+ MCl - American Chemical Society

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Solid−Liquid Equilibrium (SLE) of the N,N‑Dimethylacetamide (DMA) + MCl (M = Na, K, Rb, and Cs) + Water Ternary Systems at Multiple Temperatures Dandan Zhao, Shu’ni Li,* Quanguo Zhai, Yucheng Jiang, and Mancheng Hu* Key Laboratory of Macromolecular Science of Shaanxi Province, School of Chemistry & Chemical Engineering, Shaanxi Normal University, Xi’an, Shaanxi, 710062, P. R. China S Supporting Information *

ABSTRACT: We report herein the solid−liquid equilibria (SLE) of N,N-dimethylacetamide (DMA) + MCl (M = Na, K, Rb, and Cs) + H2O ternary systems for the first time. At the three given temperatures (T = 298.15 K, 308.15 K, and 318.15 K), the solubilities, densities, and refractive indices for these ternary systems are determined with the mass fraction of DMA in salt-free solvent system ranging from 0.0 to 1.0. The solubility of salts decreases significantly with the addition of DMA, and the saltingout ratios are calculated accordingly. The nonrandom two-liquid (NRTL) model can effectively fit the experimental solubility. Furthermore, to investigate the temperature effect on the SLE, the dynamic solubility measurement system is selected to determine the solubility of the salts in the mixed solvent (wDMA = 0.3, 0.5, and 0.7) with the temperature continuously increased. The solubility data at multiple temperatures are well fitted by the modified Apelblat equation and the λh equation.

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INTRODUCTION The phase equilibrium of the aqueous solutions containing salts are of increasing importance for the separation and purification processes in chemical engineering.1 Usually, the solid−liquid equilibrium (SLE) and liquid−liquid equilibrium (LLE) are considered as two main parts of the phase equilibrium. In fact, the majority of the running expenses of chemical plants are due to separation and purification processes. So the best application of phase equilibrium may improve the economic effectiveness of the industry. Many research groups have devoted to the research on LLE or SLE of aqueous electrolyte systems in recent years. For example, the research results obtained by Wang and Pei2,3 on the LLE of imidazolium ionic liquids + salts water aqueous biphasic systems were anticipated for the development and design of the extraction process. Marcilla and Reyes-Labarta4−7 correlated the equilibrium data of all of the equilibrium regions for water + organic + salt ternary systems using a modified nonrandom two-liquid (NRTL) equation. Ren et al.8 determined the solubilities of KCl/NaCl + [Bmim]Cl (1-butyl-3methylimidazolium chloride) + H2O at multiple temperatures. Moreover, in their study, the experimental solubility were © 2014 American Chemical Society

correlated and calculated with the modified Pitzer model. Nikam et al.9 measured the viscosity of (NH4)2SO4, K2SO4, and Al2(SO4)3 in H2O + DMF (N,N-dimethylformamide) and correlated the experimental data to discuss the structurebreaking behavior of salts in these solvents. Our research group has been devoted to the experiments and correlations of LLE and SLE of ternary or quaternary systems consisting of alkaline metal salts, especially for the Rb and Cs salts and organic solvent−water mixtures, to evaluate the application of salting-out effect in the separation and purification processes of these salts. As an extension of our continuous utilizations of the alcohol such as ethanol, 1-propanol, 2-propanol, and ethylene glycol as organic solvents, N,N-dimethylacetamide (DMA) was selected in this work. Amides and their derivatives are interesting simple models in biochemistry. In the case of DMA, due to the dominance of the general dipole−dipole interactions (dipole moment, 3.81), it can be used as a useful magnitude to examine the impact of polarity on bulk Received: November 4, 2013 Accepted: March 25, 2014 Published: April 3, 2014 1423

dx.doi.org/10.1021/je400959n | J. Chem. Eng. Data 2014, 59, 1423−1434

Journal of Chemical & Engineering Data

Article

Figure 1. System to measure the solubility at multiple temperatures: 1, thermostatic water bath; 2, syringe; 3, rubber plug; 4, temperature sensor; 5, jacketed flask; 6, laser generator; 7, magnetic stirring apparatus; 8, laser receiver; 9, light intensity display.

of 4·10−5. The two apparatus were both calibrated at atmospheric pressure with double-distilled water as a reference material before the measurement. On the other hand, the solubility at multiple temperatures is measured by utilizing the dynamic solubility measurement system depicted in Figure 1. It is also called the last crystal disappearance method. The laser monitoring observation technique was used to determine the disappearance of the solid phase in a solid + liquid mixture. The initial mass and ratio of solvent were known precisely and injected into the jacketed flask. Next, sequentially adding known masses of a solid compound to a stirred solution until a slightly excess solid was found. Then, the temperature of the mixture was raised cautiously by an interval of 0.1 K. When the last portion of salts just disappeared, the intensity of the laser beam penetrating the vessel reached the maximum, and the temperature and the salts used in the measurement were recorded. To test the reliability of this method, the solubility of KCl in water at different temperatures was measured. As depicted in Figure 2 and listed

properties.10 The boiling point of DMA (164 °C to 166 °C, 100 KPa) is higher than the alcohols, which effectively avoids the volatilization of toxicity. Moreover, DMA is widely used in industrial operations as purification, crystallization, or extraction solvent.11 However, to the best of our knowledge, there are no LLE or SLE reports on any electrolyte in DMA aqueous solution. Herein, the SLE of DMA + MCl (M = Na, K, Rb, and Cs) + H2O ternary systems are presented. As expected, the MCl solubility significantly decreases with the addition of DMA, and the salting-out ratios are calculated. The correlations of experimental solubility data via the NRTL model show satisfied results. Furthermore, the temperature effect on the SLE of these ternary systems is discussed.

