Vapor-Liquid Equilibria Study of the LiCl + CaCl2 + H2O System.

Vapor-liquid equilibrium (VLE) data are measured and reported for the LiCl + CaCl2 + H2O system. The experimental procedures were carried out with pressures between 6 and 101.3 kPa in a computer-controlled glass apparatus. We obtained the relationship between solubility of salt and vapor pressure by analyzing and summarizing the results. Then, a modified NRTL model based on the hypothesis of hydration was used in this paper. By correlation of literature and experimental data for LiCl + H2O, CaCl2 + H2O, and LiCl + CaCl2 + H2O (pressure spanning from 5 to 101.3 kPa), some parameters were modified for improving the accuracy of the calculation. Meanwhile, the model was successfully applied to predict the VLE data in LiCl + CaCl2 + H2O systems with the modified binary parameters.

Introduction

Crystallization, separation, and purification of electrolyte solutions are the key roles in technology and industrial fields. Vapor–liquid equilibrium (VLE) is widely used in chemical engineering and industries, which plays a fundamental role in chemical engineering.

Massive amounts of data with respect to phase equilibrium are reported in recent years, whereas corresponding thermodynamic models have been developed to calculate thermodynamic properties for electrolyte and nonelectrolyte systems. Because of the strong demand for separation process design, more researchers studied VLE on electrolyte systems. However, most of data were concentrated in normal pressure (101.3 kPa) and room temperature (298.15 K). Up to now, some solubility isotherms of LiCl + CaCl2 + H2O system have been measured,[1−4] whereas VLE of LiCl + H2O and CaCl2 + H2O binary systems has been obtained.[5] Nevertheless, VLE data for systems composed of LiCl + CaCl2 + H2O are still rare. For nonelectrolyte solutions, thermodynamic models such Wilson’s model,[6] NRTL model,[7] and UNIQUAC model[8] are well established. For thermodynamic property calculation of electrolyte solutions, Pitzer’s model,[9] ElecNRTL model,[10,11] Lu–Maurer’s model,[12,13] extended UNIQUAC model,[14] and Xu’s model[15] have been widely utilized. In recent years, some scholars[18−20] have done some research on the electrolyte solution systems. Despite the aforementioned research works, the calculation of VLE for mixed electrolyte systems is still confronted with great challenges.

In this paper, VLE data of the system composed of LiCl + CaCl2 + H2O are elaborately determined with a pressure varying from 10 to 101.3 kPa. The obtained data in binary systems[5,15] are used to parameterize the modified NRTL model. By this means, a complete VLE diagram of the LiCl + CaCl2 + H2O system at various pressures and model parameters is obtained.

Model Description

Xu’s Model

In Xu’s model,[5,15] the excess Gibbs energy was expressed by the NRTL term[7]where n is the number of species of solute in electrolyte solution, mx is the total molality of solute, mi is the molality of solute, mw is the molar of free water, hi is the hydration numbers of the solute, nt is the molar of solute and solvent, and Ms is the molecular weight of water.

τw,x and τx,w are the water-entity term and the entity-water term, respectively:

The relations between parameters τw,i, τi,w, and the temperature T are as follows:Based on the above descriptions, the final equation can be written as:The reference state of activity coefficients in the excess Gibbs energy model is γi → 1 as xi = (ni/nt) → 1. In the final equations, five parameters (h, τw,i(0), τw,i(1), τi,w(0), and τi,w(1)) were fitted to the experimental data.

Results and Discussion

The experimental data for LiCl + CaCl2 + H2O at different molality are listed in Tables –4. Meanwhile, experimental results were analyzed and summarized, as shown in Figures –6. Besides, the possible relationship between solubility of salt and saturated vapor pressure was obtained.

