J . Chem. Soc., Faraday Trans. 1, 1984’80, 297-308 CaC1, + KC1 + NaCl Molten-salt Mixtures Experimental and Estimated Enthalpies of Mixing BY PATRICK SEM, GERARD HATEM, JEAN-PIERRE BROS AND MARCELLE GAUNE-ESCARD* Universi te de Provence, Laboratoire de Dynamique et Thermophysique des Fluides, Rue Henri Poincare, 13397 Marseille Cedex 13, France Received 31st January, 1983 The CaC1, + KC1 + NaCl molten-salt mixture is a candidate system for thermal-energy storage. Estimates of the amount of energy which can be stored by such a system requires knowledge of the enthalpies of formation of the liquid mixtures. We have therefore performed direct measurements of the enthalpy of mixing at 1083 K for the three limiting binary systems and the ternary mixture. However, estimates of the ternary enthalpy of mixing were made from those referring to the binary limiting systems using either Kolher’s equation or the results derived from the surrounded-ion model, which was extended in the present work to ternary asymmetrical systems of the kind AX, + BX + CX.In the course of a general s t ~ d y l - ~ of the thermodynamics of molten-salt mixtures, undertaken because of their potential use for thermal-energy storage, we were led to estimate and to measure the enthalpies of formation of several systems. In the present paper we report the calculated and experimental values of the enthalpies of mixing at 1083 K of the CaCl,+KCl+NaCl ternary mixtures as well as those referring to the three limiting binary systems. EXPERIMENTAL METHODS All the enthalpies of mixing reported in this paper were measured using a high-temperature Calvet microcalorimeter. The principle of this calorimeter and its use have been the subject of several Only the main features of our apparatus will be recalled here: it can be operated up to 1300 K and the calorimetric block and the three shields were made of pure alumina.The two thermopiles, each one made up of Pt/Pt+ 10% Rh thermocouples, were connected in opposition. Each cylindrical calorimetric cell was 80 mm high and 16 mm in diameter. The whole assembly was located within a vertical cylindrical furnace heated with four resistors (two on the side wall, one on the bottom and one in the lid). Peripheral equipment consisted of a temperature regulator for the furnace, an automatic system (Apple 11) for acquisition and treatment of calorimetric data, a double potentiometric recorder (Sefram type Servorac BPD) for the measurement of temperatures and thermal effects and a thermostatted gas-tight charging device.The following points must be attended to in order to obtain reliable enthalpy-of-mixing data at high temperatures. (i) If the equation A + B+AB symbolizes the mixing reaction under investigation it is obvious that the most accurate value of the enthalpy of mixing will be obtained when the components A and B on the one hand and the mixture AB on the other are in the same reference state (liquid here) and at the same experimental temperature TE. In this way it is possible to avoid the correction term arising from the extensively used drop method,s which in some cases can exceed the actual enthalpy of mixing.This condition can be fulfilled for several experimental 297298 CaC1,KCI + NaCl MOLTEN-SALT MIXTURES device^.^. In the present investigation we used one very similar to that proposed by 0stv0ld.l~ One salt (or a binary mixture of two salts) was contained in a crucible 50 mm hgh and 9 mm diameter, the second salt (or the third component) was in a quartz ampoule (6 mm diameter) with a breakable tip. The crucible and the ampoule were located within the calorimeter at an experimental temperature of 1083 K. The mixing process was performed by breaking the tip of the ampoule. (ii) In order to obtain a homogeneous final product it was necessary to include a stirring system to this mixing device.Therefore the ampoule was connected to a long vertical quartz tube (t) which could be moved vertically, thus