Determination and Modeling of MgCl2 Solubility in Methanol, Ethanol

Article pubs.acs.org/jced

Determination and Modeling of MgCl2 Solubility in Methanol, Ethanol, 2‑Propanol, and Their Mixtures from 283 to 343 K Lanmu Zeng,†,‡ Zhibao Li,*,† and Xiaolin Wang‡ †

Key Laboratory of Green Process and Engineering, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China ‡ Beijing Key Laboratory of Membrane Materials and Engineering, Department of Chemical Engineering, Tsinghua University, Beijing 100084, China ABSTRACT: MgCl2-supported Ziegler−Natta catalyst plays an important role in polyolefin industry. The solubility of MgCl2 in various alcohols has been studied to understand the mechanisms involved in the preparation of the catalyst. The solubility of anhydrous MgCl2 in methanol, ethanol, and 2propanol and their mixtures was measured by a dynamic method at temperatures from 283.2 to 343.2 K. The solubility was found to increase with increasing temperature, but the increasing rate was dependent on the composition of solvent. In the single alcohol, the solubility value of MgCl2 is under the order of methanol > ethanol > 2-propanol at room temperature. Solubilities of MgCl2 in the mixtures of methanol + ethanol, methanol + 2-propanol, and ethanol + 2-propanol are all larger than that in the single alcohol. Three solid phases, including MgCl2·6CH3OH, MgCl2·6C2H5OH, and MgCl2·4(CH3)2CHOH, were found in the equilibrated solids by XRD characterization. The mixed-solvent model (MSE) embedded in the OLI software was applied to model the experimental solubility data. The log KSP for the dissolution reaction of MgCl2·6CH3OH, MgCl2·6C2H5OH, and MgCl2·4(CH3)2CH OH at 298.2 K were determined to be −11.5078, −13.0943, and −10.6139, respectively.

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adducts13 and obtain the final catalyst with higher activity than from ethanol. Subsequently, MgCl2-alcohol adducts were precipitated out from the solution via cooling14 or solvent evaporation.8 Then the MgCl2 supported Zeigler−Natta catalyst was prepared by the impregnation of TiCl4, and the alcohols in adducts were stripped during the treatment. The morphology of adducts is a great concern in the preparation of the catalyst because it was found that the polyolefin trends to repeat the shape of MgCl2 supports.3 Despite intensive study for nearly 60 years, there still exists rooms for gaining more understanding of this catalyst.15 It is surprisingly how little the modern nanotechnology in the control of product properties, namely, morphology, particle size, crystallinity, and so on, has been applied to the preparation of the catalyst.3 For controlling the crystallization process of the adducts, phase equilibria of the related system are priorities to investigate.16 Compared with vast data on the solubility of MgCl2 in aqueous electrolyte systems,17 the solubility data of MgCl2 in organic solvents is quite limited. Emons and Pollmer (1985)18 published the solubility of MgCl2 in water + organic solvents at 298 K. They found the solid phases in the MgCl2 + water + CH3OH system were MgCl2·6H2O, MgCl2·4H2O·2CH3OH,

INTRODUCTION MgCl2 supported high-yield Ziegler−Natta catalyst has been used for the polymerization reaction of olefins to produce polyolefin.1 Polyolefins are a group of synthetic polymers including polyethylene and polypropylene, which are widely used as grocery bags, containers, engineering plastics, and so on.2,3 After the invention of Ziegler−Natta catalysts that significantly reduced the polymers costs and enabled it to tweak the specifications of the products, polyolefin industries began their first rise in the 1950s. Later on, the discovery of MgCl2supported Ziegler−Natta catalyst led to higher activities which boosted the production of polyolefins again. Nowadays, the world polymer demand has reached 211 million metric tons.4 The modern Ziegler−Natta catalyst consists of TiCl4, alkyl aluminum, and MgCl2 as a support. Because the low surface area of MgCl2 and its poor interaction with TiCl4, MgCl2 reacts with Lewis bases such as alcohols, esters to destroy the crystalline structure of MgCl2 during the preparation of the catalyst. A common method for the synthesis of the MgCl2-alcohol adducts is recrystallization so that the morphology of the catalyst would be controlled.5,6 In this method, MgCl2 was first dissolved in alcohols or other solvents including toluene7 and ndecane.8 The most commonly used alcohol is ethanol9,10 and many other alcohols such as methanol,11 2-propanol,12 and 2butanol13 were also tested to synthesize the MgCl2-alcohol © XXXX American Chemical Society

