Ionic liquid 1-hexyl-3-methylimidazolium hexafluorophosphate, an efficient solvent for extraction of acetone from aqueous solutions

Accepted Manuscript Ionic liquid 1-hexyl-3-methylimidazolium hexafluorophosphate, an efficient solvent for extraction of acetone from aqueous solutions Javad Saien, Marjan Mohammadi Sarab Badieh, Mahdi Norouzi, Sadegh Salehzadeh PII: DOI: Reference:

S0021-9614(15)00309-2 http://dx.doi.org/10.1016/j.jct.2015.08.027 YJCHT 4373

To appear in:

J. Chem. Thermodynamics

Received Date: Revised Date: Accepted Date:

30 April 2015 13 August 2015 18 August 2015

Please cite this article as: J. Saien, M.M.S. Badieh, M. Norouzi, S. Salehzadeh, Ionic liquid 1-hexyl-3methylimidazolium hexafluorophosphate, an efficient solvent for extraction of acetone from aqueous solutions, J. Chem. Thermodynamics (2015), doi: http://dx.doi.org/10.1016/j.jct.2015.08.027

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Ionic liquid 1-hexyl-3-methylimidazolium hexafluorophosphate, an efficient solvent for extraction of acetone from aqueous solutions Javad Saien a,∗, Marjan Mohammadi Sarab Badieha, Mahdi Norouzib, Sadegh Salehzadehc a

Department of Applied Chemistry, Bu-Ali Sina University, Hamedan 65174, Iran

b c

Department of Chemical and Chemical Engineering, Malek-Ashtar University of Technology, 3454, Tehran, Iran

Department of Inorganic Chemistry, Bu-Ali Sina University, Hamedan 65174, Iran

ABSTRACT Liquid–liquid equilibrium (LLE) of the chemical system of {water + acetone + 1-Hexyl-3methylimidazolium hexafluorophosphate (HMIMPF6) ionic liquid} was studied at different temperatures of (293.2, 298.2 and 303.2) K and under atmospheric pressure of 81.5 kPa. The results show that HMIMPF6 provides the acetone distribution coefficient and separation factor values within (0.8813 - 1.2351) and (3.0 - 54.4), respectively; indicating the high capability of the ionic liquid for extraction of acetone from aqueous solutions. In most cases, acetone solubility in the ionic liquid is higher than in water, especially at higher solute concentrations. Meanwhile, higher separation factor is relevant to the lower temperature due to lower water–ionic liquid miscibility. The consistency of tie line data, at each temperature, was examined with OthmerTobias correlation. The values were nicely reproduced with the well-known NRTL and UNIQUAC models. Accordingly, the required thermodynamic properties of HMIMPF6 were obtained by the Density Functional Theory (DFT) calculations, carried out at the M06/6311++G** level of theory. The root mean square deviations (RMSD) between experimental and model concentration values were 0.0192 and 0.0255, respectively; indicating close agreement of the both models. Keywords: Experimental LLE, Ionic liquid, Acetone, Separation factor, LLE correlation

∗

Corresponding author. Tel. and Fax: +98 81 38282807. E-mail address: [email protected] (J. Saien).

1

1. Introduction Liquid–liquid extraction has frequently regarded as a desired process in many cases for separation and purification. Traditional extraction methods often use organic solvents in contact with aqueous phases. Environmentally safe technologies may reject such anachronistic processes due to their toxicity, flammability and volatile organic compounds (VOCs) [1]. To solve these problems, liquid–liquid extraction has been recently introduced with the aid of specific green solvents such as room temperature ionic liquids (RTILs or simply ILs) [2,3]. ILs exhibit excellent properties such as negligible vapour pressure, non-flammability and tunable physiochemical properties; thus they have been known as “designer solvents” for particular applications [4]. Their negligible vapour pressure permits the extracted products to be separated from ILs by conventional low pressure distillation. Non-volatile or thermal sensitive products could also be recovered from ILs by supercritical carbon dioxide [4,5]. One major requirement in evaluating the performance of the liquid–liquid extraction process is the systems equilibrium data. Currently, liquid–liquid equilibrium (LLE) of ternary components, containing ILs and organic molecules has been studied. These mixtures mostly are comprised of one IL and two organic molecules that have close boiling points or form an azeotrope, such as (IL + aromatic + aliphatic), (IL + ether + alcohol), (IL + alkane + alkene), and so on [4]. The work has been developed further for the mixture of hydrophobic ILs in contact with aqueous solutions containing organic solutes such as alcohols [6-8]. The method of LLE analysis, on the other hand, conventionally includes direct components analysis and indirect analysis. The method of direct analysis consists of letting a ternary mixture to separate into two liquid phases and detecting their composition by direct quantitative analysing of the components. In the indirect analysis technique, a relationship between the compositions and a property (density or refractive index) is first established from the known cloud solutions data at a desired temperature. Whenever this relationship is provided, only the concentration of one component in each phase would be sufficient to determine a tie line. In this regard, “cloud-point with refractive index measurement” is a method that has been frequently employed [9-11]. One problem in the field of ILs is detecting their concentration in the solutions. Using cloud point method is therefore preferred [12].

