Solubility and Thermodynamics of Lithium Carbonate in Its Precipitation Mother Liquors

Abstract

This study systematically investigated the dissolution equilibrium of lithium carbonate (Li₂CO₃) in mixed Na₂CO₃-NaCl aqueous solutions through isothermal dissolution experiments spanning 283.15–353.15 K. Precise solubility determinations were conducted using a gravimetric analysis under controlled thermodynamic conditions. The obtained solubility data were successfully correlated with the Extended Debye–Hückel (E-DH) model, yielding residual standard deviations below 0.09, which validates the model’s applicability in this ternary system. Both experimental observations and theoretical predictions confirmed that increasing the salt molality enhances the synergistic suppression of the Li₂CO₃ solubility through combined common-ion and salt effects. The thermodynamic analysis revealed the dissolution process to be exothermic (ΔH_d < 0), and entropy change dominates (ξ_S ≈ 78%), with negative entropy changes (ΔS_d < 0) indicating predominant hydration ordering effects. These mechanistic insights establish critical thermodynamic benchmarks for optimizing lithium carbonate precipitation processes in brine lithium extraction operations.

1. Introduction

Lithium, a naturally occurring trace element, is widely distributed in geological formations, including igneous rocks, soils, brine deposits, seawater, and biological systems, across plant and animal organisms. Based on incomplete statistical data, current global lithium reserves are estimated at approximately 13 million metric tons (in lithium metal equivalent). Brine lithium resources are primarily concentrated in Bolivia, Chile, China, and the United States [1]. Li₂CO₃, a commercially vital compound in lithium salt production, functions both as a flux agent and performance-enhancing additive in glass and ceramic manufacturing. This inorganic salt also serves as a fundamental precursor for synthesizing specialized lithium compounds, including lithium tantalate (LiTaO₃) and lithium niobate (LiNbO₃) monocrystals—materials essential for manufacturing surface acoustic wave elements with optimized elastic properties [2,3]. Recent technological developments have revealed significant potential for high-purity lithium salts in emerging applications, particularly within new energy systems, advanced materials, and high-tech industries. These compounds have emerged as critical components in electric vehicle technologies, demonstrating a growing importance in sustainable transportation solutions.

Contemporary lithium extraction primarily focuses on pegmatite-type lithium minerals and lithium-enriched brine deposits, containing lithium-bearing minerals such as spodumene, petalite, lepidolite, and amblygonite. Prior to the 1990s, lithium production predominantly relied on solid mineral processing, a method constrained by high energy consumption, challenging tailings/wastewater management, and significant environmental impacts. Since 1996, salt lake brine extraction has emerged as the dominant global lithium production method, accounting for 80% of the worldwide Li₂CO₃ output. Major lithium-bearing salt lakes with proven reserves exceeding one million metric tons include Salar de Uyuni, Salar de Hombre Muerto, Salar de Atacama, and the Zabuye Salt Lake [4,5]. China possesses the world’s second-largest lithium resource reserves after Bolivia, with brine deposits constituting approximately 79% of its total lithium reserves. The Qinghai–Tibet Plateau hosts China’s primary salt lake lithium resources, which demonstrate comparable proven reserves to global counterparts and substantial economic potential, forming a critical foundation for national lithium industry development [6]. Notably, the Qaidam Basin in Qinghai contains brine lithium reserves of 15.201 million metric tons (as LiCl equivalent) [7].

Conventional brine lithium extraction techniques include precipitation, calcination-leaching, selective membrane separation, adsorption, and solvent extraction methods [7,8,9,10,11,12,13]. The industrial process involving LiCl production from brine followed by reaction crystallization with Na₂CO₃ to precipitate Li₂CO₃ faces persistent challenges: a low lithium yield, product purity limitations, a poor crystal morphology, and severe particle agglomeration. The Li₂CO₃ precipitation process represents a critical yet underdeveloped stage in the lithium production chain, combining purification/enrichment with precipitation. While purification techniques receive substantial research attention, precipitation technology remains relatively primitive.