Received: July 20, 2015 Accepted: January 11, 2016

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DOI: 10.1021/acs.jced.5b00624 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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and MgCl2·6CH3OH. However, the existence of MgCl2·4H2O· 2CH3OH is skeptical because it can be considered as the mixture of MgCl2·6H2O and MgCl2·6CH3OH. Zhang et al.19 conducted the solubility test of MgCl2 in the single solvent of methanol, ethanol, and n-butanol for the development of a dehydration process of MgCl2 by alcohol distillation. In the determination of the solid−liquid phase diagram for the MgCl2 + NH3 + CH3OH system at 298 K, Pownceby et al.20 reported the solubility of MgCl2 in pure methanol. The above discussion suggests that the solubility of MgCl2 in alcohols still require investigation, especially in the mixed solvent systems at various temperatures. Several thermodynamic models are available for the modeling of the solubility of electrolytes in organic solvents. For example, the electrolyte nonrandom two-liquid (eNRTL) model developed by Chen and his co-workers has been proven feasible in the modeling of mixed solvent system.21 Another example is the LIQUAC model which is derived from the UNIQUAC model.22−24 Li et al.23 used the LIQUAC model to represent the solubility of a salt (NaCl, KCl, NaBr, KBr, and so on) in a binary solvent mixture (water + methanol, water + ethanol). Recently, Wang et al. proposed a so-called mixedsolvent electrolyte (MSE) model, which is capable of estimating the phase equilibria of electrolytes in water, organic, or mixed solvents.25−27 A successful application of the MSE model is the calculation of the phase equilibria of the ethylene glycol + water + inorganic salts system.26 In this work, the solubilities of MgCl2 in methanol, ethanol, and 2-propanol as well as in their binary mixtures, are determined experimentally by a dynamic method in the temperature range of 283−343 K. The solubilities are affected by the physical interactions between various species in the solution, and the formation of different solid phases which are dependent on the solvent concentrations and temperature. By taking into accounting those effects, a thermodynamic model framework was established to calculate the measured solubility data.

Figure 1. Schematic drawing of the solubility measurement apparatus: (A) magnetic stirring plate; (B) glass vessel; (C) magnetic rotor; (D) thermostat.

anhydrous MgCl2 and the nucleation often requires a long induction time at low supersaturation, no solid would precipitate out even if the solution is supersaturated.31 This “temperature-swing” process can ensure that true thermodynamic equilibrium was reached. This process was replicated at various temperatures. After completing the solubility tests, equilibrated solid were obtained by adding small amount of excess MgCl2 into the solution. The collected solids were washed with acetone and filtered then subjected to X-ray diffraction (XRD) characterization. The XRD patterns were recorded by using Cu/Kα radiation operating at 40 kV/40 mA with a scanning rate of 0.02 deg/s.

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CHEMICAL MODELING FRAMEWORK Chemical Equilibrium Relationships. Various solvated forms, such as MgCl2·6CH3OH and MgCl2·6C2H5OH, are known to exist when MgCl2-adducts precipitated out from alcohol solutions. For example, Gnanakumar et al.11 synthesized MgCl2·6CH3OH in a solution containing 0.1 mol·L−1 MgCl2 and 1.2 mol·L−1 methanol. The crystal structure of MgCl2·6C2H5OH collected from MgCl2 + ethanol solution was studied by Valle et al.14 Thushara et al.12 obtained MgCl2· 4(CH3)2CHOH by azeotropic distillation method from the mixture of MgCl2 + 2-propanol + toluene. Based on those findings, three solid phases including MgCl2·6CH3OH, MgCl2· 6C2H5OH, and MgCl2·4(CH3)2CHOH were assumed to be presented in the MgCl2 + alcohols (methanol, ethanol, and 2propanol) system. Although MgCl2−alcohol adducts with different molar ratios of alcohol to MgCl2 can be synthesized,9 the XRD characterization results of the equilibrated solids indicated that the three MgCl2−alcohol adducts with fixed molar ratio formed. The equilibria for the dissolution of the MgCl2−alcohol adducts are given by

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MATERIALS AND METHODS Experimental Materials. Analytical grade anhydrous MgCl2 (99%) supplied by Alfa Aesar was used. Ethanol and acetone were supplied by Beijing Chemical Plant with minimum purities of 99.7% and 99.5%, respectively. Methanol (99.5%) and 2-propanol (99.7%) from Xilong Chemical Group were used. All reagents were used directly without further purification. Determination of Solubility. A dynamic method similar to literatures28−30 was adopted to determine the solubility of MgCl2 in the alcohols. Preweighted anhydrous MgCl2 and alcohol solutions with known composition were added to the 250 mL jacket quartz glass vessel, as shown in Figure 1. Circulating water from a thermostat controlled the temperature of the vessel within ±0.1 K, while the magnetic stirrer provided constant agitation. At the beginning, the temperature of the solution was maintained at a relatively high temperature to ensure that the added MgCl2 dissolved completely. Then the temperature was dropped to 5−10 °C so that the solution was supersaturated and white precipitates were formed. The equilibration of the MgCl2 + alcohols solution was reached by elevating the temperature carefully until the precipitate disappeared. The equilibrium concentration can be calculated from the weight of the added MgCl2 and the solvents. As the equilibrated solids are MgCl2−alcohol adducts instead of