ensuring the homogeneity of the mixture. (iii) The calorimeter must be calibrated under the experimental conditions. This condition was achieved by dropping National Bureau of Standards a-alumina reference samples during the experimental runs. Insertion of this material was guided by the tube (t). Knowledge of the molar enthalpy increment of alumina between room temperature & and the experimental temperature TE allowed us to obtain the calorimeter constant. A gas-tight and thermostatted charging device12 allowed the calibration samples to be dropped without any perturbation of the gas atmosphere. Several blank runs (crucible and ampoule filled with the same salt) showed that the thermal effect from breaking the ampoule was negligible.MATERIALS The purity of the salts and their handling play an important role in the reproducibility of the experimental results. Sodium and potassium chlorides were suprapur reagents from Merck of 99.9980 and 99.9984% purity, respectively; they were dried under vaccum at 573 K for eight days. Particular attention was paid to the dehydration of calcium chloride (suprapur reagent from Merck of 99.9985%. The salt was gradually heated to its melting point under a flow of gaseous chlorine13 and then chlorine was allowed to bubble into the melt for 1 h. The excess gas was removed using a flow of pure and dry argon and the calcium chloride then solidified. All further handling of the dehydrated salts was performed in a dry-box. The argon used during the dehydratation procedure and for the calorimetric experiments was Argon-U supplied by Air Liquide.The chlorine gas was purchased from Merck. ACCURACY In isoperibol calorimetry the accuracy of the results depends on the operational temperature and on the number of the experimental steps required to reach the final result. The investigation of a ternary mixture is more difficult and therefore less precise than that of a binary system since two experimental determinations are necessary, namely the enthalpies associated with the reactions A + B+AB and AB + C-+ABC. This difficulty increases with temperature. A general study of the precision of calorimetric measurements of the enthalpy of mixing14 has allowed us to estimate the uncertainty of the present experimental results using the operating conditions given above as ca. 9%.RESULTS All calorimetric experiments were performed at 1083 K, a temperature at which the binary and ternary mixtures were single-phase liquids over the whole concentration range. The calorimetric results obtained for the systems NaCl+ KCl, CaCI, + KCl and CaCl, + NaCl are reported in table 1, together with those already published by Hersh and Kleppa14 and by Ostvoldlo in order to enable a critical comparison of all these data to be made. NaCl + KCI SYSTEM This mixture has weak thermicity. Our experimental results are compared with those obtained by Hersh and Kleppa14 at the same temperature (see table 1). They fit the equation AH/J mol = -xNa( 1 - xNa) (1921 + 53xNa)P.SEM, G. HATEM, J-P. BROS AND M. GAUNE-ESCARD 299 Table 1. Experimental molar enthalpies of mixing for liquid NaCl + KCl, CaCl, + KCl and CaCl + NaCl systems XNaCl AHIJ mol-1 AHIJ mo1-I AHIJ mo1-I XNaCl XNaCl XNaCl AHIJ rno1-I AH/J mo1-l XNaCl XCaC12 AH/kJ mo1-I 0.1 13 0.303 0.463 0.673 - 427 0.851" - 287" - 189 -418 - 500 0.096' 0.259 0.499 0.702' - 3.68' - 7.57 - 8.97 - 8.75' 0.101' - 1.64b 0.300' - 3.49' 0.5 18 - 3.65 0.751 - 2.40 NaCl + KCl 0.1 47" 0.1 48" 0.350 0.399" - 436 - 517" 0.495" 0.499" - 541" - 550a 0.700 0.701" - 400 - 472a 0.853" 0.892 - 262" - 264" - 292" - 161 CaCl, + KCl 0.099' 0.199' -3.74' -6.53' 0.307' 0.351 0.500 0.600' 0.750 0.751 -8.58' -8.33 - 9.37 8.41' - 6.25 - 5.93 CaC1, + NaCl 0.201' 0.249 0.406' 0.482 0.596' 0.699' 0.905' -2.88' - 1.98 - 3.85' - 3.65 - 3.54' - 2.92' - 1.1 1' 0.171 0.418" - 47ga 0.501 - 506 0.763 - 269 -381 0.200 0.427 0.604' 0.798' -6.59 -9.21 -8.16' - 5.23' 0.250 0.498' 0.749 - 3.14 - 