Song et al. [14] systematically investigated Li₂CO₃ solubility and supersolubility in aqueous systems through a thermodynamic analysis. Wang et al. [15] extended this work to LiCl-NaCl-KCl-Na₂SO₄ mixed solutions, examining salt effects on Li₂CO₃’s metastable zone. Cheng et al. [16] determined the solubility of lithium carbonate (Li₂CO₃) in Na-K-Cl systems and employed the Pitzer model to fit its solubility in these solutions. Gisele Azimi et al. [17] carried out an in-depth study on the crystallization process of lithium carbonate; when mixing lithium sulfate and a sodium carbonate solution, the sodium sulfate was removed by freezing, the recovery of lithium was 90%, and the purity of the lithium carbonate was 99.0%.

Although significant progress has been made in lithium carbonate preparation using sodium carbonate precipitation, the resulting mother liquor system retains a mixed solution of NaCl and Na₂CO₃. Notably, the lithium loss during the carbonation precipitation process reaches up to 15%, highlighting the technical bottleneck that underscores the necessity for systematic investigation into the solubility mechanisms within the lithium carbonate precipitation system. However, fundamental studies on the solubility of Li₂CO₃ in Na₂CO₃-NaCl aqueous solutions remain critically lacking. This deficiency in phase equilibrium data directly impedes the optimization of lithium recovery efficiency in precipitation processes, despite its pivotal role in advancing industrial-scale lithium extraction. This study systematically examines the solubility of Li₂CO₃ in mixed Na₂CO₃-NaCl aqueous solutions across a temperature range of 278.15–358.15 K. Experimental solubility data were correlated using the Extended Debye–Hückel equation with subsequent thermodynamic parameter derivation through established thermodynamic modeling. The combined experimental and theoretical investigation aims to elucidate the dissolution behavior of Li₂CO₃ in mixed Na₂CO₃-NaCl aqueous solutions, while establishing fundamental data to optimize Li₂CO₃ precipitation processes.

2. Experimental Section

2.1. Instruments and Reagents

The main chemical reagents and instruments used in the experiments are listed in

Table 1. Reagent description table.

Chemical Reagents	CAS No.	Initial Purity w (w %)	Purified Method	Final Purity w (w %)	Source
NaCl	7647-14-5	≥95.0%	Recrystallization	≥99.5%	Sinopharm Chemical Reagent Co., Ltd., Shanghai, China.
Na2CO3	497-19-8	≥95.0%	Recrystallization	≥99.5%
Li2CO3	554-13-2	≥98.0%		≥98.0%

and

Table 2. Experimental apparatus.

Instruments	Type	Source
Magnetic Stirring Thermostat	HXC-500-8A	Beijing Huicheng Jiayi Technology Co., Beijing, China
Thermostatic Water Bath	VIVO RT4	ULEB Technology (Beijing) Co., Beijing, China
Automatic Electronic Analyzing Balance	BT224S	Sartorius Scientific Instruments Co., Beijing, China
Inductively Coupled Plasma Emission Spectrometer	PerkinElmer Avio 200	PerkinElmer Inc., Wellesley, MA, USA
X-ray Diffraction instrument	D8 Discover	Bruker Co., Billerica, MA, USA

, respectively. All experimental solutions were prepared through direct dissolution of analytical-grade reagents with strict quality control. Secondary deionized water (DDW) with conductivity < 1 × 10⁻⁴ S·m⁻¹ served as the solvent system. Prior to application, the DDW was decarbonized by sequential heating and boiling processes, attaining a stable pH value of 6.60.

