Solubility Prediction and Measurement of the System KNO3

Article pubs.acs.org/jced

Solubility Prediction and Measurement of the System KNO3−LiNO3−NaNO3−H2O Xia Yin,*,† Xiuli Yu,† Xiaoya Wu,† Xiaoyi Fu,† Han Wu,† and Dewen Zeng‡ †

College of Chemistry and Chemical Engineering, Hunan University, Changsha, 410082, China, Qinghai Institute of Salt Lakes, Chinese Academy of Science, Xining, 810008, China

‡

S Supporting Information *

ABSTRACT: A Pitzer−Simonson−Clegg model has been applied to calculate the isotherms of the system KNO3− LiNO3−NaNO3−H2O and its subsystems. The model parameters are fitted against experimental solubility and water activity in the sub-binary and sub-ternary systems of the titled quaternary system. The solubility of the system KNO3− LiNO3−NaNO3−H2O at 298.1 and 308.5 K and its subsystems KNO3−LiNO3−H2O at 283.1 K and LiNO3−NaNO3−H2O at 323.1 K are elaborately measured for verifying the reliability of the model prediction. Comparisons indicated that the calculated values are in agreement with our experimental data and literature data.

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INTRODUCTION Lithium salts have great practical values in the fields of energy and new materials science because of their large heat storage density, especially used for phase change materials (PCMs) which can store or release latent heat during phase change processes. According to our previous work,1,2 it is possible that the eutectic PCM with a melting point at room temperature will exist in the quaternary system KNO3−LiNO3−NaNO3− H2O in which the content of these salts are abundant in the salt lake of China. Solubility data of the quaternary system KNO3−LiNO3−NaNO3−H2O and its subsystems are of essential importance for developing new phase change materials (PCMs). Because of the lack of complete phase equilibrium information of this system, it is difficult to obtain the correct ratio of eutectic components just using experimental methods which consume time and money.3 Our previous work1,2 has manifested that the theoretical prediction of the phase diagram of prospective systems may be an effective way for searching the desirable eutectic materials, but whether the calculated results can be reliable needs to be verified with experimental data. In this work, we calculate phase diagrams of the system KNO3−LiNO3−NaNO3−H2O and its subsystems using a Pitzer−Simonson−Clegg model (PSC model).4−7 To verify the reliability of the model values, we elaborately measure part of the solubility data of these systems and compare these experimental data with model results.

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Figure 1. Schematic diagram of self-made thermostat: (1) thermostat, (2) multiposition magnetic stirrer, (3) reference solution, (4) soft iron magnetic stirrer, (5) sample, (6) temperature sensor, (7) lamp.

Shanghai China-Lithium Industry Co. Ltd.) with nitric acid (AR from China National Pharmaceutical Industry Co. Ltd.) and was purified by double crystallization for three times with 50 % salt recovery in each time. Sodium tetraphenylborate (> 0.99, mass fraction), potassium nitrate (> 0.99, mass fraction), and sodium nitrate (> 0.99, mass fraction) were purchased from China National Pharmaceutical Industry, and the last two were purified by double crystallization for three times with 50 % salt recovery in each time. Doubly distilled water (S < 1.5·10−4 S·m−1) was used in the experiment.

EXPERIMENTAL SECTION

Received: March 13, 2013 Accepted: May 7, 2013

Chemicals and Apparatus. Lithium nitrate was prepared by neutralizing lithium carbonate (mass fraction purity > 0.9999, © XXXX American Chemical Society

A

dx.doi.org/10.1021/je400233v | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. The Binary PSC Parameters WW,ca = W1 + W2T

