# Density, pH, and Boron Species in the Ternary System NaBO2–Na2SO4–H2O at 298.15 K and 323.15 K

Authors: Xiaohui Song; Shuaiqi Sun; Lingzong Meng; Rongjian Ying; Yafei Guo; Tianlong Deng
Journal: Journal of Chemistry
 (2021)

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## Abstract

The densities and pH values in the system NaBO2–Na2SO4–H2O at 298.15 K and 323.15 K were investigated. Combining the equilibrium constants for different boron species, the distributions of six boron species in the mixed solution were calculated with total boron concentration and pH values. The molar fractions of the six boron species are mainly affected by the total boron concentration and temperature, but rarely affected by the concentration of SO42–. The dominant boron species in the mixed solution at the two temperatures is B(OH)4‒. The mole fraction of B(OH)3, B5O6(OH)4‒, and B3O3(OH)4‒ can be neglected. The polyborate ions are easier to form as the temperature increases. The results of distribution for boron species in this study and those with the Pitzer model can both be used to describe the distribution of boron species in the mixed solution.


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## Body

## 1. Introduction

The Qaidam Basin in Qinghai Province is rich in boron resources. Boron is usually distributed in liquid brine boron deposits and solid borate deposits [1]. With the continuous development of social progress and high-tech, borates are widely used in glass production, agricultural and sideline products, and pharmaceuticals, and the application of boron-containing compounds is in aerospace and defense construction [2]. Borates are gaining more and more attention, and global demand for boron will continue to grow over time [3]. In chemical engineering, the formation conditions and transformation rules of borate and hydrated borate crystals were expounded, and borate minerals were comprehensively developed and utilized to select the optimal extraction process [4]. In the last century, high-quality solid boron deposits were almost depleted. Therefore, it is urgent to solve the problem of developing liquid boron resources in western China as soon as possible. Aqueous boron species can be found in natural waters, including seawater, salt lakes, oilfield brine, and hydrothermal fluids [5].The behavior of borate solution extremely complicated, and it can exist in several different species in aqueous solution, such as metaborate B(OH)4−, B2O(OH)62−, B3O3(OH)4−, B4O5(OH)42−, B5O6(OH)4−, and B6O7(OH)62− [6, 7]. The concentrations of various boron species in different aqueous borate solution can be calculated theoretically by the Pitzer model. In the quaternary system NaCl−NaBO2−Na2B4O7−H2O at 298.15 K, the distributions of boron species in the liquid phase were calculated with the Pitzer model [8]. The main boron species in the mixed borate solution are B(OH)4‒ and B4O5(OH)42‒. The distributions of boron species in the system NaCl−NaSO4−NaBO2−H2O were also calculated in our previous work [9]. The preponderant boron species is B(OH)4−, whose mole fraction is more than 0.95. The calculated results for distribution of boron species in the system KCl−K2SO4−K2B4O7−H2O at 298.15 K show that the mole fraction of the boron species is mainly affected by the concentration of boron but no other anions in the solution [10].Boron form depends on boron concentration, pH, temperature, and ionic strength [11]. With the pH values in the solution and equilibrium constant between different boron species, the distribution of boron species was calculated [12–15]. The calculated results in these literatures [13, 14] are in agreement with those with the Pitzer model in the systems NaBO2−H2O and K2B4O7−H2O [9, 10]. The concentration of boron species was calculated in references [12–15], and it was considered that the activity coefficients of all boron ions were 1.0. Although the calculation may not be correct, the calculated results can also describe the distribution of boron species in the solution.The total boron concentration, pH value, metal cations, and temperature in the medium all affect the existence form and equilibrium relationship of borate anions, among which the total boron concentration and pH value are particularly important. At present, there are relatively few studies on the distribution of chemical species in the solution of multiple systems. NaBO2 is an important boron compound, especially in the industrial production of NaBH4 [16, 17], and it is a promising hydrogen solid carrier due to its easy hydrolysis and adjustable hydrogen release [18]. The physicochemical properties and distribution in the system NaBO2−H2O were presented [13], and the distributions for boron species in the mixed system Na2SO4–NaBO2–H2O at 298.15 K were also calculated with the Pitzer model [9]. However, the physicochemical properties including pH and density in the system were not reported. The distribution balance of boron species in the solution changes with temperature. In this work, the pH values and density values of the system Na2SO4–NaBO2–H2O at 298.15 K and 323.15 K were presented, and the distribution of boron species was also calculated.