2.2. Experimental Method

This study employed the isothermal dissolution method [18] to determine lithium carbonate (Li₂CO₃) solubility. Sodium carbonate (Na₂CO₃) and sodium chloride (NaCl) mixed solutions of varying molalities were separately prepared. Each 150 mL aliquot was transferred to a polyethylene conical flask containing 5 g Li₂CO₃ excess solid. The sealed flasks were immersed in a thermostated magnetic stirring bath, maintaining constant temperature (±0.05 °C) with continuous agitation throughout the experiment. Following five-day equilibration with daily sampling verification, supernatants were syringe-filtered through 0.22 μm microporous membranes (25 mm diameter) to eliminate residual particulates. Filtered aliquots were quantitatively transferred to 10 mL polyethylene vials and diluted to 250 mL with deionized water for subsequent analysis. Equilibrium was confirmed when consecutive daily measurements showed <0.5% variation in ionic molalities, at which point the final stabilized values were recorded as solubility data. Solid phases were immediately collected via vacuum filtration to minimize atmospheric exposure. Phase composition of equilibrium solids was verified by X-ray diffraction (XRD) analysis. Powder XRD patterns were collected on a diffractometer using Cu Kα radiation (Kα1 = 1.540598 Å and Kα2 = 1.544426, Ratio K-α2/K-α1 = 0.5) over a 2θ range of 5–80°, with a step size of 0.02° and a counting time of 38 s per step.

2.3. Analytical Methods

Lithium ion (Li⁺) molalities were analyzed using inductively coupled plasma optical emission spectrometry (ICP-OES). Carbonate (CO₃²⁻) molalities were analyzed via standardized hydrochloric acid titration. Chloride (Cl⁻) molalities were analyzed through mercurimetric titration with Hg(NO₃)₂ standard solution, employing diphenylcarbazide–bromophenol blue mixed indicator system [19].

3. Results and Discussion

3.1. Solubility of Li₂CO₃ in Mixed Solution

To validate the experimental accuracy of Li₂CO₃ solubility determinations, the molal solubility in deionized water was experimentally measured (

Table 3. Solubility of Li₂CO₃ in pure water (p = 77.3 KPa) ^a.

T (K)	Solubility of Li2CO3 (Pure Water)				100 × ε
	Experimental Data (mol·kg−1)	Literature Data [14] (mol·kg−1)	Literature Data [17] (mol·kg−1)	Literature Data [18] (mol·kg−1)	Literature [14]	Literature [17]	Literature [18]
283.15	0.1932	-	-		-	-	-
293.15	0.1838	0.1841	0.1801	0.18041	−0.16	2.08	−1.84
303.15	0.1689	0.1676	0.1705	0.16893	0.80	−0.93	0.02
313.15	0.1571	0.1554	0.1583	0.15648	1.11	−0.74	−0.39
323.15	0.1464	0.1487		0.14819	−1.56	-	1.22
333.15	0.1374	0.1388	0.1367	0.13706	−0.99	0.51	−0.25
343.15	0.1291	0.1310		0.12596	−1.48		−2.43
353.15	0.1168	0.1179	0.1151	0.11542	−0.97	1.51	−1.18

^a The standard uncertainties u are u(T) = 0.03 K, u(p) = 5 kPa, and u(m) for Li₂CO₃ is 0.0060.

). The comparative analysis revealed relative deviations (RDs) below 0.0243 versus the literature values, demonstrating an excellent agreement between experimental and published solubility data.

The solubility of Li₂CO₃ in mixed Na₂CO₃-NaCl aqueous solutions was experimentally determined across the temperature range of 283.15–353.15 K, with the comprehensive dataset tabulated in

Table 4. Solubility of Li₂CO₃ in mixed solutions of Na₂CO₃ and NaCl at 283.15–353.15 K and pressure of p = 77.3 kPa ^a.