MgCl2· 6CH3OH(s) = Mg 2 +(aq) + 2Cl−(aq) + 6CH3OH(aq)

(1)

MgCl2· 6C2H5OH(s) = Mg 2 +(aq) + 2Cl−(aq) + 6C2H5OH(aq)

(2)

MgCl2· 4(CH3)2 CHOH(s) = Mg 2 +(aq) + 2Cl−(aq) + 4(CH3)2 CHOH(aq) B

(3)



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Taking MgCl2·6C2H5OH as an example, the solubility product for reaction 1 is expressed as

Bij (Ix) = bij + cij exp( − Ix + 0.01 )

where bij and cij are functions of temperature:

KSP(MgCl2·6C2H5OH) 2

bij = BMD0 + BMD1 × T + BMD2 /T + BMD3 × T 2

6

= γMg 2+x Mg 2+(γCl−xCl−) (γC H OHxC2H5OH) 2

5

(4)

+ BMD4 × ln T

where xi and γi are the concentration in mole fraction and mole fraction-based activity coefficient of relevant species i, respectively. KSP is mole fraction-based solubility product. Thermodynamic Framework. It can be seen in eq 4 that the calculation of solubility requires the value of solubility product and activity coefficient of the relevant species. The solubility product can be estimated from the standard-state chemical potentials of the equilibrium species. The standardstate chemical potentials are calculated from various thermodynamic data according to standard thermodynamic relationships, such as entropy, enthalpy, and heat capacity. Alternatively, an empirical equation can be used in the case of accurate thermodynamic data is not available: log K = A +

B + CT + DT 2 T

+ CMD4 × ln T

(5)

aij = Q 0, ij + Q 1, ij × T + Q 2, ij × T 2

(12)

where Q0,ij, Q1,ij, and Q2,ij are adjustable UNIQUAC interaction parameters for the activity coefficient calculations in the MSE model.

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RESULTS AND DISCUSSION Solubility of MgCl2 in Single Alcohol. The solubility of MgCl2 in methanol, ethanol, and 2-propanol was determined by the method mentioned above from 283.2 to 342.2 K. The results are tabulated in Tables 1−3 and display graphically in

(6)

Table 1. Mole Fraction Solubility of MgCl2 in Methanol at Pressure p = 0.1 MPaa

(7)

The first term Gex LR represents the contribution of long-range electrostatic interactions. Gex SR is the short-range contribution resulting from molecule/molecule, molecule/ion, and ion/ion interactions; and an additional middle-range term Gex MR accounts for ionic interactions that are not included in the long-range term. The long-range interaction contribution voices by the Pitzer−Debye−Hückel formula. The middle-range interaction contribution is calculated from a second virial coefficient-type expression: ex GMR = −(∑ ni) ∑ ∑ xixjBij (Ix) RT i i j

(11)

where BMD0, BMD1, CMD0, and CMD1, and so forth, are the adjustable middle-range interaction parameters. For most aqueous electrolyte systems, the middle-range interaction contribution accounting for the interactions between ion−ion and ion−neutral molecules is the most important one. Whereas in mixed solvent systems, the shortrange interaction contribution should be introduced to account for molecular interactions. The short-range interaction is expressed by the UNIQUAC equation. The dependence of unsymmetrical energetic parameters aij on the temperature is expressed as

where Δn is the numbers of the species participated in the reaction that excludes water and solid phases. The MSE model embedded in OLI software was adopted in this work for the calculation of solubility because of its versatility in estimating the thermodynamic properties of the mixed solvent system. Detailed description of the MSE model can be found elsewhere.25,32 In the MSE model, the excess Gibbs free energy, which can be used for deriving the activity coefficient, is expressed as a sum of three terms: G ex G ex G ex Gex = LR + MR + SR RT RT RT RT

(10)

cij = CMD0 + CMD1 × T + CMD2 /T + CMD3 × T 2

where A, B, C, and D are empirical parameters. T is the temperature (K). It should be noted that the solubility product given by the standard-state chemical potentials or the empirical equation is molality-based. The molality-based solubility product can be converted to mole fraction-based solubility product expressed in eq 4 by the following equation: K (m) = K (x) × 55.5082Δn

(9)

T (K)

MgCl2 (mole fraction)

283.2 289.2 300.2 305.7 311.2 313.2 317.2 323.2 328.2 334.2

0.0488 0.0498 0.0516 0.0526 0.0538 0.0545 0.0552 0.0559 0.0564 0.0573

a

Standard uncertainties u are u(T) = 0.1 K, ur(p) = 0.05, and u(x(MgCl2)) = 0.001.