2

The aim of this paper is to utilise an IL, formed by 1-hexyl-3-methylimidazolium (HMIM+) cation and hexafluorophosphate (PF6–) anion introduced as “HMIMPF6” (figure 1), in the liquid– liquid extraction process for the first time. This IL behaves as an hydrophobic solvent due to the lack of hydrogen-bond accepting (HBA) ability [13,14]. HMIMPF6 has also relatively low viscosity and is considered as a low price IL [15,16]. The LLE of the ternary system of (water + acetone + HMIMPF6) is studied herein and corresponding data are determined via the cloud-point method as well as water content determination. Acetone and water components have been involved in one standard chemical test system recommended by the European Federation of Chemical Engineers (EFCE) [17]. Accordingly, distribution coefficients and separation factors are determined. In the modelling section, the well-known NRTL and UNIQUAC thermodynamic models are employed and the interaction parameters are determined using Aspen Plus simulator based on the obtained experimental values as well as results obtained from a satisfactory method to evaluate thermodynamic properties of HMIMPF6 by the Density Functional Theory (DFT) calculations. PF 6 5

N

4

2

N

FIGURE 1. The chemical structure of HMIMPF6.

2. Experimental 2.1. Chemicals The 1-methylimidazole, 1-chlorohexane, ethyl acetate (raw materials for the IL synthesis) and acetone were purchased from Merck. Hexafluorophosphate acid (HPF6) was obtained from Acros Organics. The chemicals were used without further purification. In table 1, there is summarized the provenance and mass fraction purity of the materials used in this work. Fresh deionised water was generated from a deioniser apparatus (Hastaran Co.), producing water with electrical conductivity of less than 0.08 µS·cm−1.

3

TABLE 1 Supplier and mass fraction purity of the used materials. Chemical Acetone 1-methylimidazole 1-chlorohexane ethyl acetate hexafluorophosphate acid HMIMPF6 *

Supplier Merck Merck Merck Merck Acros Organics synthesized

Mass fraction purity* 0.999 0.99 0.99 0.995 0.60 0.99

informed by the suppliers except for HMIMPF6 that was determined by the standard chloride titration method.

2.2. Synthesis of the ionic liquid The HMIMPF6 was synthesized according to the instruction proposed by Pereiro et al. [13]. Equal molar amounts of 1-methylimidazole and 1-chlorohexane were added to a round-bottomed flask equipped with a reflux condenser and a magnetic stirrer. The reaction mixture was heated at 343.2 K while stirring for 72 h. Then, the viscous liquid product was cooled to room temperature and washed by ethyl acetate. The used ethyl acetate was decanted and the procedure repeated three times using fresh ethyl acetate every time. After the last washing, the remaining ethyl acetate was eliminated by heating at 343.2 K under vacuum condition. The resulting liquid1-hexyl-3methylimidazolium chloride (HMIMCl) was diluted by addition of deionized water (500 cm3·mol−1 HMIMCl). An aqueous solution of 0.60 mass fraction of HPF6 was added slowly (to minimize heat generation) to aqueous solution of HMIMCl in a 1.1:1 molar ratio, respectively. After mixture stirring for 12 h to 16 h; the liquid phases were separated. The upper acidic aqueous layer was decanted and lower ionic liquid layer was washed ten times with deionized water until the water phase did not react with AgNO3 aqueous solution and the pH of the upper phase reached 5.5 [18]. The obtained ionic liquid was dried under high vacuum (2×10−1 Pa) for 18 h. The water content in the prepared IL was determined by Karl Fischer titration method using the KF Coulometer (Metrohm, model 831) that indicated a maximum water content mass fraction of 0.00051 in the sample. The produced IL was characterized using 1HNMR,