Na2CO3 (mol·kg−1)	NaCl (mol·kg−1)	Li2CO3 (mol·kg−1)
		283.15 K	293.15 K	303.15 K	313.15 K	323.15 K	333.15 K	343.15 K	353.15 K
0.500	0	-	-	0.1295	0.1215	0.1141	0.1077	0.0976	0.0835
0.500	0.100	-	0.1379	0.1283	0.1204	0.1135	0.1066	0.0955	0.0827
0.500	0.200	-	0.1360	0.1270	0.1189	0.1122	0.1055	0.0943	0.0818
0.500	0.500	0.1449	0.1349	0.1227	0.1160	0.1081	0.1020	0.0916	0.0790
0.500	1.000	0.1439	0.1308	0.1144	0.1085	0.1027	0.0954	0.0861	0.0737
0.500	1.500	0.1428	0.1239	0.1045	0.0987	0.0929	0.0878	0.0794	0.0675
0.500	2.000	0.1394	0.1126	0.0932	0.0870	0.0828	0.0792	0.0707	0.0606
0.500	2.500	0.1319	0.1006	0.0803	0.0757	0.0725	0.0696	0.0611	0.0529
0.500	3.000	0.1217	0.0880	0.0660	0.0634	0.0618	0.0590	0.0520	0.0444
0	1.000	0.1091	0.0743	0.1418	0.1352	0.1229	0.1147	0.1029	0.0902
0.050	1.000	0.0966	0.1504	0.1388	0.1342	0.1207	0.1125	0.1007	0.0884
0.100	1.000	0.0823	0.1471	0.1359	0.1276	0.1186	0.1104	0.0987	0.0866
0.250	1.000	0.1584	0.1449	0.1273	0.1205	0.1124	0.1044	0.0942	0.0815
0.500	1.000	0.1550	0.1369	0.1144	0.1085	0.1027	0.0954	0.0861	0.0737
0.760	1.000	0.1528	0.1239	0.1025	0.0982	0.0933	0.0874	0.0787	0.0665
1.000	1.000	0.1449	0.1117	0.0930	0.0891	0.0854	0.0812	0.0712	0.0608
1.250	1.000	0.1319	0.1001	0.0846	0.0810	0.0778	0.0743	0.0654	0.0558
1.500	1.000	0.1196	0.0914	0.0777	0.0733	0.0710	0.0685	0.0602	0.0517

^a The standard uncertainties u are u(T) = 0.03 K and u(p) = 5 kPa. u_r(m) for Na₂CO₃ and for NaCl are 0.0050 and 0.0050, respectively. u(m) for Li₂CO₃ is 0.0060.

. Figure 1 displays the X-ray diffraction (XRD) patterns characterizing the equilibrated solid phases. The XRD analysis confirmed the absence of Na₂CO₃ and NaCl crystalline phases in the equilibrium solids. This observation establishes that the measured molality of Li₂CO₃ in the liquid phase directly represents its thermodynamic solubility under the experimental conditions.

To systematically investigate the influence of the main components in the lithium precipitation mother liquor, Na₂CO₃ and NaCl, on the solubility of Li₂CO₃, we fixed Na₂CO₃ at 0.5 mol·kg⁻¹ and NaCl at 1.0 mol·kg⁻¹ based on the ionic concentrations in the mother liquor, respectively, while varying the concentration of the other salt. We plotted the Li₂CO₃ solubility values as a function of the temperature and the molality of the two salts, as shown in Figure 2. The solubility of Li₂CO₃ in the mixed electrolyte system exhibits a clear negative correlation with the temperature, which is consistent with the inverse relationship observed in pure water systems. As the molality of either constituent salt increases, the solubility gradually decreases. This dissolution behavior results from the combined effects of (i) the common-ion effect primarily attributed to the carbonate ions from Na₂CO₃ and (ii) the non-common-ion salt effect arising from collective ionic interactions in the mixed electrolyte system.