## 2. Experimental

### 2.1. Materials and Apparatus

The chemical reagents used in this experiment are given in Table1. Experimental water was double deionized water (DDW) with the conductivity less than 1.2·10−4 S·m−1 and pH = 6.60 at 298.15 K. The values of pH were determined by an imported pH meter (Orion 310P-01A from US, the accuracy of ±0.001 for pH determination).Table 1
Chemical reagents in this work.
ChemicalCAS reg. no.SourceMass fraction purityAnalysis methodNaBO2·4H2O10555-76-7Aladdin Industrial Corp., China0.990Analysis for BO2–Na2SO47757-82-6Sinopharm Chemical Reagent Co., Ltd., China0.990Analysis for SO42–


### 2.2. Experimental Method

To affirm the effect from Na2SO4 to the boron species distribution in the system NaBO2–Na2SO4–H2O, the mix solution with different ratios of Na2SO4 and NaB(OH)4 (m(Na2SO4)/m(NaB(OH)4)) was prepared. First, the saturated solution in the systems NaBO2–H2O and Na2SO4–H2O was prepared, respectively. Then, the mixed solution with different ratios of Na2SO4 and NaB(OH)4 was prepared by mixing the two saturated solutions and DDW according to the solubility data of the NaBO2–Na2SO4–H2O ternary system at 298.15 K and 323.15 K [19, 20]. The concentration of NaBO2 and Na2SO4 was tabulated, as shown in Figure 1.Figure 1
The concentration in the system Na2SO4–NaBO2–H2O at different temperatures. Black dotted line, 298.15 K [13]; brown dotted line, 323.15 K [14]. This work: black solid line, m(Na2SO4): m(NaB(OH)4) = 1 : 8; red solid line, m(Na2SO4): m(NaB(OH)4) = 1 : 4; blue solid line, m(Na2SO4): m(NaB(OH)4) = 3 : 8; green solid line, m(Na2SO4): m(NaB(OH)4) = 1 : 2.The mixed solution was then used for physicochemical property measurement. The densities (ρ) were measured using a density bottle with an uncertainty less than ±0.002 g·cm−3. The pH values were measured three times with the pH meter, and the uncertainty between the measurement results is 0.002. The concentration of SO42‒ was determined by the barium sulfate gravimetric method, and the relative error is less than ±0.0005 [21]. The concentration of BO2‒ was obtained by the modified mannitol gravimetric method [21, 22] with the relative error less than 0.003.


## 2.1. Materials and Apparatus

The chemical reagents used in this experiment are given in Table1. Experimental water was double deionized water (DDW) with the conductivity less than 1.2·10−4 S·m−1 and pH = 6.60 at 298.15 K. The values of pH were determined by an imported pH meter (Orion 310P-01A from US, the accuracy of ±0.001 for pH determination).Table 1
Chemical reagents in this work.
ChemicalCAS reg. no.SourceMass fraction purityAnalysis methodNaBO2·4H2O10555-76-7Aladdin Industrial Corp., China0.990Analysis for BO2–Na2SO47757-82-6Sinopharm Chemical Reagent Co., Ltd., China0.990Analysis for SO42–


## 2.2. Experimental Method

To affirm the effect from Na2SO4 to the boron species distribution in the system NaBO2–Na2SO4–H2O, the mix solution with different ratios of Na2SO4 and NaB(OH)4 (m(Na2SO4)/m(NaB(OH)4)) was prepared. First, the saturated solution in the systems NaBO2–H2O and Na2SO4–H2O was prepared, respectively. Then, the mixed solution with different ratios of Na2SO4 and NaB(OH)4 was prepared by mixing the two saturated solutions and DDW according to the solubility data of the NaBO2–Na2SO4–H2O ternary system at 298.15 K and 323.15 K [19, 20]. The concentration of NaBO2 and Na2SO4 was tabulated, as shown in Figure 1.Figure 1
The concentration in the system Na2SO4–NaBO2–H2O at different temperatures. Black dotted line, 298.15 K [13]; brown dotted line, 323.15 K [14]. This work: black solid line, m(Na2SO4): m(NaB(OH)4) = 1 : 8; red solid line, m(Na2SO4): m(NaB(OH)4) = 1 : 4; blue solid line, m(Na2SO4): m(NaB(OH)4) = 3 : 8; green solid line, m(Na2SO4): m(NaB(OH)4) = 1 : 2.The mixed solution was then used for physicochemical property measurement. The densities (ρ) were measured using a density bottle with an uncertainty less than ±0.002 g·cm−3. The pH values were measured three times with the pH meter, and the uncertainty between the measurement results is 0.002. The concentration of SO42‒ was determined by the barium sulfate gravimetric method, and the relative error is less than ±0.0005 [21]. The concentration of BO2‒ was obtained by the modified mannitol gravimetric method [21, 22] with the relative error less than 0.003.