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EXPERIMENTAL SECTION Materials. All of the chemicals (purity > 99.5 %), including sodium chloride, potassium chloride, rubidium chloride, cesium chloride, potassium chromate, silver nitrate, and DMA, were purchased from Sinopharm Chemical Reagent Co., Ltd. and used without further purification. The water utilized was double-distilled water. The salt was dried to constant weight for 48 h at 120 °C and stored in desiccators prior to use. Apparatus and Procedure. Two methods were utilized in this work to investigate the SLE of the selected systems. For the solubility at a given temperature (T = 298.15 K, 308.15 K, and 318.15 K), the experimental apparatus and process are the same as those reported in our former work.12 The mixed solvent (DMA and water) was first placed in a 10 mL syringe with the DMA mass fraction varying from 0.0 to 1.0. Excessive amounts of MCl (M = Na, K, Rb or Cs) salt were then dissolved in these mixed solvents. All of the samples were weighed on an analytical balance (Shanghai, AL204) with a precision of ± 0.0001 g. Then the samples were stirred for 48 h and settled for a further 24 h to ensure that equilibrium was established. The temperature was controlled within an accuracy of ± 0.1 K. After equilibrium was achieved, the solutions were withdrawn and analyzed. The solubilities of salts were analyzed by the Mohr method, which uses chromate ions as an indicator in the titration of chloride ions with a silver nitrate solution standardized with 0.1 mol·L−1 NaCl.13,14 The contents of DMA and water were ascertained by the fixed solvent ratio. Each result was a mean value after three parallel experiments, and the accuracy in the measurement of the mass fraction of the salt was expected to be ± 0.5 %. The density of the above saturated solution was also determined using a DMA 4500 (Anton Paar) vibrating tube densimeter with an accuracy of 1·10−5 g·cm−3. The refractive index was measured by RXA 170 (Anton Paar) with a resolution

Figure 2. Comparison of solubilities for the KCl + H2O system with the reference (w is the mass fraction of KCl in water).

in Table S1, the experimental results agree very well with the reference data.15

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RESULTS AND DISCUSSION Solubility, Density, and Refractive Index at a Fixed Temperature. The solution phase is a complex system, where the solvation environment of a molecule is determined by the interplay of many different pairwise intermolecular interactions and cooperative assembly processes.16,17 Secondary amides 1424



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Table 1. Solubility (w2), Density (ρ), and Refractive Index (nD) for DMA (1) + NaCl/KCl/RbCl/CsCl (2) + H2O (3) Systems at 298.15 K, 308.15 K, and 318.15 K with Pressure P = 0.1 MPaa ρ w1′

w2b

nD

0.0000 0.1000 0.1999 0.3000 0.4000 0.5000

0.2681 0.2313 0.1971 0.1594 0.1239 0.0869

1.37996 1.38445 1.39018 1.39659 1.40331 1.41034

0.0000 0.1000 0.1999 0.3000 0.4000 0.5000

0.2669 0.2314 0.1965 0.1616 0.1257 0.0893

1.37793 1.38354 1.38816 1.39414 1.40051 1.40713

0.0000 0.1000 0.1999 0.3000 0.4000 0.5000

0.2660 0.2338 0.2000 0.1636 0.1279 0.0914

1.37637 1.38067 1.38593 1.39184 1.39779 1.40401

0.0000 0.1001 0.2000 0.3000 0.4000 0.5001

0.2628 0.2181 0.1734 0.1298 0.0904 0.0558

1.36822 1.37314 1.37934 1.38656 1.39483 1.40377

0.0000 0.1001 0.2000 0.3000 0.4000 0.5001

0.2788 0.2352 0.1887 0.1442 0.1024 0.0641

1.36927 1.37373 1.37936 1.38586 1.39304 1.40119

0.0000 0.1001 0.2000 0.3000 0.4000 0.5001

0.2918 0.2460 0.2014 0.1542 0.1119 0.0724

1.36910 1.37298 1.37848 1.38426 1.39136 1.39876

0.0000 0.1001 0.2000 0.3000 0.4000 0.5000

0.4798 0.4136 0.3506 0.2887 0.2183 0.1427

1.38798 1.38967 1.39271 1.39702 1.40233 1.40874

0.0000 0.1001 0.2000 0.3000 0.4000 0.5000

0.4967 0.4442 0.3731 0.3171 0.2467 0.1691

1.38931 1.39058 1.39210 1.39666 1.40107 1.40639

ρ −3

w1′

g·cm

c

298.15 K DMA (1) + NaCl (2) + H2O (3) 1.19815 0.6000 1.16664 0.6999 1.13747 0.8000 1.10957 0.9000 1.08212 1.0000 1.05489 308.15 K DMA (1) + NaCl (2) + H2O (3) 1.19303 0.6000 1.16180 0.6999 1.13256 0.8000 1.10425 0.9000 1.07624 1.0000 1.04838 318.15 K DMA (1) + NaCl (2) + H2O (3) 1.18959 0.6000 1.15799 0.6999 1.12800 0.8000 1.09944 0.9000 1.07069 1.0000 1.04185 298.15 K DMA (1) + KCl (2) + H2O (3) 1.17471 0.5999 1.13952 0.7000 1.10759 0.8000 1.07887 0.9000 1.05287 1.0000 1.03058 308.15 K DMA (1) + KCl (2) + H2O (3) 1.18370 0.5999 1.14747 0.7000 1.11405 0.8000 1.08273 0.9000 1.05363 1.0000 1.02830 318.15 K DMA (1) + KCl (2) + H2O (3) 1.18618 0.5999 1.14786 0.7000 1.11505 0.8000 1.08180 0.9000 1.05207 1.0000 1.02452 298.15 K DMA (1) + RbCl (2) + H2O (3) 1.49537 0.6000 1.41039 0.7000 1.32989 0.8000 1.25211 0.9001 1.17776 1.0000 1.11120 308.15 K DMA (1) + RbCl (2) + H2O (3) 1.51914 0.6000 1.43668 0.7000 1.34358 0.7999 1.27397 0.9001 1.19637 1.0000 1.12341 1425