To isolate the individual effects of Na₂CO₃ and NaCl on the Li₂CO₃ solubility, Figure 3 illustrates the solubility variations under controlled conditions with incremental salt additions. Experimental data demonstrate systematic decreases in the Li₂CO₃ solubility with increasing concentrations of both salts, albeit through distinct mechanisms. As shown in Figure 3a, at a fixed Na₂CO₃ concentration (0.5 mol·kg⁻¹), the Li₂CO₃ solubility decreases monotonically with the rising NaCl concentration. This behavior originates from a non-specific salting-out effect induced by Na⁺ and Cl⁻: Na⁺ compresses the ionic atmosphere surrounding CO₃²⁻ through electrostatic screening, significantly reducing the activity coefficient of CO₃²⁻ (γCO₃²⁻). Simultaneously, Cl⁻ enhances the solution polarity, promoting Li⁺ hydration and decreasing the free Li⁺ concentration. The temperature elevation intensifies this suppression: the reduced dielectric constant (ε) of water strengthens the electrostatic attraction between Na⁺ and CO₃²⁻, further inhibiting the dissolution equilibrium. Figure 3b reveals that at a fixed NaCl concentration (1.0 mol·kg⁻¹), the increasing Na₂CO₃ concentration also reduces the solubility but with a progressively diminishing rate. This non-linear response stems from competing ion interaction mechanisms: (i) the common-ion effect (CO₃²⁻) directly suppresses Li₂CO₃ dissociation, while high Na⁺ concentrations compete with Li⁺ for CO₃²⁻ binding, forming NaCO₃⁻ ion pairs and reducing free carbonate, and (ii) at elevated Na₂CO₃ concentrations, a high CO₃²⁻ density promotes Li⁺-CO₃²⁻ ion pair formation (LiCO₃⁻), generating a salting-in effect. Concurrently, the dielectric constant reduction due to the increased ionic strength enhances the Li⁺-CO₃²⁻ electrostatic attraction, partially offsetting the common-ion suppression. It is particularly noteworthy that the temperature exerts a dominant influence: Li₂CO₃ maintains an inverse solubility–temperature dependence across all salt concentrations, which is consistent with its behavior in pure water. Elevated temperatures primarily facilitate ion association by weakening hydration shells while simultaneously reducing ε^r to intensify interionic electrostatic forces (inhibiting dissolution). These mechanistic insights reveal limitations in industrial precipitation processes: the competitive shielding of CO₃²⁻ by Na⁺ and the saturation of ion association effects prevent the linear enhancement of the lithium recovery efficiency with excessive Na₂CO₃ additions.

3.2. Solubility Model

The dissolution equilibrium of Li₂CO₃ in mixed Na₂CO₃-NaCl aqueous solutions under isothermal conditions is governed by two competing mechanisms: the common-ion (homoionic) effect and ionic strength-mediated salt effects. The common-ion effect modifies the dissolution equilibrium through solubility product (K_sp) constraints, while the salt effect operates via the ionic strength-dependent modulation of activity coefficients for Li⁺ and CO₃²⁻ ions in the solution. Following the classical solubility product theory, the dissolution equilibrium for Li₂CO₃ in this ternary system can be formally expressed as

$$K_{sp}(T)=m_{{\mathrm{Li}}^{+}}^2{m}_{{\mathrm{CO}}_3^{2-}}$$

(1)

Using experimental solubility data of Li₂CO₃ in pure water, Cheng et al. [16] derived new parameters for the Li⁺-CO₃²⁻ ion pair within the Pitzer activity coefficient model, enabling the successful prediction of Li₂CO₃ solubility in NaCl, KCl, LiCl, and NaCl-KCl mixed solutions. While such ion-specific models provide accurate predictions, they require extensive parametrization for complex systems. To develop a more streamlined approach for quantifying concentration-dependent solubility variations across mixed electrolytes, we established reference solubility products (K_sp(T)) for Li₂CO₃ in defined baseline solutions (0.5 mol·kg⁻¹ Na₂CO₃ + 1.0 mol·kg⁻¹ NaCl). These reference values were subsequently incorporated into an Extended Debye–Hückel (E-DH) framework to construct a predictive solubility model for multi-component systems [20].

$$\lg (\beta )=\lg ({\displaystyle \frac{K_{sp}(T)}{K_{sp}^0(T)}})=-{\displaystyle \frac{8A\sqrt{I}}{(1+Ba\sqrt{I})}}-CI-D{I}^2$$

(2)

$$I={\displaystyle \frac{1}{2}}{\displaystyle {\sum }_i{m}_i}{Z}_i^2+{\displaystyle \frac{1}{2}}{\displaystyle {\sum }_j{m}_j}{Z}_j^2$$

(3)

$$A={\displaystyle \frac{1}{2.303}}{({\displaystyle \frac{2\pi N_A}{1000}})}^{0.5}{({\displaystyle \frac{e^2}{DkT}})}^{1.5}$$

(4)

where I denotes the ionic strength of the solution at the dissolution equilibrium, mol·kg⁻¹; A denotes the Debye–Hückel limiting slope, which is calculated by listing A in

Table 5. Parameters and standard deviations of Debye–Hückel extension model at different temperatures.