13

CNMR,

19

FNMR

(500 MHz, DMSO) and mass spectroscopy. Data of characterization were in compliance with the 4

expected structure. The purity was confirmed by giving just the IL peaks and none for reactants and/or by-products. The details of spectra are: - 1HNMR: δ= 0.815 (3H,t), 1.220 (6H,m), 1.742 (2H,m), 3.797 (3H,s), 4.100 (2H,t), 7.602 (H,d), 7.672 (H,d), 9.012 (H,s). - 13C NMR: δ= 14.57, 22.69, 25.97, 30.16, 31.38, 36.47, 49.65, 123.03, 124.38, 137.30. According to the spectrum, the total carbon numbers obtained equalled 10. -

19

F NMR: This spectrum consist of two peaks, one at δ= -71.48 and the other at δ= -69.967, corresponding to the splitting of 19F (I = 1⁄2) by 31P (I = 1⁄2).

- Mass spectroscopy: molar mass of HMIMPF6 was obtained equal to 313 g·mol−1, in agreement with the exact molar mass of 312.2 g·mol−1. All the obtained spectra are given in supplementary information. Further, chloride impurities have been reported to have a detrimental effect in ILs. Therefore, standard chloride titration method [19] was employed, indicating very low chloride impurity content. The IL product can therefore be introduced with a mass fraction purity of more than 0.99. Given in table 2 are density (ρ) and refractive index (nd) of the used components in comparison with the literature values. Densities were measured by means of an oscillating U-tube densimeter (Anton Paar DMA4500, Austria), provided with automatic viscosity correction. With respect to the purity of materials, the relative uncertainty of density measurements was estimated ±0.001 [20]. All experiments were conducted under atmospheric pressure of (81.5 ±0.3) kPa. TABLE 2 Density (ρ) and refractive index (nd) of the components, compared with literature at different temperatures and under atmospheric pressure of 81.5 kPa.*

ρ / (g.cm−3) a Component

T/K

HMIMPF6

acetone

water

nd

b

Exp.

Lit.

Exp.

Lit.

293.2

1.29491

1.297 [21]

1.41760

1.41844 [22]

298.2

1.29088

1.2937 [13]

1.41640

1.41787 [13]

303.2

1.28685

1.288 [23]

1.41515

1.41610 [23]

293.2

0.79066

0.7902 [24]

1.35880

1.35880 [24]

298.2

0.78440

0.7845 [24]

1.35575

1.35566 [13]

303.2

0.77870

0.7785 [24]

-

293.2

0.99820

0.99820 [24]

1.35265 1.33305

1.33299 [25]

298.2

0.99704

0.99693 [24]

1.33250

1.33250 [25]

5

303.2

0.99565

0.99568 [24]

1.33195

1.33194 [25]

*

Standard average uncertainties are u(nd) = ±0.00005, u(T) = ±0.1 K and u(p) = ±0.3 kPa, and relative uncertainty of density ur(ρ) = ±0.001. a Measured with Anton Paar DMA 4500 densimeter, Austria b Measured with Abbe AR4 Kruss refractometer, Germany

2.3. Apparatus and procedure The solubility of components was characterized by the cloud point method [26] using a thermostatted miniature cell with about 5 cm3 volume, equipped with a magnetic stirrer and isothermal fluid jacketed. The temperature was held constant by circulating water from a water bath (Julabo, Germany) through the jacket of the cell, and with temperature uncertainty of ± 0.1 K (examined by means of an accurate thermometer, Amadigit, ad 3000th, Percica, Germany). Analysis by UV absorbance, for instance, is difficult here, because the imidazolium cation absorbs UV light with shorter wavelengths than 230 nm [12]. Binary mixtures of (water + acetone) or (HMIMPF6 + acetone) with known compositions (weighted with an electronic Ohaus balance, Adventurer, Pro AV264, Switzerland, ±0.00001 g·cm−3) were introduced to the cell and stirred at constant temperature. The corresponding third component (HMIMPF6 or water) was titrated into the cell from a microburet with an uncertainty of ±0.1 mm3. The end point was detected by observing the transition from a homogeneous to a heterogeneous cloud mixture. Then, it was allowed to rest 1 h for phase splitting, and 3 samples of the mixture were taken. The refractive index of samples was then measured and the average value was considered. Refractive indexes was determined with an Abbe refractometer (AR4, Kruss, Germany) having an accuracy of 0.00005. Also, temperature of the refractometer was retained at the same temperature of mixtures by circulating water from the water bath. This procedure was performed at temperatures of (293.2, 298.2 and 303.2) K. The perfect samples composition and the refractive indexes for this part of work are given in the supplementary information. As presented in figure 2, there is a close agreement between obtained results with those reported in the literature [27,28] for the case of absence of acetone. Generally, wi1 and wi3 refer to the mass fractions of the ith (water = 1, acetone = 2 and HMIMPF6 = 3) component in the aqueous and the IL phases, respectively. Figures 3 and 4 indicate dependency of refractive index on compositions in cloudy solutions, typically at 298.2 K. For other temperatures, similar trends were obtained.

