Apparent Molar Volumes of Aqueous Solutions of Lithium Pentaborate

Article pubs.acs.org/jced

Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Apparent Molar Volumes of Aqueous Solutions of Lithium Pentaborate from 283.15 to 363.15 K and 101.325 kPa: An Experimental and Theoretical Study Kaiyu Zhao,† Long Li,† Yafei Guo,*,† Lingzong Meng,‡ Mingli Li,§ Ji Duo,§ and Tianlong Deng† †

J. Chem. Eng. Data Downloaded from pubs.acs.org by TULANE UNIV on 02/08/19. For personal use only.

Tianjin Key Laboratory of Marine Resources and Chemistry, College of Chemical Engineering and Materials Science, Tianjin University of Science and Technology, Tianjin, 300457, People's Republic of China ‡ School of Chemistry and Chemical Engineering, Linyi University, Linyi, 276000, People's Republic of China § Central Laboratory of Tibet Autonomous Region Bureau of Geological & Mineral Resources, Lasa, 850033, People's Republic of China S Supporting Information *

ABSTRACT: Densities of LiB5O6(OH)4(aq) at molalities of 0.09859−0.89493 mol·kg−1 were measured at 5 K intervals from 283.15 to 363.15 K at 101.325 kPa using a precise Anton Paar Digital vibrating-tube densimeter. The apparent molar volumes (Vϕ), thermal expansion coefficients (α), and partial molar volumes (V̅ B) were obtained. On the basis of experimental data, diagrams of the thermodynamic parameters (α, Vϕ, and V̅ B) against molality at different temperatures were plotted. According to the Pitzer model of apparent molar volume, the Pitzer parameters V̅ B, (1)v (2)v v ß(0)v M,X, ßM,X, ßM,X, and CM,X and the coefficients ai of the temperature-dependence formula f(i, p, T) = a1 + a2 ln(T/298.15) + a3(T − 298.15) + a4/(620 − T) + a5(T − 227) (where T is the temperature in Kelvin) for LiB5O6(OH)4 were fitted by the least-squares method. The predictive apparent molar volumes agree well with the experimental values, and those results indicated that the single salt parameters and the temperature-dependence formula are reliable.

1. INTRODUCTION

developing new separation processes of lithium borates from salt-lake brines. According to the multitemperature phase diagram of (Li2O + B2O3 + H2O), Ge et al.7 synthesized LiB5O6(OH)4·3H2O previously, and the basic physicochemical properties of LiB5O6(OH)4(aq) such as pH, electrical conductivity, and density were reported. To get accurate thermodynamic behaviors of aqueous solution containing boron and lithium, the standard molar enthalpy of formation for LiB5O6(OH)4 aqueous solution was measured by a Calvet low temperature microcalorimeter;8 as for the solid minerals, Cui et al. reported the heat capacity of LiB5O6(OH)4·3H2O at temperatures from 297 to 375 K and the results were correlated with a thermodynamic function.9 However, the volumetric property of aqueous solution containing lithium pentaborate is not reported in the literature. In this paper, the apparent molar volumes, thermal expansion coefficients, and partial molar volumes of the binary system (LiB5O6(OH)4 + H2O) at molalities of 0.09859− 0.89493 mol·kg−1 and at 5 K intervals from 283.15 to 363.15 K at 101.325 kPa were obtained and represented by the Pitzer model.

Lithium borates not only occupy an important position in modern inorganic industry but also have been widely used in electronic manufacturing, glasses production, and chemical analysis for their excellent characteristics. Li2B4O7, which was a new type of piezoelectric material, could achieve the conversion between mechanical and electrical energy, so it was widely used to produce sensors of mobile phones. Due to the special structure of LiBO2, it was a potential ultraviolet nonlinear optical material used in modern glasses production.1,2 Salt lakes with high concentrations of lithium and boron are widely distributed in the Qaidam Basin of China and in the lithium triangle of Chile, Bolivia, and Argentina as well as brine lakes of salar de Atacama, salar de Uyuni, and salar del Hombre Muerto.3 The borates in brines mainly exist as [B(OH)4]−, [B4O5(OH)4]2−, and [B5O6(OH)4]− based on the construction formulas;4 meanwhile, three types of hydrated lithium borate mineralsLiB(OH)4·6H2O, Li2B4O5(OH)4· H2O, and LiB5O6(OH)4·3H2Oare naturally formed in salt lakes when combined with lithium ion.5 Due to the complex structure of B−O bonds and supersaturated phenomenon of lithium borates, 6 it is highly desirable to study the thermodynamic properties and behaviors of its aqueous electrolyte solution and fully understand the ion interactions among each ion. The basic information is significant for © XXXX American Chemical Society

