# Phase Equilibria and Phase Diagrams for the Ternary Aqueous System Containing Lithium, Sodium, and Pentaborate Ions at 298.15 and 323.15 K and 101.325 kPa

Authors: Panpan Li; Kaiyu Zhao; Shangqing Chen; Jiayin Hu; Yafei Guo; Mingli Li; Ji Duo; Tianlong Deng
Journal: Journal of Chemistry
 (2019)

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## Abstract

Phase equilibria and phase diagrams for the ternary aqueous system containing lithium, sodium, and pentaborate ions at 298.15 and 323.15 K and 101.325 kPa were investigated by the methods of isothermal dissolution equilibrium. From the experimental data, the phase diagrams and the diagrams of physicochemical properties versus composition of lithium pentaborate in the equilibrium systems were plotted, respectively. The phase diagrams of the ternary system LiB5O8 + NaB5O8 + H2O at two temperatures contain one invariant point, two univariant curves, and two crystallization regions corresponding to sodium pentaborate pentahydrate (NaB5O8·5H2O) and lithium pentaborate pentahydrate (LiB5O8·5H2O). Due to the different dissolution behaviors of pentaborate salts in the aqueous systems, the component of LiB5O8 has a relatively strong effect on the solubility of NaB5O8. It was found that this system belongs to a simple eutectic type at two temperatures, and neither double salts nor solid solutions were formed. The densities and refractive indices in the ternary system at 298.15 and 323.15 K are as similar as changing regularly with the increase of LiB5O8 concentration. On the basis of empirical equations of the density and refractive index in electrolytes, the calculated values of density and refractive index agreed well with the experimental values at two temperatures.


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## Body

## 1. Introduction

Borates not only occupy an important role in the modern inorganic salt industry but also have been widely used in electronic manufacturing, new type of electrode materials, and nonlinear optical materials for their excellent characteristics, so the demand for borates is sharply increasing nowadays [1–3]. Due to the rapid depletion of solid boron mineral resources, the comprehensive exploitation for brine resources such as salt lake brines, underground brines, and geothermal waters has become the research hotspots around the world at present [4]. The phase diagram and phase equilibrium as well as the corresponding physicochemical properties are essential to give a theoretical guidance for exploiting the available brine resources and describing the thermodynamic behaviors for the salt minerals. It is well known that salt lake brine located in the Qaidam Basin of Qinghai-Tibet Plateau is famous for its high concentrations of lithium, sodium, potassium, and boron. Therefore, it is highly desirable to study the phase equilibria and phase diagram for the systems containing lithium, sodium, and boron [5, 6].In recent years, lots of phase diagram containing borates including LiBO2 + CaB2O4 + H2O at 288.15 and 298.15 K [7], MgCl2 + MgSO4 + MgB6O10 + H2O at 323.15 K [8], MgB4O7 + Na2B4O7 + Li2B4O7 + H2O at 288 K [9], K2B4O7 + Na2B4O7 + Li2B4O7 + H2O at 273 K [10], MgCl2 + MgB6O10 + H2O and MgSO4 + MgB6O10 + H2O at 323.15 K [11], and Li2B4O7 + MgB4O7 + H2O and K2B4O7 + MgB4O7 + H2O at 273 K [12] have been reported. The existed forms of borates in the reported phase diagrams are mainly concentrated on BO2−, B4O72−, and B6O102−. However, the solubility data containing B5O8− are still lacking in the literature. In order to make comprehensive utilization and give a theoretical guidance for the actual production of salt lake brines containing pentaborate ions, the solubilities and corresponding physicochemical properties of the ternary systems LiB5O8 + NaB5O8 + H2O at 298.15 and 323.15 K were reported for the first time in this paper.