w2b

nD

g·cm−3

0.0537 0.0269 0.0107 0.0032 0.0007

1.41743 1.42455 1.43086 1.43519 1.43698

1.02893 1.00548 0.98437 0.96228 0.94189

0.0552 0.0284 0.0116 0.0036 0.0005

1.41377 1.42039 1.42629 1.43046 1.43213

1.02166 0.99723 0.97528 0.95296 0.92966

0.0579 0.0307 0.0125 0.0036 0.0006

1.41028 1.41635 1.42194 1.42588 1.42753

1.01462 0.98927 0.96646 0.94406 0.92160

0.0283 0.0131 0.0052 0.0009 0.0005

1.41316 1.42219 1.42944 1.43426 1.43624

1.01186 0.99623 0.98035 0.96100 0.93714

0.0345 0.0154 0.0056 0.0017 0.0005

1.40970 1.41811 1.42512 1.42982 1.43188

1.00655 0.98853 0.97142 0.95174 0.92828

0.0394 0.0167 0.0064 0.0017 0.0019

1.40632 1.41431 1.42080 1.42510 1.42755

1.00044 0.98032 0.96232 0.94515 0.91942

0.0881 0.0397 0.0119 0.0046 0.0017

1.41601 1.42360 1.43027 1.43476 1.43660

1.05575 1.01489 0.98637 0.96214 0.93708

0.0984 0.0460 0.0150 0.0045 0.0011

1.41263 1.41918 1.42548 1.42952 1.43212

1.06003 1.01326 0.97804 0.95771 0.93228



Article

Table 1. continued ρ w1′

w2b

nD

0.0000 0.1001 0.2000 0.3000 0.4000 0.5000

0.5184 0.4605 0.4167 0.3387 0.2609 0.1835

1.38975 1.39103 1.39288 1.39643 1.40010 1.40472

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000

0.6596 0.6135 0.5616 0.4762 0.3908 0.2935

1.41970 1.41795 1.41702 1.41654 1.41718 1.41880

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000

0.6661 0.6234 0.5664 0.5013 0.4173 0.3240

1.42044 1.41902 1.41783 1.41694 1.41696 1.41777

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000

0.6718 0.6399 0.5966 0.5238 0.4434 0.3488

1.42113 1.41949 1.41858 1.41801 1.41731 1.41715

ρ −3

w2b

nD

g·cm−3

g·cm

w1′

318.15 K DMA (1) 1.53371 1.45037 1.36198 1.28612 1.20349 1.12624 298.15 K DMA (1) 1.92206 1.80108 1.67404 1.54060 1.40415 1.27055 308.15 K DMA (1) 1.94748 1.82715 1.70328 1.57160 1.43142 1.29494 318.15 K DMA (1) 1.98435 1.84886 1.72562 1.60128 1.45710 1.31896

+ RbCl (2) + H2O (3) 0.6000 0.7000 0.8000 0.9001 1.0000

0.1094 0.0511 0.0182 0.0053 0.0012

1.41020 1.41594 1.42167 1.42565 1.42806

1.06068 1.00747 0.97430 0.94811 0.92220

+ CsCl (2) + H2O (3) 0.6000 0.7000 0.7999 0.8999 1.0000

0.1850 0.0875 0.0269 0.0047 0.0006

1.42190 1.42619 1.43085 1.43477 1.43663

1.15040 1.05703 0.99756 0.96345 0.93676

+ CsCl (2) + H2O (3) 0.6000 0.7000 0.7999 0.8999 1.0000

0.2067 0.1034 0.0345 0.0073 0.0040

1.42004 1.42271 1.42668 1.43016 1.43237

1.16518 1.06181 0.99300 0.95562 0.92958

+ CsCl (2) + H2O (3) 0.6000 0.7000 0.7999 0.8999 1.0000

0.2322 0.1219 0.0406 0.0080 0.0013

1.41825 1.42023 1.42314 1.42631 1.42844

1.18060 1.06679 0.98848 0.94753 0.92107

c

Standard uncertainties u are u(w2) = 0.0022, u(ρ) = 0.0001 g·cm−3, u(nD) = 0.00004, u(T) = 0.1 K, and u(P) = 10 kPa. bw2 is the mass fraction of salts in the mixed solution. cw1′ is the mass fraction of DMA in the salt-free solvent.

a

a fixed temperature shows a trend similar to that for solubility (Figure 4). However, the effect of the temperature on the density differed from that of solubility. There is a crosspoint at different concentrations of DMA for the systems at the three temperatures except for the NaCl + DMA + H2O system. Before the crossing point, the sequence is 298.15 K < 308.15 K < 318.15 K, while after, the order is 298.15 K > 308.15 K > 318.15 K. This is because that the salt concentration and temperature are two basic factors of influence with opposite natures. Before the crosspoint, the concentration of the salt effect is higher, and the trend is similar to what we see on the solubility curves. After the crosspoint, the temperature effect is slightly higher. For the NaCl + DMA + H2O system, the final results are caused by the temperature effect. Figure S1 shows a combination of the ternary system with two binary systems (RbCl + H2O and DMA + H2O), and the data are listed in Table S3. The density of the RbCl + H2O system nearly covers the entire area of the ternary system for DMA + RbCl + H2O, but the density of the DMA + H2O system basically remains unchanged after w3 reaches about 0.4. It is interesting that the refractive indices of the systems are much more different from that of solubility and density as plotted in Figure 5. First, the refractive indices increased with the addition of DMA. Second, the crosspoint of the curves at different temperatures vary clearly for the different alkaline metal chloride. The phenomenon is due to the three factors that influenced the refractive index: the concentration of the salt, the temperature, and the properties of DMA (nD = 1.439 at 20 °C).

