English

• Salt lakes are widely distributed in the Qinghai-Tibet plateau and abundant in high concentration of lithium, potassium and boron. The composition of salt lake brine can be represented as Li⁺-Na⁺-K⁺-Mg²⁺-Cl^--SO₄^2--B₂O₃-H₂O system. Knowledge of the volumetric characteristics, such as density, volume of mixing, has a guiding role in salt lake brine evaporation process control and solar pond design^[1]. Such data also provide valuable insight into the interaction behavior of mixed electrolyte solutions. To the best of our knowledge, volumetric properties for aqueous ternary subsystems of complex salt lake brine are not available due to the scarcity of reliable density data. Oscillating U-tube densimeter was employed in densities determination of Li₂SO₄-Na₂SO₄-H₂O and Li₂SO₄-K₂SO₄-H₂O by Guo et al and Bu et al respectively^{[2, 3]}. But the main purposes of the above-mentioned publications focused on phase equilibrium research. Volumetric properties were not conducted in these publications.

  In this study, the densities of aqueous solutions of Li₂SO₄-Na₂SO₄-H₂O, Li₂SO₄-K₂SO₄-H₂O over the temperature range 288 ≤ T/K ≤ 318 were determined with high precision vibrating-tube densimetry. The experimental densities were correlated with the Pitzer thermodynamic model. The volume of mixing at constant ionic strength and at 298.15 K for each of the ternary systems was calculated.

  1.   Experimental

  1.1   Reagents

  All reagents (purchased from Aladdin Co.) were of analytical reagent grade and used directly without further purification (lithium sulfate 99.9%, sodium sulfate ≥99.0%, potassium sulfate 99.99%). The stock solutions were prepared by dissolving solutes in distilled deionized water, respectively. The molalities of the sulfate stock solutions were determined gravimetrically by precipitation of sulfate as BaSO₄(s). Stock solution molality determinations were done with 5 replicate samples and reproducible to ≤0.08%. The tested ternary aqueous solutions were prepared by using an analytical balance with a precision of ±0.1mg, the two stock solutions and the water were weighed in appropriate proportions according to the desired concentrations using mass burettes.

  1.2   Density Determination

  Densities were measured using an Anton Paar (Austria) vibrating-tube densitometer (DMA 5000) following the experimental protocol described in detail previously^[4]. Temperatures were controlled to ±0.002K at the intervals of 288≤T/K≤318. The densitometer was calibrated with laboratory air and high purity degassed water at 293K before measure-ment. Following the calibration, densities of water and target solutions were measured. The reprod-ucibility of the densities were always within the range ±(2~10) μg·cm^-3.

  2.   Methods

  The density of a mixture of aqueous electrolytes is expressed as:

  $ \rho = \left( {1000 + \sum {{m_i}{M_i}} } \right)/\left( {\frac{{1000}}{{{\rho _0}}} + \sum {{m_i}\bar V_i^0 + {V^{ex}}} } \right) $

  (1)

  where m_i and M_i are the molality and the molecular weight of the electrolyte i in the mixture, respectively. ${\bar V_i^0}$ is the apparent molar volume of electrolyte i at infinite dilution. ρ₀ is the water density. V_ex represents the excess volume of the mixture. V_ex is determined with the Pitzer model, whose general equation is:

  $ \begin{array}{l} V_{mix}^{ex} = {A_V}\left( {\frac{1}{b}} \right)\ln \left( {1 + b{I^{\frac{1}{2}}}} \right) + \\ RT\left\{ {2\sum\limits_c {\sum\limits_a {{m_c}{m_a}\left[ {B_{c, a}^V + \left( {\sum\limits_c {{m_c}{z_c}} } \right)C_{c, a}^V} \right]} } + } \right.\\ \sum\limits_c {\sum\limits_{c'} {{m_c}{m_c}\left( {2\theta _{c, c'}^V + \sum\limits_a {{m_a}\mathit{\Psi }_{c, c', a}^V} } \right) + } } \\ \left. {\sum\limits_a {\sum\limits_{a'} {{m_a}{m_{a'}}\left( {2\theta _{a, a'}^V + \sum\limits_c {{m_c}\mathit{\Psi }_{a, a', c}^V} } \right)} } } \right\} \end{array} $