Figure 2. As can be seen, the solubility of MgCl2 in single methanol, ethanol, or 2-propanol all increases with increasing temperature. However, the effect of temperature on the solubility in ethanol is greater than that in methanol. For example, the solubility in methanol is larger than the one in ethanol at temperature below 317.2 K, while the solubility in ethanol is higher when the temperature is elevated. The solubility in these alcohols at room temperature decreases in the order of methanol, ethanol, and 2-propanol. Therefore, it can be inferred that weak polarity of the alcohol would depress the dissolution of MgCl2.

(8)

where x is the mole fraction of the species, Ix is the mole fraction-based ionic strength. Bij (Ix) is a symmetric (Bij = Bji, and Bii = Bjj = 0) binary interaction parameter between species i and j (ion or molecule). Bij (Ix) is ionic strength-dependent expressed by the following empirical expression: C



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Table 2. Mole Fraction Solubility of MgCl2 in Ethanol at Pressure p = 0.1 MPaa T (K)


287.2 295.7 302.7 308.2 314.2 318.2 324.2 328.7 332.7 342.2

0.0213 0.0289 0.0359 0.0426 0.0495 0.0544 0.0607 0.0668 0.0726 0.0848

a

Standard uncertainties u are u(T) = 0.1 K, ur(p) = 0.05, and u(x(MgCl2)) = 0.001.

Table 3. Mole Fraction Solubility of MgCl2 in 2-Propanol at Pressure p = 0.1 MPaa T (K) 283.2 288.2 298.2 302.7 309.2 313.2 319.7 325.7 328.2 332.2 337.2 342.2

Figure 3. Comparisons of the solubility of MgCl2 in alcohols from different sources: (solid square) solubility in methanol measured in this work, (solid circle) solubility in ethanol measured in this work, (open square) solubility in methanol reported by Lloyd et al., (open circle) solubility in ethanol reported by Lloyd et al., (open triangle) solubility in methanol reported by Pownceby et al.

MgCl2 (mole fraction) 1.53 1.57 1.69 1.73 1.83 1.89 2.06 2.37 2.47 2.74 3.13 3.76

× × × × × × × × × × × ×

10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

temperatures exceed 320 K. Moreover, the solubility in methanol determined by Pownceby et al. at 298 K is larger than the ones reported by us and Lloyd et al. For the solubility in ethanol, the data presented in this work is in good agreement with the literature values of Lloyd et al. The deviations of solubility collected from different sources may attribute to the different experimental procedure. For example, Pownceby et al. measured the solubility of MgCl2 in methanol by incrementally adding MgCl2 into methanol solution at constant temperature until saturation was reached. While in this work, a “temperature-swing” process was used to determine the solulibity. The log of the solubilities in single alcohol as a function of 1/ T is demonstrated in Figure 4. The relationship of the log of solubilities in methanol and ethanol and 1/T can be expressed in linear functions. However, a noticeable deviation is observed between the linear function and the log of solubility vs 1/T in the case of 2-propanol. This results suggests that log KSP of

a Standard uncertainties u are u(T) = 0.1 K, ur(p) = 0.05, and u(x(MgCl2)) = 0.001.

Figure 2. Mole fraction solubility of MgCl2 in methanol, ethanol, and 2-propanol as a function of temperature. The points represent the measured solubility data; the lines are the calculating values.

The solubility of methanol and ethanol reported in the works of Lloyd et al.33 and Pownceby et al.20 are compared with our measured data, and the results are shown in Figure 3. It can be seen that the solubility in methanol measured in this work is agreed with the values reported by Lloyd et al. at temperature below 310 K. However, the deviations become larger as

Figure 4. Log of the measured solubility in methanol, ethanol, and 2propanol as a function of 1/T; the lines are linear fittings of the data. D



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MgCl2·6CH3OH and MgCl2·6C2H5OH should be fitted as a linear function of 1/T, while more coefficients would be required for the log KSP of MgCl2·4(CH3)2CHOH. Solubility of MgCl2 in the Mixed Alcohols. Tables 4−6 list the solubility of MgCl2 in the mixtures of methanol +

Table 5. Mole Fraction Solubility of MgCl2 in the Mixtures of Methanol + 2-Propanol at Pressure p = 0.1 MPaa T (K)

methanol (mole fraction)