Received: September 12, 2018 Accepted: January 30, 2019

A

DOI: 10.1021/acs.jced.8b00814 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

2. EXPERIMENTAL SECTION 2.1. Materials. LiB5O6(OH)4·3H2O was synthesized by the chemicals of LiOH·H2O and H3BO3 listed in Table 1, and the

The densities of lithium pentaborate aqueous solutions were measured by an Anton Paar Digital vibrating-tube densimeter (DMA4500, Anton Paar Co.Ltd., Austria), and the temperature of the densimeter was automatically thermostatic by a heating attachment within a precision of 0.01 K. Before each measurement, the densimeter was calibrated by dry air and freshly degassed DDW at 293.15 K. Then, the density of pure water was measured at 10 K intervals from 279.15 to 369.15 K at 101.325 kPa by the calibrated densimeter, which were in good agreement with the literature.12 Finally, the densities of diluted samples at different molalities were measured at 5 K intervals from 283.15 to 363.15 K at 101.325 kPa.

Table 1. Source and Purity of Chemicals Used in This Worka chemical name

source of chemicals

LiOH·H2O

Macklin Chemical

H3BO3

Simopharm Chemical

purification method no further purification recrystallization

in mass fraction 0.999 0.997

Used for synthesis of the chemical of LiB5O6(OH)4·3H2O.

a

3. RESULTS AND DISCUSSION 3.1. Density and Thermal Expansion Coefficient of LiB5O6(OH)4 Aqueous Solution. All of the measured densities of LiB5O6(OH)4(aq) were listed in Table 3, and it can clearly be seen that the densities increased with increasing molality and decreasing temperature. Then, a comparison between the experimental density and data reported in the literature for the LiB5O6(OH)4 aqueous solution at 288.15, 298.15, 308.15, and 318.15 K13 was presented in Figure 1, which have the same changing tendency, the little deviation could be caused by the measuring method of density bottle in the literature. At constant molality and pressure, the relationships between density (ρ) and temperature (T) could be represented by an empirical equation,14 as follows

deionized distilled water (DDW) as the pure water was produced by ULUP-II-10T (China) with a conductivity less than 1 × 10−4 S·m−1 and pH ≈ 6.60 at 298.15 K. The synthesized method has been described previously in detail.10 The synthesized LiB5O6(OH)4·3H2O was identified by the X-ray diffractometer (MSAL XD-3, Beijing Purkinje General Instrument Co. Ltd., China) and TG-DSC (Labsys, Setaram, France); the results are shown in Figures S1 and S2 (Supporting Information), respectively. In Figure S1, it can clearly be seen that the peak position and intensity of the synthesized LiB5O6(OH)4·3H2O were in great agreement with the standard map, and in Figure S2, the actual water loss rate 32.28% of LiB5O6(OH)4·3H2O was basically consistent with the theoretical value 32.26% with an uncertainty of ±0.0071. The purity of synthesized LiB5O6(OH)4·3H2O was analyzed by the chemical analysis method. The concentration of Li+ was measured by ICP-OES (Prodigy, Leman Corporation, America) with an uncertainty of ±0.0064 in mass fraction; the concentration of [B5O6(OH)4]− was analyzed by the gravimetric method of mannitol with an uncertainty of ±0.0005.11 The analytical result shown in Table 2 indicated that the purity of the synthesis of LiB5O6(OH)4·3H2O reached 0.99 in mass fraction. 2.2. Experimental Methods. The stock solution was prepared with DDW and the synthesized LiB5O6(OH)4·3H2O in a glovebox (UNIlab Plus, MBraun, Germany) filled with nitrogen by weighting with the analytical balance (Mettler Toledo, Swiss) with a precision of 0.0001 g. All aqueous LiB5O6(OH)4 solution to be measured was freshly prepared by mass dilution from stock solution, and the molalities of diluted solution were titrated by the mannitol gravimetric method with a known concentration of NaOH aqueous solution using the mixed indicator of methyl red and phenolphthalein. The reaction equation could be described as in the following:

ρ = A 0 + A1(T − 273.15) + A 2 (T − 273.15)2

(1)

where ρ is the density of LiB5O6(OH)4 aqueous solution (g· cm−3), T is the temperature in Kelvin, and Ai is the coefficient of eq 1, which was fitted by the least-squares method and shown in Table 4 with the correlation coefficients (r) and standard deviations within 0.999 and 0.00005, respectively. The coefficient of thermal expansion for the aqueous solution, α,14 is defined as follows: α=

1 ij ∂V yz 1 i ∂ρ y jj zz = − jjj zzz V k ∂T { P , m ρ k ∂T { P , m

(2)

α = −{A1 + 2A 2 (T − 273.15)}/ρ

(3)

According to eqs 1−3, the coefficients of thermal expansion at different molalities and temperatures were calculated by eq 3, and the results of thermal expansion coefficients were listed in Table S1 (Supporting Information) with an uncertainty of 0.0005 K−1. On the basis of experimental results, the diagram for the coefficient of thermal expansion versus the molality at different temperatures was plotted in Figure 2. It can clearly be seen that the coefficient of thermal expansion for LiB5O6(OH)4 aqueous solution increased with increasing molality at low temperature and decreased with increasing molality at high temperature. Generally, the coefficient of

H3BO3 + C6H14O6 → C6H8(OH)2 · (BO3H)2 + 4H 2O C6H8(OH)2 ·(BO3H)2 + 2NaOH → C6H8(OH)2 · (BO3Na)2 + 2H 2O

Table 2. Results of Chemical Analysis for the Synthesis of LiB5O6(OH)4·3H2Oa LiB5O6(OH)4·3H2Ob

Li2O

B2O3

H2O

mole ratio Li2O:B2O3:H2O

theoretical value experimental value

0.06250 0.06171

0.31250 0.31135

0.62500 0.62694

1:5:10 1:5.05:10.16

a

Standard uncertainties u are u(xLi2O) = 0.00021, u(xB2O3) = 0.00002, and u(xH2O) = 0.00032 in mole fraction. bThe molar mass and purity for LiB5O6(OH)4·3H2O are 278.99 g·mol−1 and 0.9963 in mass fraction. B



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Table 3. Results of Densities (ρs) and Apparent Molar Volumes (Vϕ) of the Binary System (LiB5O6(OH)4 + H2O) at Different Temperatures (T) and Molalities (mi) at 101.325 kPaa mi (mol·kg−1)

ρs (g·cm−3)

0.09859 0.19272 0.26487 0.47730 0.57389 0.66232 0.81723 0.89493 0.00000

1.01477 1.02896 1.03965 1.07029 1.08393 1.09750 1.12416 1.13759 0.99966

0.09859 0.19272 0.26487 0.47730 0.57389 0.66232 0.81723 0.89493 0.00000

1.01174 1.02558 1.03603 1.06602 1.07940 1.09271 1.11889 1.13210 0.99707

0.09859 0.19272 0.26487 0.47730 0.57389 0.66232 0.81723 0.89493 0.00000

1.00669 1.02032 1.03061 1.06017 1.07336 1.08649 1.11235 1.12541 0.99232

0.09859 0.19272 0.26487 0.47730 0.57389 0.66232 0.81723 0.89493 0.00000

1.00006 1.01355 1.02373 1.05301 1.06607 1.07909 1.10472 1.11766 0.98587

0.09859 0.19272 0.26487 0.47730 0.57389 0.66232 0.81723 0.89493 0.00000

0.99209 1.00550 1.01562 1.04472 1.05770 1.07063 1.09612 1.10899 0.97802

0.09859 0.19272 0.26487 0.47730 0.57389 0.66232 0.81723 0.89493 0.00000

0.98296 0.99632 1.00641 1.03541 1.04835 1.06123 1.08663 1.09945 0.96895

Vϕ (cm3·mol−1) T = 283.15 K 70.6316 70.8507 71.1393 71.9080 72.0518 70.3577 64.5758 62.2494 T = 298.15 K 74.8737 74.7078 74.7736 75.1468 75.1417 73.3636 67.4657 65.0682 T = 313.15 K 77.5858 77.0105 76.9551 77.0979 77.0333 75.2041 69.2033 66.7525 T = 328.15 K 78.9910 78.2416 78.1498 78.1650 78.0794 76.1994 70.1305 67.6564 T = 343.15 K 79.6989 78.7603 78.6162 78.5913 78.4975 76.6108 70.4566 67.9490 T = 358.15 K 79.6885 78.7075 78.5277 78.5074 78.4104 76.5129 70.2872 67.7576

