Binodal Curves and Tie-Lines of Aliphatic Alcohols + Diammonium

Publication Date (Web): May 14, 2012 ... Fax: 984113340191. ... Additionally, tie-line compositions are reported at 298.15 K, and the electrolyte nonr...
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Binodal Curves and Tie-Lines of Aliphatic Alcohols + Diammonium Hydrogen Citrate + Water Ternary Systems: Measurement and Modeling Ebrahim Nemati-Kande,† Hemayat Shekaari,*,‡ and Mohammed Taghi Zafarani-Moattar‡ †

Department of Chemistry, Faculty of Science, Parsabad Mogan Branch, Islamic Azad University, Parsabad, Iran Department of Physical Chemistry, Faculty of Science, University of Tabriz, Tabriz 51664, Iran

‡

S Supporting Information *

ABSTRACT: The liquid−liquid equilibrium of 1-propanol, 2propanol, 2-methyl-2-propanol, or 2-butanol + diammonium hydrogen citrate aqueous biphasic systems was studied at 298.15 K. The binodal curves of investigated systems at (298.15 and 308.15) K were measured; the dielectric constant and densities were used to modify the empirical Merchuk equation, and the obtained equation was used for the correlation of all measured binodal data simultaneously. The temperature effect on the studied systems in the (293.15 to 323.15) K temperature range was discussed using the measured cloud-point data at constant salt-to-water mole fraction ratios. Additionally, tie-line compositions are reported at 298.15 K, and the electrolyte nonrandom two-liquid (NRTL) model was satisfactorily used for the correlation of these data; the restricted binary interaction parameters were also obtained. An acceptable agreement between the calculated and the experimental tie-line data was obtained.

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INTRODUCTION Mixing appropriate amounts of aqueous solutions of a shortchain alcohol and a kosmotropic salt (water structure-making salt) above critical concentrations formed an aqueous biphasic system (ABS). This type of the biphasic systems is a proper substitution of the usual organic−water solvent extraction systems, because of its technical, commercial, and biological advantages.1−3 Furthermore, the design of the methods for the recovery of chemicals is an important part of the planning for large-scale processes. This part of the planning needs the physicochemical properties of alternatives, and to this end, Greve and Kula1 recommended utilizing the ABS's composed of alcohol + water + salt for recycling the salt in ternary polymer + salt + water−protein extraction systems. In recent years many research groups have focused on the measurement of new two-phase equilibrium data for aqueous alcohol + salt systems. As examples, Taboada,4 Hu et al.,5 Tanioka and Chou,3 and Zafarani-Moattar et al.6 reported the effect of salt and alcohol type on the phase-forming ability of the relevant ABS's. The effect of temperature on the ABS's composed of some aliphatic alcohols + potassium carbonate + water was discussed by Salabat and Hashemi.7 Furthermore, in a previous work8 we studied the effect of alcohol type and temperature on the phase separation ability of some aliphatic alcohols + dipotassium oxalate + water systems. Some common kosmotropic salts and different alcohols have been used to form effective ABS's in the studied aliphatic alcohols + salts systems. The most used salts are the inorganic salts;1−8 however, the use of nontoxic and biodegradable © 2012 American Chemical Society

materials to form an ABS is one of the favorite branches of these studies. In this regard, Vernau and Kula9 investigated citrates as appropriate substitutes for inorganic salts in polymer−salt ABS's, because citrate anions are nontoxic and biodegradable and therefore can be used as green alternatives. Furthermore, the thermodynamic investigation of the liquid−liquid equilibrium (LLE) data using reliable models in such ABS's is an important goal for these studies. The nonrandom two-liquid (NRTL), electrolyte-NRTL (e-NRTL), universal quasichemical (UNIQUAC), or universal functional (UNIFAC) models are extensively used to represent the LLE data in alcohol + salt + water systems.10−18 The group contribution based models (i.e., UNIQUAC or UNIFAC) are the molecular structure dependent models, and the use of them needs to calculate the volume and surface parameters. On the other hand, local composition-based models (i.e., NRTL or eNRTL) are nondependent to the structure of the molecules and can be used for the correlation of the LLE data without any knowledge of the molecular structure of the studied molecules. It is evident that, for accurate representation of such ABS's, the effect of the mixed organic−aqueous solvent and the influence of the ionic species should be considered in an appropriate model, and Chen and Song,16 considering these two restrictions, generalized the e-NRTL model11 for the investigation of the mixed-solvent electrolyte systems and used Received: December 6, 2011 Accepted: May 7, 2012 Published: May 14, 2012 1678

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Table 1. Properties of the Pure Component purity

a

chemical

CAS No.

source

mass fraction

1-propanol 2-propanol 2-methyl-2-propanol 2-butanol diammonium hydrogen citrate

71-23-8 67-63-0 75-65-0 78-92-2 7632-50-0

Rankem (India) Rankem (India) Lobachemie (India) Lobachemie (India) Riedel-de Haën (Germany)

> > > > >

0.995 0.997 0.99 0.99 0.99

d/kg·m−3

M g·mol

−1

60.096 60.096 74.123 74.123 226.19

298.15

a

799.54 781.10 788.70 806.30

308.15

ε/C2·J−1·m−1 b

792.27 772.88 768.36 793.21

298.15c

308.15c

20.18 19.85 12.47 15.90

19.05 17.76 10.80 14.50

Taken from ref 35. bTaken from ref 36. cTaken from ref 21.

