Activity and activity coefficient studies of aqueous binary and ternary solutions of 4-nitrophenol, sodium salt of 4-nitrophenol, hydroquinone and α-cyclodextrin at 298.15 K

Journal of Molecular Liquids 139 (2008) 61 – 71 www.elsevier.com/locate/molliq

Activity and activity coefficient studies of aqueous binary and ternary solutions of 4-nitrophenol, sodium salt of 4-nitrophenol, hydroquinone and α-cyclodextrin at 298.15 K Santosh S. Terdale, Dilip H. Dagade, Kesharsingh J. Patil ⁎ Department of Chemistry, Shivaji University, Kolhapur-416 004, India Received 7 September 2007; received in revised form 28 October 2007; accepted 5 November 2007 Available online 17 November 2007

Abstract Osmotic coefficient measurements are reported for binary aqueous solutions of 4-nitrophenol, sodium salt of 4-nitrophenol and hydroquinone at 298.15 K. The data are analyzed to obtain activities and activity coefficients of solute as a function of solute concentration using appropriate thermodynamic equations and methods of integration. The measurements of solvent activity are made for ternary aqueous solutions containing fixed concentration of α-cyclodextrin (α-CD) and varying amount of 4-nitrophenol, sodium salt of 4-nitrophenol and hydroquinone. The solvent activity data have been used to obtain the individual activity coefficients of the components as a function of solute concentration at 298.15 K. It is observed that there is a lowering of activity coefficients of the phenols as well as of hydroquinone in presence of α-CD, which is being attributed to incorporation of these solute molecules into the CD cavity to form inclusion complexes. The salting-in constant and thermodynamic equilibrium constant values for the formation of 1:1 complexes have been determined using Dagade and Patil's method based on the application of the McMillan–Mayer virial coefficient theory. The results are further discussed in terms of neutral and anionic complex formation, water structural effects and hydrophobic interactions. © 2007 Elsevier B.V. All rights reserved. Keywords: Osmotic coefficient; Molecular complex; McMillan–Mayer theory; Osmotic second virial coefficient; Salting constant

1. Introduction Thermodynamic aspects of interactions of neutral and ionic species in aqueous solutions containing 18-Crown-6 have been of interest to us. Using the osmotic coefficient data, we evolved a method to obtain activity coefficients and thermodynamic equilibrium constant values for the host–guest type of complexes in solution phase [1,2]. It has been noted that for the stability of such supra-molecular species in solution phase, the size, nature and charge of the guest molecules along with the hydrophobic interaction are important. The knowledge of the activity coefficient and the use of the statistical mechanical McMillan–Mayer theory of solution enabled us to obtain

⁎ Corresponding author. E-mail address: [email protected] (K.J. Patil). 0167-7322/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.molliq.2007.11.001

information needed to probe molecular recognition phenomena on primary level. Earlier we reported the thermodynamic studies of molecular interactions in aqueous α-CD solutions by applying the McMillan–Mayer and Kirkwood–Buff theories [3]. We observed that the hydration of α-CD in aqueous solution is dependent on the temperature and conformational characteristic of α-CD, while an ideal mixing is observed at 301 and 311 K. The dissolution of α-CD in water is being characterized by enthalpy–entropy compensation phenomena and hydrophobic interaction, which increase with increase in temperature of the system. The increasing number of publications in recent years shows the many spectacular applications related to host–guest and supra-molecular chemistry [4,5]. Cyclodextrins are cyclic oligosaccharides, formed by a variable number of D (+) glucopyranose units connected by α-1, 4 linkages. They have hydrophobic cavities and a hydrophilic exterior. They are

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known to interact strongly with different type of molecules (neutral or ionic) or even with solvent molecules [6,7]. The major requirement seems to be that the guest molecule fits into the cyclodextrin cavity and a variety of factors have been considered as driving forces for the binding process. Cyclodextrins have important technological applications in drug delivery systems, separation techniques and food industry [8,9]. Complex formation between cyclodextrins and their guest molecules is the subject of comprehensive literature [10]. In an aqueous solution, the slightly apolar cyclodextrin cavity is occupied by water molecules which are energetically unfavoured and therefore can be readily displaced by appropriately sized guest molecules. Most frequently the host–guest ratio (1:1) is the essence of molecular encapsulation. Recently, we reported the drug-binding equilibria studies with α-CD in aqueous solutions [11]. Cyclodextrins form complexes in aqueous solutions with azo dyes, nitrophenol, and other substances [12]. Although there is no direct proof for a fixation of the guest molecules within the void space of the cyclodextrins, the complexes are usually regarded as inclusion compounds in which hydrogen bonding, Van der Waals forces and hydrophobic interactions are the main binding forces. This explains the interest cyclodextrins have found as models for studying the primary step of enzyme or antigen–antibody reaction [13]. 4-Nitrophenol as well as its anion is known to form complexes with α-CD. Cramer et al. have studied the thermodynamics and kinetics of the complexes using spectrophotometric data [12]. They suggested that the removal of some water molecules from

the inside of the cyclodextrin is rate determining for the complex formation of the nitrophenol with α-CD. Equilibrium constants for the formation of 1:1 inclusion complexes of α-CD and nitrophenols have also been studied by Hamai et. al using thermodynamic and NMR techniques [14]. Their results indicate that the interactions between the anionic phenols and CD are stronger than the neutral phenols and that the inclusion complexes of anionic species have more rigid structures than those of neutral species. Considering the above limited information about the α-CD complexes with the phenolic species as guest and the importance of interaction, we have extended our studies of activity coefficients to solutions of α-CD containing guest species. We obtained the activity coefficients at varied phenol concentrations (neutral and salt) in ternary solution having fixed concentration of α-CD at 298.15 K by making solvent activity measurements using vapour pressure osmometer. We did not make the measurements in buffer solutions or at different pH of solutions but in neutral water (at atmospheric conditions). In order to evaluate the equilibrium constant values of the complexed species, it was necessary to have knowledge about the binary aqueous solutions of phenols. Hence, measurements of osmotic coefficients for aqueous solutions of 4-nitrophenol and sodium salt of 4-nitrophenol at different concentrations were made. The results have been used to calculate the activity coefficients of all the three components in the ternary mixture, which were further used to calculate the transfer Gibbs free energy of a solute from binary to ternary solutions. The estimated values of the transfer Gibbs free energies are used to