ρs (g·cm−3) 1.01403 1.02808 1.03867 1.06907 1.08261 1.09608 1.12256 1.13591 0.99909 1.01026 1.02402 1.03441 1.06423 1.07754 1.09078 1.11685 1.13000 0.99570 1.00464 1.01821 1.02847 1.05792 1.07106 1.08415 1.10992 1.12294 0.99034 0.99754 1.01100 1.02116 1.05036 1.06340 1.07638 1.10196 1.11487 0.98340 0.98917 1.00256 1.01267 1.04172 1.05469 1.06760 1.09305 1.10590 0.97513 0.97969 0.99304 1.00313 1.03210 1.04503 1.05791 1.08328 1.09610 0.96571 C

Vϕ (cm3·mol−1) T = 288.15 K 72.2989 72.3930 72.6151 73.1860 73.2705 71.5439 65.7141 63.3569 T = 303.15 K 75.8893 75.5891 75.6109 75.9163 75.8835 74.0892 68.1420 65.7299 T = 318.15 K 78.1654 77.5516 77.4251 77.5311 77.4588 75.6085 69.5892 67.1248 T = 333.15 K 79.3400 78.4945 78.3658 78.3861 78.2739 76.4005 70.2974 67.8154 T = 348.15 K 79.8124 78.8257 78.6499 78.6380 78.5260 76.6344 70.4605 67.9451

ρs (g·cm−3) 1.01301 1.02694 1.03746 1.06764 1.08109 1.09448 1.12080 1.13407 0.99821 1.00857 1.02226 1.03260 1.06228 1.07552 1.08871 1.11466 1.12776 0.99411 1.00243 1.01595 1.02617 1.05553 1.06863 1.08168 1.10738 1.12035 0.98818 0.99488 1.00831 1.01846 1.04760 1.06060 1.07356 1.09909 1.11198 0.98078 0.98613 0.99950 1.00960 1.03862 1.05157 1.06447 1.08989 1.10272 0.97211

Vϕ (cm3·mol−1) T = 293.15 K 73.6440 73.6602 73.7757 74.2441 74.2882 72.5254 66.6609 64.2883 T = 308.15 K 76.7929 76.3564 76.3252 76.5527 76.5139 74.6879 68.7248 66.2945 T = 323.15 K 78.5303 77.9268 77.8102 77.8726 77.7899 75.9300 69.8821 67.4221 T = 338.15 K 79.5763 78.6854 78.4957 78.5143 78.4251 76.5327 70.4062 67.9094 T = 353.15 K 79.8100 78.8269 78.6341 78.6107 78.5094 76.6024 70.4047 67.8857

T = 363.15 K 79.7739 78.6887 78.4522 78.4392 78.3392 76.4152 70.1729 67.6202



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Table 3. continued Standard uncertainties u are u(T) = 0.01 K and u(p) = 5 kPa. u(m) for the LiB5O6(OH)4 aqueous solution is 0.00015 mol·kg−1, u(ρ) for ρ is 0.00095 g·cm−3, and u(Vϕ) for Vϕ is 0.0035 cm3·mol−1. a

Figure 1. Comparison between the experimental density and literature13 for the binary system (LiB5O6(OH)4 + H2O) at 288.15 (a), 298.15 (b), 308.15 (c), and 318.15 (d) K.

3.2. Apparent Molar Volume and Partial Molar Volume of Aqueous LiB5O6(OH)4. The apparent molar volumes were calculated by the measuring densities of LiB5O6(OH)4 aqueous solution and pure water listed in Table 3 according to the following equation

Table 4. Coefficients (Ai) with Three-Dimensional Variables of eq 1 with the Correlation Coefficients (r) and Standard Deviations m (mol·kg−1)