## 2. Experimental

### 2.1. Reagents and Apparatus

The chemicals used in this work are shown in Table1. And, LiB5O8·5H2O and NaB5O8·5H2O were successfully synthesized in our laboratory based on the method described previously in detail [13]. In brief, according to the molar ratio of LiOH·H2O : H3BO3 : H2O = 1 : 5 : 10 and Na2B4O7·10H2O : H3BO3 : H2O = 1 : 5 : 10, a certain amount of LiOH·H2O or Na2B4O7·10H2O, H3BO3, and fresh CO2-free deionized distilled water (DDW) were added in two beakers to synthesize LiB5O8·5H2O and NaB5O8·5H2O, respectively. Then, they were stirred for homogeneity at room temperature, and then transferred into two reactors to react for 7 d at 60°C under stirring with 200°rmp, respectively. Finally, LiB5O8·5H2O and NaB5O8·5H2O were produced after separation, filtration, washing and recrystallization, and drying at 35°C for use. And the synthetic samples were analyzed by chemical analysis and identified by the X-ray diffraction, and the results are shown in Table 1 and Figures 1 and 2, respectively. From the XRD patterns, it is shown that the peak positions and intensities of the synthesized chemicals LiB5O8·5H2O and NaB5O8·5H2O agree well with that of the standard samples. The DDW produced using a deionizer (ULUP-II-10T Sichuan Ulupure Co. Ltd., China) with conductivity less than 1 × 10−4 S·m−1 and pH = 6.60 at 298.15 K was used during the whole experiment [14].Table 1
Chemical samples used in this study.
Chemical
Source
Initial mass fraction
Purification method
Final mass fraction
Analytical method
H3BO3
bA.R.
0.99
No further purification
—
Gravimetric method for B(OH)3
LiOH·H2O
aA.R.
0.99
No further purification
—
Titration method for OH−
Na2B4O7·10H2O
bA.R.
0.99
No further purification
—
Gravimetric method for B4O72−
LiB5O8·5H2O
cA.R.
0.99
Recrystallization
0.998
Gravimetric method for B5O8−
NaB5O8·5H2O
cA.R.
0.99
Recrystallization
0.998
Gravimetric method for B5O8−
aA.R. from the Shanghai Macklin Biochemical Co. Ltd. bA.R. from the Simopharm Chemical Reagent Co. Ltd. cA.R. synthesized in our laboratory.Figure 1
X-ray diffraction pattern of NaB5O8·5H2O.Figure 2
X-ray diffraction pattern of LiB5O8·5H2O.A magnetic stirring thermostatic water bath (HXC-500-6A, Beijing Fortune Joy Science Technology Co. Ltd, China) was employed for controlling the temperature with a precision of ±0.1 K for the phase equilibrium experiments. The refractive indices (nD) were measured by an Abbe refractometer (Abbemat 550, Anton Paar, Austria) with an uncertainty of ±0.0003. The densities (ρ) were measured using a digital U-tube densimeter (DMA 4500, Anton Paar, Austria) with an uncertainty of ±0.5 mg·cm−3. The standard uncertainties u(x) for pressure, temperature, and composition are u(p) = 5 kPa, u(T) = 0.1 K, u(LiB5O8) = 0.00063, and u(NaB5O8) = 0.00060. An X-ray diffractometer (MSAL XD-3, Beijing Purkinje Instrument Co. Ltd, China) was used to identified the solid phase [15].


