Solubility isotherm of the system LiNO 3 KNO 3 H 2 O at 373 K

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Monatsh Chem (2018) 149:283 288 https://doi.org/10.

1 Monatsh Chem (2018) 149: ORIGINAL PAPER Solubility isotherm of the system LiNO 3 KNO 3 H 2 O at 373 K Heidelore Voigt 1 Wolfgang Voigt 1 Received: 26 August 2017 / Accepted: 26 November 2017 / Published online: 21 December 2017 Ó Springer-Verlag GmbH Austria, part of Springer Nature 2017 Abstract The solubility isotherm in the system LiNO 3 KNO 3 H 2 O was determined with an analytical method at 373 K. The data were compared with calculations from a six-parameter model of Pitzer and Simonson (J Phys Chem 90:3009, 1986) with parameters derived solely from water activities in a comparable temperature composition range. A two-parameter BET model could predict the solubility data equally good if a regular solution term from data of the anhydrous molten system was added. Graphical abstract Keywords Solubility Multi-component reaction Thermodynamic modelling Water activity Molten salt In memoriam of Prof. Dr. Heinz Gamsjäger. & Wolfgang Voigt wolfgang.voigt@chemie.tu-freiberg.de 1 Institute of Inorganic Chemistry, TU Bergakademie Freiberg, Freiberg, Germany Introduction Alkaline metal nitrates possess low melting points and extremely high solubility at elevated temperatures. Therefore, these systems were in the focus for tests of thermodynamic models covering broad concentration ranges from aqueous solutions to the molten salt limit. In this respect, the system LiNO 3 KNO 3 H 2 O is of particular interest, since the eutectic temperature of the anhydrous mixture is as low as 410 K [1]. Tripp and Braunstein [2] published vapour pressure measurements from 392 to 423 K at molar water/salt ratios from 1 to 0.05 with Li? mole fractions of the salt mixture between 0.45 and Additional vapour pressure measurements for this system have been performed by Simonson and Pitzer for the equimolar LiNO 3 / KNO 3 mixture and the binary subsystem KNO 3 H 2 Oat K [3]. The mole fraction of water was in the range The latter authors derived parameters for a thermodynamic model published in an accompanying paper [4]. The model is formulated on a mole fraction basis and contains a Debye Hückel term and Margules expansion expressions for the specific interactions water salt and salt salt. Their data analysis included the vapour pressure data mentioned above and isopiestic data from Braunstein and Braunstein [5]. The authors demonstrated that six interaction parameters were sufficient to describe the water activities within the investigated temperature composition range. Four of the parameters were given as linearly dependent on temperature in the vicinity of 373 K. For the proposed model also the equations for the salt activity coefficients were given. In this work, we will prove how accurately the given parameterization derived from solvent activities can predict the solubility of the salt components.