Fig. 1. TGA–DTA plot of sodium 4-nitrophenolate.

S.S. Terdale et al. / Journal of Molecular Liquids 139 (2008) 61–71

evaluate pair and triplet interactions by means of a virial expansion of the transfer Gibbs free energy as a function of both α-CD and phenol concentration. The resulting salting-in parameter and equilibrium constant values for the complexation reaction are reported and discussed in following pages. 2. Experimental work α-cyclodextrin (α-CD) procured from Lancaster, 4-nitrophenol procured from Merck-Schuchard and hydroquinone procured from Merck were used without further purification. The amount of water of hydration in α-CD (6.24 water molecules per α-CD molecule) was estimated using the thermogravimetric analysis (Model: Thermal Analyzer, TG-DTADSC, TA Inc. SDT-2790) and microprocessor controlled automatic Karl-Fischer Titrator (Model: TKF-55, M/s Toshniwal Company) analysis. The details about water of hydration and preparation of solutions of α-CD are being given elsewhere [3,11]. The 4-nitrophenol was dried under vacuum for 24 h before use. The sodium salt of 4-nitrophenol was prepared in the laboratory. Its purity was checked by the method of TLC as well as by thermo-gravimetric analysis. The TGA–DTA curve obtained (Fig. 1) showed resemblance to the reported one [15]. The thermo-gravimetric analysis showed the presence of two water molecules in sodium 4-nitrophenolate. The material was used without removing the water content and the calculated concentrations were correspondingly corrected. The solutions were prepared using doubly quartz distilled water on molality basis and converted to molarity scale whenever required using density data. The density measurements of aqueous solutions of 4-nitrophenol, sodium 4-nitrophenolate and hydroquinone were made using Anton Paar digital densitometer (DMA 60/602) at 298.15 K. The uncertainty in the density data was found to be ± 0.005 kg m− 3. The osmotic coefficients of binary and ternary aqueous solutions were measured using KNAUER K-7000 vapour pressure osmometer having temperature control of ± 0.001 K. The uncertainty in the osmotic coefficient data was found to be ± 0.001. The details about the density and osmotic pressure measurements were reported earlier [3].

63

osmotic coefficient data for these systems can be expressed as a function of concentration using the polynomial equation [16] /¼1þ

n X

ð2Þ

Ai mi=m

i¼1

where ϕ is the osmotic coefficients of solute molecules in aqueous binary solutions, ν is the number of ions formed by the dissociation of solute and for aqueous electrolyte solutions A1 is the Debye– Hückel constant equal to −0.3908 at 298.15 K [16]. The variations of osmotic coefficient as a function of solute concentration, for all the systems, are given in Fig. 2 and the data are collected in Table 1. The coefficients Ai in Eq. (2) have been obtained by the method of least squares (the constraint of coefficient A1, a Debye–Hückel constant, is applied during least square fit for aqueous electrolyte solutions) and are given in Table 2. The activity coefficient of solute molecule (γ2) (for non-electrolyte it is molal activity coefficient γ2, whereas for electrolyte it is to be replaced by mean molal activity coefficient γ±) in binary aqueous solutions can be expressed in terms of osmotic coefficient using the equation Z

m1=m

ln g2 ¼ ð/  1Þ þ m

ð/  1Þd ln m1=m

ð3Þ

0

Using Eq. (2) and solving the right hand side integral of Eq. (3), one can write ln g2 ¼

n X mþi Ai mi=m i i¼1

ð4Þ

where A1 for electrolyte is the Debye–Hückel constant for the osmotic coefficient (−0.3908 at 298.15 K). The solute activity coefficient values have been calculated using Eq. (4) and the data for all the systems are collected in Table 1. The variation of ln γ2 with the solute concentration for non-electrolyte and electrolyte solutes is shown in Fig. 3a and b respectively. The activity

3. Results 3.1. Binary aqueous solutions 3.1.1. Osmotic and activity coefficient The osmotic coefficient (ϕ) values were determined for aqueous binary guest solutions at 298.15 K. Using the data of osmotic coefficient, the water activity (aw) values have been estimated using the equation 
 x2 U ¼  lnaw = x1

ð1Þ

where x1 and x2 are the mole fraction of water and of solute respectively in the aqueous solution. The water activity was used to obtain the solvent activity coefficient (γ1). The experimental

Fig. 2. The variation of osmotic coefficient (ϕ) with concentration at 298.15 K for ♦; 4-nitrophenol, ○; hydroquinone and ▲; sodium 4-nitrophenolate.