UW,ca = U1 + U2T

VW,ca = V1 + V2T

electrolyte

B1

Bca = B1 + B2T B2

W1

W2

U1

U2

V1

V2

T/K

ref

KNO3 LiNO3 NaNO3

−65.03 100.6 −517.39

0.1905 −0.287 1.7565

1.28 −7.125 −3.066

−0.0024 0.00998 0.00812

−6.79 2.70 −7.859

0.0158 −0.0035 0.02376

0 −8.848 8.114

0 0.02233 −0.02721

298.15 to 425.5 298.15 to 373.4 298.15 to 424.9

13, 17 13, 16 14, 15

Table 2. The Parameters ln k of Solid Phase in the System KNO3−LiNO3−NaNO3−H2O ln k = A + B/T + CT + D ln T solid phase

A

B

C

D

solubility source

KNO3 LiNO3 LiNO3·3H2O NaNO3

1366.210 74.431 7.898 −84.734

−40957.9 −3004.1 −3242.5 1317.8

0.36917 0 0 0

−236.448 −11.015 0 13.137

18 19 19 18

Table 3. The Ternary PSC Model Parameters Wijk = a + b(T/K)

QW,ijk = c + d(T/K)

Uijk = e + f(T/K)

system

a

b

c

d

e

f

T /K

ref

KNO3−LiNO3−H2O KNO3−NaNO3−H2O LiNO3−NaNO3−H2O

−18.563 6.605 −13.432

0.03972 −0.02604 0.0316

4.852 −8.35 23.229

−0.0144 0.028 −0.06752

−19.265 0 −1.0713

0.06401 0 0.0036

298 to 373 298 to 323 298 to 323

16, 20, 23 18 21, 22

Figure 2. Comparison of calculated and experimental solubility of the system KNO3−LiNO3−H2O. The lines represent the calculated values according to Tables 1 to 3, the symbols represent the experimental data: ☆, 273.1 K;20 ○, 298.1 K;20 △, 298.1 K.23

Figure 3. Comparison of calculated and experimental solubility of the system KNO3−NaNO3−H2O. The lines represent the calculated values according to Table 1 to 3, the symbols represent the experimental data:18 □, 273.1 K; ○, 298.1 K; △, 313.1 K; ▽, 323.1 K; ■, 333.1 K; ☆, 348.1 K.

In this work, solubility measurements were carried out in a thermostat (TECHNE 18/TE-10D, England) with temperature stability of ± 0.03 K or were carried out in a self-made isothermal box (Figure 1). A Sartorius BS224S balance was used for weighing with an error of ± 0.1 mg. Measurement of the Solubility of the System KNO3− LiNO3−H2O at 283.1 K. The solid−liquid phase equilibrium experiments were carried out in a 250 cm3 Erlenmeyer flask with ground glass stopper,8 and the flask was immersed in the thermostat. The sample of the saturated solution KNO3− LiNO3−H2O containing different ratios of KNO3 and LiNO3 salt was stirred with a magnetic stirrer for 74 h and then kept static for about 6 h; the sample of saturated solution was taken with a syringe into a weighed 30 cm3 quartz bottle with cover

and was weighed accurately. The content of H2O in the sample was determined by evaporation to dryness at 503 K, cooling and weighing. The KNO3 content in the sample was analyzed with sodium tetraphenylborate9 where the error of method can be controlled less than 0.5 % in mass percentage. The wet solid was taken out with a glass scoop and analyzed the same way as for the solution. Duplicate analyses of every sample including solution and wet solid gave a maximum deviation of 0.05 %, and the total errors of experimental solubility results can be reasonably evaluated to be less than 0.7 % in mass percentage for the ternary system KNO3−LiNO3−H2O. B



Article

Figure 5. Isothermal solubility of the system KNO3−LiNO3−H2O at 283.1 K. symbols represent experimental data in this work: ●, liquid phase composition; ○, corresponding wet solid phase; , predicted isotherm with model parameters of Tables 1 to 3.

