Phase Equilibrium of the Quaternary System LiBr-Li₂SO₄-KBr-K₂SO₄-H₂O at 308.15 K

Abstract

The phase equilibria of the reciprocal quaternary system LiBr-Li₂SO₄-KBr-K₂SO₄-H₂O and its ternary sub-systems LiBr-Li₂SO₄-H₂O and KBr-K₂SO₄-H₂O at 308.15 K were studied using the isothermal dissolution equilibrium method. Then, the solubility data of the equilibrium solutions were collected, and the phase diagrams were plotted. The phase diagrams of the ternary sub-systems at 308.15 K were compared with those at other temperatures. This study found that the phase diagram of the LiBr-Li₂SO₄-H₂O system at 308.15 K consisted of an invariant point, two solid-phase crystallization regions of Li₂SO₄·H₂O and LiBr·2H₂O, and their corresponding solubility curves. The system generated two hydrated salts, which belonged to the hydrate type I phase diagram. The phase diagram of the KBr-K₂SO₄-H₂O system at 308.15 K consisted of an invariant point, two univariant solubility curves, and two solid-phase crystallization regions of KBr and K₂SO₄, and no solid solution and double salts were formed. Thus, it belonged to a simple co-saturation type phase diagram. In the LiBr-Li₂SO₄-KBr-K₂SO₄-H₂O system, K₂SO₄·Li₂SO₄ double salt formed at 308.15 K, and the phase diagram consisted of three invariant points, five crystallization regions, and seven univariant solubility curves.

1. Introduction

Lithium and its compounds have been widely used in aerospace, battery materials, ceramic glass, aluminum electrolysis, medicine, and other fields [1]. Lithium resources mainly exist in salt-lake brine and ore, among which lithium reserves in brine account for about 70–80% of total lithium resources [2,3]. To meet the increasing demand for lithium resources, the development and extraction of lithium from brine are needed [4]. Global lithium resources are mainly distributed in South American countries, Australia, and China [5]. The Sichuan Basin in China contains rich brine reserves and has a long mining history. Before 1949, salt mines were mined mainly for human consumption, thus only sodium chloride was extracted, and some useful resources, such as Li⁺, K⁺, Br⁻, B³⁺, Sr²⁺, Rb⁺, Cs⁺, I⁻, have been underutilized [6]. Since the beginning of the 21st century, due to the rapid development of new energy vehicles, the demand for lithium resources has grown, which drives the research on lithium extraction from brine [7].

Because brine is a complex electrolyte system, its comprehensive utilization depends on the guidance of the water–salt system phase diagram. In recent years, numerous studies have been conducted around the brine system in the Sichuan Basin [8], and the results indicated that the LiBr-KBr-H₂O system at 273.15 K [9], 288.15 K [10], 298.15 K [11], 308.15 K [9] and 323.15 K [12] showed simple co-saturation phase diagrams, confirming that double salt K₂SO₄·Li₂SO₄ will form in the Li₂SO₄-K₂SO₄-H₂O system at these temperatures [13,14,15,16]. In the LiBr-Li₂SO₄-H₂O system, the corresponding solid phases of the saturation point at 298.15 K were Li₂SO₄·H₂O and LiBr·2H₂O [17]. The KBr-K₂SO₄-H₂O system at multiple temperatures [18,19,20] all showed simple co-saturation type phase diagrams.

To realize the utilization of underground brine in the Sichuan Basin, the phase diagram of LiBr-Li₂SO₄-KBr-K₂SO₄-H₂O and its sub-systems (LiBr-Li₂SO₄-H₂O, KBr-K₂SO₄-H₂O) were studied at 308.15 K and 100.5 kPa in this work. Many studies have been conducted on related quaternary systems, such as the LiBr-Li₂SO₄-NaBr-Na₂SO₄-H₂O [21], LiCl-Li₂SO₄-KCl-K₂SO₄-H₂O [22,23], NaBr-Na₂SO₄-KBr-K₂SO₄-H₂O [24,25,26], and NaCl-Na₂SO₄-KCl-K₂SO₄-H₂O systems [27]. On the basis of these research results, the phase diagrams of these quaternary systems were compared, and the phase equilibrium characteristics of these quaternary systems were summarized.