3.78' - 2.69 0.242 - 339 0.447" -541" 0.543 0.800 - 483 -318 0.250 0.499' 0.696' 0.90 1 ' - 7.32 -9.17 - 7.12' - 2.85' 0.250 0.500 0.770' - 3.39 - 4.09 - 2.45' 0.300 - 446 0.448" 530a 0.58 1 - 494 0.850" - 252" a Ref. (14); ref. (10). while Hersh and Kleppa obtained a similar expression AH/J mol-l = - xNa( 1 - xNa) (2038 + 296~,,). At the equimolar composition the difference between both sets of results is ca. 50 J mo1-l. The limiting partial enthalpies obtained in the present work are, respectively, A@&(K)/J mol-l = - 1921 ARg(Na)/J mo1-1 = - 1974 and will be used in the rest of the paper.300 CaC1,KCl + NaCl MOLTEN-SALT MIXTURES CaCl, + KC1 SYSTEM 0stvold's results,lo shown in table 1, were represented by the analytical expression AH/kJ mo1-I = -xCa (1 -xCa) (43.72 - 1 3 .6 3 ~ ~ ~ ) . As they were very close to our experimental values at 1083 K, they were used to represent the enthalpy of mixing using the surrounded-ion model. First developed for binary systems with ions of the same valency,15 this model was later extended to systems with ions of different valency16 (CaCl, + KCl, for instance). The enthalpy of mixing was found to be described by the equation AH/kJ mol-1 = -(1 +x,,)x~,(l -xEa) (21.57+8.50~~,) where xEa = 2 xca/(l +xc,) is the equivalent ionic fraction as defined by F1~1r1and.l~ A@,,,,/kJ mo1-l = -43.14 AHg(ca)/kJ mol-l = -30.07.The limiting partial enthalpies are, respectively, CaCl, + NaCl SYSTEM This system has already been investigated by Ostvold,lo who fitted his experimental enthalpies of mixing (see table 1) to the equation AH/kJ mol-1 = -xca(l -xCa) (18.76-6.70). Our results at 1083 K, reported table 1, are in good agreement, and therefore we used both sets of values to represent the enthalpy of mixing using the surrounded-ion model. l6 The following expression was obtained AH/kJ mol-l = - (1 + xCa) xEa( 1 - xEa) (9.50 + 2.88~:~) which led to the limiting partial molar enthalpies AH/,",,,,,/kJ mol-1 = - 19.00 A ~ / g a a C , , / k J mol-1 = - 12.38. CaCl, + NaCl + KCl SYSTEM This system was investigated at 1083 K. The ternary mixture was obtained either by adding NaCl to a binary CaCl,+KCl mixture or by adding KCl to a binary CaCl, + NaCl mixture.The ternary mole fractions were such that the same composition could be obtained from both procedures, which provided a test of the internal consistency of the measurements; on the Gibbs composition triangle they were located either on constant x,/x,, quasi-binary sections (with xK/xCa = 1, 1/3 and 3) or on constant xNa/xCa quasi-binary sections (with xNa/xCa = 1, 1/3 and 3). The reactions of formation of the ABC ternary mixture can be written as nAA+nBB*(nAA+n,B) (nA A +n, B) +n, C --+ (nA A + nB B + n, C) with the corresponding enthalpies of formation AhAB and Ah. The ternary molar enthalpy of mixing A H is thus obtained from the experimentalP.SEM, G. HATEM, J-P. BROS AND M. GAUNE-ESCARD 30 1 Table 2. Experimental enthalpies of formation of ternary mixtures obtained by mixing liquid NaCl with binary KCI + CaCI, melts at 1083 K. Ah *K + nCa nK + nNa -k %a AH XNaCl / kJ / mol / l 0-3 mol /kJ mol-l 0.200 0.200 0.428 0.692 0.144 0.154 0.332 0.500 0.502 0.601 0.197 0.199 0.201 0.20 1 0.427 0.428 xK/xCa = 1/3, AHK(Ca) = -6.19 kJ mol-1 -8.58 6.516 8.143 - 6.79 5.358 6.697 - 10.57 3.706 6.483 - 15.52 2.873 9.330 xK/xCa = 1, = -9.08 kJ mol-l - 2.49 9.487 1 1.066 - 3.06 8.618 10.182 - 4.00 6.541 9.773 - 2.52 3.969 7.937 - 3.65 4.566 9.143 - 5.85 5.398 13.505 xK/xCa = 3, AH,(,,) = -7.49 kJ mo1-I -0.81 1 1.896 14.823 - 0.30 8.517 10.620 - 0.2 1 8.684 10.863 - 0.88 13.259 16.588 -0.15 6.162 10.760 - 0.25 6.091 10.656 - 6.00 - 5.96 - 5.16 - 3.57 - 8.01 - 7.99 - 6.49 -4.86 - 4.93 - 4.06 - 6.07 -6.03 - 6.00 - 6.04 -4.31 - 4.3 1 enthalpy Ah and from the enthalpy of mixing of the AB binary system, which was measured previously : Ah nA +nB +n, AH = + (1 + x c ) AHAB.Tables 2 and 3 report our experimental results at xK/xCa and xNa/xCa = 1,1/3 and 3, respectively. We also indicate in these tables the binary enthalpies of mixing of KCI + CaCI, and NaCl + CACl,, at the same binary mole fraction ratio, which were used in the calculation of the ternary enthalpy of mixing. ESTIMATION OF ENTHALPY OF MIXING Many relationships have been proposed to estimate the excess thermodynamic functions of multicomponent systems from those referring to the limiting binary mixtures. These relations are either empirica11s-20 or obtained from models based on energetic c~nsiderations.