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S.S. Terdale et al. / Journal of Molecular Liquids 139 (2008) 61–71

Table 1 Water activity, osmotic coefficient and activity coefficient data, at 298.15 K m (mol kg− 1)

x2

ϕ

aw

γ1

γ2

ΔGm (J mol− 1)

ΔGE (J mol− 1)

4-Nitrophenol + H2O 0.00000 0.02032 0.03032 0.04152 0.05170 0.06224 0.07111 0.07771 0.10263

0.00000 0.00037 0.00055 0.00075 0.00093 0.00112 0.00128 0.00140 0.00185

1.0000 0.9977 0.9817 0.9638 0.9475 0.9306 0.9164 0.9059 0.8660

1.00000 0.99964 0.99946 0.99928 0.99912 0.99896 0.99883 0.99874 0.99840

1.00000 1.00000 1.00001 1.00002 1.00005 1.00008 1.00011 1.00013 1.00024

1.00000 0.99109 0.97606 0.95337 0.92908 0.90194 0.87860 0.86151 0.80433

0.00 − 8.09 −11.53 − 15.21 − 18.46 − 21.73 − 24.44 − 26.42 − 33.75

0.00 0.00 − 0.01 − 0.03 − 0.05 − 0.09 − 0.14 − 0.18 − 0.38

Hydroquinone + H2O 0.00000 0.01907 0.03908 0.05753 0.07795 0.09725 0.11686 0.13613 0.15632 0.17464 0.19616 0.25026 0.29966

0.00000 0.00034 0.00070 0.00104 0.00140 0.00175 0.00210 0.00245 0.00281 0.00314 0.00352 0.00449 0.00537

1.0000 0.9964 0.9856 0.9766 0.9677 0.9603 0.9538 0.9484 0.9439 0.9407 0.9381 0.9370 0.9429

1.00000 0.99966 0.99931 0.99899 0.99864 0.99832 0.99799 0.99768 0.99735 0.99704 0.99669 0.99578 0.99492

1.00000 1.00000 1.00001 1.00002 1.00004 1.00007 1.00010 1.00012 1.00015 1.00018 1.00021 1.00027 1.00029

1.00000 0.98698 0.97191 0.95747 0.94157 0.92716 0.91352 0.90142 0.89030 0.88171 0.87342 0.86048 0.85510

0.00 − 7.65 − 14.43 − 20.25 − 26.41 − 32.01 − 37.53 − 42.83 − 48.26 − 53.08 − 58.65 − 72.19 − 84.13

0.00 − 0.01 − 0.02 − 0.05 − 0.09 − 0.15 − 0.23 − 0.31 − 0.41 − 0.51 − 0.63 − 0.95 − 1.29

Sodium 4-nitrophenolate + H2O 0.00000 0.00000 0.03930 0.00141 0.06030 0.00217 0.07926 0.00285 0.09920 0.00356 0.12041 0.00432 0.15957 0.00572 0.17643 0.00632 0.20008 0.00716

1.0000 0.9949 0.9929 0.9872 0.9787 0.9683 0.9491 0.9422 0.9350

1.00000 0.99859 0.99785 0.99718 0.99651 0.99581 0.99456 0.99403 0.99328

1.00000 1.00001 1.00001 1.00003 1.00007 1.00013 1.00028 1.00035 1.00044

1.00000 0.93836 0.93418 0.92646 0.91522 0.90111 0.87381 0.86307 0.85032

0.00 − 26.71 − 38.66 − 48.88 − 59.19 − 69.78 − 88.54 − 96.36 − 107.10

0.00 − 0.21 − 0.33 − 0.46 − 0.61 − 0.80 − 1.23 − 1.45 − 1.79

coefficient data, which have been converted to mole fraction scale, were used to calculate the Gibbs free energy of mixing (ΔGm), excess Gibbs free energy (ΔGE) of binary aqueous solutions and the values are given in Table 1 for all the systems.

rigorous statistical mechanical theories [18]. The solute–solvent 0 cluster integral b11 is given by equation [19]

3.1.2. Densities and apparent molal volumes The apparent molal volumes (ϕv) were obtained from the density data at 298.15 K. For the electrolyte solutions the apparent molal volume data is expressed by the equation

where k is the Boltzmann constant, υ20 is the partial molecular volume of the solute at infinite dilution, T is the absolute temperature, and κ is the isothermal compressibility coefficient of the pure solvent. The values for solute–solvent interaction 0 *0 (where B11 *0 = − b11 NB11 ) for aqueous solutions calculated using Eq. (6) are given in Table 3.

/v ¼ /0v þ Av c1=2 þ Bv c

ð5Þ

where ϕv0 is apparent molar volume at infinite dilution, Av is Debye–Hückel limiting law coefficient and Bv is deviation constant [17]. The variation of ϕv against c for binary 4-nitrophenol and hydroquinone system and of the parameter ϕv − Avc1 / 2 against c for the binary sodium 4-nitrophenolate system are shown in Fig. 4a and b respectively. 3.1.3. Application of the McMillan–Mayer theory The relative magnitudes of solute–solute and solute–solvent interactions have been studied for non-electrolytes using

b011 ¼ υ02 þ kT j

ð6Þ

Table 2 Coefficients Ai in Eq. (2)

A1 A2 A3 A4 A5 a

α-Cyclodextrin a

4-Nitrophenol

Hydroquinone

Sodium 4-nitrophenolate

0.2222 0.0000 – – –

0.2099 − 31.1220 160.1862 − –

− 0.3168 − 2.1304 15.2782 − 22.6073 –

−0.3908 3.8234 − 11.3090 4.8413 9.1124

Obtained from the data published earlier, Ref. [32].