2. Experimental Materials and Methods

2.1. Experimental Reagents and Instruments

Table 1. Chemical Reagents.

Chemical Reagent	CAS Reg. No.	Mass Fraction Purity	Supplier
LiBr	7550-35-8	≥99.90%	Aladdin Industrial Corporation
Li2SO4	10377-48-7	≥99.99%	Aladdin Industrial Corporation
KBr	7758-02-3	≥99.95%	Aladdin Industrial Corporation
K2SO4	7778-80-5	≥99.99%	Aladdin Industrial Corporation

lists the main experimental reagents. The pH of the distilled water in the experiment was 6.65 and the conductivity was less than 0.8 × 10⁻⁴ S/m.

The main instruments used in the experiment are shown in

Table 2. Chemical Instruments.

Instrument Name	Type	Accuracy of Measurement	Supplier
X-ray diffraction	DSFOCUS	-	Da Vinci type, Brucker AXS, Germany
A magnetic stirring thermostatic bath	HXC-500-8A	±0.05 K	Changzhou Langyue Instrument Manufacturing Co., Ltd., China
Electric blast drying oven	101-1ABS	±1 K	Beijing Yongguangming Medical Instrument Factory, China
Electronic balance	FA2204B	±0.0001 g	Shanghai Youke Instrument Co., Ltd., China

. The composition of the solid phase in equilibrium was determined by X-ray diffraction. The magnetic stirring thermostatic bath was used to ensure the constant stirring speed and temperature of the solution during the reaction process.

2.2. Experimental Methods

The solubility of each system in this work was obtained by the isothermal dissolution method. First, the solubility of KBr, K₂SO₄, LiBr, and Li₂SO₄ at 308.15 K were determined and verified. Subsequently, additional salt was introduced into the saturated binary system solution gradually, and the solubilities of the ternary systems were obtained after they reached the dissolution equilibrium. Finally, a third salt was gradually introduced to the invariant-point solution of the ternary sub-system to obtain the phase solubility of the LiBr-Li₂SO₄-KBr-K₂SO₄-H₂O system. During experimentation, the prepared solution was stirred for 12 h and allowed to stand for 10 h to obtain the supernatant. Then, the liquid phase composition of the supernatant was determined. These experimental procedures were repeated until the liquid phase composition of the solution showed no more changes, indicating that the system reached equilibrium. The experimental results show that the LiBr-Li₂SO₄-KBr-K₂SO₄-H₂O system reached equilibrium after 6–9 days at 308.15 K. This equilibrium time was consistent with the literature [19,21,22].

In the quaternary system calculations, the Jänecke index (J) values of each ion, and H₂O were used, and the calculation methods are shown in Equations (1)–(6). In this paper, the proportion of different ions in the saturated solution was expressed by mass fraction (w).

$$\mathrm{A}=\frac{{w(\mathrm{Li}}^{+})}{13.882}+\frac{{w(\mathrm{K}}^{+})}{78.197}+\frac{{w(\mathrm{Br}}^{-})}{159.808}+\frac{{w(\mathrm{SO}}_4^{2-})}{96.063}$$

(1)

$$\mathrm{J}\left({\mathrm{Li}}_2^{2+}\right)=\frac{{w(\mathrm{Li}}^{+})}{\mathrm{A} \times 13.882} \times 100 \times 2$$

(2)

$$\mathrm{J}\left({\mathrm{K}}_2^{2+}\right)=\frac{{w(\mathrm{K}}^{+})}{\mathrm{A} \times 78.197} \times 100 \times 2$$

(3)

$$\mathrm{J}\left({\mathrm{Br}}_2^{2-}\right)=\frac{{w(\mathrm{Br}}^{-})}{\mathrm{A} \times 159.808} \times 100 \times 2$$

(4)

$$\mathrm{J}\left({\mathrm{SO}}_4^{2-}\right)=\frac{{w(\mathrm{SO}}_4^{2-})}{\mathrm{A} \times 96.063} \times 100 \times 2$$