294.2 306.7 311.2 313.7 317.2 320.2 325.7 329.7

0.1920 0.1916 0.1914 0.1913 0.1912 0.1910 0.1908 0.1905

293.2 298.2 300.7 306.7 311.2 315.2 320.7 325.2 328.2

0.5796 0.5788 0.5781 0.5768 0.5753 0.5738 0.5719 0.5702 0.5683

286.2 289.7 300.7 305.7 308.2 311.7 315.7 320.2 324.2 328.2

0.7690 0.7682 0.7665 0.7653 0.7646 0.7639 0.7628 0.7615 0.7604 0.7591

Table 4. Mole Fraction Solubility of MgCl2 in the Mixtures of Methanol + Ethanol at Pressure p = 0.1 MPaa T (K)

methanol (mole fraction)

298.2 304.2 308.2 314.7 319.2 324.2 329.2 334.7 341.2

0.1900 0.1892 0.1882 0.1872 0.1864 0.1854 0.1845 0.1835 0.1823

298.2 303.7 309.7 319.2 327.7 330.2 336.2

0.3627 0.3608 0.3582 0.3563 0.3547 0.3539 0.3529

298.2 303.7 314.2 329.2 332.2 343.2

0.5564 0.5555 0.5513 0.5488 0.5484 0.5474

298.2 307.2 316.2 318.7 337.2

0.7588 0.7576 0.7580 0.7577 0.7566

ethanol (mole fraction)

Methanol (Salt-Free) = 0.7455 0.7425 0.7386 0.7345 0.7314 0.7274 0.7242 0.7200 0.7156 Methanol (Salt-Free) = 0.5507 0.5479 0.5439 0.5409 0.5386 0.5373 0.5358 Methanol (Salt-Free) = 0.3726 0.3720 0.3731 0.3714 0.3712 0.3705 Methanol (Salt-Free) = 0.1859 0.1856 0.1848 0.1847 0.1845


0.2 0.0645 0.0683 0.0732 0.0783 0.0822 0.0873 0.0912 0.0965 0.1021 0.4 0.0867 0.0913 0.0978 0.1028 0.1067 0.1087 0.1113 0.6 0.0710 0.0725 0.0757 0.0797 0.0804 0.0821

2-propanol (mole fraction)

Methanol (Salt-Free) = 0.2 0.7719 0.7704 0.7698 0.7694 0.7688 0.7682 0.7673 0.7661 Methanol (Salt-Free) = 0.6 0.3891 0.3886 0.3881 0.3872 0.3862 0.3852 0.3840 0.3828 0.3816 Methanol (Salt-Free) = 0.8 0.1929 0.1927 0.1923 0.1920 0.1918 0.1916 0.1913 0.1910 0.1907 0.1904

MgCl2 (mole fraction) 0.0362 0.0380 0.0388 0.0393 0.0400 0.0408 0.0419 0.0434 0.0313 0.0327 0.0338 0.0360 0.0385 0.0409 0.0441 0.0471 0.0501 0.0382 0.0391 0.0413 0.0427 0.0436 0.0444 0.0458 0.0475 0.0489 0.0505

a

Standard uncertainties u are u(T) = 0.1 K, ur(p) = 0.05, u(x(MgCl2)) = 0.001, and u(x(alcohol)) = 0.0001.

0.8 0.0554 0.0568 0.0572 0.0576 0.0589

The solubility of MgCl2 in the mixtures of ethanol + 2propanol is displayed in Figure 7. It can be observed that solubility is enhanced in the mixed alcohols solution similar to those in the mixtures of methanol + ethanol and methanol + 2propanol. The solubility at the ethanol concentration of 20% and 40% increases at the same rate with increasing temperature, which suggests that the equilibrated solid phases are the same under those conditions. The solubility curve in the 60% ethanol can be divided into two parts: a quick increment with increasing temperature below 316.2 K and slow growth with further prolonged temperature, indicating the phase transition of the equilibrated solid. Identification of Equilibrated Solids. The XRD results of the equilibrated solids are listed in Table 7. By comparison with the literature XRD data,11,12 it was found that MgCl2·6CH3OH, MgCl2·6C2H5OH, and MgCl2·4(CH3)2CHOH were formed in single methanol, ethanol, and 2-propanol solutions, respectively. In the mixtures of methanol + ethanol, MgCl2·6C2H5OH was identified at the methanol concentration of 20 and 40%, while the equilibrated solids were MgCl2·6CH3OH at higher methanol concentration. The XRD characterization in the mixtures of methanol + ethanol is consisted with experimental solubility data. In the mixtures of methanol + 2-propanol, the equilibrated solid changed from MgCl2·4(CH3)2CHOH to MgCl2·6CH3OH at the methanol concentration higher than

a

Standard uncertainties u are u(T) = 0.1 K, ur(p) = 0.05, u(x(MgCl2)) = 0.001, and u(x(alcohol)) = 0.0001.

