Modeling the Water Solubility in Imidazolium-Based Ionic Liquids

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Modeling the Water Solubility in ImidazoliumBased Ionic Liquids Using the Peng-Robinson EoS Jeremías Martínez, Maria Antonieta Zuñiga-Hinojosa, and Ricardo Macías-Salinas Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b05153 • Publication Date (Web): 15 Feb 2019 Downloaded from http://pubs.acs.org on February 19, 2019

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Industrial & Engineering Chemistry Research

Modeling the Water Solubility in Imidazolium-Based Ionic Liquids Using the Peng-Robinson EoS Jeremías Martínez,ǁ, María A. Zúñiga-Hinojosa,§ Ricardo Macías-Salinas§,* ǁ

Facultad de Química, Universidad Autónoma del Estado de México, Paseo Colón y Paseo Tollocan S/N, Toluca, Estado de México, C.P. 50120, México.



Centro Conjunto de Investigación en Química Sustentable UAEM-UNAM, Carretera TolucaAtlacomulco, km 14.5, Toluca, Estado de México, C.P. 50200, México.

§

Instituto Politécnico Nacional, Departamento de Ingeniería Química, ESIQIE, Ciudad de México, México, C.P. 07738.

ABSTRACT: Ionic liquids (ILs), also known as liquid salts or ionic fluids, are organic salts with a low fusion point. They behave as a liquid at low temperature or ambient temperature. Accordingly, they are prominent solvents to be used in the green chemical processes because of their attractive physicochemical properties such as low vapor pressure, high thermal stability, an excellent solvation behavior, and high gas solubility. Recently, various experimental researches have reported the water solubility in different imidazolium-based ionic liquids at different temperature, pressure, and composition conditions. In this study, we present the modeling of the vapor-liquid equilibrium of the H2O-IL system using the PengRobinson cubic equation of state coupled with the Wong-Sandler mixing rules; eight binary systems were studied for this purpose. Additionally, improved temperature-dependent parameters were introduced into the equation of state as those proposed by Stryjek and Vera for water and by Yokozeki for the IL. The studied ionic liquids were: [CxMIM][Cl] (x=2,4,6), [C4MIM][PF6], [C2MIM][BF4], [C4MIM][BF4], [OHC2MIM][BF4] and [OHC2MIM][Cl]. The obtained results showed a satisfactory agreement between the experimental and the calculated solubility data using the present modeling approach at different conditions of temperature, pressure, and composition.

INTRODUCTION Ionic liquids (ILs) have recently attracted the attention within the research and industrial community since they are considered as new potential solvents for replacing the traditional organic solvents. They present an extremely low vapor pressure what avoids their evaporation at room conditions; accordingly, ILs are ACS Paragon Plus Environment

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called “green solvents.”1,2 Other properties include their high thermal stability and their high capacity for solubilizing several gases; additionally, they remain in a liquid state over a wide range of temperatures. In this context, the vapor-liquid equilibrium (VLE) of the H2O-IL system has potential applications in different separation process, e.g., the extractive distillation (breaking azeotropes),2-6 and absorption.7 ILs could be also used in refrigeration and air conditioning industries, in which refrigerant-absorbent pairs such as H2O-LiBr and H2O-NH38,9 are commonly used. Traditional refrigerant-absorbent pairs have some disadvantages such as crystal formation, toxicity and flammability.10 Several studies have shown that ILs can be used in the gas industry to prevent the hydrate formation since they modify the dissociation equilibrium curve of gas hydrates. This is, ILs show a dual function: behaving simultaneously as thermodynamic and kinetic inhibitor.7,11-13 This peculiar characteristic is due to a strong electrostatic charge and a high tendency to create hydrogen bonds.11 Ionic liquids are organic salts formed by large and asymmetric organic cations, e.g., imidazolium cation, bonded to alkyl groups, and organic and inorganic anions. Therefore, synthesizing a significant amount of ILs for fitting some physicochemical properties is possible.14,15 The physical and chemical properties of ILs present many advantages over traditional solvents. Accordingly, it is necessary to have a vast knowledge of ILs before overtaking in a process at industrial scale. However, to create an extensive phase equilibrium database of H2O-IL systems, it is necessary to perform an extensive experimental investigation; consequently, what is time and money consuming. In this context, modeling is of vital importance, allowing to calculate and to predict physicochemical properties, and the phase equilibrium behavior. Despite the complexity in predicting the water solubility in the ionic liquids, several thermodynamic models have been used, such as activity coefficient models, equations of state, and unimolecular quantum chemical calculations. Calvar et al.3 and Carvalho et al.16 used the Nonrandom Two-Liquid (NRTL) model to correlate the experimental data of the H2O-[CxMIM][Cl] (x=2,4,6) systems, obtaining absolute average deviation (AAD) values less than 1%. Whereas, Yokozeki and Shiflett17,18 used the Redlich-Kwong EoS19 with the empirical modification in the temperature-dependent parameter of the pure component, and the modified van der Waals-Berthelot mixing rule.20 Vetere21 calculated the critical properties of ILs by using a compressibility factor of 0.256. The solubilities of the [C2MIM][BF4] and [C4MIM][BF4] ILs in water were predicted with AAD values less than 0.02%. The Statistical Associating Fluid Theory (SAFT) proposed by Chapman et al.22 and Huan and Radosz23 in their variations have also been used for several research groups to model the H2O-IL solution. Passos et al.24 applied the PC-SAFT approach for calculating water solubility in diverse ILs using the cation ACS Paragon Plus Environment

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[C4MIM+] as a base. In this case, ILs were considered as associating species with two association sites. The model parameters were calculated by simultaneous adjustment to pure ILs densities, water activity coefficients at 298.15 K, and VLE experimental data at 0.1 MPa. Their results showed a satisfactory agreement between the experimental and calculated data obtaining AAD values between 1.01 and 7.85. Vega et al.25,26 modeled the water-IL system using the soft-SAFT equation, where the IL was considered as a homonuclear chain, i.e., cation and anion as one molecule with a specific association number of sites; independently, the alkyl chain length in imidazolium cation and the corresponding anion were modeled. In regards to the equation parameters of the model for the system [CxMIM][Cl] (x=2,4,6), the segment diameter parameter was set at an average value, whereas a variation in the chain length and the dispersive energy parameters were observed as the alkyl chain length of the cation increased. In this particular case, the AAD value obtained by Vega et al. was 0.1%.25,26 Freire et al.27 modeled the H2O-[C4MIM][BF4] and H2O-[C4MIM][PF6] systems using the Conductor-like Screening for Real Solvents (COSMO-RS) model; nevertheless, they only showed qualitative results. This model, based on the statistical thermodynamics, calculates the chemical potential of any species in any mixture and does not have a concentration dependency in the excess Gibbs free energy function (UNIFAC).28 In contrast Zhou et al.29 and Khan et al.30 obtained results with a better precision using COSMO-RS.