Table 2

Experimental VLE Data for Temperature T, Pressure P, and Molality m (ma: LiCl, mb: CaCl2) for the LiCl + CaCl2 + H2O Systema

ma = 20.08 mol·kg–-1, mb = 0 mol·kg–1		ma = 15.63 mol·kg–1, mb = 1.3 mol·kg–1		ma = 10.4 mol·kg–1, mb = 3.14 mol·kg–1		ma = 8.83 mol·kg–1, mb = 4.07 mol·kg–1
T (K)	P (kPa)	T (K)	P (kPa)	T (K)	P (kPa)	T (K)	P (kPa)
329.25	6.46	322.55	6.005	325.35	5.935	327.45	6.065
341.15	11.69	337.95	11.425	336.65	10.425	339.15	11.22
348.05	13.9	346.35	16.135	347.65	16.86	347.45	15.875
355.05	21.025	353.85	21.7	353.15	20.71	354.05	20.83
360.95	26.94	359.05	26.75	359.25	26.41	359.55	25.76
363.85	30.275	362.75	30.965	363.45	31.13	365.25	32.275
369.45	36.82	367.45	36.83	367.95	37.005	368.85	37.275
372.15	40.755	370.25	41.01	370.85	41.06	371.95	41.6
376.45	47.275	373.15	45.645	374.35	46.72	375.05	46.74
378.35	50.335	376.35	51.035	376.95	51.26	378.45	52.29
381.55	55.795	379.25	56.395	379.45	56.045	380.25	55.655
384.55	61.82	381.05	60.29	382.55	61.96	382.65	60.855
386.55	66.375	383.45	65.38	384.35	65.77	385.85	67.385
388.55	71.07	386.35	71.995	386.75	71.65	387.65	72.395
390.75	76.355	388.25	76.15	388.95	77.325	389.45	75.935
393.05	81.74	390.35	81.79	390.75	82.03	391.45	81.91
394.85	86.21	392.05	86.77	392.25	86.485	393.55	87.5
396.45	91.295	393.65	90.945	393.95	91.5	394.75	92.16
398.25	96.385	395.55	97.045	395.45	96.43	395.95	95.84
400.05	101.205	397.05	101.205	397.05	101.205	397.85	101.195

Standard uncertainties u are u(P) = 0.1 kPa, u(T) = 0.05 K, and u(m) = 0.0001 g.

Table 4

Experimental VLE Data for Temperature T, Pressure P, and Molality m (ma: LiCl, mb: CaCl2) for the LiCl + CaCl2 + H2O Systema

ma = 1.66 mol·kg–1, mb = 7.14 mol·kg–1		ma = 0 mol·kg–1, mb = 7.72 mol·kg–1
T (K)	P (kPa)	T (K)	P (kPa)
334.65	6.54	334.45	6.985
343.25	10.825	343.85	11.185
352.15	16.115	352.95	16.88
358.05	20.735	358.05	21.075
363.65	26.155	364.05	26.795
369.05	32.045	367.85	30.765
372.15	35.995	372.15	36.335
376.25	41.84	375.25	40.58
378.95	46.18	379.15	46.925
381.85	50.815	381.95	51.39
384.85	56.81	384.45	56.33
387.45	61.85	387.65	62.385
389.45	65.805	389.45	66.785
391.75	71.405	391.35	71.43
393.75	76.64	393.45	76.465
395.55	81.34	395.25	81.47
397.25	85.935	396.95	86.19
399.15	91.69	398.85	91.465
400.65	96.31	400.45	96.275
402.15	101.215	401.85	101.205

Standard uncertainties u are u(P) = 0.1 kPa, u(T) = 0.05 K, and u(m) = 0.0001 g.