(2400 cycles·min−1) twice using a shaker (Labtron model LS100, Iran) for 3 min. After the first shaking, the samples were immersed in a thermostatted water bath at constant temperature of 298.15 K for about an hour. Afterward, the samples were shaken for the second time and placed in the same bath to reach the equilibrium. As we know, in the equilibrium condition any macroscopic property of the systems is stable, and therefore to ensure the occurrence of the thermodynamic equilibrium, the refractive index of some samples of the both phases (i.e., top and bottom) of several feed samples was measured, using a refractometer (Atago, model DR-A1, Japan) with an uncertainty of the ± 0.0002 in the refractive index measurement, at one hour periods. Periodic measurements show that the necessary rest time to ensure the thermodynamic equilibrium is about 4 h. However, the feed samples were immersed in the water bath for about (6 to 8) h to enrich the equilibrium condition. The split phases were separated using long needle syringes and prepared by diluting for refractive index measurement. The concentration of diammonium hydrogen citrate in both phases was analyzed using a back-titration method. In the used method, a known and extra amount of standard sodium hydroxide solution (0.5 molar) was added to a known amount of samples (about 1.5 g). The solution was then diluted by adding about 10 g of doubly distilled water, and the diluted solution is brought to a boil to draw out the ammonia. The wet litmus paper was used to ensure complete removal of the ammonia in the gas form. Subsequently, the excess hydroxide ion was titrated with standard hydrochloric acid (0.5 molar), using bromothymol blue as an indicator. The concentration of diammonium hydrogen citrate was calculated considering the amount of sodium hydroxide and hydrochloric acid standard solutions. The gravimetric analyses reveal that the uncertainty of the obtained salt concentration using this method was better than ± 0.04 % (in mass fraction percent). The refractive index measurement was performed to determine the alcohol concentration of the both split phases. In this regard, the refractive index of known solutions of the ternary alcohol (m) + diammonium hydrogen citrate (ca) + water (w) systems in the mass fraction range of 0 ≤ wm ≤ 0.1 and 0 ≤ wca ≤ 0.05 was measured at 298.15 K to find a proper relation between the refractive index and alcohol concentration. A satisfactory result was obtained when the experimental refractive index data was fitted to the following simple relation:

the proposed model for the correlation of the mean ionic activity coefficients over the entire concentration range. This paper is one of the series of our group studies on different ABS's in which the LLE of 1-propanol, 2-propanol, 2methyl-2-propanol, or 2-butanol + diammonium hydrogen citrate + water ternary systems was studied. In this work, the binodal curves of the investigated systems at (298.15 and 308.15) K were measured, and the Merchuk19 equation was modified taking into account the mixed-solvent properties and used to correlate all obtained binodal curves, concurrently. The effect of temperature on the investigated systems was discussed using the measured cloud point data at different alcohol mole fractions and in the (293.15 to 323.15) K temperature range with 5 K successive intervals. Moreover, the tie-line compositions were reported at 298.15 K and correlated using the e-NRTL model.16 The binary interaction parameters were also reported.

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EXPERIMENTAL SECTION Chemicals. The physicochemical properties of the used chemicals are described in Table 1. Apparatus and Procedure. The cloud-point titration method was performed to collect the binodal curve data. In this method, an appropriate amount of aqueous solution of diammonium hydrogen citrate solution or alcohol was placed in a double-wall glass cell, and the solution was stirred using a magnetic stirrer. The water at constant temperature was circulated between the walls of the double-wall cell to control the temperature of the cell. The temperature was controlled with an accuracy of ± 0.03 K using a thermostat (JULABO model ED, Germany). After the necessary rest time to establish the constant temperature, the droplets of aqueous solution of another component (i.e., alcohol, or salt) were added to the cell using a normal syringe, until the solution was appeared cloudy. This point indicates that the system is in the biphasic region. Subsequently, the tiny droplets of the double distilled water were added to the cloudy solution watchfully until the cloudiness was vanished. This point indicates a node on the binodal curve. The mass changes were measured by an analytical balance (Sartorius model TE214S, Switzerland) and used to calculate the composition of the alcohol and diammonium hydrogen citrate in binodal curve. The precision of the mass balance was ± 1·10−7 kg. The procedure was repeated at least five times, and the uncertainty of the obtained binodal data was found to be better than ± 0.3 % (in mass fraction percent). To determine the tie-line compositions, appropriate amounts of the concentrate solutions of the salt and the pure alcohol were mixed in glass cells and diluted by adding doubly distilled deionized water to form adequate feed samples (about 10 cm3) which are in the biphasic region. These samples were shaken

nD = n w0 + amwm + acawca

(1)