  (2)

  with

  $ B_{{\rm{c, a}}}^{\rm{V}} = \beta _{{\rm{c, a}}}^{\left( 0 \right){\rm{V}}} + \beta _{{\rm{c, a}}}^{\left( 1 \right){\rm{V}}} \cdot {\rm{g}}\left( {{\alpha _1}\sqrt I } \right) + \beta _{{\rm{c, a}}}^{\left( 2 \right){\rm{V}}} \cdot {\rm{g}}\left( {{\alpha _2}\sqrt I } \right) $

  (3)

  $ \begin{array}{l} \;\;\;\;\;\;{\rm{g}}\left( {{\alpha _i} \cdot \sqrt I } \right) = \frac{2}{{{{\left( {{\alpha _i}\sqrt I } \right)}^2}}} \cdot \\ \left[ {1 - \left( {1 + {\alpha _i}\sqrt I } \right) \cdot \exp \left( { - {\alpha _i}\sqrt I } \right)} \right] \end{array} $

  (4)

  where the symbols have the usual meanings^[5]. Theoretical Debye-Hückel slope (A_V) used in the fit was obtained using the equations developed by Krumgalz^[6].

  The volume of mixing at constant ionic strength is defined as the difference between the excess of the mixture volume and the sum of the excess volume of the pure-electrolyte components.

  $ {V_{\rm{M}}} = {V^{{\rm{ex}}}}\left( {{\rm{mixture}}} \right) - \left[ {{y_2}{V^{{\rm{ex}}}}\left( 2 \right) + \left( {1 - {y_2}} \right){V^{{\rm{ex}}}}\left( 1 \right)} \right. $

  (5)

  where y₂ is the ionic strength fraction of Na₂SO₄ or K₂SO₄ in the ternary systems and is defined by y₂=I₂/(I₁+I₂).

  3.   Results and Discussion

  Experimental density data of ternary systems Li₂SO₄-Na₂SO₄-H₂O and Li₂SO₄-K₂SO₄-H₂O are summarized in Tab. 1. I represents the total ionic strength, and m₂ represents the molality of the second electrolyte Na₂SO₄ or K₂SO₄ in ternary systems. Solution densities, ρ, are based on the water densities, ρ_w, at the target temperatures. The standard densities of water were calculated from the polynomial proposed by Kell^[7]. The measured quantity Δρ=ρ-ρ_w is independent of the model representing ρ_w. From the data in Tab. 1, the solution densities can be trivially calculated.

  Table 1

  

  表 1  实验测定的各温度下Li₂SO₄-Na₂SO₄-H₂O和Li₂SO₄-K₂SO₄-H₂O溶液密度与纯水的密度差Δρ

  Table 1.  Results of experimental measurements of density differences Δρ of Li₂SO₄-Na₂SO₄-H₂O, Li₂SO₄-K₂SO₄-H₂O systems with respect to pure water at temperatures T^a