## 3. Results and Discussion

### 3.1. Density

The density values of the NaBO2–Na2SO4–H2O ternary system at 298.15 K and 323.15 K are given in Tables 2 and 3, respectively. The density diagrams with the concentration of boron (m(B)) as the abscissa were plotted, as shown in Figure 2. In the same ratio of Na2SO4 and NaB(OH)4, the densities increase as m(B) increases, as shown in Figure 2. The densities also increase at the same concentration of one salt as the concentration of the other salt increases. However, the densities decrease at the same concentration with the increase of temperature. With the changing trends in the density diagrams, shown in Figure 2, the densities can be used to roughly estimate the concentrations of Na2SO4 and NaB(OH)4 in the ternary system.Table 2
Density and pH values in the system NaBO2–Na2SO4–H2O at 298.15 K.
m/(mol·kg−1·H2O)ρ/g·cm−3 experimentalpHm(B)m(SO42‒)3.34480.46331.266212.5993.05810.44461.231512.4832.55370.61611.198912.3752.21570.54671.174812.2951.76770.21391.151112.1741.34980.24731.140512.1011.21750.05801.126012.0851.06040.08731.118912.0440.82670.12031.101211.8900.52990.11951.083611.6750.36750.09631.058511.4700.24190.04981.030011.2800.13490.02191.012511.0802.81240.65911.264812.4082.17810.56381.211712.2581.86460.43361.195512.1641.66350.41561.179812.0851.39540.47101.154712.0431.25280.07451.153611.9511.09490.16031.141511.9100.95430.16521.126511.8460.72170.18681.109811.6200.51930.18361.092711.5360.33620.08831.072411.3500.23750.06431.056811.2040.13680.05131.045111.0402.48510.89871.272212.2522.29520.85141.244712.1851.97840.81571.218512.0421.56740.62491.191811.8871.39670.71111.177511.8281.26240.14651.168811.7881.04480.29501.158111.6890.76110.33271.138011.5230.58370.27861.115611.3680.44020.20371.101711.2300.23030.09671.065411.0360.13760.06451.055910.9402.28521.22241.303312.2481.95851.05441.248912.1081.72301.00461.224512.0341.47650.86621.204411.9011.35920.93171.188511.8931.24430.11841.182311.8431.15130.26791.173611.7810.95070.31881.160511.6900.82490.38851.148111.6050.61310.40121.138211.4800.37380.23261.123111.2590.23410.15641.091211.080Table 3
Density and pH values in the system NaBO2–Na2SO4–H2O at 323.15 K.
m/(mol·kg−1·H2O)ρ/g·cm−3pHm(B)m(SO42‒)3.79750.47241.221011.8213.34480.46331.194911.8033.05810.44461.151911.7632.55370.61611.138511.7422.21570.54901.127411.7231.78720.21391.100111.7081.36390.24771.077411.6181.23070.05021.065711.5881.05330.08791.052311.5010.83550.10401.046611.3540.57650.10021.031211.1422.81240.65911.244811.5932.17810.56381.202011.5840.37480.11271.018510.9760.24480.05801.012410.8390.14700.02580.999110.6743.30840.76581.285211.6851.86460.43361.165211.5541.65440.42291.145211.5011.46970.47101.132411.2011.25580.14841.125611.4571.00430.21141.105611.3580.72110.18981.082611.1410.51210.13601.065410.9410.33500.08941.043110.7540.24960.05771.035010.6540.16050.04321.021210.4982.90230.98951.290911.5892.69130.96671.271611.4742.45820.90621.238511.4521.97840.81571.207711.4081.58460.62491.178111.3681.45680.65781.166911.3871.27600.14651.156211.3271.05600.25161.139911.2340.76930.33271.118711.0850.58990.24491.098210.8330.49720.26591.084510.7600.39130.13061.071210.5500.23270.02271.051310.5500.15260.01511.036510.3802.28521.22241.284711.4132.14381.19451.269611.3872.10610.98191.247211.3261.87260.88001.225611.2981.47640.86631.190511.2531.36340.92531.187511.2331.31530.94861.182111.2231.15130.28271.172711.2040.96090.37021.156811.1530.83370.40021.145510.9310.57910.46591.117410.7540.43630.30711.101710.6210.30330.17171.079310.5180.13780.09021.064110.331Figure 2
The density of mixed solution of the NaBO2–Na2SO4–H2O system. (a) 298.15 K. (b) 323.15 K. Black line, m(Na2SO4): m(NaB(OH)4) = 1 : 8; red line, m(Na2SO4): m(NaB(OH)4) = 1 : 4; blue line, m(Na2SO4): m(NaB(OH)4) = 3 : 8; green line, m(Na2SO4): m(NaB(OH)4) = 1 : 2.
(a)(b)