~~-~~ In the present work we used both kinds of procedure to estimate the ternary enthalpy of mixing.Thus we use Kohler’s equationla where the enthalpy of formation AH of the ternary liquid mixture ABC is a weighted function of the binary enthalpies of mixing AHij along the quasi-binary sections corresponding to constant x i / x j molar fraction ratio. We also estimated this ternary enthalpy of mixing from the surrounded-ion model, which was extended to the kind of system investigated in the present work. Indeed the formulation of the enthalpy 11 FAR 1302 CaC1,KCl-t NaCl MOLTEN-SALT MIXTURES Table 3. Experimental enthalpies of formation of ternary mixtures obtained by mixing liquid KC1 with binary NaCl+ CaC1, melts at 1083 K Ah *Na+%a nNa +nK +nCa AH XKCl kJ / mol / 1 0-3 mol /kJ mol-l 0.078 0.199 0.199 0.199 0.199 0.428 0.428 0.692 0.692 0.138 0.142 0.329 0.329 0.450 0.450 0.454 0.599 0.599 0.739 0.077 0.077 0.201 0.201 0.429 0.428 0.692 0.691 0.692 xNa/xCa = 1/3, AHNa(ca) = -2.56 kJ mol-1 - 11.74 6.632 7.195 - 22.25 5.073 6.338 -31.48 6.033 7.541 - 27.03 5.403 6.750 - 25.83 5.372 6.709 - 60.24 5.849 10.225 - 39.28 3.48 1 6.095 - 36.36 1.939 6.306 - 34.97 1.974 6.425 xNa/xCa = 1, AHNa(Ca) = -3.80 kJ mo1-I - 18.22 7.683 8.915 - 20.79 7.90 1 9.216 - 20.98 3.759 5.610 - 25.53 4.476 6.680 -31.53 4.018 7.469 -32.17 4.1 12 7.486 -34.17 4.055 7.438 - 44.36 4.177 10.444 -46.29 4.563 1 1.400 -31.90 2.399 9.207 XNa/XCa = 39 AHNa(Ca) = - - 8.74 13.692 - 8.58 12.880 - 14.14 7.320 - 14.00 7.2 10 - 18.23 4.796 - 18.59 4.910 - 18.38 3.189 - 16.59 2.974 - 15.64 2.567 .3.19 kJ mol-1 14.835 13.953 9.157 9.018 8.398 8.591 10.367 9.65 1 8.337 - 4.00 - 5.56 - 6.23 - 6.06 - 5.91 - 7.36 - 7.91 -6.56 - 6.23 - 5.32 - 5.52 - 6.29 - 6.37 - 6.32 - 6.23 - 6.67 - 5.77 - 5.59 - 4.46 -3.54 - 3.56 -4.10 -4.11 - 4.00 - 3.99 - 2.75 - 2.70 - 2.86 of mixing of a ternary molten-salt mixture has been previously establishedz3 for salts where the ions having the same valency.For the AX + BX + CX system, for one mole, the expression is AH = X,XB[XB AH&) + (1 - Xg) AR~(A)] where xi and AH., are the ionic ternary fractions and the limiting partial enthalpies of the component i in the i+j binary system, respectively. this equation was extended to As already done for ternary reciprocalP.SEM, G. HATEM, J-P. BROS AND M. GAUNE-ESCARD 303 ternary additive mixtures containing ions of different valencies. The reaction of formation of such a system AX,+BX+CX can be symbolized as: n A AX, + nB BX + nc CX+(nA AX, + nB BX + nc c x ) with the corresponding molar enthalpy increment AH. For divalent salts, L~msden,~ introduced the concept of ' equivalent salt' : one mole of the AX, real salt is assimilated to two moles of the A,,,X (equivalent) fictitious salt, which assumes that the fictitious ion occupies a single cationic site in a quasi-lattice model of the melt. Following this assumption, the previous reaction of mixing can be written: 2n~Ao.,X+n~ BX + ~ c C X + ( ~ ~ A A O . ~ X + nBBX + ncC,) which denotes the formation of a ternary mixture from the three symmetrical salts Ao.5X, BX and CX.The enthalpy of formation AH* is thus derived from eqn (1) AH* = xl;xg[~;AHz:(~)+(l -x;)AH~*(A,,.