Figure 4. Comparison of calculated and experimental solubility of the system LiNO3−NaNO3−H2O. The lines represent the calculated values according to Table 1 to 3, the symbols represent the experimental data: □, 298.1 K;21 ○, 323.1 K.22

Table 5. Solubility of the Ternary System LiNO3−NaNO3− H2O at 323.1 K

Measurement of the Solubility of the Systems LiNO3− NaNO3−H2O and KNO3−LiNO3−NaNO3−H2O. For the solution including Li+ and Na+, it is difficult to analyze accurately the concentration of both ions in the meantime. So a solid disappearance method10−12 was used for measuring the solubility of the systems LiNO3−NaNO3−H2O at 323.1 K and KNO3−LiNO3−NaNO3−H2O at 298.1 K and 308.5 K. The procedures in detail are repeated briefly as follows: (1) MNO3 (M = K, Li, Na) stock solution was prepared using the salts purified in this work, and the concentration of solution was determined by evaporation to dryness at 503 K. (2) A sample mixture of known mass of every stock solution was put into a weighed 150 cm3 flask with a ground glass stopper and a soft iron magnetic stirrer. The flask was placed in a self-made thermostat with an accuracy of ± 0.1 K (see Figure 1) and was kept at a certain constant temperature. (3) The mixture was isothermally evaporated slowly until a small amount of crystal appeared. (4) The mixed solutions were placed in a refrigerator and frozen in a long enough time to ensure that all possible crystal types had formed, and then the frozen sample was moved to the self-made thermostat and kept at the same temperature for 24 h. (5) A drop of water (about 0.005 g) was added to the sample mixture using a syringe every 2 h. When the turbidity of the solution was decreased, the duration between additions of water was increased to 5 h. (6) When the

composition of saturation solution (100 w) LiNO3

H2O

NaNO3

predicted solid phase

0 15.17 19.83 42.07 53.10 57.84 61.00 63.23

46.80 48.54 48.61 42.35 35.32 32.51 34.87 36.77

53.20 36.29 31.56 15.58 11.58 9.65 4.13 0

NaNO3 NaNO3 NaNO3 NaNO3 NaNO3 LiNO3 LiNO3 LiNO3

last trace of salts was observed to disappear and a clear solution was obtained, the total amount of mixture solution and flask was weighed, so the mass percents of dry salts and water in the saturated solution at a constant temperature were calculated. (7) We repeated steps 3, 4, 5, and 6 until the relative error between the weighed total mass at step 6 was less than 0.3 %.

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THERMODYNAMIC CALCULATION The expressions of the PSC model for the activity coefficients of the solvent, cation M and anion X are given in the Supporting Information. The binary parameters Bca, WW,ca, UW,ca and VW,ca at various temperature were fitted against experimental water activity

Table 4. Solubility of the Ternary System KNO3−LiNO3−H2O at 283.1 K composition of solution (100 w)

composition of wet-solid-phase (100 w)

LiNO3

KNO3

H2O

LiNO3

KNO3

H2O

solid phase

37.22 4.63 9.85 20.91 35.26 36.91 36.45 0.00

0.00 13.66 10.96 9.14 10.32 2.45 6.14 17.20

62.78 81.71 79.19 69.95 54.42 60.64 57.41 82.80

1.85 5.34 11.27 42.99 46.05 46.53

54.53 56.64 50.17 8.92 1.24 3.00

43.62 38.02 38.56 48.09 52.71 50.47

LiNO3·3H2O LiNO3·3H2O LiNO3·3H2O LiNO3·3H2O LiNO3·3H2O + KNO3 KNO3 KNO3 KNO3

C



Article

The parameters of ln k are obtained from the solubility data18,19 of the binary systems and presented in Table 2. The ternary parameters Wijk, Uijk, and QW,ijk of the systems KNO3−LiNO3−H2O, KNO3−NaNO3−H2O and LiNO3− NaNO3−H2O were determined by regressing ternary experimental solubility and water activity16,18,20−23 and listed in Table 3. Solubility isotherms in the ternary systems were predicted and compared with experimental data by applying the parameters of Table 1 to 3, and were shown in Figures 2 to 4. The results showed that the calculated values agree with the experimental values very well.

