Solubility Phase Diagram of the Ca(NO3)2–Mg(NO3)2−H2O System

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Solubility Phase Diagram of the Ca(NO3)2−Mg(NO3)2−H2O System Xia Yin,† Dongdong Li,‡ Yuqi Tan,† Xiaoya Wu,† Xiuli Yu,† and Dewen Zeng*,‡ †

College of Chemistry and Chemical Engineering, Hunan University, Changsha 410082, China Key Laboratory of Salt Lake Resources and Chemistry, Qinghai Institute of Salt Lake, Chinese Academy of Sciences, Xining 810007, China

‡

ABSTRACT: The Ca(NO3)2−Mg(NO3)2−H2O ternary system is a prospective system for heat storage, and its polythermal phase diagram is the basis for phase change materials design. However, the existing experimental data are dispersed and inconsistent with each other. In this work, we elaborately determined solubility isotherms of the ternary system at T = (273.15, 298.15, and 323.15) K by an isothermal equilibrium method, and chose a Brunauer− Emmett−Teller model to simulate and to construct the phase diagram of the ternary system from (273.15 to 373.15) K. The determined phase diagram indicates that there are two stable solubility isotherms at (273.15 and 298.15) K corresponding to solid phase Ca(NO3)2·4H2O and Mg(NO3)2·6H2O. No stable solubility isotherm for solid phase Ca(NO3)2·3H2O at (273.15 and 298.15) K has been found, different from the results reported in several references.

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INTRODUCTION The existence of several dystectic points in the binary systems Ca(NO3)2−H2O and Mg(NO3)2−H2O makes the ternary system Ca(NO3)2−Mg(NO3)2−H2O a prospective one where new phase change materials (PCMs) with lower eutectic temperature could exist. For the design of the new PCMs, the solubility phase diagram of the ternary system Ca(NO3)2− Mg(NO3)2−H2O is an essential prerequisite. However, the existing literature data1−3 are different in solubility data from each other. For example, Goloshchapov1 reported the solubility data of the ternary system which shows Ca(NO3)2·3H2O existing as stable solid phase at (273.15, 283.15, and 293.15) K. However, Frolov et al.2 reported the compositions of invariant points at the temperature range from (243.15 to 400.55) K and drew the phase diagram of the Ca(NO3)2−Mg(NO3)2−H2O system which indicates no phase region of Ca(NO3)2·3H2O existing below 297.15 K. The question if Ca(NO3)2·3H2O exists as stable phase at room temperatures is worth discussing. In this work, we elaborately measured the solubility isotherms of the system Ca(NO3)2−Mg(NO3)2−H2O including the corresponding equilibrium solid phase at T = (273.15, 298.15, and 323.15) K. Applying the modified Brunauer− Emmett−Teller (BET) model,4−6 which was proved to be suitable for phase diagrams simulation of highly soluble saltwater systems in our previous work,7−10 we constructed a relatively complete phase diagram of the ternary system at the temperature range from (273.15 to 373.15) K.

acid (EDTA) and ammonium oxalate were analytically pure and purchased from China National Pharmaceutical Industry; doubly distilled water (S < 1.5·10−4 S·m−1) was used in the experiment. A thermostat (TECHNE 18/TE-10D, Staffordshire, U.K.) with temperature stability of ± 0.03 K was used to determine isotherm solubility, and a Sartorius BS224S balance was used for weighing with an error of ± 0.1 mg. Determination of the Solubility. Each sample of the saturated solution Ca(NO3)2−Mg(NO3)2−H2O, with different samples containing different ratios of Ca(NO3)2 and Mg(NO3)2 salt, was put into a 250 cm3 Erlenmeyer flask with a ground glass stopper,7 which was immersed into a thermostat. The solution and solid in the flask were stirred with a magnetic stirrer about (240 to 360) h and then kept static for about 8 h. The sample of saturated solution was taken with a syringe into a weighed 30 cm3 quartz bottle with a cover and was weighed accurately. The total substance amount of Ca(NO3)2 and Mg(NO3)2 in the sample was analyzed with the method of EDTA gravimetric titration,11 in which the sample containing a buffered solution of NH4Cl−NH3·H2O and indicator eriochrome black T was titrated with EDTA solution to an azure end point, and the Ca(NO3)2 content was determined by calcium oxalate precipitation;12 the Mg(NO3)2 and H2O contents were calculated by subtraction. The wet solid was sampled with a glass scoop into a weighed 30 cm3 quartz bottle with a cover, weighed accurately, and then was thoroughly transferred to a 150 cm3 volumetric flask. The sample was diluted with water to the 150 cm3 mark line and analyzed in the same way as for the solution, and the