### 3.2. pH Data and Boron Species Distribution

The experimental pH of the NaBO2‒Na2SO4‒H2O ternary system with different ratios is given in Tables 2 and 3. From the pH data, the pH diagrams are shown in Figure 3 to show the relationship between m(B) and pH at 298.15 K and 323.15 K. On the same scale, the pH value increases with the increase of the total boron concentration. But more than 1.2 mol·kg−1·H2O growth rate showed a downward trend. On the same total boron concentration line, the pH value decreases with the increase of Na2SO4 mole fraction. The data show that the pH of the solution in the system NaBO2–Na2SO4–H2O is mainly affected by m(B). The mole fraction of Na2SO4 for hydrolysis is lesser than that of NaBO2.Figure 3
The pH of mixed solution in the NaB(OH)4–Na2SO4–H2O system. (a) 298.15 K. (b) 323.15 K. Black line, m(Na2SO4): m(NaB(OH)4) = 1 : 8; red line, m(Na2SO4): m(NaB(OH)4) = 1 : 4; blue line, m(Na2SO4): m(NaB(OH)4) = 3 : 8; green line, m(Na2SO4): m(NaB(OH)4) = 1 : 2.
(a)(b)From the literature [12–15], B(OH)3 was assumed as the reactants B(OH)4‒, B3O3(OH)4‒, B3O3 (OH)52‒, B4O5(OH)42‒, and B5O6(OH)4‒ were formed with B(OH)3 and H2O. The reaction equation between boron species can be represented as(1)pBOH3+nH2O=BpOH3p+qH2On−qq−+qH+The ion equilibrium constants among different boron species were reported under different ionic strengths in different media by potentiometric titration of hydrogen electrode. According to the calculation method in the literature [12–15], the total boron concentration, the measured pH value, and the equilibrium constant are mentioned in the literature [23, 24], as shown in equation (2). The mole fractions of different boron species were calculated using equation (3).(2)Total boron=BOH3+BOH4−+3B3O3OH4−+3B3O3OH52−+4B4O5OH42−+5B5O6OH4−=BOH3+K11BOH3H++3K31BOH33H++3K32BOH33H+2+4K42BOH34H+2+5K51BOH35H+,(3)xBPOH3qqH2O=P×BPOH3qqH2On−qq−Total boronIn equation (2), K11, K31, K32, K32, and K51 represent the equilibrium constant equations for B(OH)4‒, B3O3(OH)4‒, B3O3(OH)52‒, B4O5(OH)42‒, and B5O6(OH)4‒. The relationship between molar fraction of different boron species and total boron concentration is shown in Figure 4.Figure 4
Boron species distribution in mixed aqueous solution of Na2SO4 and NaBO2 at 298.15 K and 323.15 K. , (B(OH)3; , B(OH)4‒; , B3O3(OH)4‒; , B3O3(OH)52‒; , B4O5(OH)42‒;  B5O6(OH)4‒.
(a)(b)The mole fraction (x) of B(OH)4‒ in the mixed solution at 298.15 K is no less than 0.98 in the concentration range (0.1349∼3.3448 mol·kg −1). The x(B(OH)3) can reach about 0.01 when m(B) is less than 0.14 mol·kg −1, but decreases to a very small value with the increase of m(B). x(B(OH)3) will be no more than 0.001 if the m(B) is more than 1.3 mol·kg −1. The x for B3O3(OH)52‒, which was not considered in the calculation with Pitzer model [9], cannot be neglected in this calculation. x(B3O3(OH)52‒) increases as m(B) increases and reach about 0.11 when m(B) is about 4.0 mol·kg −1. The mole fraction for B3O3(OH)4‒ is always below 0.0005 and can be neglected. The x(B5O6(OH)4‒) is about 1.0 × 10−9, which can be considered that B5O6(OH)4‒ does not exist in the mixed solution at 298.15 K. In Figure 3(b), the dominant boron species is also B(OH)4‒, but x(B(OH)4‒) decreases as the concentration of total boron increases. x(B(OH)4‒) is no less than 0.95 when m(B) is less than 1.2 mol·kg−1. x(B(OH)4‒) maintains no less than 0.85 when m(B) is more than 1.2 mol·kg−1. x(B3O3(OH)52‒) shows an uptrend and can occupy about 0.1 when m(B) is more than 2.4 mol·kg−1. x(B4O5(OH)42‒) also increase as m(B) increases and can reach the maximum data about 0.02. x(B(OH)3) decreases as m(B) increases. If m(B) is greater than 0.5 mol·kg−1, x(B(OH)3) will not exceed 0.005. x(B3O3(OH)4‒) is always lower than 0.0015 and can be ignored in the solution. B5O6(OH)4‒ in the solution can also be considered to be nonexistent at 323.15 K.From the changing trend for the six boron species in the mixed solution in the system NaBO2–Na2SO4–H2O at 298.15 K and 323.15 K, the boron species may react with the equations (4)–(7). The reaction is shown in Figure 5.(4)BOH4−=BOH3+OH−(5)BOH4−+2BOH3=B3O3OH4−+3H2O(6)B3O3OH4−+OH−=B3O3OH52−(7)B3O3OH52−+BOH4−=B4O5OH42−+OH−+2H2OFigure 5