~)] + X~X;[X: AHg;) + (1 - x:) AEz&)] + x: xl;[xZ ARz;o.5) + (1 -a A~z:(c)l where 2nA - 2XA -- x); = 2nA+nB+n, 1 +xA are the equivalent ionic fractions defined by Farland'' and the ARGY are, as previously, the limiting partial enthalpies of component i in the i+j binary system: AHzo:(B), for instance, is the limiting partial enthalpy of the Ao.5X salt in the A,.,X + BX binary system. It can easily be shown that AR'o:(B) = +ART(B) and APg&5, = ARg(A) ARE;, = A@$)(,, and ARS& = ARSB) = A E z A ) and ARTAcc, = ;AH&). The relation between the ternary molar enthalpies AH and AH* is also immediate AH*(~~A +- nB + n,) - A H = - AH*(l +XA).nA + bB + n, These equalities, introduced in eqn (2), yield the enthalpy of formation A H of the AX, + BX + CX ternary liquid mixture - AH= ( l + x A ) x : x ~ ( x ~ ~ AH'(^) + (1 - xg) ARE(^,) 11-2304 CaC1,KCI + NaCL MOLTEN-SALT MIXTURES XNa 0.5 1 O P - 2 - I - 0 E - Y 3 - 4 -6 Fig. 1. Ternary molar enthalpies of mixing along the xK/xCa = 1/3 section. *, Experimental; (-) calculated using Kohler’s equation ; (- - -) calculated using surrounded-ion model. Fig. 2. Ternary molar enthalpies of mixing along the xK/xCa = 1 section. *, Experimental; (-) calculated using Kohler’s equation ; (- - -) calculated using surrounded-ion model.P. SEM, G. HATEM, J-P. BROS AND M.GAUNE-ESCARD Na 305 Fig. 3. Ternary molar enthalpies of mixing along the xK/xCa = 3 section. *, Experimental; (-) calculated using Kohler’s equation ; (- - -) calculated using surrounded-ion model. XK 0.5 1 ____. - I I I I I - 2 I I * I - 0 E - -4 Y 5 - 6 - 8 Fig. 4. Ternary molar enthalpies of mixing along the xNa/xCa = 1 /3 section. *, Experimental; (-) calculated using Kohler’s equation ; (- - -) calculated using surrounded-ion model.306 0 - 2 - I - g - 4 v .Y 5 -6 - 8 CaC1,KCl + NaCl MOLTEN-SALT MIXTURES XK I 0 . 5 1 / / / / / I / / Fig. 5. Ternary molar enthalpies of mixing along the xNa/xCa = 1 section. *, Experimental; (-) calculated using Kohler’s equation ; (- - -) calculated using surrounded-ion model. XK 0.5 1 I I /’ / / / / Fig. 6. Ternary molar enthalpies of mixing along the xNa/xCa = 3 section.*, Experimental; (-) calculated using Kohler’s equation ; (- - -) calculated using surrounded-ion model. This equation was applied to the CaCl,+NaCl+KCl ternary mixture (A = Ca, B -= Na, C = K). Using the values given above for the binary limiting partial enthalpies, we obtained for the ternary molar enthalpy of mixing (in kJ mol-l) AH = (1 + xCa) xGa[ - 9.50 x;Ga - 12.38 (1 - x$,)] + (1 + xCJ xSa xi;[ - 1.92 xi; - 1.97 (1 - x;)] +( 1 +x,,) X$ xEJ - 30.07 x&- 21.57 (1 -x&)].P. SEM, G. HATEM, J-P. BROS AND M. GAUNE-ESCARD 307 We show in fig. 1-6 the enthalpies calculated in this way for comparison with the experimental values reported in tables 2 and 3. On the same figures we also show the enthalpies estimated from Kohler’s equation.Note that in most cases better agreement was obtained between estimated and experimental values when using the equation derived from the surrounded-ion model. Therefore, we used this equation to evaluate the iso-enthalpy curves over the whole ternary composition range, shown in fig. 7. Whichever relationship is selected for the calculation, the differences between the estimated and measured enthalpies of mixing were small and of the order of magnitude of the experimental uncertainty. So, for most ionic ternary mixtures of this kind, an a priori calculation of the enthalpy of mixing should be sufficient to obtain a correct estimate of the thermal energy which can be stored by such system,s. A / \ Na C1 K C I Fig. 7. Ternary iso-enthalpy curves (kJ mol-I) calculated from the surrounded-ion model.1 J-P. Bros and M. Gaune-Escard, Rev. Int. Hautes Temp. Refract., 1978, 15, 99. 3 J. L. Bouju, J-P. Bros, R. Doyen, M. Gaune-Escard, J. Pantaloni and R. Santini, Proc. Utilisation J-P. Bros and M, Gaune-Escard, Rev. Phys. Appl., 1979,14, 107. rationnelle de l’dnergie (DGRST, Grenoble, 198 1). M. Gaune-Escard and J-P. Bros, to be published. E. Calvet and H. Prat, Microcalorimdtrie (Masson, Pans, 1955). 0. J. Kleppa, J. Phys. Chem., 1960,64, 1937. 0. Kubaschewski and C. B. 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