Figure 4

Experimental VLE data for the LiCl + CaCl2 + H2O system. Symbols (black box solid, ma = 20.08 mol/kg, mb = 0 mol/kg; red solid circle, ma = 15.63 mol/kg, mb = 1.3 mol/kg; blue triangle up solid, ma = 10.4 mol/kg, mb = 3.14 mol/kg; pink triangle down solid, ma = 8.83 mol/kg, mb = 4.07 mol/kg; green diamond solid, ma = 7.46 mol/kg, mb = 4.68 mol/kg; navy blue triangle left-pointing solid, ma = 5.41 mol/kg, mb = 5.95 mol/kg; purple amethyst triangle right-pointing solid, ma = 3.73 mol/kg, mb = 6.73 mol/kg; purple hexagon solid, ma = 2.43 mol/kg, mb = 7.08 mol/kg; dark red star solid, ma = 1.66 mol/kg, mb = 7.14 mol/kg; pickle green pentagon solid, ma = 0 mol/kg, mb = 7.72 mol/kg) for experimental data (this work).

Figure 6

Prediction of experimental VLE data for the LiCl+CaCl2+H2O system. Symbols (black box solid, ma = 20.08 mol/kg, mb = 0 mol/kg; red solid circle, ma = 10.4 mol/kg, mb = 3.14 mol/kg; blue triangle up solid, ma = 7.46 mol/kg, mb = 4.68 mol/kg; pink triangle down solid, ma = 3.73 mol/kg, mb = 6.73 mol/kg; pickle green diamond solid, ma = 1.66 mol/kg, mb = 7.14 mol/kg) for experimental data (this work) and lines for prediction of the model.

Then, the thermodynamic model was studied, and Xu’s model was employed to correlate and predict VLE for the system. Xu’s model, ElecNRTL model,[10,11] and Pitzer’s model[9] were used to correlate VLE data in electrolyte systems, and VLE behaviors of LiCl + CaCl2 + H2O were investigated.

Discussion of Experimental Results

LiCl + H2O, CaCl2 + H2O, and LiCl + CaCl2 + H2O systems were chosen to study the VLE law, as shown in Tables –4 and Figures –6. From the tables and figures, we can see that the VLE law of LiCl + H2O, CaCl2 + H2O, and LiCl + CaCl2 + H2O is similar. For LiCl + H2O and CaCl2 + H2O systems, as the salt concentration increases, the saturated vapor pressure of water decreases regularly. From the results, we can see that as the temperature increases, the saturated vapor pressure also rises regularly. From Tables –4 and Figure , we can see that as the VLE pressure of mLiCl = 2.43 mol/kg and mCaCl2 = 7.08 mol/kg in the LiCl + CaCl2 + H2O system is lowest, the activity at the same temperature is lowest, and as the VLE pressure of mLiCl = 15.63 mol/kg and mCaCl2 = 1.30 mol/kg in LiCl + CaCl2 + H2O system is highest, the activity at the same temperature is highest. Simultaneously, the CaCl2 + H2O curve at saturated solubility and normal temperature is lower than LiCl + H2O.

From the analysis of results, we can see that the hygroscopicity at some mixed concentration is also relatively strong, and we can calculate the strongest concentration of moisture absorption by modeling.

Results of the Modeling

Correlation of the VLE

The model described above was used to correlate VLE data for the LiCl + CaCl2 + H2O system. The results of correlation for LiCl + H2O, CaCl2 + H2O, and LiCl + CaCl2 + H2O systems are listed in Table and Figure in the form of mean deviation between literature and calculated values. Parameters τ1,20, τ2,10, τ1,30, τ3,10, τ2,30, τ3,20, τ1,21, τ2,11, τ1,31, τ3,11, τ2,31, τ3,21, h1, and h2 were obtained from the correlation of the experimental and literature data, as listed in Table . For LiCl + CaCl2 + H2O, it can be seen from Table that dY = 0.27 kPa and dP = 1.03%. dY and dP were calculated via the following equationswhere N denotes the number of data points and Pexp and Pcal denote the experimental vapor pressure and the calculated vapor pressure, respectively.