(5)

$$\mathrm{J}\left({\mathrm{H}}_2\mathrm{O}\right)=\frac{{w(\mathrm{H}}_2\mathrm{O})}{\mathrm{A} \times 18.02} \times 100 \times 2$$

(6)

2.3. Analysis Methods

The chemical analysis method for each ion in this work was as follows. The concentration of Li⁺ was obtained according to the atomic absorption assisted subtraction method (uncertainty within ± 0.005), the concentration of K⁺ content was measured by the atomic absorption method (uncertainty within ± 0.005), the concentration of Br⁻ was determined according to the silver nitrate titration method (uncertainty within ± 0.005), and the concentration of SO₄²⁻ was determined by the sulfate gravimetric method (uncertainty within ± 0.005). The solid phase composition at equilibrium was measured by the wet-residue method and X-ray diffraction crystallography.

3. Results and Discussion

3.1. Phase Equilibrium of the LiBr-Li₂SO₄-H₂O System

Table 3. Solubility of LiBr-Li₂SO₄-H₂O at 308.15 K and 100.5 kPa ^a.

No.	Composition of Liquid Phase/w (%)		Wet Solid Phase/w (%)		Solid Phase
	LiBr	Li2SO4	LiBr	Li2SO4
1, C1	0.00	25.35	-	-	Ls1
2	4.63	21.10	1.72	63.04	Ls1
3	11.08	15.27	5.60	50.93	Ls1
4	21.32	9.07	9.99	49.87	Ls1
5	27.15	6.03	8.68	60.49	Ls1
6	33.31	2.71	12.35	54.77	Ls1
7	39.61	0.63	11.82	60.57	Ls1
8	42.48	0.18	9.99	66.06	Ls1
9	45.17	0.10	14.90	57.54	Ls1
10	49.88	0.05	11.82	65.73	Ls1
11	52.52	0.03	15.90	60.08	Ls1
12	56.54	0.02	14.18	64.26	Ls1
13, E1	63.21	0.01	54.77	17.13	Ls1 + Lb2
14, D1	63.93	0.00	-	-	Lb2

^a Standard uncertainties: u(T) = 0.05 K; u(P) = 2 kPa; u(mass fraction) = 0.03; Ls1, Li₂SO₄·H₂O, Lb2, LiBr·2H₂O.

shows the solubility data in the LiBr-Li₂SO₄-H₂O system at 308.15 K. The XRD characterization patterns of invariant point E₁ are shown in Figure 1. According to Table 3, the phase diagram of the LiBr-Li₂SO₄-H₂O system at 308.15 K was drawn (Figure 2a), and Figure 2b shows a partially enlarged view near invariant point E₁.

A₁ and B₁ represented the pure solid phase points of Li₂SO₄·H₂O and LiBr·2H₂O (Figure 2), respectively, C₁ and D₁ were the saturation points of Li₂SO₄-H₂O and LiBr-H₂O, respectively, E₁ denoted the invariant point of the system, and the liquid phase compositions at this point were w(LiBr) = 63.21%, w(Li₂SO₄) = 0.01%, and w(H₂O) = 36.78%. The equilibrium solid phases at this point were Li₂SO₄·H₂O and LiBr·2H₂O. Curve C₁E₁ indicated the solubility curve of Li₂SO₄·H₂O, and curve D₁E₁ corresponded to the solubility curve of LiBr·2H₂O. Fields A₁C₁E₁ and B₁D₁E₁ denoted the crystallization regions of Li₂SO₄·H₂O, and LiBr·2H₂O, respectively. Fields A₁E₁B₁ was the crystallization region of Li₂SO₄·H₂O and LiBr·2H₂O.

The phase diagram consisted of two solid crystalline regions Li₂SO₄·H₂O and LiBr·2H₂O, two solubility curves C₁E₁ and D₁E₁, and one saturation point E₁. The system generated two hydrated salts; therefore, its phase diagram belonged to hydrate type I. The C₁E₁ curve in Figure 2a indicated that the mass percentage of Li₂SO₄ decreased sharply with LiBr addition. When the mass percentage of LiBr was 39.61%, the content of Li₂SO₄ dropped below 1%, and the crystallization region of LiBr·2H₂O occupied a very small area in the phase diagram. This shows that LiBr had a strong salting-out effect on Li₂SO₄·H₂O, making it easier to separate from the solution.

