Effect of 1-carboxymethyl-3-methylimidazolium

Fluid Phase Equilibria 379 (2014) 86–95

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Effect of 1-carboxymethyl-3-methylimidazolium chloride ionic liquid on thermodynamic and solubility of l-threonine in water at 298.15 K and atmospheric pressure Mohammed Taghi Zafarani-Moattar ∗ , Behnaz Asadzadeh Physical Chemistry Department, University of Tabriz, Tabriz, Iran

a r t i c l e

i n f o

Article history: Received 21 January 2014 Received in revised form 30 June 2014 Accepted 1 July 2014 Available online 23 July 2014 Keywords: l-Threonine Ionic liquid Water activity Solubility Transfer Gibbs free energies

a b s t r a c t Vapor–liquid equilibrium data (water activity, vapor pressure and osmotic coefficient) of the mixed aqueous solutions, l-threonine + 1-carboxymethyl-3-methylimidazolium chloride and the corresponding binary aqueous amino acid solutions have been measured by the isopiestic method at temperature 298.15 K and atmospheric pressure. The experimental data for the activity of water were accurately correlated with segment-based local composition models of the Wilson, NRTL, modified NRTL and NRF-NRTL. From these data, the corresponding activity coefficients have been calculated. For the same system, the solubility of the l-threonine at various ionic liquid (IL) concentrations was measured at 298.15 K using gravimetric method. Also the above local composition models were used to describe the solubility of amino acid in pure water and in aqueous IL solutions. To provide information regarding solute–solute interactions, transfer Gibbs free energies (Gtr ) of amino acid from water to aqueous IL solutions have been determined from the solubility measurements and activity coefficient of amino acid in water and [Cmmim][Cl] + water solutions calculated from different models, as a function of IL concentration at 298.15 K. © 2014 Elsevier B.V. All rights reserved.

1. Introduction The biological and industrial importance of amino acids is well known as well as the knowledge of their physical and chemical properties. Amino acids are the basic building blocks of proteins and peptides, and the development of more accurate and efficient processes for their separation, concentration and purification of those has been a subject of main interest, particularly for pharmaceutical and food industries [1]. On the other hand, the reverse micellar extraction of proteins or amino acids with an electrolyte or an organic solvent has been recently considered of great interest. The importance of studying the behavior of biomolecules in aqueous systems containing electrolytes will be evident when the high cost of their separation and purification processes is considered [2,3]. To design these processes, the fundamental physical properties of biomolecules, such as solubility and activity coefficient, must be obtained [4]. The effects of co-solvents on the solubility and conformational stability of proteins have been of intense interest for decades. Obviously, the stability of biomolecules under co-solvent

∗ Corresponding author. Tel.: +98 411 3393135; fax: +98 411 3340191. E-mail address: [email protected] (M.T. Zafarani-Moattar). http://dx.doi.org/10.1016/j.fluid.2014.07.001 0378-3812/© 2014 Elsevier B.V. All rights reserved.

conditions is dependent on the nature of the co-solvent; which can alter a protein’s properties and structural effects through biomolecular interactions between its functional groups and the co-solvent particles [5]. Ionic liquids (ILs) are a new class of organic salts and as green solvents have significant effect in many biochemical and chemical processes. The introduction of structural functionalities on the cationic or anionic part has made it possible to design new ILs with targeted properties. A new kind of ionic liquid has been developed recently, and these are called “task specific” ionic liquids. In task specific ionic liquids the alkyl group is functionalized [6]. We guess that the functionalized IL, which is studied in the present work, by virtue of its functional group, promotes remarkable changes in the solubility of the studied amino acid due to new interactions may arise between IL and amino acid. The solubility behavior of biomolecules in aqueous electrolyte solutions assumes a very important role in the life sciences and biotechnological developments [7]. The successful representation of the solubility is directly related to the ability to correlate and predict the activity coefficients of amino acids in solution. One of the important tools to investigate the interactions between ionic salts and amino acids is thermodynamic transfer properties such as free energy, entropy and enthalpy, of amino acids in aqueous IL solutions. These results lead to the conclusion that some of the electrolytes can

M.T. Zafarani-Moattar, B. Asadzadeh / Fluid Phase Equilibria 379 (2014) 86–95

Nomenclature Ax a A a, b, c B C D Dev E f G e G g H h Ix k Ks m M NA NP OF P R S T V x X Z

Pitzer–Debye–Hückel constant activity or binary parameter in the NRTL, mNRTL, NRF-NRTL model amino acid coefficients of Eq. (14) second virial coefficient coordination number dielectric constant relative percentage deviation binary parameter in the Wilson model fugacity of the amino acid transfer Gibbs free energy of the amino acid electronic charge binary parameter in the NRTL, mNRTL, NRF-NRTL model Gibbs energy of interaction or Gibbs energy binary parameter in the Wilson model enthalpy of interaction ionic strength on the mole fraction scale Boltzmann constant equilibrium constant molality molar mass Avogadro’s number number of experimental data objective function vapor pressure gas constant solubility of amino acid temperature molar volume mole fraction effective mole fraction charge number

Greek letters ˛ nonrandomness factor ε permitivity of vacuum stoichiometric parameter closest approach parameter activity coefficient binary parameter in the NRTL, mNRTL, NRF-NRTL model osmotic coefficient chemical potential Superscripts binary system bin cal calculated value excess ex exp experimental value long-range LR m molality base PDH Pitzer’s extension of Debye–Hückel function SR short-range ternary system ter x mole fraction base * unsymmetric convention zwitterion ± ◦ pure solvent apparent transfer properties

87

Subscripts a and c anion and cation ca electrolyte (ionic liquid) i, j, k any species, amino acid, ions and water m amino acid non-random two liquid NRTL mNRTL modified NRTL model NRF non-random factor model transfer tr w water Wilson Wilson model