S.S. Terdale et al. / Journal of Molecular Liquids 139 (2008) 61–71

Fig. 3. The variation of experimental activity coefficient (γ2) in binary aqueous solution, with concentration at 298.15 K for (a) ♦; 4-nitrophenol and ○; hydroquinone, (b) ▲; sodium 4-nitrophenolate and —; Debye–Hückel limiting law.

According to the McMillan–Mayer theory of solution [20] the osmotic pressure π is given by p ¼ n þ B2* n2 þ B*3 n3 þ N kT

ð7Þ

where n is the number density. The osmotic second and third ⁎ virial coefficients, B2 and B3⁎, were calculated from experimental activity data and the partial molar volume of solute and solvent [21]. The osmotic second and third virial coefficients can be decomposed into repulsive and attractive components as [21]  P  R2min ¼ f 4 V 20

ð8Þ

A2min ¼ R2min  NB*2

ð9Þ

 2 P0 R3min ¼ 10 V 2

ð10Þ

A3min ¼ R3min  N 2 B*3

ð11Þ

65

Fig. 4. Variation of apparent molar volume of binary aqueous solution, as a function of concentration, at 298.15 K for (a) ♦; 4-nitrophenol and ○; hydroquinone, (b) ▲; sodium 4-nitrophenolate.

where f is the factor which is the measure of the ellipticity of the molecule. For spherical molecule f is unity. During data processing the non-electrolyte solutes studied in aqueous medium were assumed as spherical. The values of osmotic second and third virial coefficients as well as the minimum attractive and repulsive contributions to the solute–solute interactions for nitrophenol and hydroquinone are given in Table 3. The third virial coefficients are not given as their authenticity considering the errors is questionable. Table 3 a) Solute–solvent interaction coefficient V¯ 02 (cm3 mol− 1) 4-Nitrophenol 99.13 Hydroquinone 88.91 Sodium 78.85 4-nitrophenolate

RTκ (cm3 mol− 1)

3 −1 NB* 110 (cm mol )

1.12 1.12 1.12

98.01 87.79 77.73

b) Solute–solute interaction coefficient 3 −1 3 −1 3 −1 NB* 2 (cm mol ) − A2min (cm mol ) R2min (cm mol )

4-Nitrophenol 312 Hydroquinone − 210 Sodium 4802 4-nitrophenolate

85 566 –

397 356 –

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S.S. Terdale et al. / Journal of Molecular Liquids 139 (2008) 61–71 Table 4 Kirkwood–Buff integrals

4-Nitrophenol Hydroquinone

0 GAB (cm3 mol− 1)

0 GAA (cm3 mol− 1)

0 GBB (cm3 mol− 1)

NB2⁎ (cm3 mol− 1)

− 93.38 − 85.58

− 16.95 − 16.99

−530.62 443.58

265.31 − 221.79

where μ10 and μ20 are the chemical potentials for pure solvent and solute respectively where as A22 and B222 are the pair and triplet interaction terms of solute particles. The A22 coefficient is related to the second osmotic virial coefficient B2⁎0 by [23] 0 A22 t01 ¼ 2B*2  t02 þ b011

ð13Þ

where υ10 and υ20 are molecular volume of pure solvent and partial molecular volume of solute at infinite dilution respectively. For a 1:1 electrolyte 2ln g2* ¼ A22P m þ B222P m2

ð14Þ

where γ2⁎ is non-electrolyte contribution to the solute activity coefficient, ω = A22 M1 / 2 (M1 is molar mass of solvent in kg mol − 1 ). Thus from Eqs. (6) and (13), one can write P0 NB2*0 ¼ A22 V10 =2 þ V 2  RT j=2:

ð15Þ

The value for solute–solute virial coefficient (B2*0) has been *0 values calculated by obtaining the value of ω. The B2*0 and B11 at 298.15 K determined for sodium 4-nitrophenolate are collected in Table 3.

Fig. 5. Plot of Kirkwood–Buff integrals for (a) 4-nitrophenol and (b) hydroquinone, as a function of mole fraction at 298.15 K. ♦; GAB, ○; GAA and ▲; GBB.

The solute–solute interactions are also evaluated for aqueous solutions of electrolyte in dilute concentration region [22]. This was done by determining the non-electrolyte contribution to the solute activity coefficient by subtracting the Debye–Hückel electrostatic contribution from solute activity coefficient. The activity coefficient of the solute (γ2) in dilute concentration range can be represented as  1 þϖm lng2 ¼ am1=2 1 þ bm1=2

ð12Þ

where α = 1.173 kg1/2 mol− 1/2 at 25 °C and b = 1.0 kg1/2 mol− 1/2 and ω is non-electrolyte solute–solute interaction parameter. Hill [23] has shown that the Gibbs free energy for mole ratio of solute to solvent ( P m)[19,22] can be expressed as 2 G A0 P mA0 1 P P ¼ 1 þ 2 P m þm ln m þ A22 P m N1 kT kT 2 kT 1 þ B222 P m 3 þ N N :: 3

3.1.4. Application of the Kirkwood–Buff theory The information of molecular interactions involved in the solution of non-electrolyte has also been obtained by applying the Kirkwood–Buff (KB) theory [24]. The KB theory is an exact theory of solutions which does not involve the assumption of pairwise additivity of the total potential energy and is applicable to both spherical as well as non-spherical molecules [25]. The Kirkwood–Buff theory links the thermodynamic properties to Kirkwood–Buff integrals Gij defined by equation Z

l

Gij ¼

 gij  1 4kr2 dr

ð16Þ

0

where gij is the radial distribution function between species i and j, r is the distance between the centers of molecules i and j. These integrals (solvent–solvent interaction GAA, solute–solute