The phase equilibrium data of the LiBr-Li₂SO₄-H₂O system at the co-saturation points of 298.15 K and 308.15 K are shown in

Table 4. Solubilities of salts at the invariant points. In ternary system LiBr-Li₂SO₄-H₂O at 298.15 K and 308.15 K.

Temperature/K	Refs	Composition of Liquid Phase/w (%)		Solid Phase
		LiBr	Li2SO4
298.15	[21]	62.16	0.00	LiBr·2H2O
		61.27	0.07	Li2SO4·H2O + LiBr·2H2O
		0.00	25.78	Li2SO4·H2O
308.15	this work	63.93	0.00	LiBr·2H2O
		63.22	0.01	Li2SO4·H2O + LiBr·2H2O
		0.00	25.35	Li2SO4·H2O

. The phase diagrams of the system at these two temperatures are shown in Figure 3. By comparison, we found that the number of saturation points, solubility curves, and crystallization zones of the system were the same at these two temperatures. The equilibrium solid phases corresponding to the saturation point were LiBr·2H₂O and Li₂SO₄·2H₂O. The difference was that when the temperature increased by 10 K, the mass fraction (w) of Li₂SO₄ in the system decreased from 25.78% to 25.35%, while the mass fraction (w) of LiBr in the system increased from 62.16% to 63.93%. Meanwhile, the crystallization zone of Li₂SO₄·2H₂O increased while that of LiBr·2H₂O decreased. Based on this observation, we could fabricate an LiBr·2H₂O crystal by lowering the temperature.

3.2. Phase Equilibrium of the KBr-K₂SO₄-H₂O System

Table 5. Solubility of KBr-K₂SO₄-H₂O at 308.15 K and 100.5 kPa ^a.

No.	Composition of Liquid Phase/w (%)		Wet Solid Phase/w (%)		Solid Phase
	KBr	K2SO4	KBr	K2SO4
1, C2	0.00	12.05	-	-	Ar
2	3.31	10.25	0.72	81.55	Ar
3	9.57	6.87	2.28	76.11	Ar
4	14.69	4.86	4.70	70.59	Ar
5	18.67	3.69	5.26	72.95	Ar
6	22.70	2.78	7.16	68.92	Ar
7	25.91	2.16	6.54	75.88	Ar
8	29.16	1.79	8.27	72.27	Ar
9	31.99	1.46	10.52	67.72	Ar
10	34.54	1.15	9.76	72.09	Ar
11	37.73	0.85	9.55	75.20	Ar
12	40.29	0.67	8.63	78.81	Ar
13, E2	41.77	0.59	40.37	20.21	Ar + KBr
14	42.03	0.30	75.17	0.13	KBr
15, D2	42.21	0.00	-	-	KBr

^a Standard uncertainties: u(T) = 0.05 K; u(P) = 2 kPa; u(mass fraction) = 0.03; Ar, K₂SO₄.

shows the solubility data of the KBr-K₂SO₄-H₂O system at 308.15 K, where the solid phase was analyzed by XRD characterization. The results indicated that the equilibrium solid phases of sample no. 13 were K₂SO₄ and KBr (Figure 4). The phase diagram (Figure 5a) was plotted based on the solubility data, and Figure 5b presents a partially enlarged view near invariant point E₂.

Points A₂ and B₂ corresponded to solid phases K₂SO₄ and KBr, respectively, while point C₂ and D₂ was the saturation point of K₂SO₄-H₂O and KBr-H₂O (Figure 5a), where w(K₂SO₄) was 12.05% and w(KBr) was 42.21%. In addition, the liquid phase composition was w(KBr) = 41.77%, w(K₂SO₄) = 0.59%, and w(H₂O) = 57.64% in saturated point E₂, and the equilibrium solid phases at this point were KBr and K₂SO₄.