2 284 H. Voigt, W. Voigt In addition, it will be of interest whether the simple twoparameter BET model can predict the solubility isotherm. For this aim, we determined the solubility isotherm at 373 K with an analytical method involving a rigorous solid liquid filtration by centrifugation at equilibrium temperature. Using the Simonson Pitzer model [3], one can calculate the solubility product for LiNO 3 and KNO 3 in the pure binary systems at 373 K and then calculate the solubility isotherm in the ternary system and compare it with the experimental ones. Results and discussion The obtained solubility data are listed in Table 1 and plotted in Fig. 1. Since molality tends to become very large when approaching the molten salt side, results are listed and plotted on the mole fraction scale (unionized basis) as well. At the temperature of investigation the anhydrous salts form the solid equilibrium phases [6]. Even a hemihydrate, LiNO 3 H 2 O, as discussed contrarily by Campbell [7] cannot exist at 373 K. The molar ratios KNO 3 :LiNO 3 :H 2 O from chemical analyses of the solids clearly indicate the anhydrous salts as equilibrium phases (Table 1, column 5). The low ratios for water in the solids demonstrate at the same time the effective solid liquid separation. From Raman spectroscopic measurements of quenched LiNO 3 /KNO 3 melts Xu [8] supposed the existence of a congruently melting compound LiNO 3 KNO 3 below the eutectic temperature. However, the present chemical analyses of the solids give no hint for such a compound. Both crystallization branches, LiNO 3 and KNO 3, approach an approximate molar salt ratio of 1:1 at the crossing point. Usually, a strong increase in molality of one component upon adding another is observed in case of complex formation, as for instance for CuCl when HCl or alkali metal chlorides are added. For the system considered here this is not true. The reason for the solubility increase is simply the smallest temperature difference to the eutectic point of the anhydrous mixture (T = 410 K; x LiNO3 = 0.45 [1] 1 ) when the salts approach a 1:1 molar ratio. In Fig. 2 our solubility data for LiNO 3 and KNO 3 in pure water are compared with literature data. The datum for KNO 3 coincides with the curve from literature [9]. In case of LiNO 3, data were available only up to 363 K [6]. The extrapolated curve of recommended data by IUPAC proceeds a bit below our solubility datum. However, considering the remarkable scatter of the data between 313 and 343 K our solubility value is well within the range of uncertainty. 1 In Table 2, x KNO3 should be x LiNO3. The solubility in the ternary system increases for both components and reaches very high molality values (Fig. 1 left). The crossing point of the two crystallization branches is difficult to fix exactly, but should be located at KNO 3 concentrations between 85 and 90 mol (kg H 2 O) -1 or at a mole fraction x KNO3 = 0.39 (Fig. 1 right). The thick lines in Fig. 1 represent the calculated solubility from the Pitzer Simonson model [3]. As can be seen the agreement with the experimental data is good. For the reference temperature (373 K), the model contains six interaction parameters: four for the solvent salt interaction, one for salt1 salt2 interaction and a ternary interaction parameter. For temperatures deviating from 373 K Pitzer and Simonson had added five linear coefficients. All these parameters had been estimated from water activity data [3]. The only solubility data necessary for the calculation are those of the binary subsystems to fix the solubility constants K L. Thus, this is an example that for the conditions of very high electrolyte concentrations and comparable concentrations of the components solubility calculations for multi-component solutions are accurate enough from a G E model, which was parameterized purely from solvent activities. We compared our results also with predictions from the modified BET model according to Ally and Braunstein [10]. This type of model is applicable for solutions with solvent activities below approx. 0.5, which is particularly well fulfilled for molten salt hydrates and their mixtures [11 15]. According to the BET model for a binary aqueous system the water activity is described by Eq. (1), originally proposed by [16]: a w ð1 x w Þ x w ð1 a w Þ ¼ 1 c r þ ðc 1Þa w : ð1þ c r The adjustable parameters r (hydration number in monolayer) and c (energy parameter) are determined from linear fits of the left-hand side expression against the water activity a w. Parameter c is related to the energy of adsorption E ad and liquification E L of water by Eq. (2): c ¼ exp f ðe ad E L Þ=RTg ¼ exp f DE=RTg : ð2þ By means of a lattice model formalism Ally and Braunstein derived expressions for the activities of salts A and B [10] 2 (Eqs. 3, 4): a A ¼ A A þ B r A X r ; ð3þ r A 2 Equations (32) and (33) in their derivation contain a misprint: in the terms c A a H (1 - Z/H) and c B a H (1 - Z/H), the factor a H has to be deleted.