6

In cloudy samples, refractive index of aqueous phase is increased with incrementing the added acetone due to higher refractive index of acetone, compared to water. It is while, a contrary variation is observed in the IL phase due to lower refractive index of acetone compared to HMIMPF6. Similar explanation can be given for variation of refractive index when water is added

0.020

0.020

0.015

0.015

0.010

0.010

0.005

0.005

0.000

w31

w13

to the samples.

0.000 290

292

294

296

298

300

302

304

T/K FIGURE 2. Comparison of the obtained mass fractions of water in IL solution (▲), w13, and IL in water solution (●), w31, with corresponding literature values [27,28], ( ), (▲), (○) and (●), respectively.

7

0.40

0.35

0.35

0.30

0.30

0.25

0.25

0.20

0.20

0.15

0.15

0.10

0.10

0.05

0.05

0.00 1.32

1.34

1.36

1.38

1.40

w23

w21

0.40

0.00 1.42

nd

FIGURE 3. Dependency of acetone compositions on the refractive index of cloudy solutions at 298.2 K for aqueous (∆) and IL (▲) solutions. 1.00

0.14

0.95 0.12 0.90 0.10

0.85 0.80

w13

w11

0.08 0.75 0.06 0.70 0.65

0.04

0.60 0.02 0.55 0.50 1.32

1.34

1.36

1.38

1.40

0.00 1.42

nd

FIGURE 4. Dependency of water compositions on the refractive index of cloudy solutions at 298.2 K for aqueous (∆) and IL (▲) solutions.

8

To obtain the tie line values at each temperature, a tightly closed miniature equilibrium cell with about 5 cm3 volume was used. Mixtures of known masses of the three components were introduced into the cell, and located inside a shaking water bath (N-BIOTEK-304) with adjustable shaking speed, and temperature uncertainty of ±0.1 K. Content of the cell was shaking for 4 h at 175 rpm and then allowed to rest 12 h for settling layers under a specified temperature. To determine each equilibrium phase composition, samples were withdrawn from each phase carefully and analysed via measuring the refractive index. Once the calibration curves were constructed, the compositions of the unknown mixtures (corresponding to the ends of tie lines) were obtained with an estimated maximum uncertainty of ±0.005 in mass fraction. Similar procedure for determination of composition of tie lines has been used by other investigators [2931]. All experiments were carried out under ambient pressure of (81.5 ±0.3) kPa.

3. Results and discussion 3.1. Tie-line data Table 3 contains the composition of two coexistence liquid phases for the ternary {water (1) + acetone (2) + HMIMPF6 (3)} system at different temperatures. Since (acetone + water), and (acetone + HMIMPF6) are two liquid pairs that are entirely miscible and the liquid pair (water + HMIMPF6) is partially miscible, the ternary system behaves as a “type-1” LLE [32]. The data show that for the most tie-lines, acetone is more soluble in the IL phase than in the aqueous phase which can be due to hydrogen bonding between acetone and the IL. Hydrogen bonding plays an important role in pure ILs and in mixtures of ILs with polar compounds that have hydrogen bond donor (HBD) and acceptor (HBA) characters. Therefore characters of the pairs IL−organic compound depends on the molecular structure of the organic compound [33,34]. Remarkably, all IL−ketone systems indicate favourable intermolecular interactions between IL and HBA organic compounds (acetone has HBA carbonyl group) [33]. The imidazolium-based ILs (HBD solvent) are similar to polar organic compounds that can form hydrogen bonding (hydrogen on carbon 2, presented in figure 1, of imidazolium-ring with oxygen in carbonyl moiety of acetone). There may also be weak van der Waals forces between alkyl groups in imidazolium-based ILs with alkyl groups of acetone [33].