ethanol, methanol + 2-propanol, and ethanol + 2-propanol. Figure 5 shows that the solubility increases sharply with increasing temperature. The increasing rate of solubility is larger at the methanol concentration (salt-free) of 20 and 40% than the rates at the methanol concentration greater than 60%. It is reasonable to assume that different solid phases are formed dependent on methanol concentration. Moreover, it could be noted that more MgCl2 dissolved in the mixed alcohols solution than in single methanol and ethanol by comparing the solubility data in Figure 5 with the ones in Figure 2. Figure 6 represents the solubility of MgCl2 in the mixed methanol + 2-propanol solution. As can be seen in Figure 6, the solubilities measured at various methanol concentrations all increase with increasing temperature, but at different rates. For example, the solubility at the methanol concentration of 60% is 0.0313 at 293.2 K. However, it increases dramatically with increasing temperature that reaches 0.0501 at 328.2 K. E



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Table 6. Mole Fraction Solubility of MgCl2 in the Mixtures of Ethanol + 2-Propanol at Pressure p = 0.1 MPaa T (K)

ethanol (mole fraction)

297.2 302.2 309.2 317.2 321.7 327.2 335.2 340.2 345.2

0.1961 0.1969 0.1967 0.1964 0.1962 0.1959 0.1955 0.1952 0.1948

303.2 317.2 323.2 332.2 337.2 344.2

0.3834 0.3796 0.3792 0.3786 0.3782 0.3699

293.2 296.7 300.2 303.2 304.2 307.7 312.2 313.2 316.2 322.2 328.2 334.2 338.2 342.2 345.2

0.5843 0.5801 0.5748 0.5706 0.5684 0.5581 0.5452 0.5460 0.5418 0.5404 0.5399 0.5394 0.5389 0.5383 0.5377

288.2 294.2 298.7 302.2 308.2 315.2 320.2 323.2 327.2 329.2 334.7 340.2

0.7856 0.7814 0.7783 0.7738 0.7659 0.7574 0.7478 0.7428 0.7381 0.7341 0.7231 0.7120

2-propanol (mole fraction)

Ethanol (Salt-Free) = 0.7876 0.7859 0.7851 0.7840 0.7833 0.7821 0.7803 0.7791 0.7777 Ethanol (Salt-Free) = 0.5640 0.5601 0.5594 0.5585 0.5580 0.5627 Ethanol (Salt-Free) = 0.3881 0.3854 0.3818 0.3791 0.3748 0.3681 0.3628 0.3600 0.3584 0.3587 0.3584 0.3580 0.3577 0.3573 0.3569 Ethanol (Salt-Free) = 0.1960 0.1950 0.1942 0.1924 0.1904 0.1883 0.1859 0.1847 0.1835 0.1825 0.1798 0.1770


0.2 0.0164 0.0172 0.0182 0.0196 0.0204 0.0219 0.0242 0.0257 0.0274 0.4 0.0527 0.0603 0.0614 0.0629 0.0638 0.0675

Figure 5. Mole fraction solubility of MgCl2 in the mixtures of methanol + ethanol as a function of temperature. The points represent the measured solubility data; the lines are the calculating values.

0.6 0.0276 0.0345 0.0434 0.0503 0.0568 0.0738 0.0920 0.0940 0.0998 0.1010 0.1017 0.1026 0.1034 0.1044 0.1054 0.8 0.0184 0.0236 0.0275 0.0338 0.0437 0.0543 0.0663 0.0726 0.0783 0.0834 0.0971 0.1110

Figure 6. Mole fraction solubility of MgCl2 in the mixtures of methanol + 2-propanol as a function of temperature. The points represent the measured solubility data; the lines are the calculating values.

to support the existence of the mixed solvate solid such as MgCl2·2CH3OH·4C2H5OH. Model Parameterization. The middle-range and UNIQUAC interaction parameters between various species, the UNIQUAC size parameters for ions and solvent molecules, and the solubility product of the equilibrated solids are required to represent the solubility of MgCl2 in alcohols. The solubility product of MgCl2·6CH3OH, MgCl2·6C2H5OH, and MgCl2· 4(CH3)2CHOH and the middle-range interaction parameters for Mg2+−methanol, Cl−−methanol, Mg2+−ethanol, Cl−− ethanol, Mg2+−2-propanol, Cl−−2-propanol, and Mg2+−Cl− were regressed based on experimental solubility data. As discussed in previous section, the relationship between log KSP of MgCl2·6CH3OH and MgCl2·6C2H5OH and 1/T can be expressed as a linear function. The solubility products of MgCl2·6CH3OH and MgCl2·6C2H5OH were fitted by only using the first two coefficients of eq 5 (A and B). While three coefficients (A, B, and C) were used for the solubility product

a Standard uncertainties u are u(T) = 0.1 K, ur(p) = 0.05, u(x(MgCl2)) = 0.001, and u(x(alcohol)) = 0.0001.

