# Thermodynamic Modeling of Boron Species in the Ternary System Na2O-B2O3-H2O at 298.15 K

Authors: Qingtao Fu; Lele Chen; Xiaohui Song; Dan Li; Xiuxiu Yang; Lingzong Meng; Yafei Guo; Tianlong Deng
Journal: Journal of Chemistry
 (2020)

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## Abstract

The solubilities; concentration of four boron species B(OH)3, B(OH)4−, B3O3(OH)4−, and B4O5(OH)42−; and H+ (OH–) in the system Na2O–B2O3–H2O were calculated with the Pitzer model. The boron species B5O6(OH)4− was not considered in the model calculation. The calculated solubility and pH data are in accordance with the experimental results. The Pitzer model can be used to describe the experimental values. The distributions of the four boron species in the solution were obtained. The mole fractions of the four boron species are mainly affected by the ratio of B2O3 and Na2O in the solution. The dominant boron species in the solution saturated with different salts vary greatly. The results can supply a theoretical reference for sodium borate separation from brine.


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## Body

## 1. Introduction

The Qaidam Basin in Qinghai is the gathering place of salt lake resources in China [1]. In addition to the rich mineral resources such as potassium, sodium, magnesium, and lithium, the salt lake brine also has a large amount of borates [2–5]. These resources have important application value for the development of industry, agriculture, and economic construction [6]. There are many boron species in the borate solution. The boron species have complex structure and are mainly affected by the boron concentration, pH, and coexisting ions in solution [7–9]. The phase equilibria of water-salt systems can supply theoretical basis for the development of salt lake brine resources [10]. Therefore, the research on the phase equilibrium of the brine systems containing boron is meaningful to the comprehensive utilization and development of boron resources from brines [11].The system Na2O-B2O3-H2O is the simple subsystem of the complicated brine system. The phase equilibria in the system in a wide temperature range (273.15∼373.15 K) were reported [12–15]. The salts H3BO3, NaB5O6(OH)4 · 3H2O, Na2B4O5(OH)4 · 8H2O, and NaB(OH)4 · 2H2O were found in the system at 298.15 K [12–14]. The different salt forms with different ratios of Na2O and B2O3 in the solution. The change trends for concentration of total boron in the solution can be obtained with the phase equilibrium results, but the exact concentration of various boron species in the solution cannot be obtained with the phase equilibrium results.The thermodynamic model is the effective method to calculate the concentration of boron species [16]. The MSE model was applied to calculate the solubilities in the system Na2O-B2O3-H2O at 303.15 K, 333.15 K, 348.15 K, and 367.15 K [17]. However, the concentrations of different boron species and H+ (OH–) in the system were not presented [17]. The Pitzer model was widely applied in the solubility calculation in the brine systems [18, 19]. The Pitzer model in the system Na+-K+-Ca2+-Mg2+-H+-Cl–-SO42–-CO2-B(OH)4–-H2O was reported by Felmy and Weare [20]. The solubilities in the system Na2O-B2O3-H2O at 293.15 K were reported with the Pitzer model. The concentration of H+ (OH–) in the system containing boric acid or borate cannot be neglected [21, 22]. However, H+ (OH–) was not considered in the Pitzer model for the system. The concentrations of different boron species in the ternary system were not yet calculated [20]. The solubilities in the systems NaCl-NaBO2-Na2B4O7-H2O and NaCl-Na2SO4-NaBO2-H2O at 298.15 K were calculated with Pitzer model in our previous work [21, 22]. The concentrations of various boron species and H+ in the mixed borate solution were also calculated. However, the Pitzer model containing H+ (OH–) in the system Na2O-B2O3-H2O at 298.15 K, which is necessary for synthesis of sodium borate, is lacking. In this paper, the Pitzer model in the system Na2O-B2O3-H2O at 298.15 K was constructed, and the concentrations of various boron species and H+ (OH–) in the system were also calculated with the model.