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  I/ (mol·kg-1)	m2 / (mol·kg-1)	y2	288K Δρ/ (kg·m-3)	293K Δρ/ (kg·m-3)	298K Δρ/ (kg·m-3)	303K Δρ/ (kg·m-3)	308K Δρ/ (kg·m-3)	313K Δρ/ (kg·m-3)	318K Δρ/ (kg·m-3)
  Li2SO4+ Na2SO4 + H2O
  0.1002	0.0069	0.2064	3.459	3.430	3.405	3.386	3.371	3.361	3.355
  0.0999	0.0131	0.3931	3.653	3.622	3.593	3.569	3.552	3.538	3.525
  0.1005	0.0203	0.6059	3.896	3.874	3.840	3.811	3.789	3.771	3.757
  0.1008	0.0266	0.7924	4.116	4.073	4.034	4.002	3.975	3.955	3.936
  0.9993	0.0666	0.1998	32.944	32.678	32.465	31.932	31.932	31.929	31.915
  1.0020	0.1337	0.4004	35.220	34.912	34.652	34.441	34.270	34.136	34.034
  0.9987	0.1998	0.6002	36.831	36.339	35.968	35.662	35.418	35.243	35.181
  0.9993	0.2665	0.8000	38.973	38.513	38.130	37.780	37.483	37.236	37.043
  2.9973	0.1997	0.1999	93.094	92.545	92.086	91.706	91.405	91.168	90.982
  2.9985	0.4000	0.4002	99.094	98.403	97.814	97.323	96.922	96.598	96.341
  3.0003	0.5999	0.5998	104.929	104.293	103.625	103.046	102.556	102.151	101.815
  2.9997	0.8001	0.8002	110.969	110.047	109.258	108.579	108.000	107.507	107.089
  4.4997	0.3000	0.2000	134.613	133.854	133.239	132.749	132.368	132.081	131.876
  4.4994	0.5999	0.4000	142.990	142.127	141.387	140.764	140.232	139.764	139.434
  4.5006	0.9001	0.6000	151.632	150.595	149.708	148.957	148.324	147.794	147.356
  4.4988	1.2000	0.8002	159.250	158.084	157.076	156.203	155.451	154.808	154.258
  Li2SO4 + K2SO4 + H2O
  0.0990	0.0066	0.2008	3.505	3.473	3.451	3.432	3.419	3.411	3.403
  0.1008	0.0133	0.3969	3.869	3.835	3.807	3.785	3.769	3.756	3.747
  0.0987	0.0198	0.6015	4.107	4.069	4.038	4.013	3.993	3.977	3.966
  0.0981	0.0266	0.8141	4.391	4.350	4.315	4.285	4.264	4.245	4.230
  0.9993	0.0665	0.1997	33.772	33.521	33.319	33.158	33.037	32.944	32.880
  0.9999	0.1334	0.4002	36.699	36.421	36.187	35.997	35.846	35.727	35.637
  0.9633	0.2009	0.6258	38.602	38.296	38.036	37.819	37.641	37.497	37.382
  0.9999	0.2667	0.8002	42.521	42.167	41.870	41.619	41.411	41.237	41.096
  1.9992	0.1334	0.2002	65.480	65.044	64.691	64.411	64.197	64.036	63.925
  1.9998	0.2666	0.4000	70.886	70.416	70.011	69.678	69.415	69.211	69.054
  1.9992	0.4002	0.6005	76.634	76.088	75.630	75.245	74.929	74.673	74.468
  1.9998	0.5334	0.8001	82.065	81.462	80.943	80.506	80.141	79.835	79.584
  2.5002	0.1666	0.1999	80.554	80.041	79.632	79.308	79.058	78.873	78.742
  2.5005	0.3333	0.3998	87.480	86.922	86.450	86.064	85.755	85.513	85.329
  2.4999	0.5003	0.6004	94.105	93.468	92.928	92.479	92.110	91.808	91.568
  a Standard uncertainties u are u(T)=0.002K, u(p)=1kPa, u(Δρ)=0.005kg·m-3, u(m)=0.0007 for Li2SO4, u(m)=0.0008 for Na2SO4 and u(m)=0.0006 for K2SO4.

  For values that have constant ion strength I, the densities of the two ternary systems decrease as the temperatures increase. It can be ascribed to the expansion of the volume of the solution, which is due to the increase of the temperature of the system. It is clear that for constant I and temperature the densities of both ternary systems increase with the increase of y₂, which tends to reach the value of density of the second electrolyte (y₂=1). This behavior occurs while the density value of the Na₂SO₄-H₂O or K₂SO₄-H₂O system is higher than that of the Li₂SO₄-H₂O system within the concentration interval evaluated this work.