60%. The phase transition at 316.2 K in the mixtures of ethanol + 2-propanol was also supported by the XRD results. The XRD patterns of MgCl2·6CH3OH are shown in Figure 8 which can be observed that the XRD patterns collected at different conditions are basically the same. Figure 9 indicates that the equilibrated solid is MgCl2·4(CH3)2CHOH when the mole fraction of 2-propanol is 20 and 40% in the methanol + 2propanol mixtures. In all circumstances, little evidence is found F



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Figure 7. Mole fraction solubility of MgCl2 in the mixtures of ethanol + 2-propanol as a function of temperature. The points represent the measured solubility data; the lines are the calculating values.

Figure 9. XRD patterns of the MgCl2·4(CH3)2CHOH collected in single 2-propanol, mixtures of methanol + 2-propanol, and ethanol + 2-propanol.

Table 7. Equilibrated Solids Corresponding to Different Conditions system MgCl2 MgCl2 MgCl2 MgCl2 MgCl2 MgCl2 MgCl2 MgCl2 MgCl2 MgCl2 MgCl2

+ methanol + ethanol + 2-propanol + (0.2, 0.4) methanol + ethanol + (0.6, 0.8) methanol + ethanol + (0.2) methanol + 2-propanol + (0.6, 0.8) methanol + 2-propanol + (0.2, 0.4) ethanol + 2-propanol + (0.6) ethanol + 2-propanol, > 316.2 K + (0.6) ethanol + 2-propanol, < 316.2 K + (0.8) ethanol + 2-propanol

propanol systems collected from the work of Winkle et al.34,35 The UNIQUAC surface area qi and volume size ri parameters for methanol, ethanol, and 2-propanol are taken directly from the default databank in the OLI software. For Mg2+ and Cl− ions, literature values reported by Mohs and Gmehling22 are adopted. All of these parameters that are needed to model the solubility data are tabulated in Tables 8−11. From the results in Table 8, the log KSP (mole fraction-based) for the dissolution reaction of MgCl2·6CH3OH, MgCl2·6C2H5OH, and MgCl2· 4(CH3)2CHOH at 298.2 K were calculated to be −11.5078, −13.0943, and −10.6139, respectively. The average absolute deviations (AAD) between the experiment data and model results for various systems are listed in Table 12. Figures 2 and 5−7 compared the measured solubility data (marked as points) with the calculated results (marked as solid lines). The model represents the solubility data with the AAD varied from 1.23 to 8.07%, while the AAD for the VLE data is in the range of 2.87−9.71%. It can be observed that the model represents the solubility data of MgCl2 in single methanol, ethanol, and 2-propanol accurately, especially for the solubility in methanol with an AAD of 1.23%. For the solubility in mixed alcohols, the minimal value of AAD is found to be at the mixtures of ethanol + 2-propanol, which is 7.34%. While for the mixtures of methanol + ethanol and methanol + 2-propanol, the model has the tendency of underestimating the solubility at the methanol concentration of 20%. The above results suggest that proper crystallization method for MgCl2-adducts should be chosen according to the solubility behavior of MgCl2 in alcohols. For example, the synthesis of MgCl2·6CH3OH from methanol by cooling is not feasible because the effect of temperature on the solubility is limited. However, the cooling method can be adopted for MgCl2· 6C2H5OH due to the strong dependence of solubility on temperature. The low solubility of MgCl2 in 2-propanol renders precipitation of MgCl2·4(CH3)2CHOH from 2-propanol inefficient. However, MgCl2·4(CH3)2CHOH can be effectively obtained by using the mixed alcohols as the solubility is greatly enhanced in the mixed solvents.

solid MgCl2·6CH3OH MgCl2·6C2H5OH MgCl2·4(CH3)2CHOH MgCl2·6C2H5OH MgCl2·6CH3OH MgCl2·4(CH3)2CHOH MgCl2·6CH3OH MgCl2·4(CH3)2CHOH MgCl2·4(CH3)2CHOH MgCl2·6C2H5OH MgCl2·6C2H5OH

Figure 8. XRD patterns of the MgCl2·6CH3OH collected in single methanol, mixtures of methanol + ethanol, and methanol + 2propanol.