always form linear polymers in concentrated solution. The amide aggregates have exposed H-bond acceptor sites, which solvate H-bond donor solutes with similar binding affinity to amide monomers.18 But DMA is a kind of tertiary amide, and the influence of association and dissociation with water makes little contribution to the solubility, density, and refractive indices. The solubilities, densities, and refractive indices for DMA (1) + NaCl/KCl/RbCl/CsCl (2) + H2O (3) systems at 298.15 K, 308.15 K, and 318.15 K are given in Table 1 and Figures 3 to 5. For comparison, the solubilities of NaCl, KCl, RbCl, and CsCl in pure water at 298.15 K are listed in Table S2, which are in good agreement with the literature values.19,20 In Figure 3, it can be observed that the solubility decreased by increasing the ratio of DMA to water in the solvent. The effect of the temperature is that higher temperatures increase the solubility. However, the NaCl system is not sensitive to the change of temperature. With a fixed ration of DMA and H2O, it is clearly from Figure S2 that the sequence of inorganic salt solubility is CsCl > RbCl > NaCl > KCl at 298.15 K. But at the other two temperatures, there is a crosspoint between NaCl and KCl systems because the solubility of KCl is sensitive to the temperature. For ternary solution density (Figure S3), the same sequence was observed at 298.15 K and 308.15 K as that of the solubility sequence for different salts. However, the density sequence at 318.15 K is CsCl > RbCl > KCl > NaCl. That is, the order for NaCl and KCl is backward. The density for all of the systems at 1426



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Figure 3. Solubility for DMA (1) + NaCl (a)/KCl (b)/RbCl (c)/CsCl (d) (2) + H2O (3) systems at 298.15 K, 308.15 K, and 318.15 K (The solid lines are obtained by the NRTL model; w1′ is the mass fraction of DMA in the salt-free solvent, and w2 is the mass fraction of salts in the mixed solution.).

solubility sequence of the salts at certain content of DMA is CsCl > RbCl > NaCl > KCl. The crosspoint is due to the two opposite effecting factor on refractive index. The increasing of the temperature will increase the solubility and thus increase the refractive index of the solution as shown before the intersection. Meanwhile, the refractive index will decrease when the temperature is increased which is the result seen after the intersection. Figure S4 shows that the refractive index basically follows the order CsCl > RbCl > NaCl > KCl at three investigated temperatures. The salting-out ratio (S−O) is defined as (So − S) /So. So and S are the solubilities of salts in pure water and in mixed solvents, respectively. For DMA + NaCl/KCl/RbCl/CsCl + H2O systems at 298.15 K, 308.15 K, and 318.15 K, the salting out ratios are listed in Table S4. As depicted in Figure 6, the temperature has little or no effect on the salting-out ratio of the salt. So the salting-out effect can be applied at room temperature. Furthermore, the salting-out sequence is KCl > NaCl ≈ RbCl > CsCl as shown in Figure S5 at 298.15 K. Similar results can be found at the other two temperatures. Fitting Models. The nonrandom two-liquid (NRTL) model21 is usually utilized to calculate the SLE data from the

The refractive index decreases with raising the temperature while increases with the addition of the mass fraction of DMA and increases with increasing the salt content. Therefore, in DMA + NaCl/KCl/RbCl + H2O system, the refractive index increases with increasing mass fractions of DMA, showing the results affected by the content of DMA. As depicted in Figure S1b, the refractive index of the DMA + H2O system covers the entire area of the ternary system for DMA + RbCl + H2O, and the refractive index of the RbCl + H2O system shows little relationship with the ternary system. But in DMA + CsCl + H2O system, the refractive index decreases to a minimum value and then increases with the increase of DMA content. This phenomenon can be explained by the salt content and DMA content. Before the lowest point, the concentration of salt is the key factor. After that point, the result is similar to the DMA + NaCl/KCl/RbCl + H2O systems. The temperature effect on refractive index is wellpresented in the DMA + NaCl + H2O system. That is, the higher temperature, the lower refractive index is. For DMA + KCl/RbCl/ CsCl + H2O systems, the crosspoint can be seen and become more and more apparent from KCl to CsCl, illustrating the influence of the solubility of the salts. From Figure 3 and Figure S2, the 1427



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Figure 4. Density for DMA (1) + NaCl (a)/KCl (b)/RbCl (c)/CsCl (d) (2) + H2O (3) systems at 298.15 K, 308.15 K, and 318.15 K (The solid lines are obtained by eq 7; w1′ is the mass fraction of DMA in the salt-free solvent).

two binary parameters corresponding to the n binary subsystems included in the multicomponent system if the nonrandomness factor is considered constant. As an activity coefficient thermodynamic model, NRTL is also a molecularinteraction-based models for phase equilibria. Gilani and Azadian22 used the model to calculate the optimum NRTL binary interaction parameters. The NRTL parameters are fitted to activity coefficients that have been derived from experimentally determined phase equilibrium data (vapor−liquid, liquid−liquid, solid−liquid) as well as from heats of mixing. Marcilla et al.23−25 successfully applied the NRTL to the simultaneous correlation of the experimental data corresponding to all equilibrium regions in ternary systems involving a solid compound. The equations are expressed as follows:

ln γi =

τij =

Δgij RT

=

⎛ ∑ x τ G ⎞⎤ ⎜⎜τij − k k kj kj ⎟⎟⎥ ∑k Gkjxk ⎠⎥⎦ ⎣ ∑k Gkjxk ⎝

∑ ⎢⎢ j

xjGji

Aij T

Gij = exp( −αijτij)