Table 1 A brief summary of the purity of the used materials. Materiala

Mass fraction purity

NaCl l-threonine N-methylimidazole Choloroacetic acid Acetonitrile Methanol

(GR, min99.5%)>0.99 >0.99 >0.99 >0.99 >0.99

a

All materials were supplied from Merck.

stabilize biological important molecules such as proteins. From the Gibbs free energy of transfer (Gtr ) studies obtained from solubility of amino acid we can elucidate the effect of ionic liquid on protein stability [8]. For calculating Gtr values the vapor–liquid equilibrium (VLE) and solubility of amino acids data are required. Only a few measurements, however, have been performed on VLE and solubility of amino acids in ILs [5,9,10]. In calculation of Gtr values a suitable correlation equations for the measured properties are also necessary. An overview of thermodynamic equations which can be used for correlating VLE and solubility of an amino acid in aqueous ionic liquid solution was given in a previous publication [9]. In continuation of our previous work, in this work the vapor–liquid equilibria of ternary system {l-threonine + 1carboxymethyl-3-methylimidazolium chloride [Cmmim][Cl] + H2 O} and the corresponding binary aqueous l-threonine system have been measured using the improved isopiestic method at T = 298.15 K. Another objective of this study is the presentation of new experimental data for the solubility of l-threonine in aqueous [Cmmim][Cl] solutions at 298.15 K using the gravimetric method. These data permit us to investigate the role of studied IL, [Cmmim][Cl], on the solubility of l-threonine. The obtained experimental data for the water activity and solubility in this work were correlated with the segment-based local composition models such as Wilson [11], NRTL [12], modified NRTL (mNRTL) [13] and NRF-NRTL [14] models. To obtain more thermodynamic information about these kinds of systems, we also calculated the transfer Gibbs free energies (Gtr ) of l-threonine from water to various concentrations of ionic liquid [Cmmim][Cl]. 2. Experimental setup 2.1. Materials Sodium chloride (solute for the isopiestic reference standard solution) was dried in the electrical oven about 383.15 K for 24 h prior to use. l-Threonine was used without further purification. The reagents used for the synthesis of [Cmmim][Cl] were N-methylimidazole, choloroacetic acid, acetonitrile and methanol purchased from Merck. The purity of the used materials is shown in

88


Table 2 Characterization of synthesized ionic liquid.

correlation given by Colin et al. [19] was used. In the measurement of water activity the uncertainty was estimated to be ±0.0005. N

OH

N

Structure:

O

Cl Name:

Molecular weight Purity: Purification method:

Method for measuring purity: 13 C NMR (100 MHz, DMSO-d6 ): 1

H NMR (400 MHz, DMSO-d6 ): ı (ppm):

FT-IR (cm−1 ):

1-Carboxymethyl-3methylimidazolium chloride 176.60 >98% After the IL was obtained washing with 3 cm3 × 20 cm3 of cold acetonitrile, and two times recrystallized from methanol and dried under vacuum for 4 h at 50 ◦ C to afford the neat IL. Argentometry titration 168.0, 137.6, 123.7, 123.1, 49.7, 35.9 3.91 (s, 3H), 5.21 (s, 2H), 7.75 (s, 1H), 7.78(s, 1H), 9.28 (s, 1H), 13.77 (s, 1H) 3163, 2580, 2490, 1735, 1573, 1169, 774, 681, 639

Table 1. All chemicals were used without further purification. The double distilled water was used.

2.3.2. Solubility measurement In this study, the gravimetric method applied without any modification that described in our previous work [9] to measure the solubility of l-threonine in the presence of [Cmmim][Cl]. The compositions of the initial solutions were accurate within ±0.1 mg. The bath was controlled to keep a constant temperature with an accuracy of ±0.01 K. The experiments were performed by preparing solutions with different molalities of IL and adding the amino acid in excess amount to that required for saturation. To reach equilibrium conditions the solution is continuously stirred for 48 h. The temperature of the solution was first maintained for 3 h at 303.15 K and then it was lowered to 298.15 K. After 48 h stirring was discontinued and the solution is allowed to settle for at least 7 h before sampling. Samples were taken of the supernatant liquid phase using a syringe with a filter of 0.22-␮m pore size. The next step is to evaporate all water in the sample, and to dry completely the crystals in a drying stove at 343.15 K for 3 days. After the evaporation, the glass vessels with the samples were weighed. The molality of the saturated amino acid dissolved was calculated from the knowledge of the initial concentration of the IL and the weight of the glass vessels empty, with the saturated solution, and with the dried sample. All experiments were replicated at least three times and the data reported are the average of the all replicates. In the measurement of solubility the uncertainty was estimated to be ±0.5 g of l-threonine per kg of water.

2.2. Synthesis of ionic liquid 2.4. Experimental results 1-Carboxymethyl-3-methylimidazolium chloride was synthesized according to a modified procedure [15–17]. More details of synthesize method and characterization of used IL have been given in our previous work [9]. The prepared ionic liquid has a purity of greater than 0.98 in mass fraction; and characterization of synthesized IL, which is studied in the present work, is summarized in Table 2. 2.3. Apparatus and procedure 2.3.1. Vapor–liquid equilibrium measurements To obtain water activity and osmotic coefficient data of studied systems at T = 298.15 K, the isopiestic method was used. The isopiestic apparatus used for determination of water activity of ternary {l-threonine + [Cmmim][Cl] + water} system was similar to the one used by Ochs et al. [18]. This apparatus has been previously used for determination of water activity of {l-serine + [Cmmim][Cl]+ water} system [9]. This apparatus consisted of seven-leg manifold attached to round-bottom flasks. Two flasks contained the standard pure NaCl solutions; one flask contained the pure IL solution, one flask contained the pure amino acid solution, two flasks contained (amino acid + IL) solutions and the central flask was used as a water reservoir. The isopiestic apparatus was immersed in a constant-temperature bath at least 120 h for equilibrium using a temperature controller (Julabo, MB, Germany) with an uncertainty of ±0.01 K. After equilibrium the apparatus was removed from the bath. Then the manifold was slowly evacuated to remove the air and to degas the solutions. It was necessary to evacuate the manifold several times because the dissolved air was slowly released from the solutions. The mass of each flask was calculated using an analytical balance (Shimadzu, 321-34553, Shimadzu Co., Japan) with an uncertainty of ±1 × 10−7 kg. When the difference between the mass fractions of two NaCl solutions was less than 0.1% we assumed that equilibrium was reached. Averages of the duplicate are considered as the isopiestic mass fractions. For the calculation of water activity of standard aqueous NaCl solutions at different concentrations the