### 2.2. Experimental Methods

The solid-liquid-phase equilibrium of the ternary system LiB5O8 + NaB5O8 + H2O at 298.15 and 323.15 K was studied by the isothermal dissolution equilibrium method as described previously [16]. On the basis of the binary solubility, a series of artificial synthetic complexes were prepared by mixing lithium pentaborate and sodium pentaborate with DDW. Then, complexes were put into the sealed polyethylene plastic bottles, which were placed in magnetic stirring thermostatic water baths with continuous stirring in order to accelerate the establishment of equilibrium states, and the temperatures were automatically controlled for T = 298.15 ± 0.1 and 323.15 ± 0.1 K using magnetic stirring thermostatic water baths, respectively. Then, the composition of the liquid phase in the bottle was for quantitative chemical analysis at seven-day intervals. If the composition of the liquid phase became constant, it indicated that the solid-liquid-phase equilibrium was achieved. Generally, the equilibration time is about 90 days. After equilibrium was achieved, the magnetic stirrer was stopped to separate the solid phase from the liquid phase for 6 hours. When the complexes in bottles were clarified, the liquid phases were taken out for quantitative chemical analysis and physicochemical properties measurements (density and refractive index). In addition, the equilibrium solid phase was identified by X-ray diffraction [17].


### 2.3. Analytical Methods

The borate ion concentration was determined by the mannitol gravimetric method with sodium hydroxide standard solution and the mixture indicator of methyl red and phenolphthalein with an uncertainty of 0.0005 in mass fraction. The concentration of Li+ and Na+ was measured using an inductively coupled plasma optical emission spectrometer (ICP-OES, Prodigy, Leman Corporation, America. Precision: ±0.01), and then evaluated using ion balance [18].


## 2.1. Reagents and Apparatus

The chemicals used in this work are shown in Table1. And, LiB5O8·5H2O and NaB5O8·5H2O were successfully synthesized in our laboratory based on the method described previously in detail [13]. In brief, according to the molar ratio of LiOH·H2O : H3BO3 : H2O = 1 : 5 : 10 and Na2B4O7·10H2O : H3BO3 : H2O = 1 : 5 : 10, a certain amount of LiOH·H2O or Na2B4O7·10H2O, H3BO3, and fresh CO2-free deionized distilled water (DDW) were added in two beakers to synthesize LiB5O8·5H2O and NaB5O8·5H2O, respectively. Then, they were stirred for homogeneity at room temperature, and then transferred into two reactors to react for 7 d at 60°C under stirring with 200°rmp, respectively. Finally, LiB5O8·5H2O and NaB5O8·5H2O were produced after separation, filtration, washing and recrystallization, and drying at 35°C for use. And the synthetic samples were analyzed by chemical analysis and identified by the X-ray diffraction, and the results are shown in Table 1 and Figures 1 and 2, respectively. From the XRD patterns, it is shown that the peak positions and intensities of the synthesized chemicals LiB5O8·5H2O and NaB5O8·5H2O agree well with that of the standard samples. The DDW produced using a deionizer (ULUP-II-10T Sichuan Ulupure Co. Ltd., China) with conductivity less than 1 × 10−4 S·m−1 and pH = 6.60 at 298.15 K was used during the whole experiment [14].Table 1
Chemical samples used in this study.
Chemical
Source
Initial mass fraction
Purification method
Final mass fraction
Analytical method
H3BO3
bA.R.
0.99
No further purification
—
Gravimetric method for B(OH)3
LiOH·H2O
aA.R.
0.99
No further purification
—
Titration method for OH−
Na2B4O7·10H2O
bA.R.
0.99
No further purification
—
Gravimetric method for B4O72−
LiB5O8·5H2O
cA.R.
0.99
Recrystallization
0.998
Gravimetric method for B5O8−
NaB5O8·5H2O
cA.R.
0.99
Recrystallization
0.998
Gravimetric method for B5O8−
aA.R. from the Shanghai Macklin Biochemical Co. Ltd. bA.R. from the Simopharm Chemical Reagent Co. Ltd. cA.R. synthesized in our laboratory.Figure 1
X-ray diffraction pattern of NaB5O8·5H2O.Figure 2
X-ray diffraction pattern of LiB5O8·5H2O.A magnetic stirring thermostatic water bath (HXC-500-6A, Beijing Fortune Joy Science Technology Co. Ltd, China) was employed for controlling the temperature with a precision of ±0.1 K for the phase equilibrium experiments. The refractive indices (nD) were measured by an Abbe refractometer (Abbemat 550, Anton Paar, Austria) with an uncertainty of ±0.0003. The densities (ρ) were measured using a digital U-tube densimeter (DMA 4500, Anton Paar, Austria) with an uncertainty of ±0.5 mg·cm−3. The standard uncertainties u(x) for pressure, temperature, and composition are u(p) = 5 kPa, u(T) = 0.1 K, u(LiB5O8) = 0.00063, and u(NaB5O8) = 0.00060. An X-ray diffractometer (MSAL XD-3, Beijing Purkinje Instrument Co. Ltd, China) was used to identified the solid phase [15].