9

TABLE 3 Experimental tie-line values for the ternary{water (1) + acetone (2) + HMIMPF6 (3)} system at different temperatures and under atmospheric pressure of 81.5 kPa.* Water-rich phase HMIMPF6-rich phase

w11

w21

w31

w13

w23

w33

0.9392

0.0538

0.0070

0.0173

0.0538

0.9289

0.8823

0.1098

0.0079

0.0223

0.1167

0.8610

0.8382

0.1500

0.0118

0.0318

0.1667

0.8015

0.8093

0.1749

0.0158

0.0408

0.1994

0.7598

0.7641

0.2118

0.0241

0.0588

0.2474

0.6938

0.6838

0.2715

0.0446

0.1039

0.3283

0.5678

0.6389

0.3020

0.0591

0.1360

0.3702

0.4938

0.6128

0.3188

0.0684

0.1571

0.3937

0.4491

0.9244

0.0673

0.0083

0.0199

0.0647

0.9153

0.8771

0.1133

0.0096

0.0260

0.1150

0.8591

0.8311

0.1546

0.0143

0.0367

0.1639

0.7994

0.7745

0.2012

0.0243

0.0557

0.2202

0.7241

0.7365

0.2302

0.0333

0.0712

0.2549

0.6739

0.7236

0.2396

0.0367

0.0768

0.2661

0.6570

0.6536

0.2878

0.0586

0.1128

0.3259

0.5613

0.5641

0.3424

0.0935

0.1676

0.3945

0.4379

0.9186

0.0709

0.0105

0.0228

0.0625

0.9147

0.8915

0.0957

0.0128

0.0258

0.0868

0.8874

0.8240

0.1534

0.0225

0.0376

0.1457

0.8167

0.7632

0.2019

0.0350

0.0535

0.1960

0.7505

0.7081

0.2432

0.0487

0.0728

0.2417

0.6855

0.6009

0.3183

0.0808

0.1195

0.3219

0.5586

0.5036

0.3816

0.1148

0.1723

0.3886

0.4391

T = 293.2 K

T = 298.2 K

T = 303.2 K

*

Standard average uncertainties are u(nd) = ±0.00005, u(T) = ±0.1 K, u(p) = ±0.3 kPa and u(w) =

±0.005.

Results also show that mutual solubility of water and the IL phases is increased with increasing acetone concentration and temperature, i.e. smaller two phase region. The higher

10

temperature of 303.2 K provides a smaller binary region due to more tendency of water-IL miscibility (figure 5). Meantime; the acetone solubility in aqueous phase relative to the IL phase increases regularly by increasing temperature. Of course solubility of the IL in water is to some extent smaller than water in the IL at all the used temperatures.

FIGURE 5. Comparison between binary regions and tie-lines at temperatures of: 293.2 K, dotted line (▲), and 303.2 K, dashed lines (○).

The consistency of experimentally determined tie-line data at each temperature can be distinguished using the Othmer–Tobias correlation [35]:

 1 − w33   1 − w11   = A + B ln  ln w w 33 11    

(1)

where A and B are constants. The Othmer–Tobias parameters are presented in table 4 for different temperatures. The coefficient of determination (R2) close to unity indicates the degree of the consistency of the data.

11

TABLE 4 The Othmer-Tobias parameters and the coefficient of determination at different temperatures.

T/K

A

B

R2

303.2

0.2089

1.0831

0.9985

298.2

0.4959

1.1667

0.9986

293.2

0.6811

1.2248

0.9949

The distribution coefficients of water (D1) and of acetone (D2) are defined as:

D1 = D2 =

w13 w11

(2)

w23 w21

(3)

Another criterion of the extraction effectiveness is separation factor (S) which is here an indication of the relative amount of acetone in the IL to aqueous phases. It is given as:

S=

D2 D1

(4)

Figure 6 shows variation of distribution coefficient of acetone (D2) as a function of acetone concentration in aqueous phase at different temperatures. Results demonstrate that solute distribution coefficient varies from 0.8813 to 1.2351 and increases uniformly with its aqueous phase concentration. This is due to strong hydrogen bonds and van der Waals forces between acetone and HMIMPF6 molecules. Decreasing temperature causes an enhancement in distribution coefficient and this effect is more for higher solute concentrations due to little miscibility between water and the IL. Meantime figure 7 shows that increasing temperature leads the water distribution coefficient (D1) to decrease. Water distribution coefficient varies from 0.0184 to 0.3422.