In the present work, we calculated the water solubility in imidazolium-based ionic liquids using the PengRobinson EoS (PR EoS)31 at different temperature, pressure, and composition conditions. Regarding the proposed modeling approach for the H2O-IL systems, we incorporated in the PR EoS the modification in the temperature dependent a parameter (cohesive energy) of the pure IL, as suggested by Yokozeki20, whereas, we included the  expression of Stryjek and Vera for water.32 Furthermore, we applied the Wong-Sandler (WS) modern mixing rules33 in combination with the UNIQUAC model34 for estimating the excess free energy. In this modeling effort, the studied ILs were 1-ethyl-3-methylimidazolium chloride,

[C2MIM][Cl];

methylimidazolium [C4MIM][PF6]; methylimidazolium tetrafluoroborate

1-butyl-3-methylimidazolium

chloride,

[C6MIM][Cl];

1-ethyl-3-methylimidazolium tetrafluoroborate [OHC2MIM][BF4]

[C4MIM][Cl];

1-butyl-3-methylimidazolium tetrafluoroborate,

[C4MIM][BF4]; and

chloride,

1-hexyl-3-

hexafluorophosphate,

[C2MIM][BF4];

1-butyl-3-

1-(2-hydroxyethyl)-3-methylimidazolium

1-(2-hydroxyethyl)-3-methylimidazolium

[OHC2MIM][Cl].

DESCRIPTION OF THE MODEL ACS Paragon Plus Environment

chloride


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The vapor-liquid phase behavior between water and IL was determined by the PR EoS,31 expressed as

P

RT a (T )  v  b v( v  b)  b( v  b)

(1)

where a and b are the constants for pure components given by

a  0.45723552821

R Tc  (T ) Pc

(2)

and

b  0.077960739039

R Tc Pc

(3)

The Soave correlation35 is defined as

 (T )  [1   1  Tr0.5 ], Tr  T Tc

(4)

where,  is only a function of the acentric factor . To model the water, we use the Stryjek and Vera32 expression, in which the  parameter was modified

   0   1 1  Tr0.5 0.7  Tr 

(5)

where

 0  0.378893  1.4897153  0.17131848 2  0.0196554 3

(6)

1 has a specific value for pure components, i.e., when the critical properties and the acentric factor of the components were known, the experimental vapor pressures were fitted to obtain the 1 value (See Table 1). For water, the 1 and  values are -0.0663532 and 0.3438,36 respectively.

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The following modification in the temperature dependent a parameter of the pure component in the PR EoS17,18 was used for the eight ILs:20

T T  α T    βk  c   k 0  T Tc  3

k

(7)

The critical properties were taken from Valderrama et al.38 The authors calculated such properties using a group contribution method (See Table 1); the k values presented in this work were fitted to PTx experimental solubility data of each binary system. We observed that 0 values approach to one; while, 2 and 3 values did not significantly affect the vapor-liquid equilibrium calculations. So that, in the temperature dependent correlation 1 was the only adjustable parameter, which will be further discussed. Therefore, we applied the equation proposed by Yokozeki in solubility calculations.20

 Tc T     T Tc 

 T   1  1 

(8)

On the other hand, Wong and Sandler33 proposed a set of mixing rules to better represent the nonideal behavior of mixtures such as the water-ILs system. These mixing rules combine an excess free energy model with a cubic EoS to produce the desired EoS behavior at both low and high densities without being density dependent. These rules allow extrapolation over a wide range of temperature and pressure. WS mixing rules are based on two significant observations. The first states that the van der Waals one-fluid mixing rules (eqns. 9 and 10) are sufficient conditions to ensure the proper composition dependence of the second virial coefficient (eq. 11) and that they are not necessary conditions since they impose constraints on the a and b parameters to satisfy eq. 12.

a   xi x j aij

(9)

b   xi x j bij

(10)

B x,T    xi x jBij T 

(11)

i

i

j

j

i

j



bm 

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am a     xi x j  b RT  R T  ij i j

(12)

To apply the combining rule (eq. 12), an interaction parameter, kij, is introduced as follows

aj  a      bi  i    b j  RT   R T  a    1  kij   b   2  R T  ij

(13)

It should be mentioned that the composition dependence of the second virial coefficient, that is the limit condition to low density, is satisfied. Additionally, eq. 12 does not provide any relationship for calculating the a and b parameters separately, but only for the sum b  a R T  , thus an additional equation is needed. The second observation indicates that the excess of the Helmholtz free energy of a mixture is less pressure dependent than the excess Gibbs free energy, i.e.,

G E T, P  low , xi   A E T, P  low , xi   A E T, P   , xi 

(14)

The first term comes from the fact that G E  AE  Pv E , and the Pv E expression is negligible at low pressures; whereas, the second one is a result of the essential pressure independence of AE term at high densities. Accordingly, the second equation for a and b parameters comes from the condition E T, P   , x   AE T, P   , x   AE T, P  low , x   GE T, P  low , x  AEoS

(15)

E where AEoS represents the excess Helmholtz free energy derived from an EoS, whereas, the AE and GE

expressions refer to excess free energies derived from an activity coefficient model. In the WS mixing rules context, for the infinite pressure limit of an equation of state, the molecules in the liquid solution are assumed to be so tightly packed that there is no free volume, i.e., lím v  b . P


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Finally, from the above set of equations, Wong and Sandler33 obtained the following expressions for am and bm:

am  R T  Q

bm 

D 1 D

(16)

Q 1 D

(17)

where

Q  bm 

am RT

(18)

ai GE D   xi  bi R T C R T

(19)

where C is an EoS specific-constant that depends on the used EoS, the C value for PR EoS is

ln



2 1

2.

To calculate the excess Gibbs free energy for water-IL systems, the UNIQUAC equation34 was used

G E G E , combinatorial G E , residual   RT RT RT

(20)

where the combinatorial term describes the dominant entropic contribution (eq. 21); which consists of two compositional variables: area fraction , and segment fraction , i.e., combinatorial part is determined by the composition, and molecular shape and size only. Additionally, z is the coordination number equal to 10.