## 2.2. Experimental Methods

The solid-liquid-phase equilibrium of the ternary system LiB5O8 + NaB5O8 + H2O at 298.15 and 323.15 K was studied by the isothermal dissolution equilibrium method as described previously [16]. On the basis of the binary solubility, a series of artificial synthetic complexes were prepared by mixing lithium pentaborate and sodium pentaborate with DDW. Then, complexes were put into the sealed polyethylene plastic bottles, which were placed in magnetic stirring thermostatic water baths with continuous stirring in order to accelerate the establishment of equilibrium states, and the temperatures were automatically controlled for T = 298.15 ± 0.1 and 323.15 ± 0.1 K using magnetic stirring thermostatic water baths, respectively. Then, the composition of the liquid phase in the bottle was for quantitative chemical analysis at seven-day intervals. If the composition of the liquid phase became constant, it indicated that the solid-liquid-phase equilibrium was achieved. Generally, the equilibration time is about 90 days. After equilibrium was achieved, the magnetic stirrer was stopped to separate the solid phase from the liquid phase for 6 hours. When the complexes in bottles were clarified, the liquid phases were taken out for quantitative chemical analysis and physicochemical properties measurements (density and refractive index). In addition, the equilibrium solid phase was identified by X-ray diffraction [17].


## 2.3. Analytical Methods

The borate ion concentration was determined by the mannitol gravimetric method with sodium hydroxide standard solution and the mixture indicator of methyl red and phenolphthalein with an uncertainty of 0.0005 in mass fraction. The concentration of Li+ and Na+ was measured using an inductively coupled plasma optical emission spectrometer (ICP-OES, Prodigy, Leman Corporation, America. Precision: ±0.01), and then evaluated using ion balance [18].