12

1.30 1.25 1.20 1.15

D2

1.10 1.05 1.00 0.95 0.90 0.85 0.80 0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

w21

FIGURE 6. Variation of acetone distribution coefficient with its concentration in aqueous phase at different temperatures: 293.2 K (■), 298.2 K (●) and 303.2 K (▲). 0.35

0.30

0.25

D1

0.20

0.15

0.10

0.05

0.00 0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

w21

FIGURE 7. Variation of water distribution coefficient with acetone concentration in aqueous phase at different temperatures: 293.2 K (■), 298.2 K (●) and 303.2 K (▲).

13

Figure 8 shows variation of separation factor with solute concentration in aqueous phase at different temperatures. HMIMPF6 provides a suitable separation factor within (3.0 - 54.4), and therefore can be proposed as a proper candidate for recovery of acetone from aqueous solutions. It is noteworthy that distribution coefficient of acetone in a number of organic compounds like esters and 1-butanol in contact with water are comparatively more than the (HMIMPF6 + water) system [34,36]. This may reflect the less hydrophobic character of the HMIMPF6, or may also be due to the strong polar contribution of the relatively high charged groups existing in HMIMPF6, compared to the organic solvents [37]. Nevertheless, the distribution coefficient and separation factor for the used IL are significantly adequate for practical applications. It can also be observed in figure 8 that separation factor decreases with solute concentration due to presence of more water in the IL phase. Meanwhile, decreasing temperature provides a considerable enhancement in separation factor in agreement with the solute distribution coefficient. When the temperature decreases, the solubility of ILs in water also decreases. Thus, the selection of a suitable extraction temperature is important. The data here shows that 293.2 K is the best choice; and acetone separation factor decreases when temperature increases within a wide range of acetone concentration. 60

50

S

40

30

20

10

0 0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

w21

FIGURE 8. Variation of acetone separation factor with its concentration in aqueous phase at different temperatures: 293.2 K (■), 298.2 K (●) and 303.2 K (▲).

14

0.45

3.2. LLE correlation There are many papers in which LLE data for ternary systems containing ionic liquids have been correlated with Non Random Two Liquid (NRTL) as well as UNIversal QUAsi Chemical (UNIQUAC) models [38-40], which were utilized in this work. The basic relationships in these models, for every component i in coexistent liquid phases at equilibrium, are as following:

xiI γ iI = xiII γ iII

(5)

∑x

(6)

I i

= ∑ xiII = 1

I II I II where xi , xi , γ i and γ i are the mole fraction and activity coefficient of component i in phases

I and II, respectively. The model parameters of the NRTL and UNIQUAC equations were distinguished via data regression using Aspen Plus (V. 7.1) simulator. This software uses an objective function called “maximum likelihood” and an algorithm called Britt-Luecke to correlate model parameters [41]. In the NRTL model, the activity coefficient for component i is represented as [42]:

∑x τ G = ∑x G j

ln γ i

ji

ji

j

k

ki

k

 ∑v xvτ vj Gvj  x j Gij  +∑ τ ij −  xk Gkj  j ∑ xk Gkj  ∑ k k  

(7)

where x is the mole fraction, and G is binary parameters for NRTL model, while i, j, k and v are indices, each of them for all of the components. Also, the binary interactions were calculated by [41,43]: τ ij= a ij +

bij

T

(8)

+ e ij ln T + f ij T

αij = α ji = cij + d ij (T − 273.2)

(9)

Gij = exp(−α ijτ ij )

(10)

where τ ij and Gij are NRTL parameters which are determined via the parameters aij, bij (K), cij, dij and eij. On the other hand, the UNIQUAC equation for the liquid phase activity coefficient is illustrated as [44]:

ln γ i = ln γ iC ( combinator ial ) + ln γ iR ( residual ) 15

(11)

where the combinatorial and residual terms of the activity coefficient are relevant to the difference in shape and energy of the molecules, respectively. These terms are given as:

 Φi  z  θi  Φi c ln γ = ln  + qi ln  + li − ∑ x j l j xi j =1  xi  2  Φi 

(12)

     c  c  θ jτ ij R ln γ i = qi 1 − ln ∑θ jτ ji  − ∑ c    j =1  j =1  θ τ ∑ k kj   k =1 

(13)

C i

     

where i, j and k are indices, c is the number of components and the UNIQUAC parameter li is: l i=

z (ri − qi ) − (ri − 1) 2

(14)

and τ ij is the adjustable parameter in this equation, presented by [43]: 

