Spencer et al, 1990), which would per­ haps require a modification of the functional form of Eq. 5. Fig. 2 shows that the aqueous solution model yields good results up to about. 11 M, which is also well beyond the range of fitted experimen­ tal data used in its construction. It has already been emphasized that Pitzer's

482

C. Monnin, M. Dubois

ion-interaction approach cannot represent the thermodynamic properties of aqueous solutions of very soluble salts (like CsCl, LiCl, (NH 4 ) 2 SO 4 , etc.) up to saturation (Pitzer, 1995; p. 308). Besides fluid inclusions, such very concentrated solutions can be found in atmospheric aerosols and a large literature is devoted to this topic (see Kim et al (1993) and references therein). For these systems, the molality scale is no longer appropriate and alternate methods based on the mole fraction scale have been successfully devel­ oped along the same lines as the molality-based Pitzer ion interaction formalism (Clegg et al, 1992). Recently Simonin (1997) has used the Mean Spherical Approximation (MSA) to success­ fully fit free-energy data for aqueous electrolytes up to very high concentrations with only three adjustable parameters. Such models are for now restricted to 25°C, but they do offer efficient and promising methods to deal with these very con­ centrated aqueous systems. Finally, it should be kept in mind that in any case, methods based on thermodynamics are always superior to data corre­ lations based on empirical polynomials in the sense that they allow the prediction of properties of multicomponent solutions.

pheric gas-aerosol equilibrium I. Thermo-dynamic model. Aerosol Sci. Techn., 19, 157-181. Lannung, A. (1934): Dampfdruckmessungen Wässeriger Losungen des Alkalihalogenide. Zeitsch. physikalischer Chemie, A 170, 144. Lilley, T.H. & Scott, R.P (1974): The osmotic coeffi­ cients of aqueous solutions of caesium chloride and the freezing temperatures of the solutions. J. Chem. Therm., 6, 1015-1017. Mariani, E. & Giacomo-Dejak, CD. (1950): Ricerche sulla teoria delle soluzioni concentrate di electtroliti forti. Gazz. Chim. ItaL, 80, 3. Momicchioli, F., De Voto, O., Grandi, G., Cocco, G. (1970): Thermodynamic properties of concentrated solutions of strong electrolytes I. Activity coeffi­ cients of water from freezing-point depressions for alkali chlorides. Ber. Bunseng. Phys. Chem., 74, 5966. Naumov, G.B., Rhyzenko, B.H., Khodakovskii I.L. (1971): Handbook of thermodynamic data. Moscow, Atomizdat (in Russian). Pitzer, K.S. (1973): Thermodynamics of electrolytes. I. Theoretical basis and general equations. J. Phys. Chem., 11, 268-277. — (1991): Ion interaction approach: theory and data cor­ relation, in "Activity coefficients in electrolyte solu­ tions", (Ed. K.S. Pitzer), 2nd edition, p. 75-155, CRC Press, New York. — (1995): Thermodynamics. Mc Graw Hill, 621 p. Simonin, J.P (1997): Real ionic solutions in the mean Spherical Approximation. 2. Non-associating pure salts up to very high concentrations and mixtures in References the primitive model. J. Phys. Chem. B, 101, 43134320. Berkeley, Earl of (1904): On some Physical constants of saturated solutions. Phil. Trans. Roy. Soc. (London), Spencer, R.J., M0ller, N., Weare, J.H. (1990): The pre­ diction of mineral solubilities in natural waters: A 203, 189-215. chemical equilibrium model for the Na-K-Ca-MgBlidin, V.P. (1953): Heterogeneous equilibria in the sys­ C1-S04-H20 system at temperatures below 25°C. tem: LiCl-RbCl-H20 and LiCl-CsCl-H2O. Izvest. Geochim. Cosmochim. Acta, 54, 575-590. Akad. Nauk. S.S.S.R. Otdel Khim. Nauk, 814-819. Wagman, D.D., Evans, W.H., Parker, V.B., Schumm, Clegg, S.L., Pitzer, K.S., Brimblecome, P. (1992): R.H., Halow, I., Bailey, S.M., Churney, K.L., Thermodynamics of multicomponent, miscible, Nuttall, R.L. (1982): The NBS tables of chemical ionic solutions. 2. Mixtures including unsymmetrithermodynamic properties. J. Phys. Chem. Ref. cal electrolytes. J. Phys. Chem., 96, 9470-9479. Data, 11, Suppl. 2. Dubois, M., Royer, J.J., Weisbrod, A., Shtuka, A. (1993): Washburn, E.W., West, C.J., Dorsay, N.E., Bichowsky, Reconstruction of low-temperature phase diagrams F.R., Klemenc, A. (1928): International critical using a constrained least squares method: Appli­ tables of numerical data: physics, chemistry and cation to the H20-CsCl system. Eur. J. Mineral, 5, technology. Mc Graw-Hill, 481 p. 1145-1152. Weare, J.H. (1987): Models of mineral solubility in con­ Foote, H.W. (1903): On the double caesium and mer­ centrated brines with application to field observa­ curic chlorides and their solubility. Amer. Chem. tion, in "Thermodynamic modeling of geological Soc. J., 30, 339-344. material: minerals, fluids and melts", (ed. I.S.E. Hinrichsen, F.W. & Sachsel, E. (1905): Über die Carmichael and H.P Eugster). Rev. Mineral, 17, Bildungs- und Loslichkeitsverhältnisse des Doppel143-174. chloride des Eisens und der Alkalimetalle. Zeitsch. Phys. Chem., 50, 81-86. Holmes, H.F. & Mesmer, R.E. (1983): Thermodynamic Received 6 July 1998 properties of aqueous solutions of the alkali metal chlorides to 250°C. J. Phys. Chem., 87, 1242-1255. Modified version received 25 January 1999 Accepted 2 February 1999 Kim, Y.P., Seinfeld, J.H., Saxena, P. (1993): Atmos­