(3) (4)

where xi and xj are the molar fractions of components i and j and the quantities τij and Gij are calculated from eqs 3 and 4. Δgij, Δgji, and αij are three adjustable parameters for each binary pair. The parameters Δgij and Δgji are related to the energy parameter of the interaction between component i and j, and the parameter related to the nonrandomness of the mixture is 0.2. Aij stands for the optimization of the binary parameters. s is the ratio of mole numbers of solid phase and mixture, (1 − s) represents the liquid phase ratio, and μS and μL are the chemical potentials of the pure solid and component i in the liquid phase in the same standard state. nLS represents the phase number of solid−liquid equilibrium. nLS denotes the number of tie-lines in the LS region. The values of ((xi)n,L)cal. are obtained

⎡ ⎛ Δh ΔC p ⎞⎛ Tf ⎞ ΔCP ⎛ Tf ⎞⎤ = s⎢ − ⎜ f − ln⎜ ⎟⎥ ⎟⎜ − 1⎟ − ⎠ ⎢⎣ ⎝ RTf R ⎠⎝ T R ⎝ T ⎠⎥⎦ c i=1

∑j Gjixj

⎡

+

(2)

M c G liquid μL GM μS GM = solid + =s + (1 − s) ∑ xiL i RT RT RT RT RT i=1

+ (1 − s) ∑ xiL ln(γi LxiL)

∑j τjiGjixj

(1) 1428



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Figure 5. Refractive index for DMA (1) + NaCl (a)/KCl (b)/RbCl (c)/CsCl (d) (2) + H2O (3) systems at 298.15 K, 308.15 K, and 318.15 K (The solid lines are obtained by eq 7; w1′ is the mass fraction of DMA in the salt-free solvent).

as the composition where the plane passing through the point xDMA = 0, and μS is tangent to the GM/RT surface in the directions given by the pure solid and experimental equilibrium point. Δhf ⎛ Tf ⎞ ΔμS GS,E ⎜1 − ⎟ = = RT RT RTf ⎝ T⎠ Tf ΔC Tf 1 1 P + ΔCP dT − dT RT T R T T

g S,E =

∫

∫

nLS

OF(LS) =

(5)

3

∑ ∑ [((xi)n,L )exp − ((xi)n,L )cal ]2 n=1 i=1

(6)

The subscripts exp and cal stand for the experimental and calculated data respectively. Δhf stands for the enthalpy of fusion at the normal melting temperature. ΔCP stands for the heat capacity of salts, and Tf stands for the melting temperature. The values of Δhf, ΔCP can be found from the handbook.26 As the presence of solid phases is considered, the Gibbs energy value of the solid is calculated as the chemical potential change from the pure liquid (reference state) to the pure solid salt under the conditions of the experiment. First of all, we calculated the values for the Gibbs energy of pure solid,

Figure 6. Salting-out ratio for DMA (1) + NaCl (a)/KCl (b)/RbCl (c)/CsCl (d) (2) + H2O (3) systems at 298.15 K, 308.15 K, and 318.15 K (w1′ is the mass fraction of DMA in the salt-free solvent). 1429



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passing through the experimental points and the point w1′ = 1 and gE,S. The values for Gibbs energy of pure solid (gS,E) NaCl/KCl/ RbCl/CsCl at three temperatures are summarized in Table 2. Correlation results (binary parameters Aij and the objective function OF (LS)) for DMA (1) + NaCl/KCl/RbCl/CsCl (2) + H2O (3) systems at 298.15 K, 308.15 K, and 318.15 K were listed in Table 3. The solubilities of NaCl/KCl/RbCl/CsCl in mixed solvent at 298.15 K, 308.15 K, and 318.15 K were fitted by the NRTL model, and the results are listed in Table S5. The objective function OF (LS) between calculated and experimental values shows good suitability of the NRTL model. On the other hand, the experimental data for solubility of the salt, refractive indices, and density of the saturated solution are also fitted by the following four-parameter equation:

then imported the experimental temperature and gS,E into eqs 1 and 2. From minimizing the objective function, the calculated xsalt can be regressed. Accordingly, these parameters were obtained at the same time. Thus the solubility (w2) can be determined after a simple unit-converter. The compositions where the lines passsing through gE,S are tangent to the GM surface are calculated. From the results that have been obtained, the binary parameters can generate the equilibrium regions for ternary systems. In this case the composition of the points of tangency have been calculated in the direction of the lines Table 2. Values for Gibbs Energy of Pure Solid NaCl/KCl/ RbCl/CsCl at 298.15 K, 308.15 K, and 318.15 K Calculated from the NRTL Model gS,E

298.15 K

308.15 K

318.15 K

NaCl KCl RbCl CsCl

−9.54 −9.65 −11.28 −7.60

−8.98 −8.88 −10.37 −7.11

−8.45 −8.16 −9.51 −6.66

ln Y = A + Bw1′ + Cw1′2 + Dw′3

(7)

where w1′ is the mass fraction of DMA in mixed solvent systems and Y stands for the mass fraction of salts (w2), the density (ρ), and refractive index (nD) of all of the systems.

Table 3. Binary Parameters Aij and the Objective Function OF (LS) for DMA (1) + NaCl/KCl/RbCl/CsCl (2) + H2O (3) Systems of the NRTL Model at 298.15 K, 308.15 K, and 318.15 K j 298.15 K