2.4.1. Vapor–liquid equilibrium results In this work, the isopiestic measurements at T = 298.15 K were carried out for {l-threonine + [Cmmim][Cl] + H2 O} solutions and the corresponding binary aqueous l-threonine system to study the vapour–liquid equilibria behavior of these systems. For the understanding of interactions in liquids, the activity or osmotic coefficients of the different components are of great interest. They are the most relevant thermodynamics reference data, and they are often the starting point of any modeling [20,21]. At isopiestic equilibrium, the activity of the solvent in the reference and sample solutions must be the same. Therefore, the isopiestic equilibrium molalities with reference standard solutions of NaCl in water enabled the calculation of the osmotic coefficient, , of the solutions in water from [22]: =

R R mR m

(1)

where mR , R and R are the molality (mol kg−1 ), osmotic coefficient and the sums of the stoichiometric numbers of anions and cations in the reference solution, respectively. Similarly, m, and are, respectively, the molality, osmotic coefficient and the sums of the stoichiometric numbers of anions and cations in the solutions. The necessary R values at any mR were calculated from the correlation given by Colin et al. [19]. From the calculated osmotic coefficient data, the activity of water and the vapor pressure of these solutions, p, were determined at isopiestic equilibrium molalities, with the help of the following relations [22]: =−

ln aw mMw

ln aw = ln

(2) p

p0w

+

0 B − Vw

RT

p − p0w

(3)

where aw is the activity of water, Mw is the molar mass of the 0 is water, and B is the second virial coefficient of water vapor. Vw


0.35

Table 3 Isopiestic equilibrium molalities (m), osmotic coefficients (), water activities (aw ), and vapor pressures (p) of l-threonine in water at T = 298.15 K and atmospheric pressure.a −1

mL-threonine (mol kg

)

0.2224 0.3881 0.4181 0.4983 0.5178 0.5626 0.5936

−1

mNaCl (mol kg

)

0.1442 0.2224 0.2401 0.2732 0.2871 0.3101 0.3296

aw

p (kPa)

1.076 0.990 0.999 0.951 0.969 0.972 0.978

0.9957 0.9931 0.9925 0.9915 0.9910 0.9902 0.9896

3.161 3.153 3.151 3.148 3.146 3.144 3.142

0.3 0.25 0.2

mIL

Table 4 Water activity (aw ), and vapor pressure (p) for the {l-threonine (3) + [Cmmim][Cl](IL) (2) + H2 O (1)} system at T = 298.15 K and atmospheric pressure.a mIL (mol kg−1 )

mL-threonine (mol kg−1 )

mNaCl (mol kg−1 )

0.1234 0.1008 0.0788 0.0000

0.0000 0.0377 0.0818 0.2224

0.1442

0.1994 0.1685 0.1460 0.0000

0.0000 0.0745 0.1305 0.3881

0.2159 0.1859 0.1624 0.0000

0.0000 0.0822 0.1414 0.4181

0.2478 0.2125 0.1827 0.0000

0.0000 0.0939 0.1590 0.4983

0.2583 0.2363 0.1875 0.0000

0.0000 0.0552 0.1805 0.5178

0.2845 0.2542 0.2019 0.0000

0.0000 0.0679 0.1678 0.5626

0.3023 0.2715 0.2179 0.0000

0.0000 0.1015 0.1869 0.5936

aw

p (kPa)

0.969 1.000 0.999 1.076

0.9957

3.161

0.2224

0.964 0.934 0.910 0.990

0.9931

3.153

0.2401

0.968 0.920 0.896 0.999

0.9925

3.151

0.2732

0.956 0.913 0.904 0.951

0.9915

0.2871

0.971 0.951 0.903 0.969

0.9910

0.3101

0.961 0.949 0.956 0.972

0.9802

0.3296

0.960 0.900 0.932 0.902

0.15 0.1

a mNaCl : molality of isopiestic reference; standard uncertainties for molality, temperature, osmotic coefficient and vapor pressure are (m) = ±0.0001 mol kg−1 ;

(T) = ±0.01 K; () = ±0.007; (aw ) = ±0.0005; (p) = ±0.001 kPa, respectively.

the molar volume. p and p0w are the vapor pressure of solutions and the pure water, respectively. The second virial coefficient of water was calculated using the equation provided by Rard and Platford [23]. Molar volumes of liquid water were calculated using density of water at different temperatures [24]. The vapor pressures of pure water were calculated using the equation of state of Saul and Wagner [25]. After the establishment of isopiestic equilibrium, water activities were calculated using Eq. (2). The values of p for studied systems were calculated using Eq. (3). The results are collected in Table 3. Table 4 reports the water activities and vapor pressures of the ternary {l-threonine + [Cmmim][Cl] + H2 O} system at T = 298.15 K. The lines of constant water activity or vapor pressure of {l-threonine + [Cmmim][Cl] + H2 O} system at T = 298.15 K are plotted in Fig. 1. As can be seen in Table 4, in fact four points on each