  Experimental data in Tab. 1 were correlated using equation (2), for which the excess molar volumes of ternary systems were derived from equation (1). The volumetric ion interaction parameters (V_MX⁰, β_MX^(0)V, β_MX^(1)V, C_MX^V) at different temperatures for single electrolytes were listed in Table 2. The parameters of Na₂SO₄, K₂SO₄ obtained from polynomial proposed by Krumgalz et al^[6]. The parameters of Li₂SO₄ were cited from our previously published paper^[8].These parameters were used in the correlation of the two ternary systems.

  Table 2

  

  表 2  不同温度下的Pitzer体积参数

  Table 2.  Volumetric Pitzer parameters at different temperatures

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  T/K	288	293	298	303	308	313	318
  Li2SO4
  VMX0 (cm3·mol-1)	11.4165	11.9965	12.4500	12.7278	12.8233	12.8062	12.6779
  β(0)V×105 (kg·mol-1·bar-1)	3.5477	3.0314	2.7393	2.4674	2.2393	2.0745	1.9358
  β(1)V×105 (kg·mol-1·bar-1)	-5.1539	-5.8359	-7.6886	-9.1991	-10.4017	-11.8396	-13.2710
  CV×106 (kg2·mol-2·bar-1)	-1.4645	-1.0967	-0.9517	-0.7997	-0.6785	-0.6111	-0.5573
  			Na2SO4
  VMX0 (cm3·mol-1)	9.0503	10.5253	11.7760	12.8156	13.6574	14.3148	14.8011
  β(0)V×105 (kg·mol-1·bar-1)	7.0225	6.0169	5.3250	4.9123	4.7440	4.7855	5.0021
  β(1)V×105 (kg·mol-1·bar-1)	1.6858	1.5150	1.2932	1.0048	0.6616	0.2750	-0.1432
  CV×106(kg2·mol-2·bar-1)	-5.0204	-3.7013	-2.9140	-2.6031	-2.7133	-3.1892	-3.9757
  			K2SO4
  VMX0 (cm3·mol-1)	29.8538	31.1524	32.2300	33.1017	33.7818	34.2839	34.6209
  β(0)V×105 (kg·mol-1·bar-1)	-1.0017	-0.3727	0.1105	0.4618	0.6948	0.8237	0.8621
  β(1)V×105 (kg·mol-1·bar-1)	6.2864	4.2352	2.6016	1.3484	0.4381	-0.1667	-0.5034
  CV×106 (kg2·mol-2·bar-1)	7.4103	4.1365	1.6192	-0.2184	-1.4529	-2.1609	-2.4191

  The mixing parameters θ_LiNa^V, θ_LiK^V, ψ_LiNaSO4^V, ψ_LiKSO4^V for the ternary systems can be calculated from experimental densities listed in Tab. 1 by using Least-Squares method. The values of Pitzer mixing parameters and the standard deviation of the two ternary systems were correlated and listed in Tab. 3.

  Table 3

  

  表 3  不同温度下的Pitzer混合参数

  Table 3.  Mixing parameters at different temperatures

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  T/K	θLiNaV×105	ψLiNaSO4V×105	SD1	θLiKV×105	ψLiKSO4V×105	SD2
  288	5.9102	-4.4308	0.00053	0.2357	-3.5767	0.00052
  	0	0	0.0016	0	0	0.00056
  293	5.6107	-4.0375	0.00054	0.1059	0.4394	0.00047
  	0	0	0.0016	0	0	0.00047
  298	5.6499	-4.0734	0.00061	0.1671	3.2257	0.00043
  	0	0	0.0017	0	0	0.00050
  303	5.8949	-4.3481	0.00066	0.2701	5.1669	0.00041
  	0	0	0.0017	0	0	0.00071
  308	5.9826	-4.3635	0.00068	0.4085	6.3911	0.00040
  	0	0	0.0013	0	0	0.00066
  313	6.0911	-4.3638	0.00071	0.6312	6.8783	0.00040
  	0	0	0.0019	0	0	0.00073
  318	6.2433	-4.4104	0.00073	0.9087	6.7930	0.00041
  	0	0	0.0020	0	0	0.00078