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EXPERIMENTAL RESULTS AND DISCUSSION The System KNO3−LiNO3−H2O. The solubility of the system KNO3−LiNO3−H2O at 283.1 K was determined, and the data are shown in Table 4. We predicted isotherm of this system at 283.1 K with the PSC model parameters listed in Tables 1 to 3 and compared with our experimental data (see Table 4 and Figure 5), and the results are in quite good agreement. The System LiNO3−NaNO3−H2O. The experimental solubility data of the ternary system LiNO3−NaNO3−H2O at 323.1 K, which were determined with the solid disappearance method in this work, are listed in Table 5. These data are most consistent with Andronova’s data22 and the calculated value of PSC model (see Figure 6), and the predicted solid phases were shown in Table 5. The results indicate that the experimental data from the solid disappearance are reliable. The System KNO3−LiNO3−NaNO3−H2O. Using the method of solid disappearance, we determined the solubility data of the system KNO3−LiNO3−NaNO3−H2O at 298.1 and

Figure 6. Isothermal solubility of the system LiNO3−NaNO3−H2O at 323.1 K: ▲, experimental data in this work; □, reference data;22 , calculated isotherm with model parameters of Tables 1 to 3.

data13−17 of the systems KNO3−H2O, LiNO3−H2O and NaNO3−H2O, and listed in Table 1. For a hydrated salt Mν+Xν−·nH2O, its solubility product ln k at a definite temperature for the dissolution reaction M ν +X ν −·nH 2O = ν+ M+ + ν− X− + nH 2O

can be expressed by ln k = ν+ ln a M+ + ν− ln a X− + n ln a H2O

Table 6. Comparison of Experimental Data of the System KNO3−LiNO3−NaNO3−H2O and Model Predicted Values at 298.1 K dry basis quality ratio (100 w)

1 2 3 4 5 6 average Red

KNO3

LiNO3

NaNO3

wH2O (exp)a

wH2O (pred)b

Re (%)c


4.31 11.78 27.57 30.13 30.32 31.33

83.49 77.21 61.12 39.46 0 20.86

12.20 11.01 11.31 30.41 69.68 47.81

46.284 42.095 35.838 44.087 41.935 43.782

46.427 42.336 35.661 44.019 41.549 43.674

0.309 0.572 0.494 0.154 0.920 0.249 0.450

LiNO3·3H2O+NaNO3 LiNO3·3H2O+NaNO3 NaNO3 NaNO3 NaNO3 NaNO3

a

: wH2O(exp) are experimental mass percent of H2O in the saturated solution. b: wH2O (pred) are PSC calculated mass percent of H2O in the saturated solution. c: Re (%) = (|wH2O (exp) − wH2O (pred)|)/(wH2O (exp))·100. d: Average Re = ∑ni Re/n.

Table 7. Comparison of Experimental Data of the System KNO3−LiNO3−NaNO3−H2O and Model Predicted Values at 308.5 K dry basis quality ratio (100 w)

1 2 3 4 5 6 7 8 Average Red

KNO3

LiNO3

NaNO3

wH2O (exp)a

wH2O (pred)b

Re (%)c


5.78 10.85 17.37 22.63 32.78 33.98 35.03 35.02

59.81 79.23 72.81 67.78 47.21 32.81 18.38 64.98

34.41 9.92 9.82 9.59 20.01 33.21 46.59 0

48.277 32.06 28.645 26.434 35.321 39.016 38.893 24.146

50.227 31.379 28.821 26.690 35.415 38.886 38.978 24.423

4.0392 2.124 0.615 0.968 0.267 0.333 0.218 2.294 1.357

NaNO3 LiNO3 LiNO3 LiNO3 NaNO3 NaNO3 KNO3+NaNO3 KNO3+LiNO3

a

: wH2O(exp) are experimental mass percent of H2O in the saturated solution. b: wH2O (pred) are PSC calculated mass percent of H2O in the saturated solution c: Re (%) = (|wH2O (exp) − wH2O (pred)|)/(wH2O (exp))·100. d: Average Re = ∑ni Re/n. D