A0

104 A1

106 A2

r

SD

0.09859 0.19272 0.26487 0.47730 0.57389 0.66232 0.81723 0.89493

1.0166 1.0310 1.0419 1.0729 1.0867 1.1004 1.1274 1.1410

−1.2137 −1.4605 −1.6378 −2.1164 −2.3172 −2.5078 −2.8581 −3.0240

−3.2411 −3.0912 −2.9856 −2.7041 −2.5883 −2.4804 −2.2832 −2.1916

0.999 0.999 0.999 0.999 1 1 1 1

0.00005. 0.00002 0.00002 0.00003 0.00002 0.00002 0.00002 0.00002

Vϕ = 1000 × (ρw − ρs )/(mi × ρs × ρw ) + Mi /ρs

(4)

where mi is the molality (mol·kg−1) of the solute in the solution, Mi is the molar mass of lithium pentaborate in the structure formula of LiB5O6(OH)4 in aqueous solution, and ρw and ρs are the densities (g·cm−3) of pure water and LiB5O6(OH)4(aq), respectively. The calculated apparent molar volumes at different temperatures and molalities with an uncertainty of 0.0035 cm3·mol−1 were listed in Table 3 and plotted in Figure 3. It can obviously be seen that the apparent molar volume of aqueous LiB5O6(OH)4 generally increased

thermal expansion for LiB5O6(OH)4 aqueous solution was gradually evaluated with increasing temperature. D



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with increasing temperature; at low temperature, it first increased and then decreased with increasing molality, and at high temperature, it gradually decreased with increasing molality. According to the changing regulars described above, a conclusion can be drawn that the ionic association of lithium and borate ions is stronger at low temperature and high concentration. In a specified temperature, the apparent molar volume could be fitted by an empirical equation as follows Vϕ = B0 + B1m1/2 + B2 m + B3m3/2 + B4 m2

(5)

where the fitted empirical coefficients Bi were listed in Table 5 and the fitting correlation coefficients (r) are within 0.99 and standard deviations are less than 0.085, which reveals that the experimental values are in good agreement with the fitted values. According to the definition of the relationship between the partial molar volumes14 and the apparent molar volume,

Figure 2. Thermal expansion coefficients of LiB5O6(OH)4·3H2O aqueous solution versus temperature and molality at 101.325 kPa.

ji ∂Vϕ zyz VB̅ = Vϕ + mjjj zz k ∂m { P , T

(6)

Simultaneous to eqs 5 and 6, the partial molar volume at a certain temperature and pressure could be calculated by eq 7: VB̅ = Vϕ +

1 3 B1m1/2 + B2 m + B3m3/2 + 2B4 m2 2 2

(7)

The calculated results with an uncertainty of 0.0035 cm3· mol−1 were listed in Table S2 (Supporting Information) and plotted in Figure 4. As shown in Figure 4, the partial molar volumes first increased and then sharply decreased with increasing molality and gradually increased with increasing temperature. 3.3. Pitzer Parameters of the Binary System (LiB5O6(OH)4 + H2O). Pitzer’s electrolyte solution theory is widely used to evaluate the thermodynamic properties of aqueous solution. The relationship between the apparent molar volumes and molality can be described by the Pitzer equation of volumetric properties employed by Archer15,16 as follows:

Figure 3. Apparent molar volumes of LiB5O6(OH)4·3H2O aqueous solution versus temperature and molality at 101.325 kPa.

Table 5. Coefficients (Bi) with Five-Dimensional Variables of Apparent Molar Volume in eq 5 with the Correlation Coefficients (r) and Standard Deviations T (K)

102 B0

102 B1

102 B2

102 B3

102 B4

r

SD

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15

0.8354 0.8495 0.8592 0.8869 0.9085 0.9255 0.9422 0.9432 0.9463 0.9722 0.9872 0.9860 0.9936 1.0017 0.9987 0.9957 1.0069

−0.7819 −0.7504 −0.7101 −0.8023 −0.8686 −0.9083 −0.9566 −0.9115 −0.9117 −1.0538 −1.1237 −1.0843 −1.1292 −1.1717 −1.1488 −1.1347 −1.1921

1.2684 1.1663 1.0365 1.2217 1.3490 1.4054 1.4883 1.3491 1.3637 1.6915 1.8321 1.6935 1.8041 1.8913 1.8278 1.7868 1.8851

−0.0389 0.0632 0.2072 0.0330 −0.0794 −0.1150 −0.1814 −0.0183 −0.0489 −0.3777 −0.5003 −0.3191 −0.4353 −0.5124 −0.4392 −0.3862 −0.4541