## 2. Model Approach

The Pitzer thermodynamic model was widely used to calculate solubility, osmotic coefficientø, ionic activity coefficients γ, and other thermodynamic properties [23–26]. These main equations for thermodynamic property calculation are as follows:(1)ø−1=2∑imi−AØI3/21+bI1/2+∑i∑imcmaBcaØ+ZCca+∑c∑<c′mcmc′Φcc′Ø+∑amaψcc′α+∑a∑<a′mama′Φaa′Ø+∑cmcψcac′+∑n∑cmnmcλnc+∑n∑amnmaλna+∑n∑c∑amnmcmaζnca,(2)lnγM=zM2F+∑ama2BMa+ZCMa+∑cmc2ΦMc+∑amaΨMca+∑a∑<a′mama′ΨMaa′+zM∑c∑amcmaCca+∑nmn2λnM+∑n∑amnmaζnaM,(3)lnγX=zX2F+∑cmc2BcX+ZCcX+∑cmc2ΦXa+∑amcΨcXa+∑c∑<c′mcmc′Ψcc′X+ZX∑c∑amcmaCca+∑nmn2λnX+∑n∑amnmcζncX,(4)lnγN=∑cmc2λNc+∑ama2λNa+∑n∑amcmaζNca,(5)lnαw=−øMW1000∑mi.In the above equations,AØ represent Debye–Hückel parameters. The subscripts M, c, c′, X, a, a′, and N express the different cations and anions, respectively. The symbols mc and Zc are the mass molality and the charge of cation c. λNc,λNa, and ζNca represent the interaction between the cations, anions, ionic species, and the neutral species. The other terms F, C, Z, B, and Φ in the above equations are defined in references [23–26]. In equation (5), αw and MW represent the water activity and molar mass of water (mol · kg−1), and the sum contains all solute species.The solubilities of brine systems can be calculated with the Pitzer parameters and solubility products of the equilibrium solid phases (Ksp). In this study, the solubilities of the system Na2O-B2O3-H2O at 298.15 K were calculated with the model based on the Pitzer model. The pH for the solution in the system Na2O-B2O3-H2O at 298.15 K is in the range from 2.50 to 14.46 [12,27], which shows the concentration of H+ or OH–cannot be neglected in the solution. Therefore, the ions Na+, H+ (OH−), B(OH)3, B(OH)4−, B3O3(OH)4−, and B4O5(OH)42− in the solution were considered in the model calculation. The boron ion B5O6(OH)4− was not mentioned in the calculation because of the lack of parameters for B5O6(OH)4−. The Pitzer parameters and μΘ/RT of different boron species in the system Na2O-B2O3-H2O at 298.15 K were obtained from Felmy and Weare [20]. The lacking Pitzer mixing ion-interaction parameters for boron ions are considered as zero.Taking the solution saturated with H3BO3 in the ternary system for example, the dissolution equilibrium equations are as follows, and the relationship between boron ions can be expressed in equations (6)–(9).(6)BOH3s=BOH3aq(7)BOH3aq+H2O=BOH4−+H+(8)3BOH3aq=B3O3OH4−+H++2H2O(9)4BOH3aq=B4O5OH42−+2H++3H2OThe equilibrium constants for equations (6)–(9), which can be calculated with the standard chemical potentials by Felmy and Weare [20, 26], are shown in equations (10)–(13).(10)K1=mBOH3aq×γBOHaq,(11)K2=mBOH4−×γBOH4−×mH+×γH+mBOH3aq×γBOH3aq×aw,(12)K3=mB3O3OH4−×γB3O3OH4×mH+×γH+×aw2mBOH3aq×γBOH3aq3,(13)K4=mB4O5OH42−×γB4O5OH42−×mH+×γH+2×aw3mBOH3aq×γBOH3aq4.In equations (10)–(13), K1, K2, K3, and K4 represent the equilibrium constant equations for equations (6)–(9). The solution is saturated with sodium borate when B(OH)3 is unsaturated, and the solution is alkaline, taking NaB4O5(OH)4 · 8H2O for example. The dissolution equilibrium equations are as follows. The relationship between boron species can be represented in equations (15)–(17).(14)NaB4O5OH4·8H2Os=2Na++B4O5OH4−+8H2O(15)BOH4−=BOH3aq+OH−(16)3BOH4−=B3O3OH4−+2OH−+3H2O(17)4BOH4−=B4O5OH42−+2OH−+5H2OThe solubility product constant of NaB4O5(OH)4 · 8H2O (K5) at a certain temperature and pressure is shown in equation (18). The equilibrium constants for equations (15)–(17) are shown in equations (19)–(21):(18)K5=mNa+×γNa+2×mB4O5OH42−×γB4O5OH42−×aw8,(19)K6=mBOH3aq×γBOH3aq3×mOH−×γOH−mBOH4−×γBOH4−,(20)K7=mB3O3OH4−×γB3O3OH4−×mOH−×γOH−2×aw3mBOH4−×γBOH4−3,(21)K8=mB4O5OH42−×γB4O5OH42−×mOH−×γOH−2×aw5mBOH4−×γBOH4−4.In equations (18)–(21), K5, K6, K7, and K8 represent the equilibrium constant equations for equations (18)–(21).B5O6(OH)4− cannot be neglected in the solution in the system NaB5O6(OH)4-H2O when the concentration of NaB5O6(OH)4 is not very low [7]. In the system Na2O-B2O3-H2O, the concentration of B5O6(OH)4− may be not neglected when the solution is saturated with NaB5O6(OH)4·3H2O. B5O6(OH)4− will convert into B(OH)3 and B3O3(OH)4− when the concentration of NaB5O6(OH)4 is low. Therefore, the dissolution equilibrium constant of B5O6(OH)4− (K9) can be calculated with equation (23) because of the lacking parameters for B5O6(OH)4−:(22)NaB5O6OH4·3H2Os=Na++B5O6OH4−+3H2O=Na++B3O3OH4?+2BOH3(23)K9=mNa+×γNa+×mB3O3OH4−×γB3O3OH4−×mBOH3×γBOH32.According to the Pitzer model, the activity and osmotic coefficients are parametric functions ofβ(0), β(1), β(2), CØ, θaa′, ψaa′c, λNc,λNa, and ζNca. β(0), β(1), β(2), and CØ are the parameters of a single salt; θaa′ represents the interaction between the two ions with the same sign, and ψaa′c represents the interactions among the three ions, in which the sign of the third ion is different from the first two ions. Combining the charge conservation and matter conservation equations, the compositions of different species at equilibrium and solubilities for the system Na2O-B2O3-H2O can be calculated with the above equations with the Pitzer parameters and standard chemical potentials (μΘ/RT) of different species.