3 Solubility isotherm of the system LiNO 3 KNO 3 H 2 O at 373 K 285 Table 1 Solubility data of the system LiNO 3 KNO 3 H 2 O at 373 K m(kno 3 )/mol/kg H 2 O m(lino 3 )/mol/kg H 2 O x(kno 3 ) mole fraction x(lino 3 ) mole fraction Molar ratio KNO 3 :LiNO 3 :H 2 Oin solids Solid equilibrium phase :0.066:0.029 KNO :0.091:0.033 KNO :0.043:0.055 KNO :0.021:0.036 KNO :0.016:0.040 KNO :1.000:0.056 LiNO :1.000:0.066 LiNO : :0.045 KNO :1.000:0.053 LiNO :1.000:0.050 LiNO :0.891:0.192 LiNO 3? KNO :0.051:0.078 KNO :0.002:0.062 KNO :0.009:0.039 KNO :0.041:0.067 KNO :1:0.057 LiNO :1:0.116 LiNO :1: LiNO :1:0.021 LiNO :0.010:0.030 KNO :0.018:0.038 KNO :0.023:0.035 KNO LiNO LiNO LiNO LiNO :1:0.016 LiNO :1:0.034 LiNO 3? KNO :0.135:0.094 KNO :1:0.015 LiNO 3 a B ¼ B q B W q ; ð4þ A þ B q B where A and B are the moles of salts, and r and q the hydration parameters for A and B. X and W represent the moles of occupied hydration sites at A and B. The activities are formulated on a molecular mole fraction basis with the reference state as a pure molten salt. Denoting A for LiNO 3 and B for KNO 3 the parameters for A are available from [17] and listed here once more: r ¼ 2:766 þ 1: ðt=kþ; DE=J mol 1 ¼ 6583:6 þ 5:495ðT=KÞ: ð5þ ð6þ The corresponding parameters for KNO 3 were estimated in this work from vapour pressure measurements published in [18, 19]. Figure 3 shows the BET plots for the water activity at temperatures 425, 452, and 492 K. To increase the number of data points in the fit activity data up to 0.7 were included. Since at 373 K the solubility of KNO 3 is not large enough to reach water activities below 0.5, a linear temperature function was established from the three-parameter sets at higher temperature. All estimated parameters are listed in Table 2. Using these parameters gives a solubility isotherm labelled with number 1 in Fig. 1. This clearly does not describe the experimental data. Varying the BET parameters systematically within meaningful ranges as was done for isotherms 2, 3, and 4 (Fig. 1) does not improve the description satisfactorily, despite the fact that the parameters for isotherm 4 are arbitrary. Abraham and Abraham [20] have shown that a mixing parameter X

4 286 H. Voigt, W. Voigt Fig. 1 Solubility isotherm of the system LiNO 3 KNO 3 H 2 O at 373 K in molality (left) and mole fraction (right) scale. Symbols: experimental data: solid phase: KNO 3 (open circles), LiNO 3 (stars); thick line: Pitzer Simonson model; labeled thin lines: BET model: labels: 1 r = c = K L = ; 2 r = 1.70 c = 0.75 K L = r = 1.00 c = 0.50 K L = ; 4 r = 0.50 c = 0.40 K L = between the pure molten salts from regular solution theory can be introduced into the BET model. Thus, the corrected activity is given as: lna A ¼ lna A ðbetþþxx 2 B =ðrtþ: ð7þ For the systems LiCl LiNO 3 H 2 O and LiNO 3 Ca(NO 3 ) 2 H 2 O, Zeng et al. [17, 21] confirmed an improved description of the solid liquid equilibria in these systems, when adjusting this parameter X. However, in these papers, the adjusted value of X from aqueous systems was not compared with an experimental value from calorimetric data in molten salts. Maeso and Largo [1] performed a thermodynamic analysis of the system LiNO 3 KNO 3 including heat of mixing data [22], heat capacities [23] and a new determined phase diagram [1]. Their temperature dependent regular solution parameter was given as: X ¼ :008ðT=KÞlnðT=KÞþ30:50ðT=KÞ; ð8þ which for T = 373 K gives X =-7205 J mol -1. Correcting the activities according to Eq. (7) with this parameter shifts the calculated solubility isotherm toward the experimental data as shown in Fig. 4. The thick-lined curve can be considered as in agreement with the experimental data. A variation of the X parameter by ± 200 J mol -1 did not cause visible changes in the solubility curves. Thus, a rough estimate of this parameter is sufficient for adequate solubility calculations. From this example, it can be concluded that the salt salt interaction Fig. 2 Solubility of KNO 3 (left) and LiNO 3 (right) in water; closed circles: our data, open circles: data from literature, KNO 3 [9], LiNO 3 accepted data by IUPAC [6], line with symbols: recommended data by IUPAC [6]