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EXPERIMENTAL SECTION Chemicals and Apparatus. Calcium nitrate and magnesium nitrate (AR from China National Pharmaceutical Industry Co. Ltd.) were purified by double crystallization for three times with 50 % salt recovery each time. Ethylenediaminetetraacetic © 2014 American Chemical Society

Received: July 6, 2014 Accepted: October 16, 2014 Published: October 30, 2014 4026

dx.doi.org/10.1021/je500629s | J. Chem. Eng. Data 2014, 59, 4026−4030

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Table 1. Solubility of the Ca(NO3)2−Mg(NO3)2−H2O System at 273.15 K and Pressure p = 0.1 MPaa composn of soln (100 w)

a

composn of wet solid phase (100 w)

Ca(NO3)2

Mg(NO3)2

H2O

Ca(NO3)2

Mg(NO3)2

H2O

solid phaseb

49.41 32.29 40.59 25.12 5.28 12.44 18.06 0

0 15.75 7.83 23.30 35.25 30.89 27.48 39.21

50.59 51.96 51.58 51.58 59.47 56.67 54.46 60.79

52.28 56.95 42.71 3.23 7.23 11.85

7.26 3.39 15.75 44.10 42.26 38.05

40.46 39.66 41.54 52.67 50.51 50.10

C4 C4 C4 C4 + M6 M6 M6 M6 M6

Standard uncertainties u are u(T) = 0.03 K and u(w) = 0.006. bC4, Ca(NO3)2·4H2O; M6, Mg(NO3)2·6H2O.

Table 2. Solubility of the Ca(NO3)2−Mg(NO3)−H2O System at 298.15 K and Pressure p = 0.1 MPaa composn of soln (100 w)

a

composn of wet solid phase (100 w)

Ca(NO3)2

Mg(NO3)2

H2O

Ca(NO3)2

Mg(NO3)2

H2O

solid phaseb

0 7.79 20.54 29.56 38.40 45.17 48.04 53.48 57.46

41.87 37.09 29.41 24.21 20.29 12.14 8.73 3.49 0

58.13 55.12 50.05 46.23 41.31 42.69 43.23 43.03 42.54

5.15 9.96 22.56 52.90 56.83 59.50 61.70

44.69 44.20 32.39 12.03 6.55 3.97 1.76

50.16 45.84 45.05 35.07 36.62 36.53 36.54

M6 M6 M6 M6 M6 + C4 C4 C4 C4 C4

Standard uncertainties u are u(T) = 0.03 K and u(w) = 0.006. bC4, Ca(NO3)2·4H2O; M6, Mg(NO3)2·6H2O.

Table 3. Solubility of the Ca(NO3)2−Mg(NO3)−H2O System at 323.15 K and Pressure p = 0.1 MPaa composn of soln (100 w)

a

composn of wet solid phase (100 w)

Ca(NO3)2

Mg(NO3)2

H2O

Ca(NO3)2

Mg(NO3)2

H2O

solid phaseb

7.82 17.04 31.28 43.64 46.24 0

41.34 36.00 28.40 23.59 23.25 45.86

50.84 46.96 40.32 32.77 30.51 54.14

4.27 12.32 24.94 31.76 31.19

48.98 42.02 34.39 32.89 34.49

46.75 45.66 40.67 35.35 34.32

M6 M6 M6 M6 M6 M6

Standard uncertainties u are u(T) = 0.03 K and u(w) = 0.006. bM6, Mg(NO3)2·6H2O.