89

0.05 0 0

0.2

0.4

0.6

0.8

mL-threonine Fig. 1. Constant water activity of the {l-threonine (3) + [Cmmim][Cl](IL) (2) + H2 O (1)} system at T = 298.15 K: , 0.9957; ♦, 0.9931; , 0.9925; , 0.9915; •, 0.9910; , 0.9902; ×, 0.9896; —, mNRTL model (Eq. (7)).

line in Fig. 1 has a constant water activity or chemical potential, and thus these points are in equilibrium. In Fig. 2, comparison of the experimental water activity data for the ([Cmmim][Cl] + H2 O) system measured in this work with those obtained previously [9] have been made at T = 298.15 K. Fig. 2 shows that there is a good agreement between two series of data. 2.4.2. Solubility results The values of the solubility of l-threonine in aqueous [Cmmim][Cl] solutions at various IL concentrations at T = 298.15 K are presented in Table 5. In this table, the value for the solubility of l-threonine in pure water measured in this work is also compared with those obtained previously [26–30]. As shown in this table, the measured value for the solubility of l-threonine in this work is in good agreement with the literature values, especially with Ref. [27]. 2.5. Thermodynamic framework For the correlation of VLE data of (amino acid–salt–water) systems, several models have been developed. However, in this work, 1.01 1 0.99 0.98

3.148

0.97

aw 3.146

0.96 0.95 0.94 0.93

3.144

0.92 0.91 0.9 0

0.9896

3.142

a mNaCl : molality of isopiestic reference; standard uncertainties for molality, temperature, osmotic coefficient and vapor pressure are (m) = ±0.0001 mol kg−1 ;

(T) = ±0.01 K; () = ±0.007; (aw ) = ±0.0005; (p) = ±0.001 kPa, respectively.

1

2

3

4

mIL Fig. 2. Water activity (aw ) of [Cmmim][Cl] for binary system (, [Cmmim][Cl] (this work); ♦, [Cmmim][Cl] (Ref. [9])) plotted against concentration of [Cmmim][Cl] (mIL ).

90


Table 5 Experimental solubility, S (g amino acid/1000 g of water), data of l-threonine in aqueous [Cmmim][Cl] solutions along with those predicted from different local composition models at T = 298.15 K.a cal SWilson

mIL

S exp

0.000

97.70 (95.9b , 97.7c , 91.5d , 93.0e ,97.46f ) 100.3 106.3 126.9 133.2 141.6

0.0412 0.1413 0.2753 0.3551 0.4270

97.62

cal SNRTL

cal SmNRTL

cal SNRF−NRTL

97.54

97.54

97.33

2.5.2. Short-range interaction contributions 2.5.2.1. The Wilson model. The segment-based local composition Wilson model, developed for phase equilibrium behavior of (aqueous electrolyte + amino acid) solutions were used for the correlation of our water activity data has the following form [11]: ex.SR gWilson

101.5 111.2 124.7 133.2 140.9

101.4 111.3 124.7 133.2 140.8

101.4 111.0 124.3 132.8 140.4

101.0 110.5 124.2 133.2 141.6

Standard uncertainties for molality, solubility and temperature are

(m) = ± 0.001 mol kg−1 ; (S) = ±0.5 (g amino acid/1000 g of water); (T) = ±0.05 K, respectively. b Ref. [26]. c Ref. [27]. d Ref. [28]. e Ref. [29]. f Ref. [30].

CRT

g ex,LR g ex,SR g ex = + RT RT RT

(4)

g ex,LR

− Xa ln

2.5.1. Long-range interaction contribution The PDH equation for excess Gibbs energy can be written as:

4Ax Ix xi

i

ln 1 + Ix0.5

(5)

where Ax =

1 2N 1/2 A

3

Vw

− Xc ln

X H +

(Xa + Xc ) Hca,m + Xm w wm Xm + Xc + Xa + Xw

X H

m m,ca + Xc + Xw Hw,ca Xm + Xc + Xw

X H

m m,ca + Xa + Xw Hw,ca Xm + Xa + Xw

Xi = xi Ki

(Ki = Zi for ions and Ki = unity for molecules)

e2 4εDw kT

(6)

In the above relations, the parameters, , NA , k, ε and e are the closest distance parameter, Avogadro’s number, Boltzmann constant, permittivity of vacuum and electronic charge, respectively. xi is the mole fraction of component i. Ix is the ionic strength in mole fraction basis. The parameter is related to the hard-core collision diameter, or distance of closest approach, of ions in solution. Therefore, the value of depends on the electrolyte as well as the expression used to represent the short-range forces. In order to maintain simplicity in equations for more complex electrolyte systems, it is desirable that should have the same value for a wide variety of salts. The value of = 14.9 has been frequently used for aqueous electrolyte solutions [31], therefore, this value was also used in this work. The Vw and Dw are the molar volume and dielectric constant of the solvent.