τ ij = exp  − 

∆ u ij  b  = a ij + ij + cij ln T + d ij T RT  T

(15)

where ∆uij is the interaction energy parameters and also aij, bij, cij and dij are UNIQUAC coefficients of the equations for binary interaction parameters. The parameters Φi (segment fraction) and θi (area fraction) are indicated as the following equations:

Φi =

xi ri

(16)

c

∑x r

j j

j =1

θi =

xi qi

(17)

c

∑x q j

j

j =1

The UNIQUAC structural parameters r (the number of segments per molecules) and q (the relative surface area per molecules) have been calculated from the number of molecular groups and the individual values of the van der Waals volume and area of the molecule using the Bondi method [45,46]. The detailed description of the meaning of parameters and equations has been represented in the literature [47]. UNIQUAC structural parameters r and q for the used ionic liquid, HMIMPF6, were determined by Santiago et al. [40] as 9.681 and 7.845, respectively. To correlate the LLE data for the ternary systems containing ionic liquids and to obtain the model parameters using Aspen Plus simulator, the molar gaseous enthalpy of formation, 16

∆f H m
(g ) , and Gibbs energy of formation, ∆f G m
( g ) , of the used IL are required. For chemical substances, these thermodynamic properties cannot be directly calculated by ab initio quantummechanical methods. However, based on a methodology described by Emel’yanenko

et al.

[48,49], the above properties were obtained for HMIMPF6. In this regard, the most corresponding following reactions were first considered: HMIMPF6 + 16CH4 → 6HF + PH3 + 5C2H4 + 8C2H6 + 2NH3

(18)

HMIMPF6 + 16CH4 → 6HF + PH3 + 4C2H4 + 8C2H6 + 2CH3NH2

(19)

HMIMPF6 + 10CH4 → 6HF + PH3 + 3C2H4 + 6C2H6 + 2HCN

(20)

Then the enthalpy of each of the above reactions was obtained by DFT calculations, using G09 set of programs [50]. For this purpose, the structure of HMIMPF6, CH4 and all products of the above reactions were optimized at M06/6-311++G** level of theory. The optimized structure of HMIMPF6 is shown in figures 9. It should be noted that based on previous studies on similar ionic liquids [33], several structures for HMIMPF6 were examined and the data showed that the present structure is the most stable one. Indeed, the existence of several interatomic interactions between the cation and anion in this IL is the reason for the fact that this structure is more stable than other possible structures. Also, the vibrational frequency analysis, calculated at the same level of theory, indicated that optimized structures are at the stationary points corresponding to local minima without any imaginary frequency. The calculations gave, therefore, the standard enthalpy and Gibss energy of each of the compounds (table 5), which were used to calculate the standard enthalpies and Gibbs energies of the reactions (18-20). Finally, since the experimental values of these properties were available for all other species involved in the above reactions, the HMIMPF6 molar gaseous enthalpy and Gibbs energy of formation were easily calculated (table 6). The averaged values, given in this table, were used here in LLE calculations.

17

FIGURE 9. The optimized structure of HMIMPF6 at M06/6-311++G** level along with the selected interatomic distances (Å).

TABLE 5 Calculated standard enthalpies and Gibbs energies at 298 K for all compounds involved in reactions (18-20), and available experimental standard enthalpies and Gibbs energies of formation (in kJ.mol−1).

Compound CH4 C2H4 C2H6 HF PH3 NH3 HCN CH3NH2 HMIMPF6

M06/6-311++G** Gom(g)/ H m(g)/ kJ·mol-1 kJ·mol-1 o

-106282.71 -206282.49 -209464.95 -263859.69 -901206.45 -148471.39 -245374.08 -251621.57 -3788913.80

-106344.34 -206349.42 -209535.55 -263911.45 -901271.82 -148531.47 -245433.99 -251693.28 -3789107.28

Experimental ∆fHom(g)/ ∆fGom(g)/ kJ·mol-1

kJ·mol-1

-74.85 52.30 -84.68 -269.00 9.25 -46.19 130.50 -28.00 -

-59.79 [51] 68.12 [51] -32.89 [52] -270.70 [53] 18.24 [53] -16.70 [54] 120.10 [55] -27.60 [53] -

TABLE 6 Calculated standard molar enthalpy and Gibbs energy of formation for HMIMPF6 in the gaseous phase at 298.15 K. ∆fHom(g)/ ∆fGom(g)/ Reaction kJ·mol-1 kJ·mol-1 18 -1913.19 -1387.05 19 -1911.24 -1502.78 20 -1937.38 -1441.50 average -1920.60 -1443.78

Listed in table 7 are the binary interaction parameters that were obtained by Aspen Plus based on the NRTL and UNIQUAC models. Comparisons between experimental and correlated 18

composition data are shown in figures 10 and 11 at typical temperature of 298.2 K. As is obvious, correlating with both of the used models exhibits satisfactory agreement, consistent for all solute concentrations and temperatures.