Reaction relationship between boron species.In the diluted solution, B(OH)3 can be formed by hydrolysis of B(OH)4‒. As the concentration of B(OH)4‒ increases, B3O3(OH)4‒ forms with B(OH)4‒ and B(OH)3 with equation (5). The solution is alkaline because of hydrolysis of B(OH)4‒, so B3O3(OH)4‒ will combine OH– to form B3O3(OH)52‒. As the increase of concentration of B3O3(OH)52‒, B4O5(OH)42‒ forms with B3O3(OH)52‒ and B(OH)4‒. Because of the OH– formation and consumption, the concentration of OH– first increases and then decreases as m(B) increases.The dominant boron species in the system NaBO2–Na2SO4–H2O at the two temperatures is B(OH)4‒ with the mole fraction no less than 0.90. From the results of solubility calculation [9, 20], it can be considered that boron species mainly exists in the form of B(OH)4‒ in the mixed solution. The mole fractions for the six boron species in the mixed solution with different ratios show a slight difference at two temperatures. The results show that the mole fractions of the six boron species in the system NaBO2–Na2SO4–H2O are mainly affected by m(B) in the solution, but rarely effected by m(SO42–). From 298.15 K to 323.15 K, the distribution of boron species in the mixed solution changed a lot. As temperature increases, the distribution of boron species becomes complicated. The polyborate ions are easily formed as the temperature increases in the NaBO2–Na2SO4–H2O system. The results show that the mole fraction of the six boron species in the system NaBO2–Na2SO4–H2O is mainly affected by the temperature.The distribution of boron species in the system NaBO2–Na2SO4–H2O at 298.15 K was also calculated with the Pitzer model in our previous work [9]. In the calculation [9], x(B(OH)4−) is more than 0.96 in the system NaBO2–Na2SO4–H2O, which shows that the boron species in the solution in the system can be considered as a single boron species B(OH)4−. The concentrations of B(OH)3 and B3O3(OH)4− in the solution can be neglected. The comparison of the mole fraction of B(OH)4− in the system NaBO2–Na2SO4–H2O at 298.15 K calculated in this work and with the Pitzer model [9] is shown in Figure 6. The results in this work are nearly the same as those calculated with the Pitzer model [9], as shown in Figure 6, which shows that the two methods are reliable for the distribution of boron species calculation. However, there are still some differences for the calculation with the two methods. Only four boron species B(OH)3, B(OH)4‒, B3O3(OH)4‒, and B4O5(OH)42‒ were considered in the Pitzer model because of not enough parameters in the literature [9], but six boron species exist in this work. From the calculated results in this work, B3O3(OH)52‒ cannot be neglected in the mixed solution. The activity coefficients for boron species were not considered in this work, but the activity coefficients were calculated with the Pitzer model. The pH values can be calculated with the Pitzer model. However, the calculation cannot be obtained in this work if the pH values were not known. The results from the two methods show a slight difference, but the two methods can both be used to describe the distribution of boron species in the mixed solution.Figure 6
Comparison of the mole fraction of B(OH)4− in the system NaBO2–Na2SO4–H2O at 298.15 K calculated in this work and with the Pitzer model [9]. , this work; , ref. [9].