In this relation nD and n0w are the refractive indices of the ternary solution and pure water at 298.15 K, respectively. Also, am and aca are the constants and acquired from the fitting of the experimental refractive indices of the standard solution to eq 1. These constants along with the relative standard deviations are 1679

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reported in Table 2, and the concentrations of the standard ternary solutions along with the measured refractive indices are Table 2. Coefficients of Equation 1 for the Investigated Systems at 298.15 Ka system

nw0

am

104 sdm

aca

104 sdca

1-propanol (m) + diammonium hydrogen citrate (ca) + water (w) 2-propanol (m) + diammonium hydrogen citrate (ca) + water (w) 2-methyl-2-propanol (m) + diammonium hydrogen citrate (ca) + water (w) 2-butanol (m) + diammonium hydrogen citrate (ca) + water (w)

1.3325

0.0938

4.40

0.1756

2.35

1.3325

0.0951

8.64

0.1730

4.75

1.3325

0.1037

5.32

0.1742

3.17

1.3325

0.1068

5.01

0.1704

3.14

a

sdj is the standard deviation between the calculated, cal, and experimental, exp, values of mass fraction, w, for component “j” (i.e., exp alcohol (m) or salt (ca)) and calculated using sdj = [∑i(wcal j,i − wj,i )/ n]1/2. Moreover, n is the number of measured refractive indices data.

Figure 1. Experimental and calculated phase diagram for the 1propanol (m) + diammonium hydrogen citrate (ca) + water (w) system at 298.15 K. □, experimental binodal curve; , calculated binodal curve from the Merchuk equation as a function of density and dielectric constant; ○, experimental tie-line data; ---×---, calculated tie-line data from the e-NRTL model; △, initial total compositions.

given in the Supporting Information tables associated with this article. It is proper to mention that all of the unknown samples were diluted to be in the calibration curve range (i.e., 0 ≤ wm ≤ 0.1 and 0 ≤ wca ≤ 0.05). Also, it was found that the accuracy of the calculation of the alcohol mass fraction using this method is better than ± 0.002 % (in mass fraction percent). The cloud-point titration method was also used to study the effect of temperature on the studied ABS's. In this regard, an appropriate amount of the aqueous solution of diammonium hydrogen citrate was titrated with tiny droplets of pure alcohol until the solution appeared cloudy, and the cell temperature was changed (decreased or increased) at 5 K intervals until the cloudiness disappeared. Afterward, droplets of the alcohol were added to the solution until anew cloudiness of the solution. As can be inferred, in this method the mole fraction of alcohol was changed, whereas the relative salt-to-water mole fraction ratio remained constant.

and excluded from the remained solution as a separated phase, when the amount of the electrolyte is increased from the specific threshold concentration. In the case of the studied ABS's in this work, all systems have the same salt (i.e., diammonium hydrogen citrate), and it seems that the intermolecular interaction between the alcohol−water and the alcohol−alcohol self-interactions should be considered to understand the ability of organic solvents in the formation of ABS's. On the one hand, the solubility of the alcohol in water is a decisive factor to demonstrate the alcohol−water intermolecular interactions (i.e., the stronger alcohol−water intermolecular interaction results in the greater solubility of alcohol). On the basis of the solubility data for the alcohols of the studied systems, we can classify these alcohols in two categories; (I) 2butanol and 2-methyl-2-propanol are slightly soluble alcohols with a solubility of 2920 and 12 (reported by the supplier) g/ (100 mL of water) at 298.15 K, respectively, and (II) 1propanol and 2-propanol are completely soluble in water, which can dissolve in water in any proportion. 21 Figure 5 demonstrates that the order of the phase-separation ability of the studied ABS's is consistent with the solubility of the relevant alcohol. On the other word, completely miscible alcohols (i.e., 1-propanol and 2-propanol) can strongly compete with a kosmotropic salt to achieve more water molecules, and a greater salt concentration needs to salt-out these alcohols as a separated phase. However, the alcohols with the lower solubility (i.e., 2-butanol and 2-methyl-2-propanol) at the lower concentrations of salt lose competition against kosmotropic ions and are more readily salted-out. From the other point of view, the boiling point may be considered as an efficient criterion to represent the selfinteraction forces between alcohol molecules, as pointed out by Wang et al.22,23 Therefore, the phase-separation ability of the studied ABS's in each of the classes (I or II) can be discussed on the basis of the boiling point of the alcohols. In the case of the class (I) ABS's (with completely miscible alcohols) the