(7b)

where C is the effective coordination number in the system, which was fixed at 10, Z is the charge number; H and E are energy parameters and gives as:

Hij = exp

−

hij − hjj

Hij,kj = exp

−

hij − hkj

= exp

CRT

−

Eij

(7c)

CRT

= exp

CRT

Ecm = Eam = Eca,m ,

−

Eij,kj

CRT

Ecw = Eaw = Eca,w

Em,ca = Emc,ac = Ema,ca ,

(7d)

(7e)

Ew,ca = Ewc,ac = Ewa,ca

Eac = Eca = Eca,ca

(7f) (7g)

In these relations, species i, j and k can be cation, anion, amino acid or water molecule. 2.5.2.2. The NRTL model. For an aqueous electrolyte–amino acid system extended NRTL model has the following form [12]: ex,SR gNRTL

3/2

(7a)

In the above relation the subscripts w, m, ca, c and a stand for water, amino acid, electrolyte, cation and anion, respectively. R and T are gas constant and absolute temperature. Xi is the effective mole fraction which is given by:

g ex,SR

where is the long-range interaction contribution, and is the short-range interaction contribution. The long-range interaction term accounts for the electrostatic interactions between ions, and the short-range interaction term considers the nonelectrostatic interactions between all species (ion, solvent and zwitterion).

g ex.PDH =− RT

Xm + Xc + Xa + Xw

− Xm ln

a

for the correlation of water activity data for the investigated systems the segment-based local composition Wilson [11], NRTL [12], modified NRTL (mNRTL) [13] and NRF-NRTL [14] models developed for phase equilibrium behavior of aqueous electrolyte solutions of amino acids were considered. In our previous work, these equations were successfully used for the correlation of VLE data of aqueous l-serine + IL solutions [9]. The excess Gibbs energy for a multi-component aqueous solution containing several electrolytes and zwitterions is expressed as the sum of two contributions:

X H +

(Xa + Xc ) Hca,w + Xw m mw

= −Xw ln

RT

= Xw

X G +

(Xa + Xc ) Gca,w ca,w m mw mw Xm Gmw + (Xa + Xc ) Gca,w + Xw

+ Xm + Xa + Xc

X G +

(Xa + Xc ) Gca,m ca,m w wm wm Xw Gwm + (Xa + Xc ) Gca,m + Xm

X G

w w,ca w,ca + Xm Gm,ca m,ca Xw Gw,ca + Xm Gm,ca + Xc

X G

w w,ca w,ca + Xm Gm,ca m,ca Xw Gw,ca + Xm Gm,ca + Xa

(8a)

where G and are energy parameters and are given by:

Gij = exp

−˛ij

= exp −˛ij

gij − gjj RT

aij RT

= exp −˛ij ij

(8b)


Gij,kj = exp

−˛ij,kj

gij − gkj

RT

= exp −˛ij , kj

aij,kj

= exp −˛ij , kj ij , kj

(8c)

RT

91

where i∞ denotes the infinite dilution activity coefficient, Mw , m and are molecular weight of water, molality and stoichiometric number of amino acid or electrolyte. To model the chemical equilibria of amino acid species in aqueous phase, we consider the following equation: A(s) ↔ A± (aq)

acm = aam = aca,m ,

acw = aaw = aca,w

am,ca = amc,ac = ama,ca ,

(8d)

aw,ca = awc,ac = awa,ca

(8e)

aac = aca = aca,ca

(8f)

where ˛ is the nonrandomness factor. The nonrandomness factor was fixed at 0.2 for binary electrolyte–molecule pairs and binary electrolyte–electrolyte pairs. It was set at 0.3 for binary molecule–molecule pairs [12]. 2.5.2.3. The mNRTL model. The modified NRTL model presented for the correlation of vapor–liquid equilibria (VLE) for (polymer–salt–water) systems [13] and successfully used for correlation of water activity in (amino acid–electrolyte–water) systems ex,SR in our previous work [9]. The obtained gmNRTL equation for an aqueous electrolyte–amino acid system has the following form: ex,SR gmNRTL

RT

= Xw

X G + (X + X )G

m mw mw c a ca,w ca,w

(12) A± (aq)

are the solid form of amino acid and where A(s) and dissolved amino acid (as neutral zwitterions), respectively. The solubility constant based on mole fraction, can be stated as: Ks = xA± Ax±

(13)

where Ks is the solubility constant, xA± and Ax± are the mole fraction and activity coefficient of amino acid in mole fraction scale dissolved in water, respectively. In this work, following Chen et al. [12], the following equation is used to calculate the temperature dependency of the solubility constant: ln Ks = a +

b + c ln T T

(14)

where a, b and c are adjustable parameters. The modeling of the solubility of amino acids in electrolyte solutions has been discussed in some detail in Ref. [32]. The binary

Xm Gmw + (Xa + Xc )Gca,w + Xw

+ Xm + Xa + Xc

X G + (X + X )G

w wm wm c a ca,m ca,m Xw Gwm + (Xa + Xc )Gca,m + Xm

X X (

w m m,ca − w,ca )(Gm,ca − Gw,ca ) + Xw Xc w,ca (Gw,ca − 1) + Xm Xc m,ca (Gm,ca − 1) (Xw Gw,ca + Xm Gm,ca + Xc )B

X X (

w m m,ca − w,ca )(Gm,ca − Gw,ca ) + Xw Xa w,ca (Gw,ca − 1) + Xm Xc m,ca (Gm,ca − 1) (Xw Gw,ca + Xm Gm,ca + Xa )A

(9a)

that A = Xm + Xa + Xw

(9b)

B = Xm + Xc + Xw

(9c)

The performance of above modified NRTL model has not been tested for (amino acid–salt–water) systems. 2.5.2.4. The NRF-NRTL model. The extended NRF-NRTL model for the correlation of VLE for (polymer–salt–water) systems [14] similar to the modified NRTL model adopted and applied for (amino acid–salt–water) systems in our previous work [9]. The following ex,SR is obtained: equation for gNRF−NRTL ex,SR gNRF−NRTL

RT

= Xw

X G + (Xa + Xc ) Gca,w ca,w m mw mw Xm Gmw + (Xa + Xc ) Gca,w + Xw

+ Xm + Xa

− (Xm mw + (Xa + Xc ) ca,w )

X G + (Xa + Xc ) Gca,m ca,m w wm wm Xw Gwm + (Xa + Xc ) Gca,m + Xm

X G w w,ca w,ca + Xm Gm,ca m,ca Xw Gw,ca + Xm Gm,ca + Xc

ln im∗ = ln ix − ln i∞ − ln

1+

Mw

1000

mi

− (Xw wm + (Xa + Xc ) ca,m )