T/K	A	Na2CO3 = 0.5 mol·kg−1			NaCl = 1.0 mol·kg−1			δ
		Bα	C	D	Bα	C	D
283.15	0.5499	36.0149	−0.1621	0.0525	7.0640	−0.4988	0.0545	0.0034
293.15	0.5212	41.9910	−0.1499	0.0534	6.9391	−0.4939	0.0544	0.0036
303.15	0.4988	34.0053	−0.1693	0.0590	7.0089	−0.4810	0.0527	0.0033
313.15	0.4759	41.4239	−0.1504	0.0555	6.4120	−0.5026	0.0555	0.0028
323.15	0.4539	85.9871	−0.1102	0.0476	5.4438	−0.5663	0.0620	0.0033
333.15	0.4336	113.7928	−0.0951	0.0442	5.1686	−0.5762	0.0620	0.0032
343.15	0.4147	50.5828	−0.1166	0.0488	4.7531	−0.6137	0.0675	0.0033
353.15	0.3971	101.3577	−0.0956	0.0459	4.8608	−0.6117	0.0674	0.0031

at different temperatures; Bα is used as a model parameter for the theoretical term (long-range force-acting term); and C and D denote the model parameter for the short-range force correction term.

Based on the solubility model equation (Equation (2)), multivariate regression analyses were performed to determine the solubility product coefficients (β) at various temperatures. This computational approach enabled the derivation of thermodynamic parameters for Li₂CO₃ in a mixed electrolyte system containing 0.5 mol·kg⁻¹ Na₂CO₃ and 1.0 mol·kg⁻¹ NaCl across the studied temperature range. The optimized parameters are summarized in Table 5. To evaluate the model’s accuracy, both the relative deviation (ε, Equation (5)) and standard deviation (δ, Equation (6)) were employed as statistical metrics, with the corresponding computational results presented in Table 5.

$$\epsilon =(m_{{\mathrm{Li}}_2{\mathrm{CO}}_3}^{\mathrm{cal}}-m_{{\mathrm{Li}}_2{\mathrm{CO}}_3}^{\exp })/m_{{\mathrm{Li}}_2{\mathrm{CO}}_3}^{\exp }$$

(5)

$$\delta =\sqrt{{\displaystyle \frac{1}{\mathrm{n}-1}}{\displaystyle {\sum }_i{(m_{{\mathrm{Li}}_2{\mathrm{CO}}_3}^{\exp }-m_{{\mathrm{Li}}_2{\mathrm{CO}}_3}^{\mathrm{cal}})}^2}}$$

(6)

The Li₂CO₃ molalities in the mixed solution were calculated according to the model parameters, respectively, and the deviation ε relative to the total ionic strength in the mixed solution is plotted in Figure 4. As can be seen in Figure 4, the relative deviations of all the experimental values of the solubility of Li₂CO₃ from the model-calculated values are within ±0.1, which suggests that the solubility model equations can better represent the solubility properties of Li₂CO₃ in the Na₂CO₃-NaCl mixed solution.

3.3. Thermodynamics of Dissolution

The solubility of Li₂CO₃ in mixed Na₂CO₃-NaCl aqueous solutions is expressed in terms of the molar fraction x, as in Equation (7):

$$x={\displaystyle \frac{m_{{\mathrm{Li}}_2{\mathrm{CO}}_3}/M_{{\mathrm{Li}}_2{\mathrm{CO}}_3}}{{\displaystyle {\sum }_i{m}_i/M_i}}}$$

(7)

where m_i is the mass of Li₂CO₃, Na₂CO₃, NaCl, and H₂O, in grams, respectively; and M_i is the molar mass of Li₂CO₃, Na₂CO₃, NaCl, and H₂O, expressed in g·mol⁻¹, respectively.