  In this table, SD₁ and SD₂ are the standard deviations of the systems Li₂SO₄-Na₂SO₄-H₂O and Li₂SO₄-K₂SO₄-H₂O respectively. In general, the quality of the fit is better when the mixing parameters are considered (option 1) than not considered ones at all (option 2). The abilities of the Pitzer model to fit the data over wide ranges of concentrations and temperatures are illustrated as deviation plots in Fig. 1 and Fig. 2. Maximum deviations between the experimental density data and those calculated from Pitzer model using the parameters in Tab. 1 and Tab. 2 were always ≤ ±0.002 (for Li₂SO₄-Na₂SO₄-H₂O system) or ≤ ±0.0015 (for Li₂SO₄-K₂SO₄-H₂O system).

  Figure 1

  

  图 1.  Li₂SO₄-Na₂SO₄-H₂O体系密度计算值与实验值偏差

  Figure 1.  Density deviations of Pitzer model from experimental data of the Li₂SO₄-Na₂SO₄-H₂O system

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  Figure 2

  

  图 2.  Li₂SO₄-K₂SO₄-H₂O体系密度计算值与实验值偏差

  Figure 2.  Density deviations of Pitzer model from experimental data of the Li₂SO₄-K₂SO₄-H₂O system

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  Values of volume of mixing at 298 K for the ternary systems were obtained by using eq.(2) and eq.(5). Fig. 3 shows the values of ΔV_M versus y₂ for the systems Li₂SO₄-Na₂SO₄-H₂O, Li₂SO₄-K₂SO₄-H₂O respectively. Open symbols are calculated values of volume of mixing and different curves correspond to different I (total ionic strength) values in each figure. It is clear that the values of volume of the mixing are obviously positive over the entire interval of y₂ for the two ternary systems. Also, the values of ΔV_M become more positive as I increase.

  Figure 3

  

  图 3.  Li₂SO₄-Na₂SO₄-H₂O(上)和Li₂SO₄-K₂SO₄-H₂O(下)体系的混合体积

  Figure 3.  Volumes of mixing of the system of Li₂SO₄-Na₂SO₄-H₂O, Li₂SO₄-K₂SO₄-H₂O (top to bottom respectively) at 298K

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  The positive ΔV_M value indicates that the excess volume of mixtures is greater than the two binary mixtures before mixing. This indicates that the final ternary mixture reaches a less-compact configuration, leading to a greater volume of the system. The presence of the two electrolytes probably does not greatly disturb the water structure because an overall decrease in the structure of water implies a breakage of hydrogen bonds, which contributes to a decrease in volume^[9]. According to Desnoyers et al^[10], mixing two solutes with the different ability to orient water molecules (one is a structure maker and the other is a structure breaker)would result in an attraction with an increase in volume.

  4.   Conclusions

  This work provides reliable experimental data of volumetric properties of mixed aqueous Li₂SO₄- Na₂SO₄-H₂O and Li₂SO₄-K₂SO₄-H₂O solutions. This information is important in the design and control of brine evaporation processes. The data obtained for wide ranges of temperatures were used for parameterization of Pitzer mixing model that describes the volumetric properties of multi-component solutions. The values of volume of mixing (ΔV_M) at 298 K were obtained, which indicates that the two binary solutes possess an opposite ability for orientating water molecular resulting in the increase of volume after mixing.