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RESULTS AND DISCUSSION The measured binodal curve data for 1-propanol, 2-propanol, 2methyl-2-propanol, or 2-butanol + diammonium hydrogen citrate + water ternary systems at (298.15 and 308.15) K are listed in Tables 3 and 4, respectively. The binodal curves of the investigated ternary systems are also plotted in Figures 1 to 4. Furthermore, the comparison between the binodal curves at (298.15 and 308.15) K are also presented in Figure 5. Figure 5 shows that the area of the biphasic region for deferent alcohols is in the following order: 2-butanol > 2-methyl-2-propanol > 1propanol > 2-propanol, and therefore, the biphasic formation ability of the studied alcohols are in the same order. This observation can be discussed on the basis of the intermolecular interaction that occurred when an electrolyte and an alcohol are mixed in aqueous solution. In these systems the alcohol molecules and dissolved ions of the electrolyte challenged to detain more solvent (i.e., water) molecules around their respective hydration shells. In this challenge the ionic species which have more intermolecular interactions with water molecules can achieve more water molecules; proportionally the other component is enforced to decrease the interactions with water molecules, and therefore its self-intermolecular interactions increased. Subsequently, the alcohol is “salted-out” 1680

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Table 3. Binodal Curve Data for Alcohol (m) + Diammonium Hydrogen Citrate (ca) + Water (w) Ternary Systems as a Function of Mass Fractions at 298.15 K 100 wm

100 wca

29.22 31.61 33.76

9.72 8.92 8.21

8.49 11.39 13.81 17.53

35.20 31.00 27.40 23.59

24.44 27.56 30.05 31.85

9.45 8.33 7.67 7.16

10.24 10.50 10.71 11.60

8.15 7.58 7.16 5.55

100 wm

100 wca

100 wm

100 wca

1-Propanol + Diammonium Hydrogen Citrate + Water 35.60 7.64 40.55 6.05 37.26 7.14 44.8 4.94 38.78 6.71 2-Propanol + Diammonium Hydrogen Citrate + Water 21.47 20.60 35.80 11.73 25.57 17.52 37.48 11.00 30.71 14.66 38.92 10.13 33.57 13.06 40.52 9.35 2-Methyl-2-propanol + Diammonium Hydrogen Citrate + Water 33.61 6.70 41.12 4.72 34.58 6.45 42.16 4.52 35.70 6.14 43.42 4.19 38.41 5.30 2-Butanol + Diammonium Hydrogen Citrate + Water 12.06 4.71 13.00 3.47 12.57 4.00 13.18 3.22 12.78 3.75 13.42 2.94

100 wm

100 wca

48.33 51.52

4.16 3.44

41.99 45.93 48.84

8.65 6.86 5.77

45.85 48.41 51.09

3.65 3.13 2.62

13.77 14.35 15.08

2.53 1.91 1.39

Table 4. Binodal Curve Data for Alcohol (m) + Diammonium Hydrogen Citrate (ca) + Water (w) Ternary Systems as a Function of Mass Fractions at 308.15 K 100 wm

100 wca

7.97 10.72 13.11

25.15 21.30 18.89

13.84 16.18 17.57 23.56 30.21

25.93 23.72 22.62 18.36 14.42

21.05 22.35 23.92 25.9

9.32 8.85 8.27 7.63

7.86 8.07 8.36 8.79

12.03 11.46 10.68 9.41

100 wm

100 wca

100 wm

100 wca

1-Propanol + Diammonium Hydrogen Citrate + Water 17.14 15.78 35.61 7.42 28.80 9.60 38.33 6.62 31.85 8.60 2-Propanol + Diammonium Hydrogen Citrate + Water 32.54 13.17 39.77 9.42 34.46 12.14 40.88 8.90 35.89 11.31 42.23 8.25 37.62 10.47 43.16 7.82 38.64 9.89 44.45 7.30 2-Methyl-2-propanol + Diammonium Hydrogen Citrate + Water 27.53 7.15 33.66 5.62 29.36 6.62 34.59 5.43 31.45 6.15 35.39 5.22 32.50 5.89 36.76 4.91 2-Butanol + Diammonium Hydrogen Citrate + Water 9.08 8.76 10.19 6.25 9.62 7.45 10.52 5.60 9.74 7.19 10.67 5.32 9.92 6.77 10.87 4.93