− (Xw w,ca + Xm m,ca ) + Xc

From the appropriate differentiation of above gex equations the relations for the mole fraction activity coefficients of amino acid or electrolyte can be obtained. Because the experimental data available in the literature are normalized in molality scale, therefore it is necessary to convert the symmetric activity coefficient in mole fraction scale (ix ) to unsymmetric activity coefficient in molality scale (im∗ ). The activity coefficients are normalized in molality scale, according to the following relation:

energy parameters for the amino acid–water and IL–water given in Table 6 and the solubility constants of the amino acids reported in Table 8 are directly used to calculate the solubility of l-threonine in aqueous IL solutions. The amino acid–IL energy parameters are treated as adjustable parameters [11]. The solubility data were also used to determine the transfer Gibbs free energy of the amino acid from water to the aqueous [Cmmim][Cl] solutions. At the solubility limit of the model compounds, solid and liquid phases are at equilibrium, and thus the fugacity of the amino acid in liquid phase is equal to that in solid

(11)

X G w w,ca w,ca + Xm Gm,ca m,ca Xw Gw,ca + Xm Gm,ca + Xa

− (Xw w,ca + Xm m,ca )

(10)

phase and can be expressed as [33]: fA± (pure solid) = xA± Ax± fA0± fA0±

(15) Ax±

is the standard-state fugacity to which refers. where Standard-state may be chosen as the solution at infinite dilution. Eq. (15) can thus be expressed, as: fA± (pure solid) = xA± Ax∗± fA± (at infinite dilution)

(16)

where Ax∗± is defined with reference to an ideal dilute solution. For this definition it is essential to distinguish between solute and

92


Table 6 Values of parameters of Wilson, NRTL, mNRTL and NRF-NRTL models for {amino acid (3)(m) + IL (2)(ca) + H2 O (1)(w) } system at T = 298.15 K. Wilson model Emw (J mol−1 )

Ewm (J mol−1 )

Eca,w (J mol−1 )

Ew,ca (J mol−1 )

Eca,m (J mol−1 )

Em,ca (J mol−1 )

Dev%b

−23,287.206

33,622.345

−19,296.115

36,477.937

13,345.975

−1968.563

0.019

NRTL model mw (J mol−1 )a

wm (J mol−1 )

ca,w (J mol−1 )

w,ca (J mol−1 )

ca,m (J mol−1 )

m,ca (J mol−1 )

Dev%

−2.601

4.009

−2.857

5.251

1.030

−0.292

0.018

mNRTL model mw (J mol−1 )

wm (J mol−1 )

ca,w (J mol−1 )

w,ca (J mol−1 )

ca,m (J mol−1 )

m,ca ·(J mol−1 )

Dev%

−2.601

4.009

−0.8177

1.304

20.514

−4.609

0.0175

mw (J mol−1 )

wm (J mol−1 )

ca,w (J mol−1 )

w,ca (J mol−1 )

ca,m (J mol−1 )

m,ca (J mol−1 )

Dev%

7.608

3.954

1.287

2.216

11.008

−2.492

0.0176

NRF-NRTL model

a

b

aij = ij RT. Dev% =

1 NP

exp NP aw,l −acal w,l exp w,l

a

, NP is the number of experimental data points.

l=1

solvent. In this case, for the ternary system containing (IL + amino acid + water), the (water + IL) is considered as the solvent. The activity coefficient at infinite dilution of amino acid is then defined as the activity coefficient when the concentration of amino acid approaches zero. The transfer Gibbs free energy of the amino acid from water to the aqueous IL solutions, Gtr , can be calculated from the following equation [34]: bin Gtr = GAter ± (at infinite dilution) − GA± (at infinite dilution) bin = ter A± (at infinite dilution) − A± (at infinite dilution)

= R · T · ln

= R · T · ln

= R · T · ln

fAter ± (at infinite dilution)

fAbin ± (at infinite dilution) Ax∗bin · xAbin ± ±

Ax∗ter · xAter± ±

xAbin ± xAter±

+ R · T · ln

Ax∗,bin ± Ax∗,ter ±

Gtr is better denoted as apparent transfer Gibbs free energies . Gtr Later, Nozaki and Tanford [36] noted that it is important to consider the activity coefficient term in calculation of transfer Gibbs free energies for some systems and proposed rather simple method for this purpose [36]. According to this assumption made by these authors [36] the interaction between solute molecules in an aqueous electrolyte solution is the same as it would be in pure water; this means that, Ax∗,ter has the same value of Ax∗,bin at the same ± ± concentration. Recently [33] this assumption has been applied to calculate activity coefficient term using NRTL equation for binary amino acid + water system. In this paper, for determining the second term on the right hand side of Eq. (17), we considered the calculation of amino acid activity coefficients rigorously by the help of solution theory models. 2.6. Correlation

(17)

The first term on the right-hand side of Eq. (17) is directly calculated from the solubility data. The second term involves activity coefficient for amino acid in water and aqueous IL solutions. While activity coefficient of amino acid in water can be easily calculated, rigorously obtaining the activity of amino acid in multi-component liquid mixtures (here, aqueous IL) from phase equilibrium data is extremely difficult without using solution theory models. In this work we presented VLE data for (l-threonine + IL + water) system and correlated the obtained water activity data with some local composition models; therefore, these models permits us to calculate the necessary amino acid activity coefficient in aqueous IL solutions. In the case of (amino acid + electrolyte + water) systems, since only very few water activity or osmotic coefficient data are available in the literature, modeling of them has attracted a little attention. In 1960–1970, Nozaki and Tanford [27,35,36] noted that the activity coefficient term is a self-interaction coefficient term and found that the ratio of the activity coefficient term makes only a small contribution to Gtr . Therefore, many researchers [8,10,33–40] have ignored the activity coefficient term on the righthand side of Eq. (17) for determining transfer Gibbs free energies of various solutions. When the activity coefficient term was neglected,