tions are 100 w = 23.3 Mg(NO3)2, 100 w = 25.12 Ca(NO3)2, and 100 w = 51.58 H2O at 273.15 K and 100 w = 29.29 Mg(NO3)2, 100 w = 38.40 Ca(NO3)2, and 100 w = 41.31 H2O at 298.15 K. When Mg(NO3)2 was added to Ca(NO3)2(aq), the viscosity of the solution increased rapidly at 323.15 K, which made it very difficult to measure the component concentration in the mixture solution accurately. Thus, we just detected the solubility isotherm for the solid phase M6 on the Mg(NO3)2 rich side at 323.15 K, and we present the results in Table 3.

composition of the solid phase in the equilibrium was determined by the Schreinemaker method. For every sample of solution or wet solid, double analyses were taken and the maximum deviation between them was less than 0.3 %. The analysis uncertainty of the Ca(NO3)2 and Mg(NO3)2 content determined with EDTA titration and calcium oxalate precipitation can be controlled within 0.3 %; when the mass ratio of Mg2+:Ca2+ is less than 10:1,13 the mass of magnesium oxalate can be ignored by controlling the amount of precipitant. So the total experimental error in this work can be evaluated to be less than 0.6 % in mass percentage.

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THERMODYNAMIC MODELING In order to get a relatively complete phase diagram of the ternary system, we applied the modified BET model4−6 combined with experimental data in this work to simulate the phase diagram including isotherms and polytherms. Modeling Methodology. The BET model was first adopted by Stokes and Robinson4 to correlate water activity aW and salt concentration m (mol·kg−1) for a single binary system (A + H2O):

EXPERIMENTAL RESULTS The solubility data of the ternary Ca(NO3)2−Mg(NO3)2−H2O system determined at T = (273.15, 298.15, and 323.15) K are presented in Tables 1−3, respectively. Our results for the two binary systems are consistent with the literature values.14 One can see in Tables 1 and 2 that the solid phases in equilibrium with saturated solutions are C4 and M6 at (273.15 and 298.15) K (Cn and Mn stand for Ca(NO3)2·nH2O and Mg(NO3)2·nH2O, respectively). The invariant point composi-

aW m /{55.51(1 − aW )} = 1/(cr ) + (c − 1)a w /(cr ) 4027

(1)

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where ΩAB denotes an empirical interaction parameter between salts A and B and can be obtained by fitting to the data of salt activity or solubility isotherm, xi is the mole fraction of salt i in the anhydrous mixture, Ni is the substance amount of component i, Ni(M) denotes the substance amount of water bound to salt i and can be obtained by solving eqs 5 and 6 when the binary parameters ci and ri are known:

Table 4. BET Parameters of the Ca(NO3)2−Mg(NO3)2− H2O System ΔEb

ra salt

a

b

c

d

ref

Ca(NO3)2 Mg(NO3)2

5.03 5.58

−0.0042 0

−4.183 0

−0.488 −3.135

15 15

r = a + bT bΔE /(kJ ·mol−1) = c + dT /100

a

NA(M)(NA(M) + NB(M)) (rANA − NA(M))(NH − NA(M) − NB(M))

Table 5. Parameters ln k of the Solid Phase in the Ca(NO3)2−Mg(NO3)2−H2O System

= cA = exp(−ΔEA /(RT ))

(5) NB(M)(NA(M) + NB(M))

ln ka solid phase

A

B

C

ref

Ca(NO3)2·4H2O Ca(NO3)2·3H2O Ca(NO3)2·2H2O Ca(NO3)2 Mg(NO3)2·6H2O Mg(NO3)2·2H2O Mg(NO3)2

6.26 0.89 1.507 −1.838 −240.049 −5.148 1.571

−5328.9 −3209.2 −2805.2 −483.7 7440.685 −2441.5 −1504.8

0 0 0 0 33.263 0 0

15 15 15 15 16 15 15

(rBNB − NB(M))(NH − NA(M) − NB(M))