The C₂E₂ curve was the solubility curve of K₂SO₄, where A₂E₂C₂ denoted the crystallization region of K₂SO₄. The solid phase corresponding to the solubility curve D₂E₂ in the partially enlarged view shown in Figure 5b was KBr, and B₂D₂E₂ was the crystallization region of KBr. As shown in Figure 5a, the region occupied by A₂E₂C₂ in the triangle was considerably larger than B₂D₂E₂, indicating that the crystallization region of KBr in this system was smaller than that of K₂SO₄, and had a strong salting-out effect on K₂SO₄. This system did not generate a solid solution or hydrated salts at 308.15 K; thus, it consisted of a simple phase diagram.

Table 6. Solid-liquid composition of saturation point. In KBr-K₂SO₄-H₂O system at different temperatures.

Temperature/K	Refs	Composition of Liquid Phase/w (%)		Solid Phase
		KBr	K2SO4
273.15	[18]	34.11	0.00	KBr
		35.54	0.68	KBr + K2SO4
		0.00	6.78	K2SO4
308.15	this work	42.21	0.00	KBr
		41.77	0.59	KBr + K2SO4
		0.00	12.05	K2SO4
373.15	[19]	50.98	0.00	KBr
		49.98	0.34	KBr + K2SO4
		0.00	19.40	K2SO4

lists the phase equilibrium data of the co-saturation points of the KBr-K₂SO₄-H₂O system at different temperatures. A comparison of phase diagrams is shown in Figure 6. The results show that the phase diagrams had the same characteristics at these three different temperatures, and the equilibrium solid phases corresponding to the saturation point were KBr and K₂SO₄. The mass percentage of K₂SO₄ in the K₂SO₄-H₂O system increased from 6.78% to 19.4%, and the mass percentage of KBr in the KBr-H₂O system increased from 34.11% to 50.98% when the temperature increased by 100 K. By analyzing the data of the saturation points at different temperatures, we found that KBr had a strong salting-out effect on K₂SO₄. These observations provided a scientific basis for the extraction and separation of K₂SO₄.

3.3. Phase Equilibrium of the LiBr-Li₂SO₄-KBr-K₂SO₄-H₂O System

Table 7. Solubility of the LiBr-Li₂SO₄-KBr-K₂SO₄-H₂O system at 308.15 K and 100.5 kPa ^a.

No.	Composition of Solution/w(%)				Jänecke Index J/(J)			Equilibrium Solid Phases
	Li+	K+	Br−	SO42−	J(Li22+)	J(SO42−)	J(H2O)
1, A3	1.26	5.31	0.00	15.23	57.16	100.00	2736.54	Ar + Db4
2	1.18	5.15	3.19	12.60	56.44	86.79	2859.03	Ar + Db4
3	1.13	5.09	6.42	10.18	55.48	72.53	2930.61	Ar + Db4
4	1.11	4.92	10.79	7.23	55.93	52.73	2951.30	Ar + Db4
5	1.10	5.37	15.00	5.18	53.56	36.50	2754.78	Ar + Db4
6	1.05	5.62	17.43	3.73	51.37	26.25	2707.28	Ar + Db4
7	1.11	6.66	23.19	1.92	48.37	12.08	2257.28	Ar + Db4
8	1.07	7.51	25.23	1.49	44.61	8.92	2072.09	Ar + Db4
9, E3	1.04	8.79	28.54	0.87	40.08	4.83	1796.40	Ar + Db4 + Kb
10, C3	0.00	13.99	28.04	0.33	0.00	1.90	1788.14	Ar + Kb
11	0.14	13.30	28.14	0.42	5.70	2.40	1784.31	Ar + Kb
12	0.35	12.13	28.03	0.48	14.01	2.75	1815.50	Ar + Kb
13	0.46	11.47	27.81	0.57	18.51	3.29	1841.01	Ar + Kb
14	0.67	10.45	28.04	0.64	26.65	3.64	1834.54	Ar + Kb
15	0.80	9.84	28.09	0.72	31.36	4.11	1832.67	Ar + Kb
16	1.43	7.59	30.97	0.57	51.43	2.98	1651.62	Db4 + Kb
17	1.80	6.31	32.78	0.48	61.57	2.37	1548.54	Db4 + Kb
18	2.34	4.14	34.74	0.41	76.10	1.93	1461.26	Db4 + Kb
19	2.76	2.95	37.26	0.32	84.07	1.40	1331.13	Db4 + Kb
20, E4	3.57	0.96	42.91	0.08	95.44	0.32	1081.07	Db4 + Kb + Ls1
21, B3	3.20	1.15	0.00	23.57	94.01	100.00	1630.50	Db4 + Ls1
22	2.95	1.11	3.78	19.53	93.77	89.58	1775.88	Db4 + Ls1
23,	2.71	1.06	8.16	15.18	93.54	75.57	1935.24	Db4 + Ls1
24	2.64	1.02	14.18	11.02	93.59	56.38	1940.70	Db4 + Ls1
25	2.50	1.05	16.91	8.39	93.05	45.23	2043.95	Db4 + Ls1
26	2.38	1.03	21.18	4.97	92.84	28.08	2121.04	Db4 + Ls1
27	2.54	1.11	26.36	3.13	92.80	16.47	1878.64	Db4 + Ls1
28	2.84	1.04	34.08	0.46	93.89	2.20	1566.76	Db4 + Ls1
29	3.91	0.91	46.82	0.05	96.04	0.17	913.66	Kb + Ls1
30	5.03	0.82	59.54	0.03	97.18	0.09	514.64	Kb + Ls1
31, E5	5.02	0.74	59.26	0.01	97.46	0.03	523.25	Kb + Ls1 + Lb2
32, F3	5.01	0.70	59.05	0.00	97.58	0.00	529.25	Kb + Lb2
33, D3	5.05	0.00	58.14	0.01	100.00	0.03	561.16	Ls1 + Lb2
34	4.68	0.46	54.77	0.01	98.78	0.03	558.94	Ls1 + Lb2