Table 5 Coefficients Bi in Eq. (23)

B0 B1 B2 B3

4-Nitrophenol

Hydroquinone

Sodium 4-nitrophenolate

− 11.4003 48.68397 − 15.7765 –

− 6.59715 22.86657 − 14.399 25.64649

−12.1013 76.4666 − 384.404 1155.74

S.S. Terdale et al. / Journal of Molecular Liquids 139 (2008) 61–71 Table 6 Water activity for ternary system, H2O + 0.1 m α-CD + guest m2 (mol kg− 1)

aW

Δ / m1m2 (observed)

Δ / m1m2 (calculated)

% Error in aw

4-Nitrophenol + 0.1 m α-CD + H2O 0.018893 0.99820 −10.4719 0.030045 0.99819 −9.9540 0.040940 0.99816 −9.4499 0.050512 0.99813 −8.9968 0.060999 0.99808 −8.4930 0.072216 0.99802 −7.9544 0.081977 0.99796 −7.4951 0.092459 0.99788 −7.0217 0.102638 0.99779 −6.5913

− 10.4861 −9.9518 −9.4336 −8.9814 −8.4894 −7.9668 −7.5154 −7.0339 −6.5697

0.0000 0.0000 0.0001 0.0001 0.0000 −0.0002 −0.0003 −0.0002 0.0004

Hydroquinone + 0.1 m α-CD + H2O 0.02149 0.99801 −6.1196 0.03882 0.99787 −5.7189 0.05652 0.99771 −5.3426 0.08047 0.99746 −4.8412 0.09958 0.99723 −4.4425 0.12068 0.99696 −4.0044 0.14039 0.99668 −3.5983 0.15873 0.99639 −3.2241 0.18269 0.99598 −2.7414 0.20223 0.99561 −2.3526

−6.1122 −5.7297 −5.3461 −4.8369 −4.4375 −4.0023 −3.5998 −3.2278 −2.7438 −2.3497

0.0000 −0.0001 0.0000 0.0001 0.0001 0.0000 0.0000 −0.0001 −0.0001 0.0001

− 10.8419 −9.81559 −8.98405 −8.18485 −7.58075 −6.93478 −6.32065 −5.80138 −4.98678

−0.0003 0.0009 0.0001 −0.0009 −0.0010 −0.0002 0.0010 0.0014 −0.0012

Sodium 4-nitrophenolate + 0.1 m α-CD + H2O 0.01801 0.99787 −10.9213 0.03557 0.99748 −9.6685 0.05239 0.99709 −8.9722 0.07129 0.99663 −8.2537 0.08746 0.99620 −7.6439 0.10611 0.99568 −6.9428 0.12417 0.99516 −6.2743 0.13884 0.99471 −5.7456 0.15968 0.99405 −5.0283

interaction GBB and solute–solvent interaction GAB) are evaluated following inversion procedure of the Kirkwood– Buff theory as described by Ben-Naim [26] from experimental data of activity, partial molar volumes and isothermal compressibility [26,27]. In this A represents the solvent and B represents the solute. The values of KB integrals are plotted in Fig. 5 as a function of solute concentration and the values obtained at infinite dilution (Gij0) are given Table 4. The coefficient GBB0 is related to the osmotic second virial coefficients B⁎2 through the equation G0BB ¼ 2NB2*

ð17Þ

where N is the Avogadro's number [25–27]. We did not make the application of this theory to aqueous solutions of sodium 4nitrophenolate as it requires single ion activity data. 3.2. Ternary aqueous mixtures 3.2.1. Activity coefficients The molal activity coefficient of non-electrolyte γ1 (α-CD) in the ternary system is expressed as a function of concentra-

67

tion of the α-CD (m1) and guest solute (m2) (i.e. 4-nitrophenol or sodium 4-nitrophenolate or hydroquinone) using the equation ln g1 ¼

l X l X i¼0

Aij mi1 mj2

ðA00 ¼ 0Þ

ð18Þ

j¼0

If we expand Eq. (6) including all the fourth order terms we get [2], lng1 ¼ lng01 þ A01 m2 þ A11 m1 m2 þ A02 m22 þ A03 m32 þ A21 m21 m2 þ A12 m1 m22 þ A31 m31 m2 þ A22 m21 m22 þ A13 m1 m32 þ A04 m42

ð19Þ

where γ10 is activity coefficient of non-electrolyte (α-CD) in binary aqueous solutions represented as lng01 ¼ A1 m1 þ A2 m21 þ A3 m31 þ A4 m41 . It is taken from the data of binary aqueous α-CD solutions reported earlier [3] and the coefficients Ai are included in Table 2. A similar expression for the

Table 7 Activity coefficient, free energies of transfer and excess free energy for ternary system H2O + 0.1 m α-CD + guest, at 298.15 K γ0 m2 (mol kg− 1)

γ1

γ2

ΔG1tr ΔG2tr ΔGE (J mol− 1) (J mol− 1) (J mol− 1)

4-Nitrophenol + 0.1 m α-CD + H2O 0.00000 0.99997 1.04464 0.32640 0.01889 1.00031 0.84957 0.35423 0.03005 1.00050 0.75810 0.36725 0.04094 1.00067 0.68218 0.37781 0.05051 1.00081 0.62468 0.38561 0.06100 1.00095 0.57006 0.39293 0.07222 1.00109 0.51988 0.39993 0.08198 1.00120 0.48211 0.40591 0.09246 1.00131 0.44679 0.41295 0.10264 1.00140 0.41698 0.42126