Using enthalpies of formation for solid Li₂CO₃ and aqueous Li⁺ and CO₃²⁻ ions from the literature, Lee et al. [21] calculated the enthalpy of dissolution (ΔH_d) for Li₂CO₃ to be −4.3 kJ·mol⁻¹ based on a 1 mol/kg standard state via a thermodynamic cycle approach. While such indirect calculations based on formation enthalpies provide valuable insights, the apparent enthalpy of the dissolution can also be directly determined from experimental solubility data using the temperature dependence expressed by the Van’t Hoff equation [22]. This fundamental thermodynamic relationship, derived from activity coefficient relationships under ideal solution approximations, establishes a linear correlation between the natural logarithm of the solute mole fraction (ln x) and the reciprocal absolute temperature (1/T), as expressed by Equation (8):

$$\ln x=-{\displaystyle \frac{\mathrm{\Delta }{H}_d}{RT}}+{\displaystyle \frac{\mathrm{\Delta }{S}_d}{R}}$$

(8)

$$\mathrm{\Delta }{G}_d=\mathrm{\Delta }{H}_d-\mathrm{\Delta }{S}_d\overline{T}$$

(9)

where R = 8.314 J·mol⁻¹·K⁻¹ (universal gas constant); ΔH_d= dissolution enthalpy (J·mol⁻¹); ΔS_d = dissolution entropy (J·mol⁻¹·K⁻¹); and T= system temperature (K).

The Gibbs energy change (ΔrG) calculated here represents the apparent standard Gibbs energy of the dissolution for lithium carbonate (Li₂CO₃) in mixed electrolytes. This macroscopic thermodynamic property is derived directly from solubility measurements using the relation Δ_rG = –RTln(K_sp). It should be noted that this approach provides the net thermodynamic driving force of the dissolution equilibrium. The values reported are apparent properties, reflecting the overall thermodynamics of the system under the given experimental conditions, without incorporating molecular-scale solvation studies. Although microscopic analyses—such as solvation energetics (e.g., ΔG_solv)—could offer further mechanistic interpretation, they are not prerequisites for establishing phase equilibrium thermodynamics.

Within the experimental temperature range, ΔH_d and ΔS_d are assumed to be temperature-independent based on the thermodynamic convention for limited temperature intervals. Using Equations (8) and (9), we determined the apparent molar dissolution enthalpy (ΔH_d) and entropy (ΔS_d) for Li₂CO₃ across various mixed solutions. Figure 5 presents these apparent thermodynamic parameters (ΔH_d, ΔS_d, ΔG_d) characterizing the Li₂CO₃ dissolution in mixed Na₂CO₃-NaCl aqueous solutions, where the corresponding Gibbs free energy change (ΔG_d) was calculated at the mean experimental temperature. The negative ΔH_d values (ΔH_d < 0) confirm the exothermic nature of the dissolution, which is consistent with the observed inverse solubility–temperature dependence. NaCl and Na₂CO₃ exhibit antagonistic modulations on the dissolution enthalpy: (a) at the fixed Na₂CO₃ (0.5 mol·kg⁻¹), ΔH_d decreases (becomes more negative) with the increasing NaCl concentration; (b) conversely, at the fixed NaCl (1.0 mol·kg⁻¹), ΔH_d increases (becomes less negative) progressively with the Na₂CO₃ concentration. This antagonistic effect suggests that NaCl enhances the temperature sensitivity of the solubility, whereas Na₂CO₃ mitigates thermal effects. The calculated ΔH_d for the dissolution in the NaCl-Na₂CO₃ system ranges from approximately −5.8 to −6.4 kJ·mol⁻¹. This value is significantly more negative than the standard dissolution enthalpy of −4.3 kJ·mol⁻¹ reported in the literature [21]. The observed difference arises primarily because the dissolution medium (NaCl-Na₂CO₃ brine) constitutes a non-ideal solution, where significant deviations from ideal behavior occur due to ionic interactions and altered activity coefficients.