## 3.1. Density

The density values of the NaBO2–Na2SO4–H2O ternary system at 298.15 K and 323.15 K are given in Tables 2 and 3, respectively. The density diagrams with the concentration of boron (m(B)) as the abscissa were plotted, as shown in Figure 2. In the same ratio of Na2SO4 and NaB(OH)4, the densities increase as m(B) increases, as shown in Figure 2. The densities also increase at the same concentration of one salt as the concentration of the other salt increases. However, the densities decrease at the same concentration with the increase of temperature. With the changing trends in the density diagrams, shown in Figure 2, the densities can be used to roughly estimate the concentrations of Na2SO4 and NaB(OH)4 in the ternary system.Table 2
Density and pH values in the system NaBO2–Na2SO4–H2O at 298.15 K.
m/(mol·kg−1·H2O)ρ/g·cm−3 experimentalpHm(B)m(SO42‒)3.34480.46331.266212.5993.05810.44461.231512.4832.55370.61611.198912.3752.21570.54671.174812.2951.76770.21391.151112.1741.34980.24731.140512.1011.21750.05801.126012.0851.06040.08731.118912.0440.82670.12031.101211.8900.52990.11951.083611.6750.36750.09631.058511.4700.24190.04981.030011.2800.13490.02191.012511.0802.81240.65911.264812.4082.17810.56381.211712.2581.86460.43361.195512.1641.66350.41561.179812.0851.39540.47101.154712.0431.25280.07451.153611.9511.09490.16031.141511.9100.95430.16521.126511.8460.72170.18681.109811.6200.51930.18361.092711.5360.33620.08831.072411.3500.23750.06431.056811.2040.13680.05131.045111.0402.48510.89871.272212.2522.29520.85141.244712.1851.97840.81571.218512.0421.56740.62491.191811.8871.39670.71111.177511.8281.26240.14651.168811.7881.04480.29501.158111.6890.76110.33271.138011.5230.58370.27861.115611.3680.44020.20371.101711.2300.23030.09671.065411.0360.13760.06451.055910.9402.28521.22241.303312.2481.95851.05441.248912.1081.72301.00461.224512.0341.47650.86621.204411.9011.35920.93171.188511.8931.24430.11841.182311.8431.15130.26791.173611.7810.95070.31881.160511.6900.82490.38851.148111.6050.61310.40121.138211.4800.37380.23261.123111.2590.23410.15641.091211.080Table 3
Density and pH values in the system NaBO2–Na2SO4–H2O at 323.15 K.
m/(mol·kg−1·H2O)ρ/g·cm−3pHm(B)m(SO42‒)3.79750.47241.221011.8213.34480.46331.194911.8033.05810.44461.151911.7632.55370.61611.138511.7422.21570.54901.127411.7231.78720.21391.100111.7081.36390.24771.077411.6181.23070.05021.065711.5881.05330.08791.052311.5010.83550.10401.046611.3540.57650.10021.031211.1422.81240.65911.244811.5932.17810.56381.202011.5840.37480.11271.018510.9760.24480.05801.012410.8390.14700.02580.999110.6743.30840.76581.285211.6851.86460.43361.165211.5541.65440.42291.145211.5011.46970.47101.132411.2011.25580.14841.125611.4571.00430.21141.105611.3580.72110.18981.082611.1410.51210.13601.065410.9410.33500.08941.043110.7540.24960.05771.035010.6540.16050.04321.021210.4982.90230.98951.290911.5892.69130.96671.271611.4742.45820.90621.238511.4521.97840.81571.207711.4081.58460.62491.178111.3681.45680.65781.166911.3871.27600.14651.156211.3271.05600.25161.139911.2340.76930.33271.118711.0850.58990.24491.098210.8330.49720.26591.084510.7600.39130.13061.071210.5500.23270.02271.051310.5500.15260.01511.036510.3802.28521.22241.284711.4132.14381.19451.269611.3872.10610.98191.247211.3261.87260.88001.225611.2981.47640.86631.190511.2531.36340.92531.187511.2331.31530.94861.182111.2231.15130.28271.172711.2040.96090.37021.156811.1530.83370.40021.145510.9310.57910.46591.117410.7540.43630.30711.101710.6210.30330.17171.079310.5180.13780.09021.064110.331Figure 2
The density of mixed solution of the NaBO2–Na2SO4–H2O system. (a) 298.15 K. (b) 323.15 K. Black line, m(Na2SO4): m(NaB(OH)4) = 1 : 8; red line, m(Na2SO4): m(NaB(OH)4) = 1 : 4; blue line, m(Na2SO4): m(NaB(OH)4) = 3 : 8; green line, m(Na2SO4): m(NaB(OH)4) = 1 : 2.
(a)(b)