Table 5

Correlation Results of VLE Data

			this work
system	p (kPa)	data points	dY (kPa)a	dP (%)b	references
CaCl2-H2O	5 to 101.3	322	0.081	1.82	(1)(2)(15), and (16)
LiCl-H2O	5 to 101.3	47	0.018	1.25	(1) and (4)
LiCl-CaCl2-H2O	5 to 101.3	200	0.27	1.03	(3)(5), and experimental data

dY = (1/N)∑|Pexp–Pcal|, where N is the number of data points.

dP = (1/N)∑|Pexp–Pcal|/Pexp × 100%, where N is the number of data points.

Figure 5

Correlation of experimental VLE data for the LiCl + CaCl2 + H2O system. Symbols (black box solid, ma = 20.08 mol/kg, mb = 0 mol/kg; red solid circle, ma = 10.4 mol/kg, mb = 3.14 mol/kg; blue triangle up solid, ma = 7.46 mol/kg, mb = 4.68 mol/kg; pink triangle down solid, ma=3.73 mol/kg, mb=6.73 mol/kg; pickle green diamond solid, ma = 1.66 mol/kg, mb = 7.14 mol/kg) for experimental data (this work) and lines for correlation of the model.

Table 6

Model Parameters (Correlated) for Mixed Electrolyte Solutions

system	component	a	h	τi,w(0)	τw,i(0)	τi,w(1)	τw,i(1)
LiCl-CaCl2-H2O	LiCl	4.49	8.52	–0.07	0.43	–267.49	15.31
	CaCl2		2.47	–0.47	0.2	–188.66	–58.31

Prediction of the VLE

Xu’s model was chosen to predict the VLE results, as shown in Figure , as well as dY = 6.8 kPa and dP = 11.31%. The parameters in Xu’s model were obtained from literature,[15] as listed in Table . It is clear that Xu’s model can be used to describe the VLE law of the ternary electrolyte systems. However, the prediction result is worse than the correlation result.

Table 7

Model Parameters (Original and Modified) for Binary Electrolyte Solutions in Xu’s Model

system	model type	a	h	τi,w(0)	τw,i(0)	τi,w(1)	τw,i(1)
CaCl2-H2O	original	0.3	1.1	–4.66	36.94	–114.25	–13200.53
LiCl-H2O	original		2.15	–0.957	2.06	–822.12	–93.41
CaCl2-H2O	modified	0.3	1.1	781.44	–3771.77	–98.47	–6010.44
LiCl-H2O	modified		2.15	–4.99	13.17	–4.29	16.17

For the LiCl + CaCl2 + H2O system, the prediction result is unsatisfactory. We have recalculated the parameters for LiCl + H2O and CaCl2 + H2O systems by using the experimental data in this work and modified the parameters for the binary electrolyte solutions, as listed in Table . Prediction results for the LiCl + CaCl2 + H2O system used the modified parameters are dY = 0.37 kPa and dP = 1.76%. The prediction with modified parameters is considered more accurate. However, the prediction results are not better than the correlation results (dY = 0.27 kPa and dP = 1.03%). If you want to calculate the VLE data more accurately, you can use the correlated model. The predicted model is relatively simple and convenient.

Comparison with Other Methods

The LiCl + CaCl2 + H2O system was selected for comparing ElecNRTL model, Pitzer’s model, and Xu’s model. Comparison results are shown in Table . Note that both ElecNRTL and Pitzer results were calculated by the software Aspen Plus 8.1.

Table 8

Comparison of Models for Electrolyte Solutions

			Chen-NRTL		Pitzer		this work (correlation used Xu’s model)		this work (prediction used Xu’s model)
system	p (kPa)	data points	dY (kPa)a	dP (%)b	dY (kPa)a	dP (%)b	dY (kPa)a	dP (%)b	dY (kPa)a	dP (%)b	references
LiCl-CaCl2-H2O	5 to 101.3	200	0.45	2.3	0.30	1.72	0.27	1.03	0.37	1.76	(1)(2), and experimental data

dY = (1/N)∑|Pexp–Pcal|, where N is the number of data points.

dP = (1/N)∑|Pexp–Pcal|/Pexp × 100%, where N is the number of data points.