G E,

combinatorial

RT

x1 ln

1 x1

 x2 ln

2

   z   x1 q1 ln 1  x2 q2 ln 2  x2 2  1 2  ACS Paragon Plus Environment

(21)


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where segment fraction, , and area fractions  and  ' are given by

i 

  ' i

i 

xi qi xi qi  x j q j

xi q'i xi q'i  x j q'j

xi ri xi ri  x j rj

i , j  1, 2

(22)

i , j  1, 2

(23)

i , j  1, 2

(24)

Parameters r, q and q’ are pure-component molecular structural constants, which depend on the molecular size and external surface areas. The UNIQUAC structural parameters of the ionic species were obtained from Lei et al.,39 by correlating the activity coefficients of solutes at infinite dilution in ILs at different temperatures; whereas the r and q values for water were taken from Prausnitz et al.37 Concerning, the q’ values both ILs and water, these were estimated by following expression 0.7  q .37

On the other hand, the residual term mainly describes the intermolecular forces which are responsible for the enthalpy of mixing and is given by

G E , residual   q1 x1 ln 1   2 2 ,1   q2 x2 ln  2  1 1,2  RT

(25)

where  1,2 and  2,1 are adjusted parameters, which are expressed as a function of characteristic energies

ΔU i, j

ln i , j  

ΔU i , j RT

i , j  1, 2

(26)


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In most of the cases, the above equation gives the primary effect of temperature on  i ,j . This work aims to predict the water solubility in ILs using the PR EoS coupled with WS mixing rules. This modeling approach is restricted to 1 parameter firstly; subsequently, to both UNIQUAC parameters ( ΔU1,2 and

ΔU 2,1 ) and finally, to the interaction parameter for the second virial coefficient

k12  k 21 . The above

mentioned parameters were fitted to experimental solubility data. All vapor-liquid equilibrium calculations were performed using the phi-phi method. The required expressions for the fugacity coefficients of each species in the mixture, based on Wong-Sandler approach, are given elsewhere.33,40

RESULTS AND DISCUSSION The ILs considered in this work are based on the imidazolium cation bonded to the [ Cl  ], [ PF6 ], and 

[BF 4 ] anions. In this context, the anion plays a more significant role than the alkyl chain length; additionally, the shape and size of the anion determine its miscibility extent in a solvent.5 For modeling purposes of the H2O-IL systems. We present in Table 2 the corresponding temperature and pressure ranges, the maximum H2O solubility measured, and the source of the experimental solubility data for all ILs considered in this study. As shown in Table 2, the temperature range is moderate (283.15-443.15 K), whereas, the pressure range is low (0.008-3.192 bar). The maximum H2O solubility is reported for the H2O-IL- Cl  system at a water molar fraction of 0.998.

The simplex optimization procedure of Nelder and Mead47 was used in the computations for searching the minimum of the following objective functions according to the reported experimental data.

N







   1  y

2

N



min f   Pjexp  Pjcalc   1  yHcalc 2O ,j j1

j1



(27)



(28)

2

or

N

min f   T jexp  T jcalc j1

2

N

j1

calc 2 H 2O ,j



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where N is the number of experimental points, Pexp and Pcalc are experimental and calculated pressures, Texp and Tcalc stand for experimental and calculated temperatures, and yHcalc is the equilibrium composition 2O of H2O in the vapor phase. It should be mentioned that in this modeling approach only water is considered in the vapor phase. In a first attempt to obtain the value of the 1, U1,2, U2,1, and k12 parameters, we correlated the experimental solubilities at 298 K as suggested by Macías-Salinas.48 However, we found that the experimental solubility data of the H2O-[C4MIM][PF6] system was only reported at 298 K in the literature. Therefore, we decided to use the solubilities at the lowest temperature, pressure or H2O molar fraction according to the available experimental data. We found that 1 value must be our priority due to its reasonable representation of the cohesive energy () for ILs. Once optimized, 1 was set constant, and the U1,2, U2,1, and k12 parameters were fitted using the same initial values in each isotherm, isobar or isopleth. It should be mentioned that U1,2 and U2,1 values showed similar values in each isobar of H2O-[CxMIM][Cl] (x=2,4,6) systems; so that, we set either U1,2 or U2,1 to optimize again the U1,2 or U2,1, and k12 parameters. When we obtained the suitable 1, U1,2 and U2,1values, we set them constant, and finally, we fitted the k12 parameter. For purposes of modeling, we chose the appropriate values of the adjusted parameters based on a k12 value less than one and the lowest percent absolute average deviation (AAD %) for each water solubility in IL calculation. Table 3 shows the correlating results of the model parameters 1, U1,2, U2,1 and k12, and the % AAD between experimental and calculated temperatures of H2O-[CxMIM][Cl] (x=2,4,6) systems. As can be seen, the 1 value for H2O-[C4MIM][Cl] is smaller than the 1 values for H2O-[C2MIM][Cl] and H2O-[C6MIM][Cl] systems. We observed an increase in U1,2 values, as the alkyl chain length increases in the 1-alkyl-3methylimidazolium cation; whereas U2,1 values do not show any tendency. Table 3 also shows k12 values, which are larger than 0.5. Additionally, the predictive capability of the modeling approach to represent the experimental data of the water solubility in ILs with Cl  anion is rather good due to the maximum AAD value of 0.22%.

Figure 1 shows the experimental and calculated solubilities with the present modeling approach for H2O[CxMIM][Cl] (x=2,4,6) systems at 0.5, 0.7, and 1 bar. In Figure 1(a), a reasonable agreement is observed between the experimental and calculated temperatures using the 3-methylimidazolium cation and the chloride anion, irrespective of the alkyl chain length of the cation and pressure. A characteristic, per se, of the WS approach, consists in reproducing the desired equation of state behavior at both low and high densities without being density dependent and allows extrapolation over a wide range of temperature and ACS Paragon Plus Environment