DMA + NaCl + H2O

i

1 2 3

1

2

3

308.15 K

DMA + RbCl + H2O

−466.38

23393.10 166157.82

i

1 2 3

−452.67 −273.01 −2596.81 OF(LS) = 4.007·10−3 j

298.15 K

DMA + KCl + H2O

i

1 2 3

1

DMA + RbCl + H2O

i

1 2 3

−607.94 −393.23 OF(LS) = 5.595·10−2

308.15 K

DMA + CsCl + H2O

−411.85

23406.56 166157.80

i

1 2 3

DMA + CsCl + H2O

i

1 2 3

3

318.15 K

DMA + NaCl + H2O

−556.08 −47.68

i

1 2 3

3

318.15 K

DMA + KCl + H2O

5476.51 421.94

i

1 2 3

−3141.62

2

−378.23 −474.72 OF(LS) = 2.028·10−2

DMA + NaCl + H2O

i

1 2 3

1

−2546.71

2 21.92

−603.49 −12.32 −2515.07 OF(LS) = 1.699·10−2 j

308.15 K

DMA + KCl + H2O

i

1 2 3

1

2 882.91

−899.19 −778.12 −2408.69 OF(LS) = 2.244·10−2

2

3 4012.01 −332.63

−2045.66

1

2

3

−204.87

24599.71 166157.82

−433.30 −62.62 −2430.38 OF(LS) = 1.518·10−3 j 1

2

3

2235.75 −1359.89 −1642.76 −2297.68 OF(LS) = 9.712·10−3 j

j 308.15 K

1

−629.98 −1800.63 OF(LS) = 5.131·10−3

2

324.23

−3114.46

348.29

−750.04

1

3 −453.45 91.36

j

j 298.15 K

2 −621.19

j 3

1

1

−500.26 −236.22 OF(LS) = 1.688·10−2

2

−401.26 −1030.55 −2525.42 OF(LS) = 5.503·10−2 j

298.15 K

j

3

318.15 K

DMA + RbCl + H2O

23387.16 166157.82

i

1 2 3

1

−391.78 78.97 OF(LS) = 6.324·10−3

23440.77 166157.80

2

3

−599.23

−551.08 1076.95

−3378.11 j

3

318.15 K

DMA + CsCl + H2O

23516.77 166157.80

i

1 2 3

1430

1

2 299.65

−334.20 −661.64 OF(LS) = 1.108·10−2

3 5553.70 118.43

−2312.12



Article

Table 4. Values of the Parameters of Equation 7 for the Solubility, Density, and Refractive Index of DMA (1) + NaCl (a)/KCl (b)/RbCl (c)/CsCl (d) (2) + H2O (3) Ternary Systems at 298.15 K, 308.15 K, and 318.15 K A

system 298.15 K; DMA NaCl + H2O 298.15 K; DMA KCl + H2O 298.15 K; DMA RbCl + H2O 298.15 K; DMA CsCl + H2O 308.15 K; DMA NaCl + H2O 308.15 K; DMA KCl + H2O 308.15 K; DMA RbCl + H2O 308.15 K; DMA CsCl + H2O 318.15 K; DMA NaCl + H2O 318.15 K; DMA KCl + H2O 318.15 K; DMA RbCl + H2O 318.15 K; DMA CsCl + H2O 298.15 K; DMA NaCl + H2O 298.15 K; DMA KCl + H2O 298.15 K; DMA RbCl + H2O 298.15 K; DMA CsCl + H2O 308.15 K; DMA NaCl + H2O 308.15 K; DMA KCl + H2O

B

C

D

100δ

+

0.2670

Mass Fraction −0.3133 −0.2390

+

0.2651

−0.4976

0.1026

0.1337

0.2672

+

0.4776

−0.5441

−0.5327

0.6048

0.4279

+

0.6525

−0.1036

−1.9993

1.4512

0.7059

+

0.2656

−0.2996

−0.2551

0.2905

0.1599

+

0.2811

−0.4825

0.0133

0.1921

0.2676

+

0.4951

−0.4315

−0.8282

0.7695

0.5208

0.2872

0.1501

+

0.6545

0.0002

−2.1391

1.4843

1.0533

+

0.2655

−0.2805

−0.2907

0.3073

0.1033

+

0.2930

−0.4677

−0.0608

0.2405

0.2249

+

0.5159

−0.3596

−1.0662

0.9165

0.5472

+

0.6607

0.1338

−2.3744

1.5755

1.0091

0.0088

0.0576

+

1.1979

−0.3111

Density 0.0466

+

1.1764

−0.4127

0.3273

−0.1518

0.1695

+

1.4958

−0.8557

0.0409

0.2824

0.2023

+

1.9232

−1.1323

−0.8217

0.9763

0.6349

+

1.1929

−0.3109

0.0411

0.0073

0.0741

+

1.1853

−0.4151

0.2621

−0.1019

0.1793

B

C

D 0.2364

0.4355

100δ

308.15 K; DMA RbCl + H2O 308.15 K; DMA CsCl + H2O 318.15 K; DMA NaCl + H2O 318.15 K; DMA KCl + H2O 318.15 K; DMA RbCl + H2O 318.15 K; DMA CsCl + H2O

+

1.5206

−0.8791

Density 0.0592

+

1.9456

−1.0357

−1.0952

1.1214

0.5643

+

1.1893

−0.3102

0.0204

0.0227

0.0623

+

1.1872

−0.4143

0.2212

−0.0718

0.2004

+

1.5352

−0.8584

−0.0614

0.3123

0.4311

+

1.9756

−1.0283

−1.1686

1.1448

0.7766

298.15 K; DMA NaCl + H2O 298.15 K; DMA KCl + H2O 298.15 K; DMA RbCl + H2O 298.15 K; DMA CsCl + H2O 308.15 K; DMA NaCl + H2O 308.15 K; DMA KCl + H2O 308.15 K; DMA RbCl + H2O 308.15 K; DMA CsCl + H2O 318.15 K; DMA NaCl + H2O 318.15 K; DMA KCl + H2O 318.15 K; DMA RbCl + H2O 318.15 K; DMA CsCl + H2O