## 3.2. pH Data and Boron Species Distribution

The experimental pH of the NaBO2‒Na2SO4‒H2O ternary system with different ratios is given in Tables 2 and 3. From the pH data, the pH diagrams are shown in Figure 3 to show the relationship between m(B) and pH at 298.15 K and 323.15 K. On the same scale, the pH value increases with the increase of the total boron concentration. But more than 1.2 mol·kg−1·H2O growth rate showed a downward trend. On the same total boron concentration line, the pH value decreases with the increase of Na2SO4 mole fraction. The data show that the pH of the solution in the system NaBO2–Na2SO4–H2O is mainly affected by m(B). The mole fraction of Na2SO4 for hydrolysis is lesser than that of NaBO2.Figure 3
The pH of mixed solution in the NaB(OH)4–Na2SO4–H2O system. (a) 298.15 K. (b) 323.15 K. Black line, m(Na2SO4): m(NaB(OH)4) = 1 : 8; red line, m(Na2SO4): m(NaB(OH)4) = 1 : 4; blue line, m(Na2SO4): m(NaB(OH)4) = 3 : 8; green line, m(Na2SO4): m(NaB(OH)4) = 1 : 2.
(a)(b)From the literature [12–15], B(OH)3 was assumed as the reactants B(OH)4‒, B3O3(OH)4‒, B3O3 (OH)52‒, B4O5(OH)42‒, and B5O6(OH)4‒ were formed with B(OH)3 and H2O. The reaction equation between boron species can be represented as(1)pBOH3+nH2O=BpOH3p+qH2On−qq−+qH+The ion equilibrium constants among different boron species were reported under different ionic strengths in different media by potentiometric titration of hydrogen electrode. According to the calculation method in the literature [12–15], the total boron concentration, the measured pH value, and the equilibrium constant are mentioned in the literature [23, 24], as shown in equation (2). The mole fractions of different boron species were calculated using equation (3).(2)Total boron=BOH3+BOH4−+3B3O3OH4−+3B3O3OH52−+4B4O5OH42−+5B5O6OH4−=BOH3+K11BOH3H++3K31BOH33H++3K32BOH33H+2+4K42BOH34H+2+5K51BOH35H+,(3)xBPOH3qqH2O=P×BPOH3qqH2On−qq−Total boronIn equation (2), K11, K31, K32, K32, and K51 represent the equilibrium constant equations for B(OH)4‒, B3O3(OH)4‒, B3O3(OH)52‒, B4O5(OH)42‒, and B5O6(OH)4‒. The relationship between molar fraction of different boron species and total boron concentration is shown in Figure 4.Figure 4
Boron species distribution in mixed aqueous solution of Na2SO4 and NaBO2 at 298.15 K and 323.15 K. , (B(OH)3; , B(OH)4‒; , B3O3(OH)4‒; , B3O3(OH)52‒; , B4O5(OH)42‒;  B5O6(OH)4‒.
(a)(b)The mole fraction (x) of B(OH)4‒ in the mixed solution at 298.15 K is no less than 0.98 in the concentration range (0.1349∼3.3448 mol·kg −1). The x(B(OH)3) can reach about 0.01 when m(B) is less than 0.14 mol·kg −1, but decreases to a very small value with the increase of m(B). x(B(OH)3) will be no more than 0.001 if the m(B) is more than 1.3 mol·kg −1. The x for B3O3(OH)52‒, which was not considered in the calculation with Pitzer model [9], cannot be neglected in this calculation. x(B3O3(OH)52‒) increases as m(B) increases and reach about 0.11 when m(B) is about 4.0 mol·kg −1. The mole fraction for B3O3(OH)4‒ is always below 0.0005 and can be neglected. The x(B5O6(OH)4‒) is about 1.0 × 10−9, which can be considered that B5O6(OH)4‒ does not exist in the mixed solution at 298.15 K. In Figure 3(b), the dominant boron species is also B(OH)4‒, but x(B(OH)4‒) decreases as the concentration of total boron increases. x(B(OH)4‒) is no less than 0.95 when m(B) is less than 1.2 mol·kg−1. x(B(OH)4‒) maintains no less than 0.85 when m(B) is more than 1.2 mol·kg−1. x(B3O3(OH)52‒) shows an uptrend and can occupy about 0.1 when m(B) is more than 2.4 mol·kg−1. x(B4O5(OH)42‒) also increase as m(B) increases and can reach the maximum data about 0.02. x(B(OH)3) decreases as m(B) increases. If m(B) is greater than 0.5 mol·kg−1, x(B(OH)3) will not exceed 0.005. x(B3O3(OH)4‒) is always lower than 0.0015 and can be ignored in the solution. B5O6(OH)4‒ in the solution can also be considered to be nonexistent at 323.15 K.From the changing trend for the six boron species in the mixed solution in the system NaBO2–Na2SO4–H2O at 298.15 K and 323.15 K, the boron species may react with the equations (4)–(7). The reaction is shown in Figure 5.(4)BOH4−=BOH3+OH−(5)BOH4−+2BOH3=B3O3OH4−+3H2O(6)B3O3OH4−+OH−=B3O3OH52−(7)B3O3OH52−+BOH4−=B4O5OH42−+OH−+2H2OFigure 5