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pressure as shown in this figure. Carvalho et al.16 showed in the vapor-liquid equilibrium for H2O[CxMIM][Cl] (x=2,4,6) systems that as alkyl chain length increases in the cation, the boiling points decrease because of weak solvation of the cations. This phenomenon can be explained through the UNIQUAC model. As mentioned above, the residual term (Eq. 25) describes the intermolecular forces that are responsible for the enthalpy of mixing; whereas, the combinatorial term describes the entropic contribution, which is determined by the composition, molecular shape, and size. Although the UNIQUAC model was not developed to describe the behavior of mixtures containing electrolyte species, it can be applied in systems of water with ionic liquid solutions, since in ionic liquids the ion charge is usually dispersed, and the long-range electrostatic forces are weak compared with the short-range intermolecular forces, so that they can be neglected. Figure 2 presents the analysis of the enthalpic and entropic contributions for H2O-[CxMIM][Cl] (x=2,4,6) systems using the UNIQUAC model at 1 bar. As can be seen in this figure, the water solubility in IL depends on enthalpic contribution noticeably. Furthermore, all systems show an exothermic behavior irrespective of alkyl chain length of the imidazolium cation. An examination of this figure also shows that as the alkyl chain length of cation increases, the enthalpic contribution increases, whereas the entropic contribution decreases to a lesser extent. A possible explanation is that the molecular interactions between H2O and IL decrease as the size of IL increases because of an increase in the alkyl chain length cation regardless of Cl  anion. Freire et al.27,49 showed that the decrease of the water solubility in IL is due to the increase of hydrophobic character of the cation, which is caused by the alkyl chain length. So that, such behavior can be related to the decrease in the polarity of the IL, no matter the type of anion. According to Zhang et al.50 a smaller alkyl chain length of the cation results in a stronger interaction between water and IL. It can be seen in Figure 2 that as the molar fraction of the H2O increases, the enthalpic contributions decrease up to a minimum value, and subsequently, they approach to zero irrespective of alkyl chain length of the cation. A maximum interaction exists between H2O and the ILs: [C2MIM][Cl], [C4MIM][Cl], and [C6MIM][Cl] at 0.69, 0.75 and 0.79 molar fraction of the H2O, respectively. This behavior suggests that at the molar fractions above mentioned, the interaction between H2O and IL is 1-1. Additionally, as the amount of water increase, the H2O-H2O interactions are dominant, i.e., the solvation behavior is predominant. Khan et al.30 predicted the activity coefficient of water in ILs and the excess enthalpies using the COSMO-RS approach. This study consisted of setting the [C4MIM  ] cation; whereas the anion was varied, being one of them the chloride anion. The results of this study showed that the addition of H2O to binary solution reduces the electrostatic interaction between the [C4MIM  ] cation and Cl  anion, and both species are attracted to H2O. As well as, the hydrogen of water presents a greater preference to bond with the lone ACS Paragon Plus Environment


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pairs of electrons of the Cl  anion. Accordingly, as the amount of water increase, the hydrogens of the molecules of water cluster around Cl  anions up to a saturation limit. The saturation limit obtained in this work is 0.75, similar to those reported in the literature. Niazi et al.51 showed the maximum saturation limit of the molar fraction of the H2O is 0.75 for H2O-[C4MIM][Cl] system by using molecular dynamics. Regarding H2O-[C4MIM][PF6] and H2O-[C2MIM][BF4] systems, when we obtained the optimized 1 value, we only observed in H2O-[C4MIM][PF6] system similar values of the U2,1 parameter. In a first attempt, we set 1 and U2,1 values and optimized U1,2 and k12 parameters in each isotherm to know the parameter variation as a function of temperature. However, we found that there existed a great deal of scatter among the adjusted U1,2 parameters. Notwithstanding this fact, we correlated the U1,2 and k12 parameters to a straight-line equation as a function of temperature To reduce the number of fitted parameters, after extensive testing of solubility calculations, we set constant the k12 parameter at the highest value (0.645). Figure 3 shows the behavior of the U1,2 parameter as a function of the temperature from H2O-[C4MIM][PF6] system at 283.15, 298.15 and 323.15 K. This figure shows that the U1,2 parameters become less positive, and even negative as the temperature increases. Therefore, we correlated them via following straight-line equation

ΔU 1,2  c T  d

(29)

where c and d are the constants of the correlation, and T is the temperature. The adjusted parameters of the modeling approach for the H2O-[C2MIM][BF4] system presented a similar behavior to the H2O[C4MIM][PF6] system. The main difference was that U1,2 values were comparable in each isotherm and

U2,1 values did not show any tendency. Thus, we followed the above mentioned approach for the fitting of the parameter. First, we fixed the value U1,2 parameter, and then the k12 parameter at the highest value (0.553). Finally, we adjusted the U2,1 parameter as a function of temperature. The corresponding results are shown in Figure 4, where it can be seen that all values are positive and they are less positive as temperature increases. This figure also showed that the values decrease in a scattered manner as temperature increases. Notwithstanding this fact, we correlated them according to the following straightline expression as a function of temperature

ΔU 2,1  e T  g

(30) ACS Paragon Plus Environment

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where e and g are the constants of the correlation, and T is the temperature. Table 4 presents the 1 ,

U1,2, U2,1, and k12 values for H2O-[C4MIM][PF6] and H2O-[C2MIM][BF4] systems. As seen in this table, the predictive capability of the present approach for calculating the H2O solubility in ILs is quite good.

Figure 5 shows the H2O solubility in [C4MIM][PF6] at 283.1, 298.15, and 323.15 K; whereas, Figure 6 presents the H2O solubility in [C2MIM][BF4] at 323.15, 328.15, and 333.15 K. These figures show that the pressure increases as the molar fraction of the H2O increases. Both figures present a satisfactory agreement between experimental and calculated solubilities, even at the dilution region, as demonstrated in Figure 5.

Figure 7 and Figure 8 depict the analysis of the entropic and enthalpic contributions with the UNIQUAC model for H2O-[C4MIM][PF6] and H2O-[C2MIM][BF4] systems, respectively. As shown in both figures, the behavior of the entropic contributions is the same at any temperature because neither the size or shape of the ILs are different. However, the behavior of the enthalpic contributions exhibits a variation as the molar fraction of the H2O is increased, as revealed in Figures 7 and 8. As can be seen in Figure 7, all enthalpic contributions are positive; it means that the behavior of these systems is endothermic. Also, it is shown that as temperature increases, the enthalpic contributions are less positive due to the stronger molecular interactions between H2O and [C4MIM][PF6]. These molecular interactions increase, in a linear manner, as the molar fraction of the H2O increases. The behavior of the enthalpic contributions is entirely different for the H2O-[C2MIM][BF4] system as shown in Figure 9. This figure presents that all enthalpic contributions are negative, and they decrease as the temperature increases at a 0.4 molar fraction of the H2O; that is the molecular interactions between H2O and [C2MIM][BF4] increase with an increase in the temperature. It is important to note that, as the molar fraction of the H2O increases at 0.5, the values of enthalpic contributions are similar; meaning that, the molecular interactions are equal regardless of the temperature. At molar fractions higher than 0.5, the enthalpic contributions become to increase with temperature. This variation indicates that the molecular interactions between H2O and [C2MIM][BF4] are less favorable at higher temperatures. The latter behavior also shows that the effect of the composition is stronger than temperature since the slope of the straight line in the range from 0.4 to 0.7 molar fraction of the H2O do not change regardless of temperature. In Figure 9, it is also shown the little effect in the enthalpic contributions at molar fractions of the H2O greater than 0.7. According to Cammarata et al.,52 ACS Paragon Plus Environment


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who studied the H2O-[C4MIM][PF6] and H2O-[C2MIM][BF4] systems with the ATR-IR spectroscopy, the increase of the H2O solubility in imidazolium-based ILs depends on the formation of the hydrogen bond between H2O and the anion of IL.