TABLE 7 NRTL and UNIQUAC binary interaction parameters for the {water (1) + acetone (2) + HMIMPF6 (3)} system.*

Component i

1

1

2

Component j

3

2

3

aij

0.00

0.05

0.00

aji

0.00

6.40

0.00

bij

2169.83

534.94

205.73

bji

463.57

1923.43

-414.12

cij

0.30

0.30

0.30

aij

0.00

-4.83

0.00

aji

0.00

8.61

0.00

bij

-112.78

1479.47

256.99

bji

-659.25

-2661.82

-217.90

NRTL

UNIQUAC

*

AAD and BIAS values for NRTL model are 0.06217 and -0.01573, and for UNIQUAC model, 0.06745 and -0.02353, respectively.

19

Acetone 0.0

1.0

0.1

0.9

0.2

0.8

0.3

0.7

0.4

0.6

0.5

0.5

0.6

0.4

0.7

0.3

0.8

0.2

0.9

0.1

1.0

0.0

HMIMPF6 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Water

FIGURE 10. Comparison between experimental tie lines, dotted line (▲), and NRTL tie lines, dashed lines (○), at 298.2 K. Acetone 0.0 0.1

1.0 0.9

0.2

0.8

0.3

0.7

0.4

0.6

0.5

0.5

0.6

0.4

0.7

0.3

0.8

0.2

0.9

0.1

1.0

HMIMPF6 0.0

0.0 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Water

FIGURE 11. Comparison between experimental tie lines, dotted line (▲), and UNIQUAC tie lines, dashed line (○), at 298.2 K.

20

To indicate the capability of the used models, the root mean square deviation (RMSD) between experimental and calculated data was obtained from:

∑∑∑(w

exp imn

RMSD =

i

m

cal 2 − wimn )

(18)

n

6N

exp cal where wimn and wimn are experimental and calculated mass fractions of components i = 1, 2, 3 in

phases, m = I, II and on tie lines n = 1, 2, ..., N. The RMSD values based on NRTL and UNIQUAC models were 0.0192 and 0.0255, respectively. These reasonable errors, as well as the corresponding maximum errors of 0.0691 and 0.1301, indicate that the NRTL and UNIQUAC models can satisfactorily be used to reproduce the experimental data. Also, it can be concluded that thermodynamic parameters for the ionic liquid, obtained by the DFT calculations, was adequate to successfully correlate using the models.

4. Conclusions The equilibrium behaviour of the ternary system of (water + acetone + HMIMPF6) was investigated at temperatures of (293.2, 298.2, and 303.2) K and under atmospheric pressure. The results showed that the used IL provides solute distribution coefficients ranging from 0.8813 to 1.2351 at the considered concentrations and temperatures. Meantime, the range of separation factor was within the range of 3.0 - 54.4. These relatively high values are due to presumed hydrogen bonds between acetone and HMIMPF6 molecules. Low temperature was preferred both for the solute distribution coefficient and separation factor criteria due to decrease in miscibility between water and the used IL. The consistency of experimental tie line data was confirmed by the Othmer–Tobias correlation. The NRTL and UNIQUAC models were employed to correlate the experimental LLE data and to estimate tie-lines of the studied ternary system. Relevant IL thermodynamic data, required for the models, were obtained from DFT calculations. As can be concluded from the RMSD values, fairly good correlations were obtained with both the NRTL and UNIQUAC models.

21

Acknowledgement The authors wish to acknowledge Iran National Science Foundation (INSF) for financial support of this work. The Bu-Ali Sina University authorities are also acknowledged.

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25

Research highlights

• • • • •

The use of HMIMPF6 as a green ionic was feasible in the extraction of acetone from water. The binodal curves were determined by cloud point measurement method. High level separation factor of acetone between the ionic liquid and water were achieved. The thermodynamic properties of HMIMPF6 were obtained by the Density Functional Theory calculations. The NRTL and UNIQUAC models were applied satisfactorily to correlate the equilibrium data.

26