For the aforementioned local composition model parameters were estimated by minimizing the following objective function:

OF =

NP

aw,l − acal w,l exp

2

(18)

l=1 exp

where NP is the number of experimental data points and aw,l and

acal are, respectively, the experimental and calculated values of w,l the water activity. The results of fitted parameters for the local composition models with the corresponding relative percentage deviations (Dev%) are shown in Table 6. All range of ionic liquid concentration that reported in this work and our previous work [9] were used to obtained the IL–water energy parameters (are listed in Table 6). On the basis of the (Dev%) values, we conclude that all these models can be satisfactory used to represent the VLE data for the studied ternary aqueous amino acid–IL solutions. Using mNRTL parameters reported in Table 6 for the investigated system we calculated isoactivity curve for each water activity value reported in Table 4 for different ionic liquid molalities as shown in Fig. 1.This figure shows that there is a fairly good agreement between experimental water activity and those calculated by the mNRTL model used in this work.


mthreonine (mol kg−1 )

m∗ Wilson

m∗ NRTL

m∗ mNRTL

m∗ NRF-NRTL

0.2224 0.3881 0.4181 0.4983 0.5178 0.5626 0.5936

0.988 0.980 0.979 0.976 0.975 0.973 0.972

0.989 0.982 0.981 0.978 0.977 0.976 0.975

0.989 0.982 0.981 0.978 0.977 0.976 0.975

0.986 0.977 0.976 0.972 0.971 0.970 0.969

Table 8 Solubility constants of l-threonine in water. Models

a

b

c

Dev%

Wilson NRTL or mNRTL NRF-NRTL

−56.639 −71.941 −76.053

1337.942 1948.388 2138.336

8.407 10.734 11.341

0.148 0.087 0.175

Using the obtained parameters given in Table 6, the unsymmetrical molal activity coefficients of the amino acid in water were calculated and the results are shown in Table 7. As can be seen, in Table 7 the obtained molal activity coefficients for l-threonine from different local composition models for aqueous l-threonine system are in good agreement. In order to check the quality of the obtained data, the unsymmetrical molal activity coefficients of the amino acid in this work have been compared with the values reported in the literature [41]. As can be seen from Fig. 3, our results are in good agreement with the literature. The adjustable parameters a, b and c in Eq. (14) were estimated by minimizing the following objective function: OF =

NP

exp

Sl

− Slcal

2

(19)

l=1

where S is the solubility in grams of amino acid per kilogram of water. The solubility data taken from Refs. [30,42] cover temperature ranges from 298.15 to 333.15 K. The values for the adjustable parameters a, b and c along with the corresponding absolute relative percentage deviations (Dev%) are given in Table 8. On the basis of the obtained deviations, from Table 8, we conclude that all the local composition models are satisfactory in representing

170 L-threonine solubility(gr/1000gr H2O)

Table 7 Molal activity coefficient ( m∗ ) of the l-threonine for the binary solutions obtained from different local composition models at T = 298.15 K.

93

160 150 140 130 120 110 100 90 80 290

300

310

320

330

340

T(K) Fig. 4. Solubility of l-threonine in water plotted vs. temperature: ♦, experimental data for l-threonine (Refs. [30,42]); —, NRTL or mNRTL model.

solubility of l-threonine in water. However, better quality of fitting is obtained with the NRTL or mNRTL models. In fact both the NRTL and mNRTL models have the same relation for water activity and solubility. Variation of the solubility of l-threonine with temperature was shown in Fig. 4 by mNRTL or NRTL model. Estimated binary parameters between amino acid–IL in water and Dev% of correlation of experimental solubility data of an amino acid in aqueous IL solutions are presented in Table 9. Using reported parameters in Table 9, the solubility of l-threonine in aqueous IL solutions at 298.15 K was calculated and also presented in Table 5. The results in Table 5 indicate successful representation of solubility of l-threonine in aqueous IL solutions by different models used. The results of modeling with the NRF-NRTL model and experimental data for the ratio of solubility of l-threonine in aqueous [Cmmim][Cl] solutions to its solubility in pure water are shown in Fig. 5. Also Fig. 5 compares the ratio of solubility of l-threonine in the presence of [Cmmim][Cl] and KCl taken from Ref. [30] as a function of electrolyte concentration. As observed in Table 5 and Fig. 5, we conclude that l-threonine exhibiting a more pronounced salting-in effect by adding a little of [Cmmim][Cl]. , calcuThe results of apparent transfer Gibbs free energies Gtr lated from the experimental solubility data are reported in Table 10.

1 Table 9 Estimated binary parameters between amino acid(m) and IL(ca) in water along with (Dev%) of correlation of experimental solubility data of an amino acid(m) in aqueous solutions of IL(ca) from the local composition models.

0.99 0.98

Model parameters

0.97

γm*

Wilson

Eca,m (J mol

−1

Dev% −1

)

Em,ca (J mol

−561.668

)

−5717.031

1.363

0.96 Model parameters NRTL

0.95

aca,m (J mol

−1

)

am,ca (J mol

−1001.443

0.94

Dev% −1

)

−5996.263

1.377

Model parameters mNRTL

0.93 0

0.5

1

1.5

2

2.5

mL-threonine m∗

Fig. 3. Activity coefficient ( ) of threonine for binary system (, threonine (this work); ♦, threonine (Ref. [41])) plotted against concentration of threonine (mthreonine ).