0.12 − 0.81 − 1.31 − 1.78 − 2.19 − 2.63 − 3.10 − 3.50 − 3.91 − 4.29

0.0 −511.5 − 793.3 − 1054.4 − 1272.2 − 1498.5 − 1726.5 − 1912.9 − 2101.0 − 2271.7

− 2771.0 − 2534.5 − 2401.9 − 2276.1 − 2167.9 − 2051.2 − 1927.3 − 1819.4 − 1702.1 − 1585.5

Hydroquinone + 0.1 m α-CD + H2O 0.00000 0.99996 1.04560 0.51490 0.02149 1.00020 0.91218 0.53148 0.03882 1.00037 0.82328 0.54472 0.05652 1.00052 0.74648 0.55822 0.08047 1.00071 0.66092 0.57660 0.09958 1.00082 0.60498 0.59156 0.12068 1.00093 0.55360 0.60858 0.14039 1.00100 0.51380 0.62520 0.15873 1.00104 0.48275 0.64151 0.18269 1.00105 0.44962 0.66441 0.20223 1.00103 0.42798 0.68477

0.11 − 0.53 − 1.01 − 1.48 − 2.08 − 2.53 − 3.01 − 3.44 − 3.82 − 4.29 − 4.64

0.0 − 337.4 − 590.7 − 832.7 −1133.3 − 1351.6 − 1570.7 − 1754.7 − 1908.3 − 2083.5 − 2204.9

− 1640.9 − 1525.2 − 1431.2 − 1335.2 − 1206.5 −1105.5 − 996.1 − 896.1 − 804.8 − 687.7 − 593.3

Sodium 4-nitrophenolate + 0.1 m α-CD + H2O 0.00000 1.00018 1.04500 0.54926 0.65 0.01801 1.00030 0.85018 0.54898 − 0.92 0.03557 1.00054 0.70933 0.57763 − 1.89 0.05239 1.00075 0.60570 0.60066 − 2.69 0.07129 1.00096 0.51507 0.62087 − 3.52 0.08746 1.00111 0.45345 0.63430 − 4.21 0.10611 1.00126 0.39606 0.64692 − 4.98 0.12417 1.00138 0.35137 0.65795 − 5.71 0.13884 1.00145 0.32144 0.66734 − 6.25 0.15968 1.00153 0.28720 0.68356 − 6.92

0.0 − 509.7 − 957.0 − 1346.8 − 1746.8 − 2061.0 − 2394.7 − 2689.7 − 2908.9 − 3186.2

− 2961.7 − 2870.5 − 2569.5 − 2352.6 − 2176.3 − 2062.7 − 1954.3 − 1856.1 − 1772.8 − 1640.1

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S.S. Terdale et al. / Journal of Molecular Liquids 139 (2008) 61–71

activity coefficient of solute (γ2) may be obtained by applying cross differentiation relation:

 ∂lng1 ∂lng2 ¼m ∂m2 m1 ∂m1 m2 where ν is the number of ions formed by the dissociation of solute molecule. The result is lng2 ¼ lng02 l X l  X þ i¼0

j¼1

 j ðiþ1Þ ð j1Þ Aij m1 m2 ði þ 1Þm

ðA00 ¼ 0Þ ð20Þ

where γ2 is activity coefficient of solute in ternary aqueous system and γ20 is that in binary aqueous system. The coefficients Aij in Eq. (18) were retained up to fourth power of concentration. These coefficients may be related to an experimental quantity Δ, which is defined as [28–30] D ¼ 55:51 ln aw  m1 /01  mm2 /02

ð21Þ

where ϕ10 and ϕ20 are the osmotic coefficients of α-CD and the solute respectively, in binary aqueous systems. By applying Gibbs–Duhem relation for both binary and ternary systems it has been shown that [31] D=m1 m2 ¼ A01 þ A11 m1 þ 2A02 m2 þ 3A03 m22 þ A21 m21 þ ð3=2ÞA12 m1 m2 þ A31 m31 þ ð4=3ÞA22 m21 m2 þ 2A13 m1 m22 þ 4A04 m32 :

Fig. 7. Variation of activity coefficient of solute (γ2) in aqueous ternary solutions containing 0.1m α-CD, as a function of concentration of solute at 298.15 K for ♦; 4-nitrophenol, ○; hydroquinone and ▲; sodium 4-nitrophenolate.

that Eq. (22) can be expressed in terms of concentration of guest (m2) as D=m1 m2 ¼ B0 þPB1 m2 þ B2 m22 þ B3 m32 i:e: D=m1 m2 ¼ Bi mi2 i¼0

where ð22Þ

Since the concentration of α-CD (m1) is kept constant in the this study, it can be incorporated into the coefficients (Aij) so

B0 ¼ A01 þ A11 m1 þ A21 m21 þ A31 m31 B1 ¼ 2A02 þ ð3=2ÞA12 m1 þ ð4=3ÞA22 m21 B2 ¼ 3A03 þ 2A13 m1 B3 ¼ 4A04

ð23Þ

The Δ / (m1m2) is obtained with the help of Eq. (21) and the coefficients Bi can be found by the method of least squares. The values of Bi coefficients are given in Table 5. Using Eq. (23), Eqs. (19) and (20) have been derived in terms Bi coefficients and are given below.  l
X 1 ðiþ1Þ ln g1 ¼ lng01 þ ð24Þ Bi m2 i þ 1 i¼0 ln g2 ¼ ln g02 þ

l h X m1 i Bi mi2 : m i¼0

ð25Þ

The values of Δ / (m1m2) are recalculated using the least square fit coefficients Bi and were further used for the recalculation of water activity. The reliability of the data is expressed in terms of percentage error given by [2] k error in aw ¼ Fig. 6. Variation of activity coefficient of 0.1 m α-CD (γ1) in aqueous ternary solutions containing solute, as a function of concentration of solute at 298.15 K for ♦; 4-nitrophenol, ○; hydroquinone and ▲; sodium 4-nitrophenolate.