Reaction relationship between boron species.In the diluted solution, B(OH)3 can be formed by hydrolysis of B(OH)4‒. As the concentration of B(OH)4‒ increases, B3O3(OH)4‒ forms with B(OH)4‒ and B(OH)3 with equation (5). The solution is alkaline because of hydrolysis of B(OH)4‒, so B3O3(OH)4‒ will combine OH– to form B3O3(OH)52‒. As the increase of concentration of B3O3(OH)52‒, B4O5(OH)42‒ forms with B3O3(OH)52‒ and B(OH)4‒. Because of the OH– formation and consumption, the concentration of OH– first increases and then decreases as m(B) increases.The dominant boron species in the system NaBO2–Na2SO4–H2O at the two temperatures is B(OH)4‒ with the mole fraction no less than 0.90. From the results of solubility calculation [9, 20], it can be considered that boron species mainly exists in the form of B(OH)4‒ in the mixed solution. The mole fractions for the six boron species in the mixed solution with different ratios show a slight difference at two temperatures. The results show that the mole fractions of the six boron species in the system NaBO2–Na2SO4–H2O are mainly affected by m(B) in the solution, but rarely effected by m(SO42–). From 298.15 K to 323.15 K, the distribution of boron species in the mixed solution changed a lot. As temperature increases, the distribution of boron species becomes complicated. The polyborate ions are easily formed as the temperature increases in the NaBO2–Na2SO4–H2O system. The results show that the mole fraction of the six boron species in the system NaBO2–Na2SO4–H2O is mainly affected by the temperature.The distribution of boron species in the system NaBO2–Na2SO4–H2O at 298.15 K was also calculated with the Pitzer model in our previous work [9]. In the calculation [9], x(B(OH)4−) is more than 0.96 in the system NaBO2–Na2SO4–H2O, which shows that the boron species in the solution in the system can be considered as a single boron species B(OH)4−. The concentrations of B(OH)3 and B3O3(OH)4− in the solution can be neglected. The comparison of the mole fraction of B(OH)4− in the system NaBO2–Na2SO4–H2O at 298.15 K calculated in this work and with the Pitzer model [9] is shown in Figure 6. The results in this work are nearly the same as those calculated with the Pitzer model [9], as shown in Figure 6, which shows that the two methods are reliable for the distribution of boron species calculation. However, there are still some differences for the calculation with the two methods. Only four boron species B(OH)3, B(OH)4‒, B3O3(OH)4‒, and B4O5(OH)42‒ were considered in the Pitzer model because of not enough parameters in the literature [9], but six boron species exist in this work. From the calculated results in this work, B3O3(OH)52‒ cannot be neglected in the mixed solution. The activity coefficients for boron species were not considered in this work, but the activity coefficients were calculated with the Pitzer model. The pH values can be calculated with the Pitzer model. However, the calculation cannot be obtained in this work if the pH values were not known. The results from the two methods show a slight difference, but the two methods can both be used to describe the distribution of boron species in the mixed solution.Figure 6
Comparison of the mole fraction of B(OH)4− in the system NaBO2–Na2SO4–H2O at 298.15 K calculated in this work and with the Pitzer model [9]. , this work; , ref. [9].


## 4. Conclusions

The densities and pH values in the system NaBO2–Na2SO4–H2O at 298.15 K and 323.15 K were investigated in this study. The densities and pH values change gradually with the changing of m(B) and m(SO42–). Combining the equilibrium constants for different boron species, the molar fractions of six boron species in the mixed solution were calculated with m(B) and pH values. The distribution of six boron species in mixed solutions was obtained. The mole fractions of boron species are mainly affected by the concentration of total boron and temperature, but rarely affected by the concentration of SO42–. The polyborate ions are easier to form as the temperature increases. The dominant boron species in the system NaBO2–Na2SO4–H2O at the two temperatures is B(OH)4‒. The mole fraction of B(OH)3 and B3O3(OH)4‒ can be neglected. B5O6(OH)4‒ in the solution in the ternary system can be considered to be nonexistent. In the solubility calculation, it can be considered that there is only one boron species B(OH)4‒ in the system. The calculation of distribution for boron species in this study and those with the Pitzer model can both be used to describe the distribution of boron species in the mixed solution. The results on physicochemical properties and boron species distribution calculation in the system NaBO2–Na2SO4–H2O can supply theoretical reference for separating sodium metaborate salts from brine and development of universal thermodynamic models of brine systems with various boron species.



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