−0.7236 −0.7581 −0.8135 −0.7523 −0.71605 −0.70869 −0.6892 −0.7560 −0.7399 −0.6201 −0.5819 −0.6625 −0.6191 −0.5950 −0.6256 −0.6503 −0.6363

0.991 0.998 0.998 0.999 0.999 0.999 0.999 1 1 0.999 0.999 0.999 0.999 0.999 1 1 1

0.085 0.033 0.026 0.022 0.022 0.022 0.022 0.020 0.020 0.022 0.022 0.022 0.022 0.022 0.018 0.020 0.015

E



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the temperature-dependent and pressure-dependent parameters for volumetric ion interaction. The Pitzer ion interaction parameters of the apparent molar volumes at different temperatures could be expressed as functions f(i, p, T): v ß(0) M,X = f (1, p , T )

(13)

v ß(1) M,X = f (2, p , T )

(14)

v ß(2) M,X = f (3, p , T )

(15)

v CM,X = f (3, p , T )

(16)

with f(i, p, T) represented as f (i , p , T ) = a1 + a 2 ln(T /298.15) + a3(T − 298.15) + a4 /(620 − T ) + a5(T − 227)

Figure 4. Partial molar volumes of LiB5O6(OH)4·3H2O aqueous solution versus temperature and molality at 101.325 kPa.

where T is the temperature in Kelvin, p is the pressure in MPa, and ai are the polynomial coefficients of the temperaturedependent eq 17. All of the thermodynamic and dielectric property parameters of water involved in this Article were calculated by the reported equations in ref 18. On the basis of the apparent molar volumes obtained in this experiment and Pitzer equations of volumetric properties, the Pitzer single salt parameters and limiting partial molar volume of LiB5O6(OH)4 aqueous solution at temperatures from 283.15 to 363.15 K at 101.325 kPa were fitted by the leastsquares method on the basis of eqs 8−12 and listed in Table 6.

Vϕ = V (mr )/nr − vw /nr + v|z Mz X| × (Av /2b) × ln[(1 + bI1/2)/(1 + bIr1/2)] + 2vM × vX v v × RT{m × BM,X (m) − mr × BM,X (m r ) v + vM × z M × CM,X × (m 2 − m r 2 )}

(8)

The relationship between BvM,X(m) and ionic strength (I) of aqueous solution was expressed as follows: v v (1)v 1/2 v 1/2 BM,X = ß(0) ) + ß(2) ) M,X + ß M,X × g (αB1· I M,X × g (αB2 · I

Table 6. Pitzer Single Salt Parameters of LiB5O6(OH)4 at Different Temperatures

(9)

g (t ) = 2 × [1 − (1 + t ) exp( − t )] /t 2

(10)

Meanwhile, eq 8 could be rearranged to yield the working equation14,15 for aqueous solution of LiB5O6(OH)4 as follows Vϕ = VB̅ 0 + v|z Mz X| × (Av /2b) × ln[(1 + bI1/2)] v + 2vM × vX × RT (m × BM,X (m) + m2 × vM × z M v × CM,X )

(11)

−1

where m (mol·kg ) is the molality of LiB5O6(OH)4 aqueous solution, vw is the volume of 1 kg of pure water, V(mr) is the volume of mr, where mr = 0.15 mol·kg−1, nr = 0.15 mol, which is the number of moles of solute in this quantity of solution, Av is the Debye−Hückel limiting-law slope for the apparent molar volume fitted by the literature,17 z are the charges of each ion, zM and zX are the charges of the cation and anion, such as LiB5O6(OH)4 (zM = 1, zX = 1), vM and vX are the numbers of M and X ions formed by stoichiometric dissociation of one molecule of MX, and v = vM + vX, as for LiB5O6(OH)4(vM = 1, vX = 1, v = 2), αB1 = 1.4 kg1/2·mol1/2, αB2 = 1.5 kg1/2·mol1/2, b = 1.2 kg1/2·mol−1/2, t represented the independent variables in eq 9, which were αB1·I1/2 and αB2·I1/2, respectively, and the ionic strength I (mol·kg−1) of the solution is calculated as I = (1/2) ∑ mizi 2

(12) −1

T (K)

V̅ 0B

β(0)v

β(1)v

β(2)v

C(0)v

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15

−7.6401 −8.0389 −7.8125 −7.9194 −7.9071 −7.7658 −7.6236 −7.7002 −7.9802 −7.8247 −7.9223 −7.2373 −8.0801 −8.1236 −8.0262 −8.3489 −7.9802