100 wm

100 wca

40.56 42.57

6.05 5.50

45.98 47.05 49.33 50.84

6.57 5.98 5.17 4.51

37.93 40.50 42.63

4.68 4.17 3.77

11.34 11.98 12.18

4.09 3.09 2.89

and constant salt-to-water mole fraction ratios. The experimental cloud-point data in the (293.15 to 323.15) K temperature range with 5 K intervals are reported in Table 5 and plotted in Figure 6. These data report the required alcohol mole fraction which results from the phase separation of the studied ternary systems at the same concentration ratio of the salt to water as a function of temperature. The CP data reported in Table 5 show that, in the case of ABS's composed of 2-propanol or 2-methyl-2-propanol, the required alcohol mole fraction slightly decreases with increasing temperature. Also, 2-methyl-2-propanol and 1-propanol ABS's show a slight decrease of the required alcohol at temperatures between (298.15 to 308.15) K and (318.15 to 328.15) K, respectively, and there is not any sensible change at other temperatures. Therefore, the phase-separation ability of all studied ABS's

boiling points are in the order of 1-propanol (370.35) > 2propanol (355.45 K). Also, in the case of the class (II) ABS's (with completely miscible alcohols) the boiling points are in the order of 2-butanol (372.66 K) > 2-methyl-2-propanol (355.55 K). Therefore, the boiling-point data demonstrate that, in both classes, the alcohol with the higher boiling point has more self-interaction forces between alcohol molecules and easily can be salted-out. It should be noted that a similar conclusion has been made by Wang et al.22,23 only about ABS's composed of completely miscible alcohols. Also, Figure 5 demonstrates that the phase separation ability of these ABS's increased when the temperature was increased. Additionally, the temperature effect on the investigated systems in larger temperature range was studied by measuring the cloud-point (CP) data at different alcohol mole fractions 1681

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Figure 2. Experimental and calculated phase diagram for the 2-propanol (m) + diammonium hydrogen citrate (ca) + water (w) system at 298.15 K. □, experimental binodal curve; , calculated binodal curve from the Merchuk equation as a function of density and dielectric constant; ○, experimental tie-line data; ---×---, calculated tie-line data from the e-NRTL model; △, initial total compositions.

Figure 3. Experimental and calculated phase diagram for the 2-methyl-2-propanol (m) + diammonium hydrogen citrate (ca) + water (w) system at 298.15 K. □, experimental binodal curve; , calculated binodal curve from the Merchuk equation as a function of density and dielectric constant;  ○, experimental tie-line data; ---×---, calculated tie-lines data from the e-NRTL model; △, initial total compositions.

ability of these ABS's in the studied temperature range. This trend is similar to the one reported previously8 for aliphatic alcohols + dipotassium oxalate + water systems.

increased with increasing the temperature at the mentioned temperature ranges. Moreover, Figure 6 confirms that the temperature does not change the order of the phase-separation 1682

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Figure 4. Experimental and calculated phase diagram for the 2-butanol (m) + diammonium hydrogen citrate (ca) + water (w) system at 298.15 K. □, experimental binodal curve; , calculated binodal curve from the Merchuk equation as a function of density and dielectric constant; ○, experimental tie-line data; ---×---, calculated tie-line data from the e-NRTL model; △, initial total compositions.

Figure 5. Comparison between the binodal curves for the alcohol (m) + diammonium hydrogen citrate (ca) + water (w) system at 298.15 K (hollow symbols) and 308.15 K (filled symbols). ●, ○, 2-propanol; ▲, △, 1-propanol; ⧫, ◊, 2-methyl-2-propanol; ■, □, 2-butanol;  and - - -, calculated from the Merchuk equation at (298.15 and 308.15) K, respectively.

Moattar et al.24,25 attributed the salting-out capability of a salt to the Gibbs free energy of hydration, ΔGhyd, of the constitutive ions of the salt. Marcus26 reported the values of (−285 and −295) kJ·mol−1 for ΔGhyd of NH4+ and K+ cations, respectively. Additionally, Zafarani-Moattar et al.,24,27 using the Marcus method,26 calculated the ΔGhyd values of (−1453 and −968) kJ·mol−1 for oxalate and hydrogen citrate anions, respectively. In the case of the studied systems, the ΔGhyd values shows that

Figure 7 compares the binodal curves of the ABS's studied in this work with the ones reported by Shekaari et al.8 for alcohols + dipotassium oxalate + water ABS's at 298.15 K. Figure 7 demonstrates that the extents of the biphasic region for the ABS's composed of dipotassium oxalate salt are more than the ones for diammonium hydrogen citrate salt. On the other word, dipotassium oxalate salt can more strongly salt-out the alcohol from the solution than diammonium hydrogen citrate. Zafarani1683