Article

values at 298.1 K and 308.5 K are less than 0.5 % and 1.36 %, respectively. The reason that the predicted values at 298 K are more accurate than the ones at 308 K may be the parametrization of model was obtained by regressing the binary and ternary experimental data at different temperatures including 298 K but without 308 K, so the prediction difficulty increases at 308.5 K. Furthermore we predicted the isothermal eutectic lines and waterlines with the same mass percent of H2O in the saturated solution at 298.1 and 308.5 K (see Figure 7 and Figure 8). The results of the predicted values and experimental data are seen to be in good agreement, so it can be reasonably believed that the phase diagram of the system KNO3−LiNO3−NaNO3−H2O predicted using the PSC model parameters of Table 1 to 3 are reliable.

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CONCLUSIONS We calculated the solubility of the ternary systems KNO3− LiNO−H2O, LiNO3−NaNO3−H2O, and KNO3−NaNO3− H2O with a PSC model, based on available experimental data, and we predicted the solubility of the quaternary system KNO3−LiNO3−NaNO3−H2O at 298.1 and 308.5 K. To check the reliability of the model calculation, the solubility of the system KNO3−LiNO3−H2O at 283.1 K was determined using the phase equilibrium method, and the solubilities of the system LiNO3−NaNO3−H2O at 323.1 K and KNO3−LiNO3− NaNO3−H2O at 298.1 and 308.5 K were measured with the solid disappearance method. Comparisons showed that the PSC model can calculate accurately the phase diagrams of the ternary salt-water systems by using available binary and ternary experimental data. That the predicted solubility data are in good agreement with the experimental results for the quaternary system indicates that the PSC model parameters determined in this work are reliable and thus can serve for the theoretical design in PCMs development.

Figure 7. Phase diagram of the system KNO3−LiNO3−NaNO3−H2O at 298.1 K: ○, experimental data in this work; lines are predicted values with PSC model: bold line, eutectic line; ---, predicted waterline with the same value, value = mass of H2O/mass of the saturated solution ×100 %.

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ASSOCIATED CONTENT

S Supporting Information *

The expressions of the PSC model for the activity coefficients of the solvent, cation M, and anion X. 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]. Figure 8. Phase diagram of the system KNO3−LiNO3−NaNO3−H2O at 308.5 K: ○, experimental data in this work; lines are predicted values with PSC model: bold line, eutectic line predicted with PSC model; ---, predicted waterline with the same value, value = mass of H2O/mass of the saturated solution ×100 %.

Funding

308.5 K and obtained the mass percents of every dry salt (KNO3, LiNO3, and NaNO3) and mass percent of H2O in the saturated solutions (see Tables 6 and 7). Combining the binary and ternary parameters of Tablex 1 to 3 with the mass percents of dry salts (columns 2 to 4 in Tables 6 and 7), we predicted the mass percent of H2O in the saturated solution of the system KNO3−LiNO3−NaNO3−H2O at 298.1 and 308.5 K and predicted the corresponding solid phases, as shown in columns 6 and 8 of Table 6 and Table 7, and gave the relative errors between the experimental mass percents of H2O and predicted values (see column 7 of Table 6 and Table 7). The average relative error between the experimental data and predicted

Notes

This work was financially supported by the National Natural Science Foundation of China (Grant J1210040, J1103312), the Hunan Provincial Natural Science Foundation of China (Grant 11JJ2011), China’s Ministry of Science and Technology (Grant 2012AA052503) The authors declare no competing financial interest.

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Solubility Prediction and Measurement of the System KNO3

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