−0.0782 −0.0708 −0.0401 −0.0798 −0.0821 −0.0819 −0.0904 −0.0841 −0.0823 −0.0990 −0.1057 −0.1003 −0.1032 −0.1058 −0.1100 −0.1023 −0.1064

2.6958 2.5186 1.7678 2.7149 2.7609 2.7516 2.9465 2.8018 2.7405 3.1181 3.2609 3.1471 3.2040 3.2599 3.3495 3.1741 3.2626

−2.6622 −2.4913 −1.7625 −2.6812 −2.7256 −2.7166 −2.9052 −2.7656 −2.7052 −3.0696 −3.2068 −3.0980 −3.1523 −3.2062 −3.2924 −3.1231 −3.2083

−0.0043 −0.0051 −0.0091 −0.0034 −0.0028 −0.0027 −0.0013 −0.0021 −0.0021 0.0005 0.0017 0.0009 0.0014 0.0020 0.0027 0.0016 0.0024

The temperature-dependent coefficients ai were fitted by eqs 13−17 and shown in Table 7, and the fitted results of each (1)v (2)v v single salt parameter ß(0)v M,X, ßM,X, ßM,X, and CM,X were in good agreement with the experimental values, which indicated that the Pitzer model we constructed is suitable to describe the volumetric properties of the binary system (LiB5O6(OH)4 + H2O). On the basis of temperature-dependent coefficients and calculated Pitzer single salt parameters, the apparent molar volume for LiB5O6(OH)4 aqueous solution at each temperature from 283.15 to 363.15 K could be predicted, not only for

−1

R = 8.314472 cm ·MPa·K ·mol is the gas constant, T is the temperature in Kelvin. V̅ 0B is the limiting partial molar volume of LiB5O6(OH)4 aqueous solution, and BvM,X(m) and CvM,X are 3

(17)

F



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Table 7. Relational Coefficients of Pitzer Parameters of LiB5O6(OH)4 polynomial coefficient Pitzer parameters

a1

β β(1)v β(2)v C(0)v

9.7287 × 10 −2.4091 × 102 2.3439 × 102 −1.3331 × 100

(0)v

a2 0

a3

−4.4445 × 10 1.0915 × 103 −1.0611 × 103 6.1181 × 100

1.6044 × 10 −3.9564 × 10° 3.8476 × 10° −2.1965 × 10−2

4. CONCLUSION The new experimental data on the volumetric properties of the binary system (LiB5O6(OH)4 + H2O) from 283.15 to 363.15 K at 101.325 kPa were reported for the first time. It reveals the changing regulars about densities, the apparent molar volumes, thermal expansion coefficients, and partial molar volumes of LiB5O6(OH)4 aqueous solution with temperature T and molality m. On the basis of the apparent molar volumes we obtained and Pitzer ion interaction theory, the Pitzer (1)v (2)v v parameters V̅ 0B, ß(0)v M,X, ßM,X, ßM,X, and CM,X and the temperature-dependence coefficient ai were obtained, and eventually, a reliable model was constructed.

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−2.8109 × 10 7.0027 × 104 −6.8166 × 104 3.8008 × 102