= c B = exp(−ΔE B/(RT ))

(6)

The binary parameters and their temperature dependence of the systems Ca(NO3)2−H2O and Mg(NO3)2−H2O are taken from previous work15 and are listed in Table 4. To calculate the phase diagram of the ternary systems, the equilibrium constant of the hydrated salt should be determined in advance. For the solid salt·nH2O, its solubility product ln k at a certain temperature for the dissolution reaction

a

ln k = A + B /T + C ln T

salt ·nH 2O(s) = salt(aq) + nH 2O(aq)

(7)

can be expressed by ln k = ln asalt + n ln a H2O

The solubility product can be obtained from the solubility data in the binary system; in this work the parameters of lnk as a function of temperature are taken from our previous work15,16 and presented in Table 5. Prediction of Phase Diagram and Discussion. We predicted the solubility isotherms in the ternary system Ca(NO3)2−Mg(NO3)2−H2O at various temperatures just using the binary parameters listed in Tables 4 and 5 (i.e., ΩAB = 0) and presented the predicted results in Figure 1 (dashed lines). The predicted isotherm agrees with our experimental data very well at 273.15 K, and the deviation between them increases at increasing temperatures. By introducing the empirical interaction parameter ΩAB in eqs 3 and 4 into the simulation and fitting its values to our experimental data at (298.15 and 323.15) K, we got the calculated results expressed by solid lines in Figure 1 and the parameters as a function of temperature: ΩAB = 13657.5 − 50T. The calculated isotherms agree with the experimental data in all three temperatures. Furthermore, a relatively complete phase diagram of the ternary system from (273.15 to 373.15) K was constructed by the binary parameters in Tables 4 and 5 and the interaction parameter ΩAB. Figures 2 and 3 are some comparisons between the results determined in this work with those reported in the literature.1−3 At 273.15 K, Goloshchapov1 gave solubility data of the ternary system and two invariant points M6 + C3 (● in Figure 2a) and C3 + C4 (■ in Figure 2a), and Frolov et al.2 and Orlova et al.3 reported that there was also only one invariant point M6 + C4 (▼ and ▲ in Figure 2a). According to our research results, there should be definitely no stable solubility isotherm for the solid C3. Goloshchapov’s results1 for the solid C3 should be suspect. We noticed that the invariant point for the solid phases M6 + C4 determined in this work locates between the two points reported in the literature.2,3

Figure 1. Calculated isotherms of the Ca(NO3)2−Mg(NO3)2−H2O system compared with experimental data: ○, 273.15 K in this work; ●, 273.15 K from literature;14 □, 298.15 K in this work; ■, 298.15 K from literature;14 Δ, 323.15 K in this work; ▲, 323.15 K from literature;14 --, predicted isotherms with binary model parameters only; −, isotherms calculated with binary and empirical interaction parameters.

where c and r are model parameters which can be obtained by regressing the experimental water activity data aW; c = exp(−ΔE/RT), ΔE = Ui − UL, Ui is the energy of monolayer adsorption of water on to the solute i, and UL is the internal energy of liquefaction of pure water. For a ternary system (A + B + H2O) the activity expressions for each component have been proposed10 as follows: aW = (NW − NA(M) − NB(M))/NW

(8)