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Table 5. Cloud-Point (CP) Data for the Alcohols (m) + Diammonium Hydrogen Citrate (ca) + Water (w) Systems as a Function of Mole Fraction of the Relevant Alcohol at the Temperature Range from (293.15 to 328.15) K T/K

xm/xw

xca

1-Propanol + Diammonium Hydrogen Citrate + Water 293.15 0.0886 0.227 298.15 0.0886 0.227 303.15 0.0886 0.227 308.15 0.0886 0.227 313.15 0.0886 0.227 318.15 0.0886 0.227 323.15 0.0886 0.219 328.15 0.0886 0.210 2-Propanol + Diammonium Hydrogen Citrate + Water 293.15 0.0885 0.268 298.15 0.0885 0.266 303.15 0.0885 0.264 308.15 0.0885 0.261 313.15 0.0885 0.259 318.15 0.0885 0.257 323.15 0.0885 0.255 328.15 0.0885 0.253 2-Methyl-2-propanol + Diammonium Hydrogen Citrate + Water 293.15 0.0887 0.138 298.15 0.0887 0.124 303.15 0.0887 0.107 308.15 0.0887 0.092 313.15 0.0887 0.080 318.15 0.0887 0.071 323.15 0.0887 0.065 328.15 0.0887 0.058 2-Butanol + Diammonium Hydrogen Citrate + Water 293.15 0.0884 0.029 298.15 0.0884 0.027 303.15 0.0884 0.026 308.15 0.0884 0.025 313.15 0.0884 0.025 318.15 0.0884 0.025 323.15 0.0884 0.025 328.15 0.0884 0.025

Figure 6. Effect of temperature on cloud point, CP, as a function of the alcohol (m) mole fractions, in the presence of aqueous solution of diammonium hydrogen citrate (ca) salt: ○, 2-propanol; ▲, 1-propanol; □, 2-methyl-2-propanol; ●, 2-butanol.

Figure 7. Comparison between the binodal curves for the alcohols (m) + diammonium hydrogen citrate (ca1) + H2O (w) systems studied in this work (solid lines and filled symbols) and alcohols (m) + dipotassium oxalate (ca2) + H2O (w) systems reported previously8 (dashed lines and hollow symbols). {■, 2-propanol + ca1 + w; ---□---, 2-propanol + ca2 + w)}; {▲, 1-propanol + ca1 + w; ---△---, 1-propanol + ca2 + w}; {○, 2-methyl-2-propanol (m) + ca1 + w; ---●---, 2-methyl-2-propanol (m) + ca2 + w} and {⧫, 2butanol (m) + ca1 + w; ---◊---, 2-butanol (m) + ca1 + w} at 298.15 K.

both potassium and oxalate ions have more affinity to arrange the water molecules around their hydration shells than ammonium and hydrogen citrate ions and can more strongly compete with the third component (i.e., alcohol molecules). In other words, the salting-out ability of the dipotassium oxalate which has the more ΔGhyd value is more than the diammonium hydrogen citrate salt. Moreover, the tie-line compositions of the studied ABS's at 298.15 K are given in Table 6 and represented in Figures 1 to 4 too. Different authors have used some empirical equations to fit the binodal curves previously;19,28−34 however, in this work, we attempt to obtain an equation for the simultaneous correlation of all binodal curves. In this regard, we considered that the dielectric constant and density of the solvent are dependent on the composition of the mixed-solvent system. This assumption is imposed to several empirical equations, and satisfactory results were obtained when the Merchuk equation19 was modified considering the dielectric constant and density of the

mixed aqueous−organic solvent. The Merchuk equation19 has the following form: wm = a exp(bwca0.5 − cwca3)

(2)

In this equation a, b, and c are the fitting parameters, and wca and wm denote the mass fraction of the salt and alcohol, respectively. To obtain an appropriate equation for simultaneous correlation, the parameters of the Merchuk equation are modified as follows: a = a0 ·εs−0.5 + a1 ln εs + a 2 ·ds−0.5 + a3 ln ds

b = b0 ·εs−0.5 + b1 ln εs + b2 ·ds−0.5 + b3 ln ds 1684

(3)

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Recently, Zafarani-Moattar et al.37 used the generalized electrolyte-NRTL (e-NRTL) model of Chen and Song16 for mixed solvent electrolyte systems to represent the LLE of some alcohol + salt + water ABS's. In this work, we decided to further examine the ability of the e-NRTL model in the correlation of the LLE data. In the correlation procedure, the Levenberg−Marquardt optimization algorithm and the value of ρ = 14.9 was used.38 The water activity data for diammonium hydrogen citrate + water binary systems at 298.15 K reported by Sadeghi et al.39 were used to obtain the water−salt, τw,ca, and salt−water, τca,w, parameters. It should be noted that, following Chen et al.,16,17 in the correlation of binary water activity data we restricted the fitting procedure to find the best set of binary interaction parameters in which τw,ca has a positive sign and τca,w has a negative sign. It was found that the quality of fitting (i.e., both binary and ternary data) using this restriction criterion was better than the one in which the correlation procedure has no criterion. The best result was obtained when the value of αw,ca = 0.1 was used. Using this nonrandomness factor and the mentioned criterion the values of τw,ca = 14.4135 and τca,w = −7.1568 were obtained. Also, the comparisons between the calculated water activity data using e-NRTL model and the experimental values reported by Sadeghi et al.38 are presented in Figure I of the Supporting Information associated with this article. These values were remained fixed in all studied alcohol + diammonium hydrogen citrate + water systems, and the following procedure was done to obtain other remaining salt− alcohol, τca,m, alcohol−salt, τm,ca, water−alcohol, τw,m, and alcohol−water, τm,w, restricted binary interaction parameters from the fitting of tie-line compositions. For multiphase systems at constant temperature and pressure, the chemical potential of any component in each phase, which are in equilibrium, should be equal. The chemical potential of any component at constant temperature and pressure in liquid phases can be rewritten as follows:

Table 6. Tie-Line Data for Alcohol (m) + Diammonium Hydrogen Citrate (ca) + Water (w) Systems as a Function of Mass Fraction at 298.15 K total composition 100 wm

100 wca

top phase 100 wm

100 wca

bottom phase 100 wm

100 wca

1-Propanol (m) + Diammonium Hydrogen Citrate (ca) + Water (w) 34.98 11.48 58.98 2.51 9.50 21.18 36.75 12.43 63.20 2.13 7.75 23.75 39.00 13.50 66.76 1.72 6.80 27.16 40.95 14.49 70.05 1.44 6.57 30.12 42.94 15.49 71.98 1.37 6.20 33.67 44.96 15.63 73.91 1.15 5.79 35.07 2-Propanol (m) + Diammonium Hydrogen Citrate (ca) + Water (w) 9.22 43.12 47.49 6.43 17.70 23.95 9.50 43.98 50.48 5.47 15.70 26.13 9.74 44.95 52.98 4.76 13.83 27.90 10.00 45.95 55.07 4.06 12.72 29.75 10.24 46.94 57.42 3.73 11.87 31.23 10.60 47.70 59.32 3.36 9.62 33.93 2-Methyl-2-propanol (m) + Diammonium Hydrogen Citrate (ca) + Water (w) 37.37 6.93 54.14 2.38 18.06 11.89 37.98 7.25 57.49 1.87 16.30 13.43 39.05 7.73 59.89 1.71 14.11 15.17 40.00 8.34 61.89 1.63 13.60 16.62 40.95 8.94 63.8 1.40 11.86 18.56 42.29 9.53 66.01 1.33 11.03 20.41 2-Butanol (m) + Diammonium Hydrogen Citrate (ca) + Water (w) 4.40 36.00 73.13 1.11 10.48 6.64 5.63 38.62 74.91 0.95 9.25 9.38 6.60 40.00 77.02 0.79 8.60 11.55 8.23 41.97 79.72 0.55 6.90 15.41 9.63 44.04 81.06 0.43 5.53 19.25

c = c0·εs−0.5 + c1 ln εs + c 2·ds−0.5 + c3 ln ds

In these relations, ai, bi, and ci (i: from 1 to 3) are new modified parameters, and εs and ds are the mixed-solvent dielectric constant and density, respectively. εs and ds values are calculated from the simple composition average mixing rules adopted by Chen et al.16 as follows: 1 = ds εs =

∑ m

∑ m

xm 1 ∑m ′ xm ′ dm xmM m εm ∑m ′ xm ′M m ′

μi (x) = RT ln(γixi)

(6)

In eq 6 μi is the chemical potential of component i, and x and γ refer to the mole fraction and activity coefficient, respectively. Also, R and T are the gas constant and absolute temperature, respectively. For studied ABS's, equilibrium conditions can be reduced as follows:

(4)

(γixi)top = (γixi)bot

(7)

In eq 7 superscripts “top” and “bot” refer to the top and bottom phases, respectively. In this respect, the following objective function (OF) was used to obtain the interaction parameters of the e-NRTL model:

(5)

where Mm and xm refer to the molecular weight and the mole fraction of the solvent m, respectively. The Levenberg−Marquardt optimization algorithm was used to correlate the obtained binodal curves to the modified Merchuk equation as a function of the mixed aqueous−organic solvent properties. Densities of water and alcohols were obtained from other papers,35,36 and also dielectric constants of the solvents were obtained from Lide.21 The obtained parameters and the consequent standard deviations (sd) are reported in Table 7. Furthermore, Figures 1 to 4 compare the experimental and calculated binodal curves. The obtained standard deviations (sd) and the results shown in Figures 1 to 4 reveal that the modified Merchuk equation can simultaneously correlate all of the binodal curves obtained in this work with an acceptable accuracy.