## 3. Result and Discussion

The experimental and calculated solubilities of boundary point saturated with B(OH)3 and invariant points for the ternary system Na2O-B2O3-H2O at 298.15 K are shown in Table 1. The comparisons of experimental and calculated phase diagrams in the system at 298.15 K are shown in Figure 1. The point A, which is saturated with B(OH)3, is the boundary point in the system Na2O-B2O3-H2O. There are three invariant points (E1, E2, and E3) and four solubility curves in the system. According to Table 1 and Figure 1, the calculated values are in agreement with the experimental values except point E3. The results show that the Pitzer model with four boron species is reliable for calculating the solubilities in the system Na2O-B2O3-H2O. From A to E2, w(B2O3) increased as w(Na2O) increases and reaches the maximum data at point E2. The point with minimum w(B2O3) in Figure 1 is shown as point B. The solubility curve saturated with Na2B4O5(OH)4 · 8H2O can be separated into two parts E2B and BE3. From E2 to B, w(B2O3) decreased sharply as w(Na2O) decreased. However, w(B2O3) increased relatively gently as w(Na2O) increases from B to E3. In the solubility curve saturated with NaB(OH)4 · 2H2O, w(B2O3) decreased with w(Na2O) increasing.Table 1
Experimental and calculated solubilities of invariant points for the system Na2O-B2O3-H2O at 298.15 K.
No.Na2OB2O3pHEquilibrium solid phaseRef.AExperimental data0.003.064.27H3BO3[12]Experimental data0.003.252.50H3BO3[27]ACalculated data0.003.073.15H3BO3This workE1Experimental data1.6910.26—H3BO3 + NaB5O8·5H2O[12]E1Experimental data1.6210.086.22H3BO3 + NaB5O8·5H2O[14]E1Calculated data1.8310.276.50H3BO3 + NaB5O8·5H2OThis workE2Experimental data2.7312.737.18NaB5O8·5H2O + Na2B4O7·10H2O[12]E2Experimental data2.8212.70—NaB5O8·5H2O + Na2B4O7·10H2O[14]E2Calculated data2.8713.106.83NaB5O8·5H2O + Na2B4O7·10H2OThis workE3Experimental data9.3810.6413.08Na2B4O7·10H2O + NaBO2·4H2O[12]E3Calculated data10.3412.0812.73Na2B4O7·10H2O + NaBO2·4H2OThis workFigure 1
Experimental and calculated phase diagrams in the system Na2O-B2O3-H2O at 298.15 K. □, data from ref.; ▲, data from ref.; ○, data from ref.; —, calculated data.The H+ or OH− concentration cannot be neglected in the system Na2O-B2O3-H2O at 298.15 K. The calculated and experimental pH diagrams were plotted, as shown in Figure 2. The mass fractions (100w) of Na2O were used as the abscissa in Figure 2. The calculated pH data are in accordance with the experimental results except some points. The pH datum for point A is 4.27 from Валяшко [12] and 2.50 from Li [27] in Table 1. Considering the experimental error, the calculated data for point A (3.15) can be considered to be in agreement with the experimental data. The pH data increased with increasing w (Na2O). The changing trend varied in different curves saturated with different salts. With the calculated pH diagram, the invariant points in the system can be roughly judged.Figure 2
Experimental and calculated pH data in the system Na2O-B2O3-H2O at 298.15  K. □, data from ref.; ▲, data from ref.; ★, calculated data in the invariant points; —, calculated data.The reasons about the difference between the calculated solubility and pH data with experimental results are complicated. On the one hand, only four boron species were considered in the solution of the system Na2O-B2O3-H2O in this model calculation. However, B5O6(OH)4– may exist in the solution in the system [7]. Moreover, the concentration of B5O6(OH)4– cannot be neglected as m (B) in the solution increases [7]. On the other hand, the lacking Pitzer parameters for boron ions cannot be considered as zero. Therefore, the difference between the experimental and calculated values is inevitable, and it was controlled to the minimum based on our current knowledge.The mole fractions (xi) for the four boron species in this ternary system calculated with the Pitzer model are shown in Figure 3. The mole fraction of the four boron species (xi) can be calculated with equations (24)–(27), which is the same as our previous work [22]. In equations (24)–(27), B42–, B3–, B–,and B represent B4O5(OH)42–, B3O3(OH)4–, B(OH)4–, and B(OH)3.(24)xB42−=4mB42−4mB42−+3mB3−+mB−+mB,(25)xB3−=3mB42−4mB42−+3mB3−+mB−+mB,(26)xB−=mB−4mB42−+3mB3−+mB−+mB,(27)xB=mB4mB42−+3mB3−+mB−+mB.Figure 3