For the LiCl + CaCl2 + H2O system, the dY value (0.27 kPa) of this work (correlation) used Xu’s model is smaller than that of ElecNRTL’s model (dY = 0.45 kPa) and Pitzer’s model (dY = 0.3 kPa). Besides, the dP value (1.03%) of this work (correlation) used Xu’s model is smaller than that of ElecNRTL’s model (dP = 2.3% ) and Pitzer’s model (dP = 1.72%).

A modified NRTL model based on the hypothesis of hydration was proposed in Xu’s work. Xu’s model for the excess Gibbs energy was derived from the NRTL equation, and the hydration hypothesis and the salt–salt mixing rule were introduced in the model. Because of the assumptions and theoretical derivations, the results in this work are considered more comprehensive and accurate.

Conclusions

In this paper, VLE data for LiCl + CaCl2 + H2O systems was measured and reported. The reliability of measurements was verified by comparing experimental data with literatures. Through the analysis of experimental data, it is shown that the solubility of salt is an important factor affecting saturated vapor pressure. As the VLE pressure of mLiCl = 2.43 mol/kg and mCaCl2 = 7.08 mol/kg is lowest, the activity at the same temperature is lowest, and the hygroscopicity at some mixed concentration is also relatively strong.

By the correlation of experimental data, modified parameters (LiCl-H2O and CaCl2-H2O) of Xu’s model were obtained. The calculations were compared to ElecNRTL model and Pitzer’s model. From comparisons, the result in this work is better than ElecNRTL model and Pitzer’s model. The model can be used to successfully predict VLE data for the LiCl + CaCl2 + H2O system with modified binary parameters.

Experimental Section

Materials

Anhydrous LiCl (purity ≥99.9%) and anhydrous CaCl2 (purity ≥99.99%) were purchased from Aladdin Industrial Corporation. Distilled water (18.2 Ω·cm) was used for the preparation of solutions.

Apparatus and Procedures

A dual circulation glass ebulliometer (40 mL) was used in the VLE measurements, as shown in Figure . The main experimental instruments are listed in Table , including a vacuum pump in the ebulliometer, a pressure controller, a heating mantle, and a temperature controller.

Figure 1

Schematic diagram of the VLE apparatus used in this work: (A) heating mantle, (B) equilibrium still, (C) sampling port, (D) thermometer well, (E) sampling port, and (F) condenser.

Table 1

Main Experimental Instruments

instrument	model	manufacturer	uncertainty
dual circulation glass ebulliometer	40 cm3	Tianjin Wuqing Beiyang Chemical Factory
pressure controller	Ruska Series 7000 controller	Ruska Instrument Corp. (Houston, TX, USA)	±0.01 kPa
temperature controller	model SRS13A	SHIMADEN (Japan)	±0.05 K
electronic balances	SECURA225D-1CEU balances	Sartorius Lab Instruments GmbH & Co. KG 37070 (Göttingen, Germany)	±0.0001 g

During the experiments, the sample was placed into the glass ebulliometer, then heated by the heating mantle, and was controlled by the temperature controller. The operation pressure was controlled by the vacuum pump, the pressure sensor, and the control valve. The procedures were carried out with a pressure between 6.3 and 101.3 kPa. The vapor sample was condensed in a spherical condenser (length 40 cm) and then returned to the mixing chamber for recirculation.

The experimental steps are as follows: (1) First, we need to check the airtightness of the entire system by controlling the pressure. (2) We need to calibrate the temperature and pressure detectors. (3) The sample (40 mL) is placed into the glass ebulliometer. (4) The temperature heater is turned on, and the temperature is set by the temperature controller (110–180 V). (5) The vacuum pump is turned on, and the pressure is controlled by an electronic pressure relief valve. (6) The time was 0.5–1 h in the first equilibrium; then, the following equilibrium time was 10–20 min. (7) When the VLE state is reached, we recorded the temperature and pressure values.