## 3. Results and Discussion

In order to evaluate and test the reliability of the experimental method in this work, a comparison of the solubilites in the boundary subsystems NaB5O8 + H2O at 298.15 and 323.15 K in literature [19] is summarized in Table 2. The results show that the experimental results in this work agree well with previous reports, demonstrating that our experimental procedure and results are rational reliable and rational. The experimental solubilities and the relevant physicochemical properties including density and refractive index for the ternary systems LiB5O8 + NaB5O8 + H2O at 298.15 and 323.15 K and 101.325 kPa are presented in Table 3, respectively. The composition of the liquid phase was expressed in mass fraction.Table 2
Solubilities in the binary subsystems NaB5O8 + H2O at 298.15 and 323.15 K and 0.1 MPaa.
Binary system
T (K)
Solubility (100wb)
Ref.
NaB5O8 + H2O
298.15
12.20
19
12.23
This work
323.15
21.80
19
20.73
This work
aStandard uncertainties u are u(T) = 0.1 K and u(p) = 5 kPa. uw for NaB5O8 is 0.00060 in mass fraction. bw is the mass fraction.Table 3
Solubilities, refractive indices, and densities for ternary system LiB5O8 + NaB5O8 + H2Oa.
No.
Composition of liquid phase (100wb)
Density,ρ (g·cm−3)
Refractive index (nD)
Equilibrium solid phasec
LiB5O8
NaB5O8
Exp. Value
Cal. Value
Relative error (%)
Exp. Value
Cal. Value
Relative error (%)
T = 298.15 K and p = 0.1 MPa
1,A
14.00
0.00
1.10136
1.096286
0.46
1.353170
1.352497
0.05
LB5
2
13.71
1.92
1.10231
1.108264
−0.54
1.353425
1.354508
−0.08
LB5
3
13.12
2.57
1.10473
1.108647
−0.35
1.353711
1.354481
−0.06
LB5
4
11.77
3.78
1.10618
1.107469
−0.12
1.353998
1.354067
−0.01
LB5
5,E
9.87
4.69
1.10757
1.099968
0.69
1.354261
1.352483
0.13
LB5 + NB5
6
4.52
8.88
1.09087
1.090923
0.00
1.349830
1.350084
−0.02
NB5
7
3.48
9.64
1.08973
1.088776
0.09
1.349583
1.349549
0.00
NB5
8
0.96
12.12
1.08658
1.088226
−0.15
1.348849
1.349059
−0.02
NB5
9,B
0.00
12.23
1.08213
1.081964
0.02
1.347858
1.347821
0.00
NB5
T = 323.15 K and p = 0.1 MPa
1,A
0.00
20.73
1.14023
1.130639
0.84
1.356293
1.354688
0.12
NB5
2
5.12
18.17
1.14082
1.151091
−0.90
1.356541
1.358206
−0.12
NB5
3
9.82
13.20
1.14404
1.150421
−0.56
1.357015
1.358158
−0.08
NB5
4
12.96
9.46
1.14623
1.146839
0.05
1.357495
1.357601
0.01
NB5
5,E
14.80
7.60
1.15309
1.147217
0.51
1.358599
1.357689
0.07
LB5 + NB5
6
15.70
6.04
1.15109
1.142560
0.74
1.358417
1.356919
0.11
LB5
7
17.55
5.21
1.14925
1.150696
0.13
1.358121
1.358310
−0.01
LB5
8
19.11
3.68
1.14793
1.151369
−0.30
1.357911
1.358444
−0.04
LB5
9,B
22.19
0.00
1.14747
1.147767
0.03
1.357777
1.357883
−0.01
LB5
aStandard uncertainties u are u(T) = 0.1 K and u(p) = 5 kPa. uw for LiB5O8 and NaB5O8 are 0.00063 and 0.00060 in mass fraction. u(x) for ρ and nD are 0.5 mg·cm−3 and 0.0003, respectively. bw is the mass fraction. cNB5, NaB5O8·5H2O; LB5, LiB5O8·5H2O.


### 3.1. Solubilities of the Binary Systems LiB5O8 + H2O and NaB5O8 + H2O at 298.15 and 323.15 K

The solubilities of binary systems LiB5O8 + H2O and NaB5O8 + H2O at 298.15 and 323.15 K were firstly obtained by the isothermal dissolution equilibrium method in this work. As shown in Table 2, the solubilities of lithium pentaborate in the binary systems LiB5O8 + H2O at 298.15 and 323.15 K in mass fraction of 100w were 14.00 and 22.19, respectively. Analogously, the solubilities of sodium pentaborate in the binary systems NaB5O8 + H2O at 298.15 and 323.15 K in mass fraction of 100w were 12.23 and 20.73, respectively. Obviously, the solubilities of single salts of LiB5O8 or NaB5O8 are increased with the increasing of temperature.