  
  
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• 

  Figure 1  Density deviations of Pitzer model from experimental data of the Li₂SO₄-Na₂SO₄-H₂O system

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  Figure 2  Density deviations of Pitzer model from experimental data of the Li₂SO₄-K₂SO₄-H₂O system

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  Figure 3  Volumes of mixing of the system of Li₂SO₄-Na₂SO₄-H₂O, Li₂SO₄-K₂SO₄-H₂O (top to bottom respectively) at 298K

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  Table 1.  Results of experimental measurements of density differences Δρ of Li₂SO₄-Na₂SO₄-H₂O, Li₂SO₄-K₂SO₄-H₂O systems with respect to pure water at temperatures T^a

  I/ (mol·kg-1)	m2 / (mol·kg-1)	y2	288K Δρ/ (kg·m-3)	293K Δρ/ (kg·m-3)	298K Δρ/ (kg·m-3)	303K Δρ/ (kg·m-3)	308K Δρ/ (kg·m-3)	313K Δρ/ (kg·m-3)	318K Δρ/ (kg·m-3)
  Li2SO4+ Na2SO4 + H2O
  0.1002	0.0069	0.2064	3.459	3.430	3.405	3.386	3.371	3.361	3.355
  0.0999	0.0131	0.3931	3.653	3.622	3.593	3.569	3.552	3.538	3.525
  0.1005	0.0203	0.6059	3.896	3.874	3.840	3.811	3.789	3.771	3.757
  0.1008	0.0266	0.7924	4.116	4.073	4.034	4.002	3.975	3.955	3.936
  0.9993	0.0666	0.1998	32.944	32.678	32.465	31.932	31.932	31.929	31.915
  1.0020	0.1337	0.4004	35.220	34.912	34.652	34.441	34.270	34.136	34.034
  0.9987	0.1998	0.6002	36.831	36.339	35.968	35.662	35.418	35.243	35.181
  0.9993	0.2665	0.8000	38.973	38.513	38.130	37.780	37.483	37.236	37.043
  2.9973	0.1997	0.1999	93.094	92.545	92.086	91.706	91.405	91.168	90.982
  2.9985	0.4000	0.4002	99.094	98.403	97.814	97.323	96.922	96.598	96.341
  3.0003	0.5999	0.5998	104.929	104.293	103.625	103.046	102.556	102.151	101.815
  2.9997	0.8001	0.8002	110.969	110.047	109.258	108.579	108.000	107.507	107.089
  4.4997	0.3000	0.2000	134.613	133.854	133.239	132.749	132.368	132.081	131.876
  4.4994	0.5999	0.4000	142.990	142.127	141.387	140.764	140.232	139.764	139.434
  4.5006	0.9001	0.6000	151.632	150.595	149.708	148.957	148.324	147.794	147.356
  4.4988	1.2000	0.8002	159.250	158.084	157.076	156.203	155.451	154.808	154.258
  Li2SO4 + K2SO4 + H2O
  0.0990	0.0066	0.2008	3.505	3.473	3.451	3.432	3.419	3.411	3.403
  0.1008	0.0133	0.3969	3.869	3.835	3.807	3.785	3.769	3.756	3.747
  0.0987	0.0198	0.6015	4.107	4.069	4.038	4.013	3.993	3.977	3.966
  0.0981	0.0266	0.8141	4.391	4.350	4.315	4.285	4.264	4.245	4.230
  0.9993	0.0665	0.1997	33.772	33.521	33.319	33.158	33.037	32.944	32.880
  0.9999	0.1334	0.4002	36.699	36.421	36.187	35.997	35.846	35.727	35.637
  0.9633	0.2009	0.6258	38.602	38.296	38.036	37.819	37.641	37.497	37.382
  0.9999	0.2667	0.8002	42.521	42.167	41.870	41.619	41.411	41.237	41.096
  1.9992	0.1334	0.2002	65.480	65.044	64.691	64.411	64.197	64.036	63.925
  1.9998	0.2666	0.4000	70.886	70.416	70.011	69.678	69.415	69.211	69.054
  1.9992	0.4002	0.6005	76.634	76.088	75.630	75.245	74.929	74.673	74.468
  1.9998	0.5334	0.8001	82.065	81.462	80.943	80.506	80.141	79.835	79.584
  2.5002	0.1666	0.1999	80.554	80.041	79.632	79.308	79.058	78.873	78.742
  2.5005	0.3333	0.3998	87.480	86.922	86.450	86.064	85.755	85.513	85.329
  2.4999	0.5003	0.6004	94.105	93.468	92.928	92.479	92.110	91.808	91.568
  a Standard uncertainties u are u(T)=0.002K, u(p)=1kPa, u(Δρ)=0.005kg·m-3, u(m)=0.0007 for Li2SO4, u(m)=0.0008 for Na2SO4 and u(m)=0.0006 for K2SO4.