of MgCl2·4(CH3)2CHOH. The UNIQUAC interaction parameters for methanol−ethanol, methanol−2-propanol, and ethanol−2-propanol were obtained through regressing the vapor−liquid equilibrium data of methanol + ethanol + 2G



Article

Table 8. Coefficients for Solubility Products (Mole Fraction-Based) of MgCl2·6CH3OH, MgCl2·6C2H5OH, and MgCl2· 4(CH3)2CHOH species

A

B

C

D

log K(MgCl2·6CH3OH) log K(MgCl2·6C2H5OH) log K(MgCl2·4(CH3)2CHOH)

−7.5644413 25.5285457 298.9315

−1175.717 −11515.41 −52575.92

0 0 −0.4467714

0 0 0

Table 9. MSE Middle-Range Interaction Parametersa

a

species

BMD0

BMD1

BMD2

CMD0

CMD1

CMD2

Mg2+−methanol Cl−−methanol Mg2+−ethanol Cl−−ethanol Mg2+−2-propanol Cl−−2-propanol Mg2+−Cl−

−48.49725 −0.5699423 64.88912 −4.582282 −157.8560 −122.3917 49.36908

0 0 9.5361690 × 10−3 −9.3016641 × 10−2 0 0.2313463 −0.7537794

3898.270 1766.595 0 0 36194.22 21047.93 36939.66

−6.586657 7.445236 −117.7853 58.26674 −42.37983 −19.24068 −17.70895

0.1168242 0 0 0 0.2595997 2.1107244 × 10−3 1.329609

0 0 0 0 0 0 −83544.93

For all of the species pairs, BMD3, BMD4, CMD3, and CMD4 are set equal to zero.

Table 10. UNIQUAC Interaction Parametersa species ethanol 2-propanol ethanol a

methanol methanol 2-propanol

Q0,ij

Q1,ij

Q0,ji

Q1,ji

−74633.32 −4055.498 2114.870

268.1980 4.488675 7.046171

−12256.72 3954.965 578.2296

27.37359 9.176213 −9.828123

For all of the species pairs, Q2,ij and Q2,ij are set equal to zero.

Table 11. UNIQUAC Surface Area Qi and Volume Size Ri Parameters

a

species

qi

ri

refs

methanol ethanol 2-propanol Mg2+ Cl−

1.4311 2.5755 3.2491 0.1484 0.9809

1.4322 2.5880 3.1240 0.0571 0.9699

a a a b b

various conditions contributes to different solubility behavior. With the regression of solubility products for MgCl2·6CH3OH, MgCl2·6C2H5OH, and MgCl2·4(CH3)2CHOH and interaction parameters for Mg2+−methanol, Cl−−methanol, Mg2+−ethanol, Cl−−ethanol, Mg2+−2-propanol, Cl−−2-propanol, Mg2+−Cl−, methanol−ethanol, methanol−2-propanol, and ethanol−2propanol, the MSE model embedded in the OLI software can be used to describe the experimental solubility data reasonably. The results obtained in this work would provide fundamental thermodynamic data for the synthesis of MgCl2−alcohol adducts.

MSEPUB databank in the OLI software. bMohs and Gmehling.22

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Table 12. Average Absolute Deviations AAD%a Between the Experiment Data and Model Results

a

system

type of data

AAD value (%)

MgCl2 + methanol MgCl2 + ethanol MgCl2 + 2-propanol MgCl2 + methanol + ethanol MgCl2 + methanol + 2-propanol MgCl2 + ethanol + 2-propanol methanol + ethanol methanol + 2-propanol ethanol + 2-propanol methanol + ethanol + 2-propanol

solubility solubility solubility solubility solubility solubility VLE VLE VLE VLE

1.23 4.86 5.57 8.06 8.07 7.34 8.83 2.87 9.71 7.48

AAD% =

∑nl [|yexp

AUTHOR INFORMATION

Corresponding Author

*Tel./fax: +86-10-62551557. E-mail: [email protected]. Funding

The authors are grateful to the financial support of National Natural Science Foundation of China (Grant No. U1407112 and 21476235), National Basic Research Program of China (973 Program with Grant No. 2013CB632605) and the Science and Technology Planning Project of Qinghai Province (2012G-213A). Notes

The authors declare no competing financial interest.

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− ycal|/yexp] × 100, n = number of data points.

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CONCLUSIONS Solubility data of anhydrous MgCl2 in single and mixed solvents of methanol, ethanol, and 2-propanol has been measured at different temperatures. The results show that temperature and the composition of the solvents both significantly influence the solubility. The formation of different solid phases (MgCl2· 6CH3OH, MgCl2·6C2H5OH, and MgCl2·4(CH3)2CHOH) at H



Article

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Determination and Modeling of MgCl2 Solubility in Methanol, Ethanol

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