### 3.2. Phase Diagrams of the Ternary System LiB5O8 + NaB5O8 + H2O at 298.15 and 323.15 K

From the experimental data in Table2, the phase diagrams and part enlargement diagrams for the ternary system at 298.15 and 323.15 K are shown in Figures 3 and 4. In Figures 3 and 4, it can be clearly seen that they are all in one invariant point corresponding to E1 at 298.15 K and E2 at 323.15 K, i.e., cosaturated with LiB5O8·5H2O and NaB5O8·5H2O, two univariant solubility curves of A1E1 and B1E1 at 298.15 K, A2E2 and B2E2 at 323.15 K, and two crystallization regions corresponding to LiB5O8·5H2O and NaB5O8·5H2O, respectively. In addition, due to the difference of the solubilities, the area of crystallization region for NaB5O8·5H2O is relatively larger than that for LiB5O8·5H2O at both temperatures. The composition for the two invariant points of LiB5O8 and NaB5O8 in the liquid phase in mass fraction of 100w is 9.87 and 4.69 at 298.15 K and 14.80 and 7.60 at 323.15 K, respectively. The points A1, A2 and B1, B2 present the solubilities of the binary systems LiB5O8 + H2O and NaB5O8 + H2O at two temperatures, respectively. At both temperatures, the component of NaB5O8 in the ternary system is decreased sharply with the increase of jLiB5O8 concentration in the solution, so it indicates that the component of lithium pentaborate existing in the solution has a strong salting-out effect of NaB5O8. The same coexisted equilibrium solid phases in the invariant points E1 and E2 identified by the powder X-ray diffraction are presented in Figure 5. A comparison for the ternary system LiB5O8 + NaB5O8 + H2O at 298.15 and 323.15 K shows is in Figure 6. It can be clearly seen that the solubilities for the ternary system LiB5O8 + NaB5O8 + H2O increased with the increase of temperature, but the crystallization regions for LiB5O8·5H2O and NaB5O8·5H2O did not change obviously with changing temperature. And, this ternary system at two temperatures belongs to a simple eutectic type, and neither double salts nor solid solutions were formed.Figure 3
Phase diagram and part enlargement of the compositions of the ternary system LiB5O8 + NaB5O8 + H2O at 298.15 K; , experimental points at 298.15 K; —, solubility curve at 298.15 K.Figure 4
Phase diagram for the ternary system LiB5O8 + NaB5O8 + H2O at 323.15 K; •, experimental points at 323.15 K; —, solubility curve at 323.15 K.Figure 5
X-ray diffraction patterns of the solid phase at invariant pointE1 LiB5O8·5H2O + NaB5O8·5H2O.Figure 6
Comparison of phase diagram of the ternary system LiB5O8 + NaB5O8 + H2O at 298.15 and 323.15 K; , experimental points at 298.15 K; , experimental points at 323.15 K; —, solubility curve at 298.15 and 323.15 K.


### 3.3. Refractive Index and Density Calculation

According to the semiempirical formulas of electrolyte aqueous solution with density and refractive index employed by Deng et al. [20], shown as equations (1) and (2), the density and refractive index of the experimental solution were calculated, and the results are listed in Table 3.(1)lnρρ0=∑Ai×wi,(2)lnnDnD0=∑Bi×wi,where ρ and ρ0 are the density of solution and pure water at the same temperature and nD and nD0 represent the refractive index of the solution and pure water at the same temperature, respectively. The ρ0 values at 298.15 and 323.15 K are 0.997041 and 0.988038 g·cm−3, respectively; the nD0 values at 298.15 and 323.15 K are 1.33250 and 1.32904, respectively; and wi is the component same as Table 2. Ai and Bi represent the coefficients for the solid phase i in this system. The Ai and Bi for LiB5O8 and NaB5O8 are shown in Table 4, and the maximal relative deviation of density between experimental and calculated values was 0.0084, as for the refractive index, the deviation was less than 0.0013, which indicates that the physicochemical properties obtained are reliable. On the basis of the data of physicochemical property (including densities and refractive indices) in Table 2, the diagrams of physicochemical properties (density and refractive index) versus the composition of lithium pentaborate in the solution are plotted in Figures 7 and 8, respectively. It could be clearly seen that the density and refractive index changed regularly with the changing of lithium pentaborate concentration in the ternary system at two temperatures, which was increased, and then decreased as the increasing of the concentration of lithium pentaborate concentration, and show a similar changing tendency.Table 4
Coefficients of densities and refractive indices in the ternary system LiB5O8 + NaB5O8 + H2O at 298.15 and 323.15 K and 0.1 MPa.
T (K)
Coefficients
LiB5O8
NaB5O8
298.15
A
i
0.006777954
0.006683650
B
i
0.001063948
0.000934748
323.15
A
i
0.006753151
0.006503464
B
i
0.000967555
0.000922052
aStandard uncertainties u(x) are u(T) = 0.1 K and u(p) = 5 kPa.Figure 7
Comparison of physicochemical properties versus composition diagram of the ternary system LiB5O8 + NaB5O8 + H2O at 298.15 K.Figure 8
Comparison of physicochemical properties versus composition diagram of the ternary system LiB5O8 + NaB5O8 + H2O at 323.15 K.