OF =

∑ ∑ ∑ (xpexp, n,k − xpcal, n,k)2 p

n

k

(8)

where p, n, k, and the “exp” and “cal” subscripts are the relative phase (i.e., top or bottom), the number of the relative tie-line, each of the components (i.e., alcohol, salt, or water), and calculated and experimental values, respectively. The obtained parameters using this method are reported in Table 8 along with the respective deviations (dev). Several values for nonrandomness factors were examined; however, in the case of all studied ABS's the best results were obtained when the fixed value of αw,m = αm,w = αca,m = αm,ca = 0.25 was used. Figures 1 to 4 compare the calculated and experimental 1685

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Table 7. Parameters of the Merchuk Equation as a Function of Density and Dielectric Constant Used for the Simultaneous Correlation of the Binodal Curves of the Alcohol (m) + Diammonium Hydrogen Citrate (ca) + Water (w) Systems at (298.15 and 308.15) K ma + ca + w

system

mb + ca + w

mc + ca + w

md + ca + w

overall

0.29

0.06

0.24

0.35

0.13

0.22

T = 298.15 K

a

a0 a1 a2 a3 b0 b1 b2 b3 10−3·c0 c1 10−3·c2 c3 sd

35.4367 2.7181 −48.2073 −2.0388 273.8982 −8.6227 −88.7942 0.6768 1.9527 317.1696 −6.7119 −212.8411

a0 a1 a2 a3 b0 b1 b2 b3 10−3·c0 c1 10−3·c2 c3 sd

4.2786 0.4178 −4.0099 −0.2906 274.2466 −3.6776 −136.3679 −2.1579 −7.3724 88.2521 3.4288 57.0406

0.38

0.16 T = 308.15 K

0.25 b

c

0.08

d

1-Propanol. 2-Propanol. 2-Methyl-2-propanol. 2-Butanol.

and 308.15) K were measured, and the Merchuk equation was modified considering the mixed organic−aqueous solvents properties and adequately used to fit all obtained binodal curves simultaneously. The measured cloud point data at different alcohol mole fractions and constant salt-to-water ratios show that the extent of the biphasic region for the studied alcohols is in the order of: 2-butanol > 2-methyl-2-propanol > 1-propanol > 2-propanol in the temperature range of (293.15 to 328.15) K. Also, the obtained results confirmed that the phase separation ability of the slightly soluble alcohols is more than the completely miscible alcohols due to the more weak intermolecular interactions with water molecules. Additionally, the boilingpoint data demonstrate that the alcohol with higher boilingpoint, in both completely miscible and slightly soluble cases, has more self-interaction forces between alcohol molecules and have more affinity to form an ABS. Also, results show that dipotassium oxalate salt can more strongly salt-out than diammonium hydrogen citrate salt, which is attributed to the more negative ΔGhyd values of potassium and oxalate ions. Additionally, the tie-lines data at 298.15 K were reported and satisfactorily correlated using the e-NRTL model, and the restricted binary interaction parameters of e-NRTL model were also reported. Good agreement between the calculated and experimental tie-line data was observed.

Table 8. Values of Restricted Binary Interaction Parameters of e-NRTL Model for the Studied ABS's at 298.15 K τw,m

τm,w

τca,m

τm,ca

deva

1-Propanol (m) + Diammonium Hydrogen Citrate (ca) + Water (w)b 2.4662 3.4427 2.8886 12.880 0.23 2-Propanol (m) + Diammonium Hydrogen Citrate (ca) + Water (w)b 6.2707 10.4485 11.2867 2.9452 0.01 2-Methyl-2-propanol (m) + Diammonium Hydrogen Citrate (ca) + Water (w)b 2.5626 3.0566 22.599 21.632 0.34 2-Butanol (m) + Diammonium Hydrogen Citrate (ca) + Water (w)b 2.6477 3.8257 5.0421 14.777 0.08 a exp 2 dev = ∑p∑n∑k ((100wcal p,n,k − 100wp,n,k) /6N) where w, p, n, k, and N are the mass fraction, relative phase (i.e., top or bottom), the number relative tie-line, each of the components (i.e., alcohol, salt, or water), and the number of tie-line data, respectively. bIn the cases of all studied ABS's the nonrandomness factors are fixed at: αw,m = αm,w = αca,m = αm,ca = 0.25.

tie-line compositions. The results shown in Figure 1 to 4 and deviations reported in Table 8 show that there is a good agreement between the calculated and the experimental tie-line data.

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CONCLUSIONS The LLE of 1-propanol, 2-propanol, 2-methyl-2-propanol, or 2butanol + diammonium hydrogen citrate + water ABS's was studied. Binodal curves of the investigated systems at (298.15 1686

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ASSOCIATED CONTENT

S Supporting Information *

Comparison between experimental and calculated values using e-NRTL model of activity of water against molality (Supplemental Figure I). This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: 984113393139. Fax: 984113340191. E-mail address: [email protected] (H.S.). Notes

The authors declare no competing financial interest.

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REFERENCES

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