Figure 10 shows the entropic and enthalpic contributions for H2O-[C4MIM][PF6] and H2O-[C2MIM][BF4] systems at 323.15 K and H2O-[C2MIM][Cl] and H2O-[C4MIM][Cl] systems at 1 bar. As can be seen, the entropic contributions are positive for H2O-[C4MIM][PF6] and H2O-[C2MIM][BF4] systems. Regarding the enthalpic contributions, they are positive for the H2O-[C4MIM][PF6] system what indicates its hydrophobic character in the H2O solubility; whereas the enthalpic contributions are negative for H2O[C2MIM][BF4] system, leading to more favorable interactions between H2O and [C2MIM][BF4] molecules. It is important to highlight that the binary solutions do not present a comparable range of molar fractions of the H2O, cation or anion, although both anions are fluorinated. However, when the H2O-[C2MIM][BF4], and H2O-[C2MIM][Cl] systems are compared, Figure 10, it can be observed that the entropic contribution for H2O-[C2MIM][BF4] system is greater than for the H2O-[C2MIM][Cl] system. Figure 10 also shown that the entropic contribution for H2O-[C2MIM][BF4] system is greater than for the H2O-[C4MIM][Cl] system; even though the [C4MIM+] cation has a larger alkyl chain length. The enthalpic contributions are negative for the three systems, what indicates an exothermic behavior and favorable molecular interactions. It can also be observed in Figure 10 that the H2O solubility degree in the H2O-[C2MIM][Cl] is more significant than in the H2O-[C2MIM][BF4] system. According to Khan et al.,30 the increase in the size of the halogenated anions causes a lesser interaction with H2O. Furthermore, they showed that the fluorinated anions decrease the interaction force between H2O and the IL. As evidenced in Figure 10, the UNIQUAC model was able to capture the size and shape effects of the anion (via entropic contribution), as well as the force in the molecular interactions between the H2O and IL, regardless of the kind of anion. Jork et al.5 and Freire et al.49 pointed out that the size or shape of anion has a more considerable effect than the alkyl chain length of the imidazolium cation in the solubility of the above mentioned systems.

To obtain the fitted parameters of the modeling approach at constant composition for the H2O[C4MIM][BF4], H2O-[OHC2MIM][BF4], and H2O-[OHC2MIM][Cl] systems, we followed the above mentioned methodology. First, we optimized 1, U1,2, U2,1, and k12 parameters, and then we chose the

1 value at the lowest AAD, P %. Subsequently, we set constant the 1 value, and U1,2, U2,1, and k12 parameters were then again optimized. At this point, we observed that U1,2 showed similar values for the ACS Paragon Plus Environment

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H2O-[C4MIM][BF4] and H2O-[OHC2MIM][BF4] systems, so that it was set constant for both systems. After that, we adjusted U2,1 and k12, and we observed a great deal of scatter among them; regardless of it, we correlated U2,1 values to a straight line equation as a function of the molar fraction of the H2O, and then we fitted the k12 parameter. Finally, we chose the highest k12 value and set it constant to optimize

ΔU 2,1 parameter again. Figure 11 shows the fitted U2,1 values as a function of the molar fraction of the H2O for the H2O-[C4MIM][BF4] system. As can be seen, all values are positive, and they increase as the molar fraction of the H2O increases. It can be observed in Figure 11(a) that at a molar fraction of 0.582 there is not a linear trend of the U2,1 parameters. Figure 12 presents the U2,1 values as a function of the molar fraction of the H2O for H2O-[OHC2MIM][BF4] system. It can be observed in Figure 12(a) that all values are negative, and they became less negative as the molar fraction of the H2O increases, except at 0.8. It can be seen in Figures 11(a) and 12(a), that the H2O-[C4MIM][BF4] and H2O-[OHC2MIM][BF4] systems show a deviation of the linear equation at the highest molar fraction of the H2O. This behavior could be attributed to the solvation effect between the H2O and the [ BF4 ] anion which has been evidenced as the amount of water is increased.30 Since this modeling approach only takes into account the short-range interactions, we decide to exclude the obtained U2,1 values at the highest molar fraction of H2O. A similar procedure for the fitting of parameters was followed for the H2O-[OHC2MIM][Cl] system. The main difference is that we set constant the U2,1 parameter and adjusted the U1,2 as a function of the molar fraction of the H2O. Figure 13(a) shows the fitted U1,2 values as a function of the molar fraction of the H2O. It is observed that the U1,2 values increase linearly from negative to positive, when the molar fraction of the H2O is increased, except at 0.988. We suggested that the presence of the hydroxyl group in the cation and the high concentration of H2O, regardless of the size of the anion, produce such behavior. However, the proposed model was not able to describe this trend because it includes only the short-range interactions. Therefore, we fitted the U1,2 values to a linear equation without taking into account the last point, as shown in Figure 13(b). The following straight-line equation was used to correlate U1,2 and U2,1 parameters as a function of the composition:

ΔU 1,2  h x  l

(31)

ΔU 2,1  n x  o

(32)



Page 16 of 40

where h, l, n, and o are the correlation constants and x is the molar fraction of the H2O. The correlating results of the 1, U1,2, U2,1, and k12 parameters and the AAD, P% are listed in Table 5. It can be seen from this table that the ADD, the P% values are high for the H2O-[C4MIM][BF4] and H2O[OHC2MIM][BF4] systems: 11.65% and 8.64%, even though the U1,2 parameter was correlated as a function of the molar fraction of H2O. Figure 14 shows the experimental and calculated solubilities with the modeling approach for H2O-[C4MIM][BF4] system at molar fraction of the H2O 0.112, 0.280, 0.398, and 0.582, H2O-[OHC2MIM][BF4] at 0.2, 0.4, 0.6, and 0.8, and H2O-[OHC2MIM][Cl] at 0.693, 0.795, 0.900, 0.955 and 0.988. As can be seen in Figures 14(a) and 14(b), there exist a poor agreement between experimental and calculated solubilities at the highest isopleths. A possible explanation of these discrepancies is that the solvation interactions are not accounted for in the modeling approach. These solvation forces are present as the concentration of water increase, especially in systems with bulky anions, e.g., [ PF6 ] and [ BF4 ]. On the other hand, Figure 14(c) shows a good agreement between the experimental and calculated solubilities probably because the size of the halide ion such Cl  is lesser than the bulky anions. Figure 15 depicts entropic and enthalpic contributions for H2O-[C4MIM][BF4], H2O-[OHC2MIM][BF4], and [OHC2MIM][Cl] systems at 0.582, 0.6, and 0.693 molar fractions of the H2O, respectively. Although it is not valid to compare such systems because they present different composition, we only exhibited them to understand the behavior of their contributions as a function of the molar composition of the H2O. As can be seen in this figure, the entropic contributions are represented by a point because the molar fractions are constant. The entropic contributions for the binary systems with the anion [ BF4 ] are positive; whereas the solution with the Cl  anion is negative. On the other hand, the enthalpic contributions are described by solid lines. These contributions are negative for H2O-[OHC2MIM][BF4] and H2O-[OHC2MIM][Cl], which indicate that the molecular interactions between H2O and the IL are favorable. However, the enthalpic contributions are positive for H2O-[C4MIM][BF4]; this behavior exhibits that the molecular interactions are unfavorable between H2O and [C4MIM][BF4]. An examination of this figure also shows a poor variation in the values of the enthalpic contributions for all systems, especially in H2O-[OHC2MIM][Cl] system. Thus, the behavior of the entropic and enthalpic contributions are not well represented by the UNIQUAC model using experimental solubility data at constant composition.