+

1.3802

Refractive Index 0.0329 0.0883 −0.0640

0.0367

+

1.3687

0.0259

0.1401

−0.0980

0.0457

+

1.3886

−0.0077

0.1420

−0.0857

0.0577

+

1.4204

−0.0378

0.0910

−0.0360

0.0719

+

1.3785

0.0343

0.0748

−0.0551

0.0476

+

1.3698

0.0229

0.1251

−0.0854

0.0497

+

1.3897

−0.0091

0.1224

−0.0706

0.0454

+

1.4210

−0.0299

0.0576

−0.0155

0.0558

+

1.3766

0.0338

0.0694

−0.0519

0.0307

+

1.3695

0.0227

0.1117

−0.0760

0.0395

+

1.3902

−0.0052

0.0983

−0.0548

0.0448

+

1.4213

−0.0207

0.0258

0.0027

0.0461

the value of C indicate the relationship between the temperatures and the enthalpy of fusion.29 The agreement between the predicted and the experimental results indicates that the experimental results are reliable (Figure 7). The λh equation was first used by Buchowski et al.30,31 to investigate the relationship of solvent, activity solubility, and temperature. Moreover, it was proved that λ and h were constant in a pure solvent system. Domanska32,33 found that the pure solvent system of the λh equation was also applicable to the ternary system assuming the binary mixture solvent to be a suppositional single component processing:

The value of A, B, C, and D listed in Table 4 represent empirical constants, together with the obtained standard deviation (δ) below. Based on the data obtained, it is easy to conclude that eq 7 can correlate the solubility, density, and refractive index of the investigated systems satisfactorily. It can be seen that the four-parameter equation can correlate the data simply within the whole range of DMA concentration. Multiple Temperature Solubility and Correlations. To investigate the influence of temperature on the SLE of DMA + MCl + H2O systems, the multiple temperature solubility is determined through the dynamic solubility measurement system, and the data are listed in Table 5. The thermodynamics model put forward by Apelblat27 was used to calculate the multiple temperature solubility as a function of temperature:28 ln w2 = A + B /T + C ln T

A

system

−ln(1 − λ(1 − w2)/w2) = λh(T −1 − Tm−1)

(9)

Tm is the melting temperature of the solute. h stands for the per mole of solute dissolving enthalpy divided by gas constant; λ is the average number of the associated solute molecules in binary systems. The value of λ, h, and the corresponding standard deviation (δ) for all of the ternary systems are listed in Table S7. As depicted in Figure 7, the multiple temperature solubility for all of the systems obtained by two experimental methods and the correlated results from the modified Apelblat equation and λh equation are in good coincidence.

(8)

where T stands for the absolute temperature; A, B, and C is the parameters in the equation and obtained by the least-squares method. The values of A, B, an dC together with the standard deviation (δ) for all of the systems are listed in Table S6. Moreover, the values of A and B represent the variation of the solution activity and nonidealities behavior of solution, whereas 1431



Article

Table 5. Solubilities for Ternary Systems of DMA + NaCl/ KCl/RbCl/CsCl + H2O at Multiple Temperatures and Results Correlated by the Modified Apelblat Equation and λh Equation Ta/K

wexpb

wApelc

wλhd

0.1643 0.1639 0.1630 0.1609 0.1591 0.1580 0.1569 0.1545

0.1644 0.1639 0.1630 0.1608 0.1590 0.1579 0.1569 0.1548

0.0937 0.0918 0.0901 0.0884 0.0868 0.0855 0.0851

0.0934 0.0916 0.0900 0.0884 0.0869 0.0857 0.0854

0.0300 0.0297 0.0293 0.0284 0.0273 0.0251 0.0246

0.0300 0.0298 0.0294 0.0284 0.0273 0.0251 0.0246

0.1621 0.1560 0.1532 0.1503 0.1471 0.1447 0.1415 0.1374 0.1351 0.1329 0.1302 0.1279 0.1267 0.1246

0.1614 0.1557 0.1530 0.1502 0.1472 0.1448 0.1416 0.1376 0.1353 0.1331 0.1303 0.1280 0.1268 0.1246

0.0797 0.0764 0.0731 0.0694 0.0681 0.0670 0.0659 0.0635 0.0624 0.0610 0.0596 0.0579 0.0566 0.0554 0.0540 0.0528

0.0795 0.0764 0.0732 0.0695 0.0683 0.0672 0.0660 0.0636 0.0625 0.0611 0.0596 0.0579 0.0566 0.0553 0.0538 0.0525

Table 5. continued

0.1649 0.1637 0.1624 0.1608 0.1591 0.1584 0.1570 0.1544

321.35 314.95 308.95 303.05 297.65 293.15 291.85

0.0938 0.0918 0.0900 0.0883 0.0868 0.0858 0.0848

325.65 323.95 321.35 315.05 308.15 293.15 289.15

0.0306 0.0298 0.0290 0.0281 0.0270 0.0252 0.0248

wexpb

329.55 321.35 315.95 311.55 308.45 306.25 303.95 300.85 297.75 294.85

0.0192 0.0173 0.0161 0.0156 0.0147 0.0141 0.0135 0.0128 0.0119 0.0113

330.35 324.05 316.55 309.35 305.05 300.55 296.75 291.85

0.3584 0.3469 0.3318 0.3173 0.3082 0.2994 0.2902 0.2791

325.75 323.75 318.95 314.15 310.05 304.95 300.25 296.35 293.35 288.85

0.2023 0.1980 0.1886 0.1784 0.1716 0.1618 0.1534 0.1460 0.1387 0.1307

KCl wDMA = 0.3

334.55 330.65 323.85 319.35 314.15 309.15 306.05 301.05 298.25 293.65 289.95

0.0596 0.0556 0.0507 0.0469 0.0442 0.0408 0.0383 0.0360 0.0337 0.0311 0.0203

0.0780 0.0758 0.0733 0.0706 0.0693 0.0680 0.0665 0.0641 0.0626 0.0611 0.0594 0.0576 0.0561 0.0551 0.0537 0.0517