aw ðcaldÞ  aðobsdÞ  100: aw ðobsdÞ

ð26Þ

The observed and calculated values of Δ / (m1m2) along with percentage error in water activity are produced in Table 6. From the

S.S. Terdale et al. / Journal of Molecular Liquids 139 (2008) 61–71

69

Table 8 Pair, triplet interaction parameters, salting coefficients and thermodynamic equilibrium constants of the system H2O + 0.1 m α-CD + guest, at 298.15 K g12 g112 g122 kS log (J kg mol− 2) (J kg2 mol− 3) (J kg2 mol− 3) (kg mol− 1) K 4-Nitrophenol − 13,960.6 Hydroquinone −8009.31 Sodium −6993.47 4-nitrophenolate

−390.292 −267.69 −246.432

19,563.57 8712.783 4381.437

− 11.3 − 6.5 − 11.3

4.9 2.8 4.9

3.2.2. Transfer free energies and salting constant The salting constant values are determined by applying the method based on the application of the McMillan–Mayer theory of solutions [2]. According to which Gibb's free energy of transfer of α-CD (1) from water (W) to an aqueous solution containing solute (2) is given by [32]

Fig. 8. Variation of Gibb's free energies of transfer of 0.1 m α-CD (ΔG1tr) from water to solutions containing solute as a function of concentration of solute at 298.15 K for ♦; 4-nitrophenol, ○; hydroquinone and ▲; sodium 4-nitrophenolate.

measured water activity, the activity coefficient of the solvent (γ0) has been calculated. The activity coefficient for α-CD (γ1) and activity coefficient for the solute (γ2) are calculated using Eqs. (24) and (25) respectively and are given in Table 7. The variation of γ1 and γ2 with solute concentration is shown in Figs. 6 and 7 respectively.

DG1tr ðW YW þ 2Þ ¼ 2mm2 g12 þ 6mm1 m2 g112 þ 3m2 m22 g122 þ N N ::

ð27Þ

where m1 and m2 are the molalities of α-CD (1) and solute (2) respectively defined per kg of water and ν is the number of ions into which electrolyte dissociates. The variation of ΔGtr1 with solute concentration is shown in Fig. 8. The g12, g112… are the pair and triplet interaction parameters, which take into account all sources of non-ideality in the ternary system. The Gibb's free energy for the transfer of solute from water to aqueous α-CD solution is given by DG2tr ðW YW þ 1Þ ¼ 2mm1 g12 þ 3mm21 g112 þ 6m2 m2 m1 g122 þ N N ::

ð28Þ

The variation of ΔGtr2 with solute concentration is shown in Fig. 9. At low α-CD and solute concentrations all triplet and higher-order terms can be neglected and the pair interaction parameter g12 can be related to the familiar salting coefficient kS by RTkS ¼ 2mg12 :

ð29Þ

Transfer free energies for transfer of α-CD from aqueous binary to ternary solutions containing other solute (i.e. 4nitrophenol or sodium 4-nitrophenolate or hydroquinone) (data are given in Table 7) have been used to calculate pair and triplet interaction parameters using Eq. (27). The salting constant values are reported in Table 8. 4. Discussion

Fig. 9. Variation of Gibb's free energies of transfer of solute (ΔG2tr) from water to 0.1m α-CD solutions as a function of concentration of solute, at 298.15 K for ♦; 4-nitrophenol, ○; hydroquinone and ▲; sodium 4-nitrophenolate.

On examination of Fig. 2, it is noted that the osmotic coefficient decreases with concentration of phenols showing the presence of non-ideality. In case of sodium 4-nitrophenolate similar behavior is observed. The activity coefficients (Fig. 3) of both non-electrolytes decrease with increase in concentration of solute in the studied concentration range while in case of nitrophenolate ions, a positive deviation from the Debye–