CONCLUSIONS ACS Paragon Plus Environment

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A formal modeling approach was devised here to calculate and predict the H2O solubility in imidazoliumbased ILs. It made use of the Peng-Robinson cubic equation of state and the Wong-Sandler mixing rules at different conditions of temperature, pressure, and composition. The following conclusions can be drawn from this work: (1) The agreement between experimental and calculated solubility data was remarkably good when the anion of the ILs are small, such as halides. However, the model requires the use of temperature-dependent U values for improving H2O-solubility estimations when the ILs present bulky anions or hydroxyl groups in cations. (2) Results of the comparison showed a poor agreement between the experimental data and the calculated values when the IL exhibits (i) a bulky anion, and (ii) a hydroxyl group in the cation. (3) The UNIQUAC model was able to predict the behavior of the molecular interactions (enthalpic contribution) at constant temperature and pressure; as well as, the effect of the alkyl chain length in cation and the size of the anion (entropic contribution).

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS J. Martínez and M. A. Zúñiga-Hinojosa gratefully acknowledge the National Council for Science and Technology of Mexico (CONACyT) for providing financial support for this work. R. Macías Salinas is also grateful for the financial support provided by the Instituto Politécnico National during the realization of this work.

LIST OF SYMBOLS a = Attractive parameter in the CEoS A = Helmholtz free energy b = Co-volume parameter in the CEoS B = As defined in eq 11 ACS Paragon Plus Environment


c = As defined in eq 29 C = CEoS-specific constant d = As defined in eq 29 D = As defined in eq 19 e = As defined in eq 30 f = Objective function g = As defined in eq 30 G = Gibbs free energy h = As defined in eq 31 k = Interaction parameter in the CEoS l = As defined in eq 31 n = As defined in eq 32

  Number of data points o = As defined in eq 32 P = Pressure q = Surface area parameter in UNIQUAC

q' = Prime surface area parameter in UNIQUAC Q = As defined in eq 18 r = Volume parameter in UNIQUAC R = Universal gas constant T = Temperature v = Molar volume x = Number of alkyl groups x = Liquid mole fraction y = Gas mole fraction z = Coordination number Subscripts c = Critical property EoE = Equation of state i,j = i-j Pair interaction m = Mixture property ACS Paragon Plus Environment

Page 18 of 40

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r = Reduced property 1 = H2O 2 = Ionic liquid Greek Letters

 

Temperature-dependent correlation of the parameter 



Fitted parameters to PTx experimental solubility data



ΔU = Energy interaction parameter in UNIQUAC  

Activity coefficient

 

Segment fraction

 0 ,1  Parameter suggested by Stryjek and Vera (1986)  

Area fraction

' =

Prime area fraction

 =

Dimensionless energy parameter in UNIQUAC

 

Acentric factor

Superscripts calc = Calculated value combinatorial = Combinatorial contribution E =

Excess property

exp = Experimental value residual =

Residual property

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Mixtures: A Review. Fluid Phase Equilib. 2004, 219, 93. (2) Quijada-Maldonado, E.; Meindersma, G. W.; de Haan, A. B. Ionic Liquid Effects on Mass Transfer Efficiency in Extractive Distillation of Water-Ethanol Mixtures. Compt. Chem. Eng. 2014, 71, 210. (3) Calvar N.; González, B.; Gómez, E.; Domínguez, A. Vapor-Liquid Equilibria for the Ternary System Ethanol+Water+1-Butyl-3-methylimidazolium Chloride and the Corresponding Binary Systems at 101.3 kPa. J. Chem. Eng. Data 2006, 51, 2178. ACS Paragon Plus Environment


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Table 1. Properties of pure components. Component Tc [K]

Page 24 of 40

Pc [bar]

r

q

q’

H2O

647.286a

220.8975a

0.920b

1.400b

1.000b

[C2MIM]Cl

748.6

34.17

12.089

10.488

7.489

[C4MIM]Cl

789.0

27.85

13.438

11.568

8.256

[C6MIM]Cl

829.2

23.50

14.787

12.648

9.031

[C4MIM][PF6]

719.4

17.28

17.405

11.006

7.858

[C2MIM][BF4]

596.2

23.59

13.808

8.550

6.105

[C4MIM][BF4]

643.2

20.38

15.157

9.630

6.876

[OHC2MIM][BF4]

691.7

24.67

14.582

9.442

6.742

[OHC2MIM]Cl a Poling et al.36 b Prausnitz et al.37

832.1

36.21

12.862

11.380

8.126


Page 25 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 2. Experimental H2O solubilities in different ionic liquids. Ionic liquids [C2MIM]Cl

[C4MIM]Cl

[C6MIM]Cl

[C4MIM][PF6]

[C2MIM][BF4]

T [K] 355.58-409.3, 364.02-421.93, 373.66-435.03 354.92-405.02, 363.49-414.97, 372.66-429.69 354.64-383.26, 363.46-393.61, 373.13-405.3 373.3-415.51 283.1, 298.15, 323.15 323.15, 328.15, 333.15

373.15 [C4MIM][BF4] 308.17443.65,298.16433.68, 285.13433.92, 284.95433.28 [OHC2MIM][BF4] 392.6-464.8, 403.0-427.4, 361.6-402.2, 325.8-383.8 [OHC2MIM]Cl 318.57-398.32, 314.82-391.60, 300.73-380.1, 301.40-375.60, 301.87-373.56

P [bar] 0.5, 0.7, 1.0

x-H2O maximum 0.998

Source Carvalho et al.16

0.5, 0.7, 1.0

0.988

Carvalho et al.16

0.5, 0.7, 1.0, 1.01

0.998

Carvalho et al.16, Calvar et al.41

0.002-0.010, 0.002-0.020, 0.005-0.050 0.057-0.097, 0.073-0.124, 0.094-0.159 0.025-0.756 0.008-0.520, 0.013-1.228, 0.009-2.001, 0.011-3.192

0.151

Anthony et al.42

0.8

Han et al.43

0.778 0.582

Jork et al.5 Guan et al.44

0.122-0.879, 0.483-1.008, 0.267-1.0, 0.0920.988 0.033-0.805, 0.041-1.023, 0.028-1.011, 0.036-1.008, 0.039-1.008