0.0217 0.0185 0.0165 0.0150 0.0140 0.0133 0.0127 0.0118 0.0110 0.0102

0.3602 0.3466 0.3308 0.3160 0.3073 0.2983 0.2908 0.2813

0.3594 0.3467 0.3315 0.3167 0.3078 0.2985 0.2905 0.2803

0.2031 0.1987 0.1884 0.1786 0.1704 0.1607 0.1521 0.1452 0.1400 0.1326

0.2024 0.1983 0.1886 0.1791 0.1711 0.1613 0.1524 0.1452 0.1397 0.1316

0.0605 0.0567 0.0506 0.0469 0.0429 0.0393 0.0372 0.0340 0.0323 0.0297 0.0277

0.0602 0.0566 0.0508 0.0472 0.0432 0.0395 0.0373 0.0340 0.0322 0.0294 0.0273

0.5462 0.5353 0.5209 0.5116 0.5013 0.4952 0.4865 0.4771 0.4716 0.4643

0.5451 0.5351 0.5215 0.5124 0.5021 0.4959 0.4869 0.4770 0.4710 0.4631

0.3610 0.3423 0.3347 0.3270 0.3145

0.3597 0.3425 0.3352 0.3277 0.3154

wDMA = 0.7

CsCl wDMA = 0.3

wDMA = 0.5 327.75 324.25 320.65 316.45 314.95 313.65 312.25 309.35 307.95 306.25 304.35 302.15 300.45 298.75 296.85 295.15

0.0195 0.0174 0.0161 0.0151 0.0144 0.0139 0.0135 0.0128 0.0123 0.0117

wDMA = 0.5

wDMA = 0.7

0.1598 0.1561 0.1537 0.1507 0.1480 0.1455 0.1421 0.1383 0.1358 0.1324 0.1302 0.1280 0.1258 0.1232

wλhd

RbCl wDMA = 0.3

wDMA = 0.5

322.95 318.55 316.45 314.25 311.85 309.95 307.45 304.25 302.35 300.55 298.35 296.45 295.45 293.65

wApelc wDMA = 0.7

NaCl wDMAe = 0.3 327.15 325.15 321.35 312.15 304.45 299.85 295.25 285.25

Ta/K

330.05 324.95 318.15 313.75 308.85 305.95 301.75 297.25 294.55 291.05

0.5433 0.5347 0.5222 0.5131 0.5036 0.4967 0.4875 0.4771 0.4703 0.4615

324.95 318.45 315.75 312.95 308.35

0.3577 0.3418 0.3359 0.3289 0.3168

wDMA = 0.5

1432



■

CONCLUSION The SLE of DMA + NaCl/KCl/RbCl/CsCl + H2O ternary systems have been carefully investigated in this work. The solubility of the inorganic salts decreases with the addition of DMA in all of the systems. The temperature has little or nearly no effect on the salting-out ratio. The density and refractive index curves both show a crosspoint for the KCl/RbCl/CsCl systems at three investigated temperatures. The MCl solubility at a fixed temperature is well fitted by the nonrandom twoliquid (NRTL) model. Furthermore, the modified Apelblat equation and λh equation are successfully utilized to correlate the multiple temperature solubility.

Table 5. continued Ta/K

wexpb

302.45 299.45 297.15 294.65 291.05

0.3000 0.2923 0.2864 0.2780 0.2659

329.55 326.85 322.85 320.35 317.25 314.45 310.35 308.15 300.05 297.45 293.85 290.85

0.1381 0.1320 0.1258 0.1209 0.1167 0.1120 0.1057 0.1014 0.0895 0.0853 0.0806 0.0752

wApelc

wλhd

0.2989 0.2911 0.2853 0.2790 0.2701

0.2995 0.2914 0.2852 0.2784 0.2687

0.1385 0.1332 0.1257 0.1212 0.1158 0.1111 0.1044 0.1010 0.0891 0.0855 0.0808 0.0770

0.1379 0.1331 0.1260 0.1216 0.1164 0.1117 0.1050 0.1015 0.0892 0.0854 0.0803 0.0762

Article

wDMA = 0.5

wDMA = 0.7

■

ASSOCIATED CONTENT

S Supporting Information *

Data for solubilities for MCl in pure water, the refractive index and density of the two binary systems of DMA + H2O and RbCl + H2O systems at 298.15 K, the salting-out ratio for DMA + MCl + H2O systems, solubilities for DMA + MCl + H2O systems fitted by the NRTL model at (298.15, 308.15, and 318.15) K, parameters of eq 8 and eq 9, solubilities of KCl in pure water at multiple temperatures. Figures for the refractive index and density of DMA + RbCl + H2O system with two binary systems at 298.15 K, solubilities, densities, refractive indices and salting-out ratio for DMA + MCl + H2O systems at

a

The uncertainty of the temperature is 0.1 K. bwexp stands for the experimental data, and the uncertainty is 0.0022. cwApel stands for the data correlated by the modified Apelblat equation. dwλh stands for the data correlated by the λh equation. ewDMA stands for the mass fraction of DMA in mixed solvents.

Figure 7. Solubilities for ternary systems of DMA (1) + NaCl (a)/KCl (b)/RbCl (c)/CsCl (d) (2) + H2O (3) at multiple temperatures and the results correlated by the modified Apelblat equation and λh equation: ■, wDMA = 0.3; ●, wDMA = 0.5; ▲, wDMA = 0.7; ★, traditional method; , the modified Apelblat equation correlated; ···, λh equation correlated; w2 is the mass fraction of salts in the mixed solution. 1433



Article

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(298.15, 308.15, and 318.15) K. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Funding

This work was supported by the National Natural Science Foundation of China (nos. 21171111 and 21301114), and Natural Science Foundation of Shaanxi Province (no. 2013JQ2009). Notes

The authors declare no competing financial interest.

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REFERENCES

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