Variation in the distribution of boron species in the system Na2O-B2O3-H2O at 298.15 K: (a) B4O5(OH)42–; (b) B3O3(OH)4–; (c) B(OH)4–; (d) B(OH)3.
(a)(b)(c)(d)The variation trends for the relationships betweenxi and w (Na2O) are different in Figure 3. With the difference, the invariant points can be judged. From Figure 3(a), x(B4O5(OH)42–) increased from point A to E2 as w(Na2O) increased. In the curve E2E3 saturated with Na2B4O5(OH)4 · 8H2O, x(B4O5(OH)42–) firstly increased sharply as w(Na2O) decreased, and then decreased sharply as w(Na2O) increased. In the curve saturated with NaB(OH)4 · 2H2O in Figure 3(a), x(B4O5(OH)42−) decreased to nearly zero. In Figure 3(b), x(B3O3(OH)4–) increased from points A to E2. From points E2 to E3, x(B3O3(OH)4–) decreased to nearly zero. x(B3O3(OH)4–) can be neglected in the curve saturated with NaB(OH)4 · 2H2O. x(B(OH)4–) in Figure 3(c) is nearly zero in the curves AE1 and E1E2. x(B(OH)4–) increased from points E2 to E3 and reached the maximum data at E3. In the curve saturated with NaB(OH)4 · 2H2O, x (B(OH)4–) increased sharply to the maximum and became stable with the mole fraction no less than 0.99. In Figure 3(d), x (B(OH)3) decreased as w (Na2O) increased from point A to E2. In the curve E2E3, x (B(OH)3) decreased to nearly zero. x (B(OH)3) can be neglected if w (Na2O) is more than 0.028. From Figure 3, the mole fraction of the four boron species is mainly affected by the ratio of B2O3 and Na2O in the solution, which affects the equilibrium solid phase in the system Na2O-B2O3-H2O.From Figure3, the dominant boron species in solutions saturated with different salts vary greatly. The main boron species are B(OH)3 and B3O3(OH)4– in the solution saturated with B(OH)3 or NaB5O6(OH)4·3H2O. B(OH)4– is the dominant boron species in the solution saturated with NaB(OH)4·2H2O. The boron species are very different in the solution saturated with Na2B4O5(OH)4·3H2O. When w(Na2O) is less than 0.028, the four boron species exist in the solution. However, the mass fraction of B3O3(OH)4− and B(OH)3 can be neglected if w(Na2O) is more than 0.028. The dominant boron species is B(OH)4− in the solution if w(Na2O) is more than 0.028.


## 4. Conclusions

The Pitzer model of boron species in the ternary system Na2O-B2O3-H2O at 298.15 K was constructed. The solubilities; concentration of four boron species B(OH)3, B(OH)4−, B3O3(OH)4−, and B4O5(OH)42−, and H+ (OH–) in the system Na2O-B2O3-H2O were calculated with the Pitzer model. The boron species B5O6(OH)4− was not considered in the model calculation. The calculated solubility and pH data are in accordance with the experimental results. The Pitzer model can be used to describe the experimental values. The distributions of the four boron species in the solution were obtained. The mole fractions of the four boron species are mainly affected by the ratio of B2O3 and Na2O in the solution. The dominant boron species in the solution saturated with different salts vary greatly. The main boron species are B(OH)3 and B3O3(OH)4– in the solution saturated with B(OH)3 or NaB5O6(OH)4·3H2O. B(OH)4– is the dominant boron species in the solution saturated with NaB(OH)4 · 2H2O. The results can supply a theoretical reference for sodium borate separation from brine.



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