0.8

Kim et al.45

0.988

Nie et al.46



Page 26 of 40

Table 3. Adjusted parameters with the PR-WS model for H2O-[CxMIM][Cl] (x=2,4,6) systems. Ionic liquid

[C2MIM]Cl

[C4MIM]Cl

[C6MIM]Cl

 

93 10.27 -1512.82 1209.13 0.663 0.14

81 0.78 -842.77 -422.43 0.876 0.22

123 10.07 -612.67 115.16 0.810 0.18

U12 [cal/mol] U21 [cal/mol] k1,2 AAD, T%

Total 297

N = Number of experimental points. Table 4. Fitted model parameters for H2O-[C4MIM][PF6] and H2O-[C2MIM][BF4] systems. Ionic liquid

Coefficients

  c d e g

U12 [cal/mol

[C4MIM][PF6]

[C2MIM][BF4]

33 4.26 -5.10 1571.38

27 13.79

1439.82

-793.89 -5.43 3618.87

k12

0.645

0.554

AAD, P %

2.50

3.90

U21 [cal/mol]

Total 60

N = Number of experimental points.

Table 5. Fitted model parameters for H2O-[C4MIM][BF4], H2O-[OHC2MIM][BF4], and H2O[OHC2MIM][Cl] systems. Ionic liquid

Coefficients

 

[C4MIM][BF4]

[OHC2MIM][BF4]

[OHC2MIM][Cl]

45

35

48

11.95

13.71

2.75

U12 [cal/mol]

h l

108.48

-757.65

U21

n

1952.74

265.16

[cal/mol]

o

432.67

-327.66

-48.05

-0.517

0.748

0.591

8.64

1.93

k12

2171.10

AAD, P % 11.65 N = Number of experimental points.


-1778.30

Total 128

Page 27 of 40

440

440

0.5 bar Carvalho et al., 2013 0.7 bar Carvalho et al., 2013 1.0 bar Carvalho et al., 2013 PR-WS model

430 420

420 Temperature, K

400 390

(a)

380

0.5 bar Carvalho et al., 2013 0.7 bar Carvalho et al., 2013 1.0 bar Carvalho et al., 2013 PR-WS model

430

410

410 400 390

(b)

380

370

370

360

360 350

350 0.5

0.6

0.7 0.8 Molar Fraction H2O

0.9

420

1

0.5

0.6


0.5 bar Carvalho et al., 2013 0.7 bar Carvalho et al., 2013 1.0 bar Carvalho et al., 2013 1.01 bar Calvar et al., 2007 PR-WS model

410 400 Temperature, K

Temperature, K

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47


390 380 370 360

(c)

350 340 330 0.5

0.6

0.7 0.8 Molar Fractions H2O

Figure 1 (Martínez et al.)


0.9

1

0.9

1


0.2 0 0.4

0.5

0.6

0.7

0.8

0.9

1

-0.2

GE/RT

-0.4 -0.6

H2O-[C2MIM][Cl] Entropic H2O-[C4MIM][Cl] Enthalpic H2O-[C4MIM][Cl] Entropic H2O-[C4MIM][Cl] Enthalpic H2O-[C6MIM][Cl] Entropic H2O-[C6MIM][Cl] Enthalpic

-0.8 -1 -1.2 -1.4

Molar Fraction H2O


150

100 Adjusted ΔU12 parameter

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 40

50

0 280

290

300

310

-50

-100 Temperature, K



320

330

Page 29 of 40

1840 1820

Adjusted ΔU21 parameter

1800 1780 1760 1740 1720 1700 1680 1660 1640 1620 322

324

326

328 Temperature, K

330

332

334


0.045 283.1 K Anthony et al., 2005 298.15 K Anthony et al., 2005 323.15 K Anthony et al., 2005 PR-WS Model

0.04 0.035 0.03 Pressure, bar

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.025 0.02 0.015 0.01 0.005 0 0

0.02

0.04

0.06 0.08 0.1 Molar Fraction H2O



0.12

0.14


0.2 323.15 K Han et al., 2016

0.18

328.15 K Han et al., 2016 333.15 K Han et al., 2016

0.16 Pressure, bar

PR-WS Model 0.14 0.12 0.1 0.08 0.06 0.04 0.4

0.5


0.8

0.9


0.4 0.35 0.3 GE/RT

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 40

0.25

283.15 K Entropic 283.15 K Enthalpic

0.2

298.15 K Entropic 298.15 K Enthalpic

0.15

323.15 K Entropic 0.1

323.15 K Enthalpic

0.05 0 0

0.05

0.1 Molar Fraction H2O



0.15

0.2

Page 31 of 40

0.5 0.4 0.3

323.15 K Entropic

GE/RT

328.15 K Entropic 0.2

333.15 K Entropic 323.15 K Enthalpic 328.15 K Enthalpic

0.1

333.15 K Enthalpic 0 0.4

0.5

0.6

0.7

0.8

0.9

0.8

0.9

-0.1 -0.2 Molar Fraction H2O


0 0.4

0.5

0.6

0.7

-0.02 323.15 K Enthalpic

-0.04

328.15 K Enthalpic

-0.06 GE/RT

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


333.15 K Enthalpic

-0.08 -0.1 -0.12 -0.14 -0.16 -0.18 Molar Fraction H2O




0.6 0.4 0.2 0 0

0.2

0.4

0.6

-0.2 GE/RT

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 40

-0.4 -0.6 -0.8 -1

H2O-[C4MIM][PF6] H2O-[C4MIM][PF6] H2O-[C2MIM][BF4] H2O-[C2MIM][BF4] H2O-[C2MIM][Cl] H2O-[C2MIM][Cl] H2O-[C4MIM][Cl] H2O-[C4MIM][Cl]

Entropic Enthalpic Entropic Enthalpic Entropic Enthalpic Entropic Enthalpic




0.8

1

4500

1300

4000

1200

3500


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47



Page 33 of 40

3000 2500 2000 1500

(a)

1000

1100 1000 900

(b)

800 700

500 0 0

0.2

0.4 Molar fraction H2O

0.6

0.8

600 0



0.1


0.4

0.5


-150 0

0.2

0.4

0.6

0.8

1

-160 0

-250

-300

-350

0.2

0.4

-180 Adjusted ΔU21 parameter

-200 Adjusted ΔU21 parameter

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

Page 34 of 40

(a)

-200 -220 -240 -260

(b)

-280 -400

Molar Fraction H2O

-300



Molar Fraction H2O

0.6

0.8


400

400

200

300

0 -200

0.6

0.7

0.8

-400 -600 -800 -1000

(a)