The reliability of measurement was verified by comparing our experimental data (i.e., H2O + CaCl2, NaCl-KCl-H2O) with those in literatures (Figures and 3). We have verified the accuracy and stability of the equipment by using the VLE data of the H2O + CaCl2 system in ref (5). The experimental data for LiCl + CaCl2 + H2O systems at different molality are listed in Tables –4.

Figure 2

Vapor–liquid equilibrium in the CaCl2 + H2O system. Empty symbols (black box, m = 1 mol/kg; red circle open, m = 3 mol/kg; pink triangle down open, m = 6 mol/kg) for literature data[16] and full symbols (black box solid, m = 1 mol/kg; red solid circle, m = 3 mol/kg; triangle down solid, m = 6 mol/kg) for experimental data.[5]

Figure 3

Vapor–liquid equilibrium in the NaCl-KCl-H2O system. Empty symbols (black box, mNaCl = 5.8 mol/kg, mKCl = 0.6 mol/kg; red circle open, mNaCl = 3 mol/kg, mKCl = 0.7 mol/kg) for literature data[17] and full symbols (black box solid, mNaCl = 5.8 mol/kg, mKCl = 0.6 mol/kg; red solid circle, mNaCl = 3 mol/kg, mKCl = 0.7 mol/kg) for experimental data.

Table 3

Experimental VLE Data for Temperature T, Pressure P, and molality m (ma: LiCl, mb: CaCl2) for the LiCl + CaCl2 + H2O Systema

ma = 7.46 mol·kg–1, mb = 4.68 mol·kg–1		ma = 5.41 mol·kg–1, mb = 5.95 mol·kg–1		ma = 3.73 mol·kg–1, mb = 6.73 mol·kg–1		ma = 2.43 mol·kg–1, mb = 7.08 mol·kg–1
T (K)	P (kPa)	T (K)	P (kPa)	T (K)	P (kPa)	T (K)	P (kPa)
330.45	6.46	329.55	6.395	331.95	7.013	330.95	6.455
341.25	11.41	342.25	11.295	342.35	10.973	343.55	11.215
349.05	16.035	350.55	15.84	351.85	15.978	352.35	16.005
355.65	21.245	357.95	21.46	358.45	20.858	358.65	20.825
359.45	26.16	362.55	25.63	365.05	26.833	364.05	26.135
366.25	31.675	368.75	32.155	369.55	31.883	369.85	32.15
371.05	38.18	371.65	36.175	372.95	36.378	372.45	35.67
372.35	40.185	375.35	41.225	376.05	40.893	376.35	41.2
376.55	46.7	378.45	46.28	379.45	46.223	379.55	46.285
379.55	51.805	381.65	51.875	382.55	51.348	382.05	50.78
382.25	56.775	384.15	56.365	384.75	55.893	385.45	56.83
384.65	61.8	386.35	61.355	387.35	61.423	388.25	62.88
386.65	65.785	388.35	65.825	389.35	65.848	389.75	66.29
389.65	73.43	390.75	71.825	391.75	71.368	391.85	71.405
390.85	76.385	392.65	75.79	393.75	76.448	394.35	77.315
392.55	81.3	394.75	81.305	395.65	81.423	396.45	82.51
394.55	86.335	396.55	86.595	397.55	86.413	397.75	86.64
396.25	91.41	398.35	91.335	399.15	90.888	399.65	91.865
397.55	96.225	400.05	96.39	400.75	96.358	401.25	96.37
399.45	101.195	401.55	101.175	402.45	101.311	402.35	101.185

Standard uncertainties u are u(P) = 0.1 kPa, u(T) = 0.05 K, and u(m) = 0.0001 g.