## 3.1. Solubilities of the Binary Systems LiB5O8 + H2O and NaB5O8 + H2O at 298.15 and 323.15 K

The solubilities of binary systems LiB5O8 + H2O and NaB5O8 + H2O at 298.15 and 323.15 K were firstly obtained by the isothermal dissolution equilibrium method in this work. As shown in Table 2, the solubilities of lithium pentaborate in the binary systems LiB5O8 + H2O at 298.15 and 323.15 K in mass fraction of 100w were 14.00 and 22.19, respectively. Analogously, the solubilities of sodium pentaborate in the binary systems NaB5O8 + H2O at 298.15 and 323.15 K in mass fraction of 100w were 12.23 and 20.73, respectively. Obviously, the solubilities of single salts of LiB5O8 or NaB5O8 are increased with the increasing of temperature.


## 3.2. Phase Diagrams of the Ternary System LiB5O8 + NaB5O8 + H2O at 298.15 and 323.15 K

From the experimental data in Table2, the phase diagrams and part enlargement diagrams for the ternary system at 298.15 and 323.15 K are shown in Figures 3 and 4. In Figures 3 and 4, it can be clearly seen that they are all in one invariant point corresponding to E1 at 298.15 K and E2 at 323.15 K, i.e., cosaturated with LiB5O8·5H2O and NaB5O8·5H2O, two univariant solubility curves of A1E1 and B1E1 at 298.15 K, A2E2 and B2E2 at 323.15 K, and two crystallization regions corresponding to LiB5O8·5H2O and NaB5O8·5H2O, respectively. In addition, due to the difference of the solubilities, the area of crystallization region for NaB5O8·5H2O is relatively larger than that for LiB5O8·5H2O at both temperatures. The composition for the two invariant points of LiB5O8 and NaB5O8 in the liquid phase in mass fraction of 100w is 9.87 and 4.69 at 298.15 K and 14.80 and 7.60 at 323.15 K, respectively. The points A1, A2 and B1, B2 present the solubilities of the binary systems LiB5O8 + H2O and NaB5O8 + H2O at two temperatures, respectively. At both temperatures, the component of NaB5O8 in the ternary system is decreased sharply with the increase of jLiB5O8 concentration in the solution, so it indicates that the component of lithium pentaborate existing in the solution has a strong salting-out effect of NaB5O8. The same coexisted equilibrium solid phases in the invariant points E1 and E2 identified by the powder X-ray diffraction are presented in Figure 5. A comparison for the ternary system LiB5O8 + NaB5O8 + H2O at 298.15 and 323.15 K shows is in Figure 6. It can be clearly seen that the solubilities for the ternary system LiB5O8 + NaB5O8 + H2O increased with the increase of temperature, but the crystallization regions for LiB5O8·5H2O and NaB5O8·5H2O did not change obviously with changing temperature. And, this ternary system at two temperatures belongs to a simple eutectic type, and neither double salts nor solid solutions were formed.Figure 3
Phase diagram and part enlargement of the compositions of the ternary system LiB5O8 + NaB5O8 + H2O at 298.15 K; , experimental points at 298.15 K; —, solubility curve at 298.15 K.Figure 4
Phase diagram for the ternary system LiB5O8 + NaB5O8 + H2O at 323.15 K; •, experimental points at 323.15 K; —, solubility curve at 323.15 K.Figure 5
X-ray diffraction patterns of the solid phase at invariant pointE1 LiB5O8·5H2O + NaB5O8·5H2O.Figure 6
Comparison of phase diagram of the ternary system LiB5O8 + NaB5O8 + H2O at 298.15 and 323.15 K; , experimental points at 298.15 K; , experimental points at 323.15 K; —, solubility curve at 298.15 and 323.15 K.