The red dashed trendline in Figure 5 delineates the molality-dependent dissolution entropy (ΔS_d) evolution. Crystalline dissolution comprises two sequential processes: (i) lattice disintegration into constituent ions and (ii) subsequent ion hydration. The first stage generates increased ionic disorder, yielding positive sublimation entropy (Δ_subS^θ_m > 0). The subsequent hydration stage induces hydration structuring around ions, producing negative hydration entropy (Δ_hydS^θ_m < 0). The net dissolution entropy (Δ_sS^θ_m) is therefore the following summation: Δ_sS_m^θ = Δ_subS^θ_m + Δ_hS^θ_m [23,24]. The observed ΔS_d < 0 indicates an overall entropy reduction during dissolution, signifying the dominance of the hydration entropy over sublimation effects. The ionic hydration process requires the destruction of the original ionic hydration in the solution and the establishment of a new mixed ionic hydration structure. The dissolution entropy (ΔS_d) exhibits an inverse relationship with the salt molality across both NaCl and Na₂CO₃ concentration gradients. The progressive salt addition depletes free water molecules available for hydration. The enhanced ion association generates ordered ionic assemblies, which amplify solution structuring effects and thereby intensify negative ΔS_d magnitudes at elevated ionic strengths.

The concentration dependence of the Gibbs free energy change (ΔG_d) for Li₂CO₃ dissolution was quantitatively evaluated using the Gibbs–Helmholtz relationship (Equation (9)). Figure 5 reveals positive ΔG_d values (ΔG_d > 0) across all experimental conditions, confirming the thermodynamically unfavorable nature of the Li₂CO₃ dissolution. The progressive increase in ΔG_d with rising salt molalities demonstrates that the concomitant addition of both salts produces synergistic solubility suppression in industrial lithium precipitation systems.

The entropic contribution to the dissolution spontaneity was quantified through the dimensionless parameter: [25,26]. As shown in Figure 6, calculated ξ_S values range from 0.781 to 0.797 across experimental conditions, exhibiting a positive correlation with the Na₂CO₃ molality. This confirms entropy-driven dominance in the Li₂CO₃ dissolution. The combined evidence of negative dissolution entropy (ΔS_d < 0) and a high entropic contribution (ξ_S ≈ 0.79) reveals that hydration structure reorganization governs dissolution thermodynamics. Specifically, Li⁺ ions exhibit exceptional hydration energy compared to other alkali cations, which intensifies water ordering effects and thereby suppresses the Li₂CO₃ solubility relative to its alkali metal analogs. This finding is consistent with the work of Lee et al. [21], who calculated thermodynamic dissolution parameters for M₂CO₃ (M = Li, Na, K) and demonstrated that dissolution entropy is the primary factor governing the solubility differences among these alkali carbonates.

4. Conclusions

Through isothermal dissolution equilibrium studies of Li₂CO₃ in lithium precipitation mother liquors across 283.15–353.15 K, with the precise determination of the equilibrium solubility, we derive the following conclusions:

(1)

Concentration dependence: Li₂CO₃ solubility exhibits an inverse proportionality to both Na₂CO₃ and NaCl molalities. Notably, Na₂CO₃ manifests dual behaviors: while its common-ion effect dominates the solubility reduction, a concurrent weak salting-in effect partially offsets this suppression. NaCl exerts unidirectional salting-out effects through ionic strength modulation.

(2)

Model validation: The Extended Debye–Hückel (E-DH) model demonstrates a strong predictive capability, yielding residual standard deviations < 0.09 across all isotherms, confirming its applicability to industrial lithium precipitation systems.

(3)

Thermodynamic analysis: The systematic evaluation of dissolution parameters reveals the apparent enthalpy of the dissolution (ΔH_d < 0), with positive ΔG_d values confirming non-spontaneous dissolution behavior. Negative ΔS_d values indicate enhanced solution ordering, with the entropy-driven percentage (ξ_S) maintaining at 78% across all salt concentrations. The predominance of entropic control suggests that dissolution dynamics are governed by the hydration structure reorganization rather than enthalpic interactions.

Investigating the thermodynamic properties of lithium carbonate dissolution in lithium precipitation mother liquors can provide critical insights for optimizing industrial processes to enhance lithium recovery yields during carbonation crystallization.