−7.5633 × 101 1.8328 × 103 −1.7791 × 103 1.0466 × 101

REFERENCES

(1) Zheng, X. J. Development and application prospects of boron and borate products. Inorg. Chem. Ind. 2014, 4, 1−4. (2) Mutailipu, M.; Xie, Z. Q.; Su, X.; Zhang, M.; Wang, Y.; Yang, Z. H.; Pan, S. L. Chemical cosubstitution-oriented design of rare-earth borates as potential ultraviolet nonlinear optical materials. J. Am. Chem. Soc. 2017, 139, 18397−18405. (3) Trocoli, R.; Battistel, A.; Mantia, F. L. Selectivity of a lithiumrecovery process based on LiFePO4. Chem. - Eur. J. 2014, 20, 9888− 9891. (4) Liu, Z. H.; Gao, S. Y.; Xia, S. P. FT-IR spectroscopic study of phase transformation of chloropinnoite in boric acid solution at 303 K. Spectrochim. Acta, Part A 2003, 59, 265−270. (5) Christ, C. L.; Clark, J. R. A crystal-chemical classification of borate structures with emphasis on hydrated borates. Phys. Chem. Miner. 1977, 2, 59−87. (6) Li, J.; Gao, S. Y. Chemistry of borates. J. Salt Lake Res. 1993, 3, 62−67. (7) Ge, H. W.; Fang, C. H.; Fang, Y.; Zhou, Y. Q.; Liu, H. Y. Physical properties of aqueous LiB5O6(OH)4 solution: Density, viscosity, conductivity and pH. J. Salt Lake Res. 2015, 1, 45−50. (8) Li, J.; Li, B.; Gao, S. Y. Thermochemistry of hydrated lithium borates. J. Chem. Thermodyn. 1998, 30, 681−688. (9) Cui, W. J.; Li, L.; Guo, Y. F.; Zhang, S. S. Heat capacity and thermodynamic property of lithium pentaborate pentahydrate. J. Chem. 2018, 2018, 7962739. (10) Zhang, S. S.; Li, L.; Guo, Y. F.; Deng, T. L. Studies on the syntheses of alkalis pentaborates. J. Salt Sci. Chem. Ind. 2017, 6, 31− 34. (11) Ge, H. W.; Yao, Y.; Deng, T. L. Improvement of boron analysis method based on mass titration of brines. Chem. Res. Appl. 2017, 29, 12−17. (12) Speight, J. M. Lange’s Handbook of Chemistry; McGraw-Hill: New York, 2005; pp 1−1815. (13) Ge, H. W.; Fang, Y.; Fang, C. H.; Zhou, Y. Q.; Zhu, F. Y.; Liu, H. Y.; Yang, Z. X.; Tang, Y. L. Density, electrical conductivity, pH and polyborate distribution of LiB(OH) 4 Li 2 B 4 O 5 (OH) 4 and LiB5O6(OH)4 solutions. J. Chem. Eng. Data 2014, 59, 4039−4048. (14) Xu, W. G.; Qin, Y.; Gao, F.; Liu, J. G.; Yan, C. W.; Yang, J. Z. Determination of volume properties of aqueous vanadyl sulfate at 283.15 to 323.15 K. Ind. Eng. Chem. Res. 2014, 53, 7217−7223. (15) Krumgalz, B. S.; Pogorelsky, R.; Iosilevskii, Y. A.; Weiser, A.; Pitzer, K. S. Ion interaction approach for volumetric calculations for solutions of single electrolytes at 25°C. J. Solution Chem. 1994, 23, 849−875. (16) Zezin, D.; Driesner, T.; Scott, S.; Sanchez-Valle, C.; Wagner, T. Volumetric properties of mixed electrolyte aqueous solutions at elevated temperatures and pressures. The systems CaCl2+ NaCl + H2O and MgCl2+ NaCl + H2O to 523.15 K, 70 MPa, and ionic strength from (0.1 to 18) mol·kg−1. J. Chem. Eng. Data 2014, 59, 2570−2588.

ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.8b00814.

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a5 3

ßvM,X Short-range interactions between M and X of Pitzer’s parameters CvM,X Triple ion interactions of volumetric Pitzer parameters ai Temperature-dependent coefficients of Pitzer single salt parameters

the experimental temperature, which is meaningful for the actual application.

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a4 −1

1

Values of the thermal expansion coefficient (a) and the partial molar volume (V̅ B) of LiB5O6(OH)4 aqueous solution in Tables S1 and S2 as well as the TG-DSC curve and XRD pattern for the synthesis of LiB5O6(OH)4·3H2O in Figures S1 and S2 (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone and Fax: +86-2260601156. ORCID

Yafei Guo: 0000-0003-0698-3565 Lingzong Meng: 0000-0002-2904-7000 Tianlong Deng: 0000-0002-1728-2943 Funding

The authors gratefully acknowledge partial financial support from the National Natural Science Foundation of China (U1607123 and 21773170), the Key Projects of Natural Science Foundation of Tianjin (18JCZDJC10040), the Major Special Projects of Tibet Autonomous Region (XZ201801-GB01), and the Yangtze Scholars and Innovative Research Team of the Chinese University (IRT_17R81). Notes

The authors declare no competing financial interest.

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ABBREVIATIONS m Molality ρ Density a Thermal expansion coefficient Vϕ Apparent molar volume V̅ B Partial molar volume G



Article

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Apparent Molar Volumes of Aqueous Solutions of Lithium Pentaborate

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