^a Standard uncertainties: u(T) = 0.05 K; u(P) = 2 kPa; u(mass fraction) = 0.03; Ar, K₂SO₄; Db4, K₂SO₄·Li₂SO₄; Kb, KBr; Ls1, Li₂SO₄·H₂O; Lb2, LiBr·2H₂O.

shows the solubility data of the LiBr-Li₂SO₄-KBr-K₂SO₄-H₂O system at 308.15 K. The XRD characterization results of the solid phase at invariant points E₃, E₄, and E₅ are shown in Figure 7. The dry salt phase diagram of the LiBr-Li₂SO₄-KBr-K₂SO₄-H₂O quaternary system at 308.15 K was plotted according to Table 7, as shown in Figure 8. Points A₃, B₃, C₃, D₃, and F₃ corresponded to the saturation points of each ternary subsystem. The liquid phase composition of each point is presented in Table 7. According to the XRD characterization results, the LiBr-Li₂SO₄-KBr-K₂SO₄-H₂O system contained three saturated points (E₃, E₄, and E₅). The equilibrium solid phases at point E₃ were K₂SO₄, KBr and K₂SO₄·Li₂SO₄, and all ion contents for this composition at this point were w(K⁺) = 8.79%, w(Li⁺) = 1.04%, w(Br⁻) = 28.54%, and w(SO₄²⁻) = 0.87%. The equilibrium solid phases at point E₄ were KBr, Li₂SO₄·H₂O, and K₂SO₄·Li₂SO₄, and all ion contents for this composition were w(K⁺) = 0.96%, w(Li⁺) = 3.57%, w(Br⁻) = 42.91%, and w(SO₄²⁻) = 0.08%. The equilibrium solid phases at point E₅ were Li₂SO₄·H₂O, LiBr·2H₂O, and KBr, and all ion contents for this composition were w(K⁺) = 0.74%, w(Li⁺) = 5.02%, w(Br⁻) = 59.26%, and w(SO₄²⁻) = 0.01%.