Dev%

aca,m (J mol−1 )

am,ca (J mol−1 )

1137.778

−15,653.743

1.452

Model parameters NRF-NRTL

−1

aca,m (J mol

87,876.616

)

Dev% −1

am,ca (J mol 6125.162

) 1.174

94


Table 10 Transfer Gibbs free energies of l-threonine from water to aqueous IL solutions at 298.15 K and atmospheric pressure. Molality of IL

0.0412

0.1413

0.2753

0.3551

0.4270

(J mol−1 ) Gtr

−60.281

−193.419

−613.936

−725.060

−866.307

A± x∗,ter A±

−4.617a (0.726)b

−19.156(2.279)

−42.283(6.697)

−1

−64.898(−59.818)

−212.576(−190.888)

−656.219(−606.979)

−4.425(0.527)

−15.393(1.632)

−33.018(4.500)

−64.706(−60.017)

−208.813(−191.535)

−646.953(−609.176)

−2.116(0.527)

−7.324(1.632)

−15.592(4.500)

−62.397(−60.017)

−200.743(−191.535)

−629.527(−609.176)

A± x∗,ter A±

−17.789(0.791)

−20.460(2.404)

−25.706(6.030)

−1

−78.070(−59.753)

−213.880(−190.763)

−639.642(−607.646)

x∗,bin

Wilson model R · T · ln

Gtr (J mol

)

x∗,bin

−57.803(7.683) −782.863(−717.741)

−73.530(8.771) −939.838(−857.421)

NRTL model R · T · ln

A± x∗,ter A±

Gtr (J mol−1 )

x∗,bin

−44.741(5.040) −769.801(−720.384)

−56.652(5.546) −922.959(−860.646)

mNRTL model R · T · ln

A± x∗,ter A±

Gtr (J mol−1 )

x∗,bin

−21.936(5.040) −746.996(−720.384)

−28.525(5.546) −894.832(−860.646)

NRF-NRTL model R · T · ln

Gtr (J mol a b

)

−29.801(6.486) −754.861(−718.938)

−34.503(6.664) −900.810(−859.527)

Obtained using the solubility data and rigorous calculation of amino acid activity coefficient data. Obtained using the solubility data and assumption used by Nozaki and Tanford [36] for calculation of amino acid activity coefficient in (electrolyte + water) solutions.

The transfer Gibbs free energies Gtr values presented in Table 10 were obtained by taking into account the activity coefficients of amino acid in water and [Cmmim][Cl] + water solutions rigorously and calculating their values using the activity coefficient relation for each model with the parameters reported in Table 6. The calculated values for activity coefficient term in Eq. (17) of each model are also tabulated in Table 10. We also calculated the transfer Gibbs free energy for l-threonine from water to [Cmmim][Cl] using the method proposed by Nozaki and Tanford [36] assuming that, Ax∗,ter ±

has the same value of Ax∗,bin at the same concentration with the ± results collected in Table 10. From the data presented in Table 10 it is concluded that regardless of method used, the activity coefficient term has a little contribution to calculated Gtr values. There are also fairly good agreement between Gtr values calculated either taking into account the amino acid activity coefficient in [Cmmim][Cl] + water rigorously as made in this work and the simple assumption proposed by Nozaki and Tanford [36]. In general,

1.7

Relative solubility(S/S0)

1.5 1.3 1.1 0.9 0.7 0.5 0.04

0.54

1.04

1.54

2.04

2.54

electrolyte molality (mol/1000 gr H2O) Fig. 5. Comparison of the ratio of the solubilities of l-threonine in two aqueous electrolyte solutions to its solubility in pure water (S/S0 ) at T = 298.15 K: , [Cmmim][Cl]; , KCl; —, NRF-NRTL model (Eq. (10)).

it is known that [38] the unfavorable interactions of solvents with amino acids or proteins account for the increase of amino acid or proteins stability, indicating that solubilities decrease with increasing the concentration of electrolyte (salting-out effect) as well as the positive contribution for the transfer Gibbs free energy. In contrast, if Gtr has a negative sign and the solubility increases with increasing the concentration of denaturants (salting-in effect), it indicates that the interactions are favorable and the denaturants destabilize the proteins or amino acids [38]. As can be seen from , and G Table 10 for the {l-threonine + [Cmmim][Cl] + H2 O}, Gtr tr are negative and these values decrease with respective to IL concentrations. The negative values for transfer Gibbs free energies suggest that interactions between the amino acid and [Cmmim][Cl] are favorable and the IL solutions destabilize the amino acid.

3. Conclusions The water activity data for the ternary system {lthreonine + [Cmmim][Cl] + H2 O}, and the corresponding binary aqueous amino acid system were measured accurately at 298.15 K using an improved isopiestic method. Values of the vapor pressure of solutions were also calculated from the experimental water activity data. The Wilson, NRTL, modified NRTL and NRF-NRTL equations were used to correlate the experimental water activity data. For the same system, the solubility of the l-threonine at various IL concentrations was measured at 298.15 K using gravimetric method. Also the above local composition models used to describe the solubility of amino acid in pure water and in aqueous IL solutions. It was found that all the models used in this work can accurately correlate the VLE and solubility data for the studied system. Furthermore, the unsymmetrical molal activity coefficients of the amino acid were calculated in the binary aqueous solutions by using local composition models; the obtained values from different models were in good agreement. Finally, to obtain some information regarding the effect of IL on the stability of l-threonine, the transfer Gibbs free energies of amino acid from water to aqueous IL solutions were determined through solubility measurements and the values of amino acid activity coefficient in water and (IL + water) solutions using the above local composition models at 298.15 K. The obtained negative values for Gtr show


that, destabilization of amino acid increases with increasing the concentration of the ionic liquid in water. Acknowledgement We are grateful to University of Tabriz Research Council for the financial support of this research.

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