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Hückel limiting law is noted. All these results indicate the importance of solute–solute and ion–ion interactions in binary aqueous solutions. The volumetric behaviour of the studied solutes yields information about solute–solvent (at infinite dilution) and solute–solute interaction via the Bv parameter (Eq. (5)). Seen in this way, it is observed from Fig. 4, that solute–solute interaction deviation parameter Bv with respect to volume properties is small in case of hydroquinone and sodium 4-nitrophenolate. In case of nitrophenol, we observe negative Bv parameter in dilute concentration region and a minimum in apparent molar volume at a concentration of about 0.05 mol kg− 1. For many monofunctional non-electrolytes such behaviour in water is well known [33,34] and is interpreted in terms of solute induced effect due to overlap of cosphere water molecules. The solute–solvent virial coefficients (NB11⁎0) obtained for these systems by the application of the McMillan–Mayer theory (Table 3a) show marginal differences with partial molar volume of these solutes. The solute–solute osmotic virial coefficient (NB2⁎) exhibit important observations. For example for 4nitrophenol and sodium 4-nitrophenolate positive virial coefficients are obtained while for hydroquinone a negative coefficient is obtained. It is thus clear that increase in number of functional groups in a molecule makes virial coefficient negative (i.e. minimum attractive contribution to second virial coefficient increases as the number of functional groups capable of participating hydrogen bond formation increases which is in harmony with the interpretation suggested by Kauzmann et al. [21] for carbohydrate solutes in water) whereas the positive virial coefficient for nitrophenol signifies importance of pairwise hydrophobic interactions. The value of NB2⁎ for electrolyte (sodium 4-nitrophenolate) is high positive indicating the importance of ion–ion interaction. The data for two non-electrolytes when subjected to scrutiny by application of KB theory, we note that the Gij integrals reveal the followings: 1) the GAA and GAB parameters representing solvent–solvent and solute–solvent interaction effects respectively are almost constant as a function of mole fraction of solute indicating presence of weak solute–solvent interaction, 2) the GBB parameter varies typically with increase in concentration of solute and goes through a maximum. It is suggested that the strength of hydrophobic interaction increases in dilute concentration region while at high concentrations due to pair, triplet and higher-order interactions the strength decreases. The infinite dilution values for both the compounds (Eq. (17)) i.e. GBB0 (Table 4) yield the second virial coefficient values which are in good agreement with those obtained by the application of the McMillan–Mayer theory of solutions. Let us examine now the data of ternary aqueous solutions of these solutes (i.e. guests) in presence of fixed concentration of αCD. Fig. 6 shows that the activity coefficient of α-CD decreases as the solute concentration is increased. The decrease is comparatively smaller in case of hydroquinone than the nitrophenol and sodium nitrophenolate. The trace activity coefficients of these solutes get lowered due to the presence of α-CD in aqueous solutions (Fig. 7). Thus the lowering of activity coefficient of α-CD as well as solute molecules can be attributed

to formation of complexed species having host–guest type equilibria. The solute activity coefficients increase with increase in concentration of solute. It was expected to have extrema at stoichiometric concentration due to complexation. However, such behaviour is not observed meaning the presence of cooperative binding interactions having a higher order in complexation. The calculations carried out using Eqs. (27) and (28) reveal that on transferring α-CD from aqueous solutions to aqueous solute solutions cause negative free energy changes (Fig. 8). Similar calculations for transfer of solute molecules from aqueous to aqueous α-CD solutions also yield negative transfer free energy changes (Fig. 9). Thus our interpretation of binding equilibria between α-CD as a host and solute molecules as guest gets justified. The concentration variation of ΔGtr2 indicate positive slopes meaning that negative free energy contribution to the process of complexation gets decreased due to occupation of α-CD structural cavities by incorporation of guest molecules. The data of transfer free energies when subjected to the analysis by the McMillan–Mayer theory of solutions, it is observed that the pair wise interaction parameters (g12) are negative while the g112 parameters are also negative. Therefore, the complexation process between host and guest molecules is spontaneous and is assisted by hydrophobic interactions (i.e. between complexed α-CD molecules). However, the g122 parameters are all positive meaning α-CD-solute–solute triplet interactions are not favourable in solution phase. The salting constant values are negative (Table 8) and the thermodynamic equilibrium constant values are positive in the order sodium 4-nitrophenolate ≈ 4-nitrophenol N hydroquinone. It is seen that the negatively charged phenolate ion is similar in complex forming capacity to that of nitrophenol. Probably this is due to very feeble charge over the entire anionic species due to low charge density. The inner cavity of α-CD is known to be hydrophobic and hence the anionic species gets stabilized by dispersive interactions as well as due to hydrophobic association between α-CD molecules. In literature, the equilibrium constant values for the solutes by various techniques are known [10,14] and are quite low as compared to the values obtained in the present work. The differences may be due to the fact that reported values are generally at different pH or in buffers. Moreover, these are based upon the neglect of activity coefficient ratios in an equilibrium equation. 5. Conclusions Osmotic coefficient and activity coefficient studies made for aqueous solutions of 4-nitrophenol and hydroquinone at different concentrations enabled us to derive useful information about the interactions. The negative deviations in case of activity coefficients signify that these molecules are solubilized by hydrophobic hydration and interaction in aqueous medium. The second virial coefficients (B2⁎) calculated by application of the Kirkwood–Buff and McMillan–Mayer theories of solutions for both the solutes are in agreement with each other, however for 4-nitrophenol, a positive while for hydroquinone a negative value of NB2⁎ appears. Thus, it is suggested that the presence of

S.S. Terdale et al. / Journal of Molecular Liquids 139 (2008) 61–71

more than one functional group affect the second virial coefficient value for such molecule. The variation of KB integral for solute–solute interaction as a function of solute concentration indicates that for both the solutes, the strength of interaction increases initially and thereafter decreases with further increase in concentration due to hydrophobic hydration. The data of osmotic and activity coefficient for electrolyte sodium 4-nitrophenolate are also obtained and analyzed with the help of Debye–Hückel limiting law. The observed positive deviation from limiting law is interpreted in terms of ion–ion interactions. The virial coefficient for the solute electrolyte is estimated by the application of the McMillan–Mayer theory and which is found to be of high positive magnitude. The high NB2⁎ values in case of sodium salt of 4-nitrophenol shows the importance of coulombic attractions. The above solutes studied in presence of α-CD indicate lowering of activity coefficients, which has been interpreted in terms of complexation of host– guest type equilibria in solution phase. The data of transfer free energies from binary to ternary solution enabled us to calculate salting-in constant and thermodynamic equilibrium constant values for the complexation reaction by the application of the McMillan–Mayer theory of virial coefficients. The high negative kS values and positive K values support the interpretation that these complexation reactions are attenuated by hydrophobic interaction between the complexed α-CD molecules. Acknowledgement We are grateful to the referee for his constructive suggestions which helped to improve the investigations reported here. References [1] [2] [3] [4]

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