Figure 8 shows that there were seven solubility curves, namely, A₃E₃, B₃E₄, C₃E₃, E₃E₄, E₄E₅, D₃E₅, and F₃E₅. The corresponding equilibrium solid phases of A₃E₃ were K₂SO₄ and K₂SO₄·Li₂SO₄, while the corresponding equilibrium solid phases of B₃E₄ were K₂SO₄·Li₂SO₄ and Li₂SO₄·H₂O, those of C₃E₃ were K₂SO₄ and KBr, those of E₃E₄ were K₂SO₄·Li₂SO₄ and KBr, those of E₄E₅ were KBr and Li₂SO₄·H₂O, those of D₃E₅ were Li₂SO₄·H₂O and LiBr·2H₂O, and those of F₃E₅ were KBr and LiBr·2H₂O. There were five crystallization regions, among which A₃E₃C₃, A₃E₃E₄B₃, C₃E₃E₄E₅F₃, B₃E₄E₅D₃, D₃E₅F₃ corresponded to the crystalline regions of K₂SO₄, K₂SO₄·Li₂SO₄, KBr, Li₂SO₄·H₂O, and LiBr·2H₂O. The area in each crystalline region was different, and among these, the crystalline region of K₂SO₄ was the largest, accounting for more than 50% of the phase diagram followed by K₂SO₄·Li₂SO₄ double salt, which accounted for about 30–40%, Li₂SO₄·H₂O and KBr accounted for a few percent, and the crystallization region of LiBr·2H₂O was very small.

Figure 9 shows the water diagram of this quaternary system plotted with J(2Li⁺) and J(H₂O). The solubility curve C₃E₃ corresponding to K₂SO₄ and KBr shows smooth fluctuations, indicating that the addition of Li₂SO₄ had a weak effect on the equilibrium. In the solubility curves A₃E₃, B₃E_4, and E₄E₅, the value of J(H₂O) varied greatly with J(2Li⁺), indicating that Br⁻-containing salts had a great influence on the phase equilibrium of this system. The values of J(H₂O) near invariant points E₄ and E₅ were substantially lower than the other parts, suggesting that the mass percentage of H₂O in the solution near the crystallization region of LiBr·2H₂O was the smallest. A comprehensive analysis of the system shows that K₂SO₄ crystals most readily precipitated from the system, followed by K₂SO₄·Li₂SO₄ double salt crystals, and the LiBr·2H₂O crystals had the most difficulty precipitating from the system. Bromide salts had a strong salting-out effect on sulfate.

By summarizing the phase diagrams of the related systems, we found that double salts occurred in sulfate-containing systems that also contained two of the three elements of lithium, sodium, and potassium [21,22,23,24,25,26,27], for example, K₂SO₄·Li₂SO₄, Na₂SO₄·Li₂SO₄, and Na₂SO₄·3K₂SO₄. After comparing the phase diagrams of the systems, we found that the region of the double salt was relatively large, indicating that the double salt had weak solubility and could be easily separated from the system. However, the salts formed by Cl⁻, Br⁻, as well as alkali metals and their hydrated salts, which exhibited strong solubility in the system, were difficult to separate from the system.

4. Conclusions

The phase equilibria of quaternary systems (LiBr-Li₂SO₄-KBr-K₂SO₄-H₂O) and their subsystems (LiBr-Li₂SO₄-H₂O, KBr-K₂SO₄-H₂O) were studied. The results showed that at 308.15 K, two hydrated salts (Li₂SO₄·H₂O and LiBr·2H₂O) formed in the LiBr-Li₂SO₄-H₂O system. The crystallization region of LiBr in this system was considerably smaller than Li₂SO₄, and LiBr had a strong salting-out effect on Li₂SO₄. Compared with the phase equilibrium data of 298.15 K, we found that LiBr·2H₂O could be precipitated by decreasing the temperature. At 308.15 K, the solid solution and compound salt were not found in the KBr-K₂SO₄-H₂O system, which belonged to a simple co-saturation phase diagram. In addition, the crystallization region of KBr in this system was smaller than K₂SO₄, and KBr had a strong salting-out effect on K₂SO₄. At 308.15 K, the phase diagram of the LiBr-Li₂SO₄-KBr-K₂SO₄-H₂O system consisted of three invariant points, seven solubility curves, and five crystallization regions, i.e., the K₂SO₄, KBr, Li₂SO₄·H₂O, LiBr·2H₂O, and K₂SO₄·Li₂SO₄ crystallization regions. In this system, the crystallization region of LiBr·2H₂O was the smallest, while K₂SO₄ was the largest, indicating that K₂SO₄ could easily be separated from the system, and this result could be used for the separation and extraction of lithium salts in brine.