1

200 100 0 0.6

0.7

0.8

Fraction Molar H2O

0.9

1

-100

(b)

-200 -300

-1200 -1400

0.9


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47


Page 35 of 40

-400



Fraction Molar H2O


1.4

x= 0.112 Guan et al., 2011 x= 0.28 Guan et al., 2011 x= 0.398 Guan et al., 2011 x= 0.582 Guan et al., 2011 PR-WS Model

2

x=0.2 Kim et al., 2004 x=0.4 Kim et al., 2004 x=0.6 Kim et al., 2004 x=0.8 Kim et al., 2004 PR-WS Model

1.2 1 Pressure, bar

1.5

1

(a)

0.8 0.6

(b)

0.4

0.5

0.2 0

0 300

320

340

360 380 400 Temperature, K

420

440

300

350

400 Temperature, K

1.20 x=0.6929 Nie et al., 2012 x= 0.7946 Nie et al., 2012 x= 0.9003 Nie et al., 2012 x= 0.9547 Nie et al., 2012 x= 0.9878 Nie et al., 2012 PR-WS Model

1.00

Pressure, bar

Pressure, bar

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

Page 36 of 40

0.80 0.60

(c)

0.40 0.20 0.00 300

320

340 360 Temperature, K



380

400

450

500

Page 37 of 40

0.6

GE/RT

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0

-0.6

0.4

0.5 x= 0.582 H2O-[C4MIM][BF4] x= 0.582 H2O-[C4MIM][BF4] x= 0.6 H2O-[OHC2MIM][BF4] x= 0.6 H2O-[OHC2MIM][BF4] x= 0.6929 H2O-[OHC2MIM][Cl] x= 0.6929 H2O-OHC2MIM][Cl]

0.6 Entropic Enthalpic Entropic Enthalpic Entropic Enthalpic

-1.2 Molar Fraction H2O



0.7


Page 38 of 40

FIGURE CAPTIONS Figure 1. Solubility of the systems with the PR-WS model: (a) H2O-[C2MIM][Cl], (b) H2O[C4MIM][Cl] at 0.5, 0.7, and 1.0 bar, and (c) H2O-[C6MIM][Cl] at 0.5, 0.7, 1.0 y 1.01 bar. Experimental (symbols), calculated (solid lines). Figure 2. Analysis of the entropic and enthalpic contributions for H2O-[CxMIM][Cl] (x=2,4,6) systems using the UNIQUAC model at 1 bar. Figure 3. Fitted U2,1 parameter as a function of temperature for H2O-[C4MIM][PF6] system. Figure 4. Fitted U2,1 parameter as a function of temperature for H2O-[C2MIM][BF4] system. Figure 5. The solubility of the H2O-[C4MIM][PF6] system at 283.1, 298.15, and 323.15 K with the PR-WS model. Experimental (symbols), calculated (solid lines). Figure 6. The solubility of the H2O-[C2MIM][BF4] system at 323.15, 328.15, and 333.15 K with the PR-WS model. Experimental (symbols), calculated (solid lines). Figure 7. Analysis of the entropic and enthalpic contributions for H2O-[C4MIM][PF6] system at 283.15, 298.15, and 323.15, K using the UNIQUAC model. Entropic contribution (dotted lines), enthalpic contribution (solid lines). Figure 8. Analysis of the entropic and enthalpic contributions for H2O-[C2MIM][BF4] system at 323.15, 328.15, and 333.15 K using the UNIQUAC model. Entropic contributions (dotted lines), enthalpic contributions (solid lines). Figure 9. Analysis of the enthalpic contribution for H2O-[C2MIM][BF4] system at 323.15, 328.15, and 333.15 K using the UNIQUAC model. Figure 10. Analysis of the entropic and enthalpic contributions for H2O-[C4MIM][PF6] and H2O[C2MIM][BF4] systems at 323.15 K and H2O-[C2MIM][Cl] and H2O-[C4MIM][Cl] systems at 1 bar, using the UNIQUAC model. Entropic contributions (dotted lines), enthalpic contributions (solid lines). Figure 11 (a) Fitted U2,1 parameter for the H2O-[C4MIM][BF4] system at 0.112, 0.280, 0.398, and 0.582 molar fraction of the H2O, and (b) fitted U2,1 parameter at 0.112, 0.280, and 0.398 molar fraction of the H2O for the H2O-[C4MIM][BF4] system. Figure 12 (a) Fitted U2,1 parameter for H2O-[OHC2MIM][BF4] system at 0.2, 0.4, 0.6, and 0.8 molar fraction of the H2O, and (b) fitted U2,1 parameter for H2O-[OHC2MIM][BF4] system at 0.2, 0.4, and 0.6 molar fraction of the H2O. Figure 13 (a) Fitted U1,2 parameter for the H2O-[OHC2MIM][Cl] system at 0.693, 0.795, 0.9, 0.955 and 0.988 molar fraction of the H2O, and (b) fitted U1,2 parameter at 0.693, 0.795, 0.9, and 0.955 molar fraction of the H2O for the H2O-[OHC2MIM][Cl]. Figure 14 Solubility of the systems with the PR-WS model: (a) H2O-[C4MIM][BF4] at 0.112, 0.280, 0.398 , and 0.582 molar fraction of the H2O, (b) H2O-[OHC2MIM][BF4] at 0.2, 0.4, 0.6 y 0.8 molar


Page 39 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


fraction of the H2O, and (c) H2O-[OHC2MIM][Cl] at 0.693, 0.795, 0.9, 0.955, and 0.988 molar fraction of the H2O. Experimental (symbols), calculated (solid lines). Figure 15 Analysis of the entropic and enthalpic contributions using the UNIQUAC model for H2O[C4MIM][BF4], H2O-[OHC2MIM][BF4], and [OHC2MIM][Cl] systems at 0.582, 0.6, and 0.693 molar fraction of the H2O, respectively. Entropic contribution (symbols), enthalpic contributions (solid lines).



GRAPHICAL ABSTRACT 0.6 0.4 0.2 0 0

0.2

0.4

0.6

0.8

1

-0.2 GE/RT

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 40 of 40

-0.4 -0.6 -0.8 -1

H2O-[C4MIM][PF6] H2O-[C4MIM][PF6] H2O-[C2MIM][BF4] H2O-[C2MIM][BF4] H2O-[C2MIM][Cl] H2O-[C2MIM][Cl] H2O-[C4MIM][Cl] H2O-[C4MIM][Cl]

Entropic Enthalpic Entropic Enthalpic Entropic Enthalpic Entropic Enthalpic


Analysis of the entropic and enthalpic contributions using the UNIQUAC model for H2O-IL systems. Entropic contributions (dotted lines), enthalpic contributions (solid lines).


Modeling the Water Solubility in Imidazolium-Based Ionic Liquids

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