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  Table 2.  Volumetric Pitzer parameters at different temperatures

  T/K	288	293	298	303	308	313	318
  Li2SO4
  VMX0 (cm3·mol-1)	11.4165	11.9965	12.4500	12.7278	12.8233	12.8062	12.6779
  β(0)V×105 (kg·mol-1·bar-1)	3.5477	3.0314	2.7393	2.4674	2.2393	2.0745	1.9358
  β(1)V×105 (kg·mol-1·bar-1)	-5.1539	-5.8359	-7.6886	-9.1991	-10.4017	-11.8396	-13.2710
  CV×106 (kg2·mol-2·bar-1)	-1.4645	-1.0967	-0.9517	-0.7997	-0.6785	-0.6111	-0.5573
  			Na2SO4
  VMX0 (cm3·mol-1)	9.0503	10.5253	11.7760	12.8156	13.6574	14.3148	14.8011
  β(0)V×105 (kg·mol-1·bar-1)	7.0225	6.0169	5.3250	4.9123	4.7440	4.7855	5.0021
  β(1)V×105 (kg·mol-1·bar-1)	1.6858	1.5150	1.2932	1.0048	0.6616	0.2750	-0.1432
  CV×106(kg2·mol-2·bar-1)	-5.0204	-3.7013	-2.9140	-2.6031	-2.7133	-3.1892	-3.9757
  			K2SO4
  VMX0 (cm3·mol-1)	29.8538	31.1524	32.2300	33.1017	33.7818	34.2839	34.6209
  β(0)V×105 (kg·mol-1·bar-1)	-1.0017	-0.3727	0.1105	0.4618	0.6948	0.8237	0.8621
  β(1)V×105 (kg·mol-1·bar-1)	6.2864	4.2352	2.6016	1.3484	0.4381	-0.1667	-0.5034
  CV×106 (kg2·mol-2·bar-1)	7.4103	4.1365	1.6192	-0.2184	-1.4529	-2.1609	-2.4191

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  Table 3.  Mixing parameters at different temperatures

  T/K	θLiNaV×105	ψLiNaSO4V×105	SD1	θLiKV×105	ψLiKSO4V×105	SD2
  288	5.9102	-4.4308	0.00053	0.2357	-3.5767	0.00052
  	0	0	0.0016	0	0	0.00056
  293	5.6107	-4.0375	0.00054	0.1059	0.4394	0.00047
  	0	0	0.0016	0	0	0.00047
  298	5.6499	-4.0734	0.00061	0.1671	3.2257	0.00043
  	0	0	0.0017	0	0	0.00050
  303	5.8949	-4.3481	0.00066	0.2701	5.1669	0.00041
  	0	0	0.0017	0	0	0.00071
  308	5.9826	-4.3635	0.00068	0.4085	6.3911	0.00040
  	0	0	0.0013	0	0	0.00066
  313	6.0911	-4.3638	0.00071	0.6312	6.8783	0.00040
  	0	0	0.0019	0	0	0.00073
  318	6.2433	-4.4104	0.00073	0.9087	6.7930	0.00041
  	0	0	0.0020	0	0	0.00078

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