5 Solubility isotherm of the system LiNO 3 KNO 3 H 2 O at 373 K 287 component (KNO 3 ) the BET parameters can be determined only roughly. Of course, for an exact description of the experimental data some adjustment of the parameters would be necessary, but this was not the intention of this work. Conclusion Fig. 3 BET plots for the system KNO 3 H 2 O at three temperatures. Symbols: data from [18, 19], lines: linear regression The solubility isotherm in the system LiNO 3 KNO 3 H 2 O was experimentally determined for T = 373 K. Use of a high-temperature centrifuge allowed application of an analytical method. Calculations with the six-parameter Pitzer Simonson model, parameterized exclusively through water activities, reproduced the solubility curves. The same agreement was achieved with the two-parameter BET model, if a regular solution term from measurements of the anhydrous molten salt mixture is added. Table 2 BET parameters for the system KNO 3 H 2 O T/K r c DE/kJ mol a a From r = 1.409? (T/K) c = ? (T/K) Experimental Reagent grade chemicals were used. KNO 3 and LiNO 3 were dried at 110 C. Approx. 20 g of salt mixture and g water were weighed into Teflon cups of about 20 cm 3. The latter were inserted into autoclaves, which are described in detail in [24]. Due to the strong change in solubility, the appropriate amounts of salts and water had to be estimated from parts of the solubility curve already determined in preliminary experiments. Equilibration time was 65 h at (373 ± 0.06) K. After filtration by centrifugation (Teflon filtre with 0.45 lm pore size) both liquid and solid phases were analyzed. Potassium content was determined gravimetrically with sodium tetraphenyl borate (± 0.37% uncertainty). The total water content was determined by drying approx. 1 g of sample at 110 C until constant weight (ca. 100 h). The amount of LiNO 3 was calculated from the difference of total weight and the amounts of KNO 3 and water. Identification of solids was additionally checked by X-ray powder diffraction. References Fig. 4 Solubility isotherm of the system LiNO 3 KNO 3 H 2 O at 373 K. Symbols: experimental data, thin line: BET model with parameters from Table 2; thick line: same BET parameters plus added X term parameter becomes particularly important, when the hydration is not strong as for KNO 3. The BET model again provides good estimates for activities for very highly concentrated electrolyte solutions, even if for one 1. Maeso MJ, Largo J (1993) Thermochim Acta 223: Tripp TB, Braunstein J (1969) J Phys Chem 73: Simonson JM, Pitzer KS (1986) J Phys Chem 90: Pitzer KS, Simonson JM (1986) J Phys Chem 90: Braunstein H, Braunstein J (1971) J Chem Thermodyn 14: Eysseltova J (2005) Monatsh Chem 136: Campbell AN (1942) J Am Chem Soc 64: Xu K (1999) J Phys Chem Solids 60:5 9. Linke WF, Seidell A (1965) Solubilities: inorganic and metalorganic compounds, 4th edn. American Chemical Society, Washington, D.C.

6 288 H. Voigt, W. Voigt 10. Ally MR, Braunstein J (1998) J Chem Thermodyn 30: Voigt W (1993) Monatsh Chem 124: Voigt W, Zeng D (2002) Pure Appl Chem 74: Zeng D, Voigt W (2003) Calphad 27: Marcus Y (2005) J Solut Chem 34: Ally MR, Braunstein J (1993) Fluid Phase Equilib 87: Stokes RH, Robinson RA (1948) J Am Chem Soc 70: Zeng D, Ming J, Voigt W (2008) J Chem Thermodyn 40: Barry JC, Richter J, Stich E (1988) Ber Bunsenges Phys Chem 92: Stich E (1985) Aktivitätskoeffizienten aus Dampfdruckmessungen an Wasser-Salz-Mischungen über den gesamten Konzentrationsbereich. Dissertation, RWTH Aachen 20. Abraham M, Abraham M-C (2000) Electrochim Acta 46: Jiang J, Yin X, Li D (2016) J Chem Eng Data 61: Kleppa OJ, Hersh LS (1961) J Chem Phys 34: Maeso MJ, Largo J (1993) Thermochim Acta 222: Freyer D, Voigt W (2004) Geochim Cosmochim Acta 68:307

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