(2) 2

aA = {NA /(NA + NB)}{(rANA − NA(M))/(rANA )}rA exp(ΩAB / RT )xB (3) 2

aB = {NB/(NA + NB)}{(rBNB − NB(M))/(rBNB)}rB exp(ΩAB / RT )xA (4) 4028

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Figure 2. Predicted phase diagram of the Ca(NO3)2−Mg(NO3)2−H2O system compared with the results in the literature in symbols: (a) , predicted polytherm in this work, T = 273.15 K; , predicted isotherm; ○, isotherm equilibrium with M·6;1 □, isotherm equilibrium with C4;1 ●, invariant point M6 + C3;1 ■, invariant point C3 + C4;1 ▼, invariant point M6 + C4;2 ▲, invariant point M6 + C4.3 (b) , predicted polytherm in this work, T = 283.15 K; , predicted isotherm; ○, isotherm equilibrium with M6;1 □, isotherm equilibrium with C3;1 ●, isotherm equilibrium with C4;1 ◐, invariant point M6 + C3;1 ◑, invariant point C3+C4.1 (c) , predicted polytherm in this work, T = 293.15 K; , predicted isotherm; ▽, isotherm equilibrium with M6;1 ◁, isotherm equilibrium with C3;1 ▷, isotherm equilibrium with C4;1 ▼, invariant point M6 + C3;1 ▶, invariant point C3 + C4.1

Goloshchapov1 also reported there exists a stable formation field for the solid phase C3 at (283.15 and 293.15) K (the symbols in Figure 2b,c), which should be false according to our research results. The predicted phase diagram of the Ca(NO3)2−Mg(NO3)2− H2O system at the temperature range from (273.15 to 373.15) K is shown in Figure 3a. Frolov et al.2 reported the invariant points at temperature ranging from (234.15 to 400.15) K and drew the phase diagram according to these invariant points, which are shown in Figure 3b. We can see that the predicted phase diagram in this work is different from the results of Frolov et al.,2 and there is no field of crystallization of C2 in the phase diagram of Frolov, which is distinguished from our results.

results show that there are two solubility branches for C4 and M6 at (273.15 and 298.15) K. The modified BET model was chosen to simulate the experimental results, and a relatively complete phase diagram of the ternary Ca(NO3)2−Mg(NO3)2−H2O system was constructed over the temperature range from (273.15 to 373.15) K. The simulated results agree with our experimental values very well. Phase equilibrium data from literature were compared with those determined in this work, and their reliability was discussed based on the phase diagram constructed in this work. One definite conclusion can be drawn in this work: that there exists no stable formation field for solid phase Ca(NO3)2· 3H2O at temperatures equal to or below 298.15 K.

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CONCLUSION We elaborately determined the solubility isotherms of the ternary Ca(NO3)2−Mg(NO3)2−H2O system at T = (273.15, 298.15, and 323.15) K using the isothermal method. The

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. 4029

dx.doi.org/10.1021/je500629s | J. Chem. Eng. Data 2014, 59, 4026−4030

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Figure 3. Predicted phase diagram of the Ca(NO3)2−Mg(NO3)2−H2O system compared with the results of the literature: (a), , predicted polytherm in this work; , predicted isotherm at 273.15 K. (b) , predicted polytherm in this work; --, polytherm from the literature;2 ○, invariant point in the literature.2 The numbers in the figure are the temperatures in Celsius degrees of invariant points.2

Funding

(12) Analytical laboratory of Qinghai Institute of Salt Lakes at Chinese Academy of Sciences. Analytic method of brines and salts, 2nd ed.; Science Press: Beijing, 1988; pp 37−39. (13) Wu, H.; Yu, X. L.; Wu, X. Y.; Fu, X. Y.; Yin, X. Method for accurate determination of solution containing calcium and magnesium. J. Salt Lake Res. 2014, 21, 29−33. (14) Linke, W. F.; Seidell, A. Solubilities: Inorganic and metal-organic compounds, 4th ed.; American Chemical Society: Washington, DC, USA; 1965. (15) Zeng, D. W.; Voigt, W. Phase diagram calculation of molten salt hydrates using the modified BET equation. Comput. Coupling Phase Diagrams Thermochem. 2003, 27, 243−251. (16) Zhou, Q. B.; Yin, X.; Wang, Q.; Wang, C. Phase diagram prediction of the system Mg(NO3)2-MgCl2-H2O as phase change materials. Acta Chim. Sin. 2011, 69, 1725−1730.

This work was financially supported by KLSLRC (Grant KLSLRC-KF-13-HX-3), the National Natural Science Foundation of China (Grants J1210040 and J1103312), and the Chinese Ministry of Science and Technology (Grant 2012AA052503). Notes

The authors declare no competing financial interest.

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REFERENCES

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