## 3.3. Refractive Index and Density Calculation

According to the semiempirical formulas of electrolyte aqueous solution with density and refractive index employed by Deng et al. [20], shown as equations (1) and (2), the density and refractive index of the experimental solution were calculated, and the results are listed in Table 3.(1)lnρρ0=∑Ai×wi,(2)lnnDnD0=∑Bi×wi,where ρ and ρ0 are the density of solution and pure water at the same temperature and nD and nD0 represent the refractive index of the solution and pure water at the same temperature, respectively. The ρ0 values at 298.15 and 323.15 K are 0.997041 and 0.988038 g·cm−3, respectively; the nD0 values at 298.15 and 323.15 K are 1.33250 and 1.32904, respectively; and wi is the component same as Table 2. Ai and Bi represent the coefficients for the solid phase i in this system. The Ai and Bi for LiB5O8 and NaB5O8 are shown in Table 4, and the maximal relative deviation of density between experimental and calculated values was 0.0084, as for the refractive index, the deviation was less than 0.0013, which indicates that the physicochemical properties obtained are reliable. On the basis of the data of physicochemical property (including densities and refractive indices) in Table 2, the diagrams of physicochemical properties (density and refractive index) versus the composition of lithium pentaborate in the solution are plotted in Figures 7 and 8, respectively. It could be clearly seen that the density and refractive index changed regularly with the changing of lithium pentaborate concentration in the ternary system at two temperatures, which was increased, and then decreased as the increasing of the concentration of lithium pentaborate concentration, and show a similar changing tendency.Table 4
Coefficients of densities and refractive indices in the ternary system LiB5O8 + NaB5O8 + H2O at 298.15 and 323.15 K and 0.1 MPa.
T (K)
Coefficients
LiB5O8
NaB5O8
298.15
A
i
0.006777954
0.006683650
B
i
0.001063948
0.000934748
323.15
A
i
0.006753151
0.006503464
B
i
0.000967555
0.000922052
aStandard uncertainties u(x) are u(T) = 0.1 K and u(p) = 5 kPa.Figure 7
Comparison of physicochemical properties versus composition diagram of the ternary system LiB5O8 + NaB5O8 + H2O at 298.15 K.Figure 8
Comparison of physicochemical properties versus composition diagram of the ternary system LiB5O8 + NaB5O8 + H2O at 323.15 K.


## 4. Conclusions

Phase equilibria and phase diagrams for the ternary systems of LiB5O8 + NaB5O8 + H2O at 298.15 and 323.15 K were studied by the isothermal dissolution equilibrium method, and the solubilities and relevant physicochemical properties including density and refractive index were firstly obtained. For this system at two temperatures, the phase diagrams contain one invariant point, two univariant solubility curves, and two crystallization regions corresponding to LiB5O8·5H2O and NaB5O8·5H2O, and the area of crystallization region of NaB5O8·5H2O at each temperature is relatively larger than that of LiB5O8·5H2O. This ternary system at two temperatures belongs to simple eutectic type, and neither double salts nor solid solution was found. The density and refractive index in the two ternary systems at 298.15 and 323.15 K increased firstly and then decreased with increasing of LiB5O8 concentration. In addition, the density and refractive index for salt-water electrolytes were theoretically calculated by empirical equations, which agree well with the experimental values.



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