Thermodynamic Studies of Aqueous Solutions of 2,2,2-Cryptand at

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Thermodynamic Studies of Aqueous Solutions of 2,2,2-Cryptand at 298.15 K: Enthalpy−Entropy Compensation, Partial Entropies, and Complexation with K+ Ions Vasim R. Shaikh,† Santosh S. Terdale,‡ Abdul Ahamad,† Gaurav R. Gupta,† Dilip H. Dagade,§ Dilip G. Hundiwale,† and Kesharsingh J. Patil*,† †

School of Chemical Sciences, North Maharashtra University, Jalgaon-425001, India Department of Chemistry, University of Pune, Pune-411007, India § Department of Chemistry, Shivaji University, Kolhapur-416004, India ‡

ABSTRACT: The osmotic coefficient measurements for binary aqueous solutions of 2,2,2-cryptand (4,7,13,16,21,24hexaoxa-1,10-diazabicyclo[8.8.8] hexacosane) in the concentration range of ∼0.009 to ∼0.24 mol·kg−1 and in ternary aqueous solutions containing a fixed concentration of 2,2,2cryptand of ∼0.1 mol·kg−1 with varying concentration of KBr (∼0.06 to ∼0.16 mol·kg−1) have been reported at 298.15 K. The diamine gets hydrolyzed in aqueous solutions and needs proper approach to obtain meaningful thermodynamic properties. The measured osmotic coefficient values are corrected for hydrolysis and are used to determine the solvent activity and mean ionic activity coefficients of solute as a function of concentration. Strong ion-pair formation is observed, and the ion-pair dissociation constant for the species [CrptH]+[OH−] is reported. The excess and mixing thermodynamic properties (Gibbs free energy, enthalpy, and entropy changes) have been obtained using the activity data from this study and the heat data reported in the literature. Further, the data are utilized to compute the partial molal entropies of solvent and solute at finite as well as infinite dilution of 2,2,2-cryptand in water. The concentration dependent non-linear enthalpy−entropy compensation effect has been observed for the studied system, and the compensation temperature along with entropic parameter are reported. Using solute activity coefficient data in ternary solutions, the transfer Gibbs free energies for transfer of the cryptand from water to aqueous KBr as well as transfer of KBr from water to aqueous cryptand were obtained and utilized to obtain the salting constant (ks) and thermodynamic equilibrium constant (log K) values for the complex (2,2,2-cryptand:K+) at 298.15 K. The value of log K = 5.8 ± 0.1 obtained in this work is found to be in good agreement with that reported by Lehn and Sauvage. The standard molar entropy for complexation is also estimated for the 2,2,2-cryptand−KBr complex in aqueous medium.

1. INTRODUCTION Supramolecular chemistry, broadly the chemistry of multicomponent molecular assemblies in which the component structural units are typically held together by a variety of weaker (non-covalent) interactions, has rapidly developed in the last about two decades.1,2 This involves the design and investigation of preorganized molecular receptors that are capable of binding specific substrates with high efficiency and selectivity. Pedersen,3 Lehn,4 Cram,5 and others published the synthesis of macrocyclic molecules (crown ethers, cryptands, spherands, and so forth) that are able to selectively bind ions or small organic molecules as well as water molecules via non-covalent interactions. The concepts developed in supramolecular chemistry are increasingly used in fields like material science, surface science, sensor technology, and nanotechnology. In biology and chemistry, it is expected that with the help of the studies on the supramolecular entities a better understanding on the roles of enzymes with their catalytic activities can be achieved. Cryptands are a novel class of macrocyclic ligands discovered by Lehn6,7 that form stable complexes with a variety of cations; © XXXX American Chemical Society

these complexes are known as cryptates. Numerous studies have been reported on the thermodynamics of complexing of cations by cryptands in water7−10 and other solvents11−13 and also on the rates of complex formation and dissociation.12−15 The standard molal free energies, enthalpies, and entropies have been studied especially for 2,2,2-cryptand in water (wherein protonation is avoided by addition of bases like KOH or NaOH) as well in methanol.16 Heat capacity and volume changes for monoprotonation and diprotonation of 2,2,2-cryptand in water have been studied by Morel-Desrosiers et al.17,18 Although the interactions between the solvent and the cryptate cations have received wide attention, the exact nature of these interactions and the balance between the external effects and the internal modifications of the ligand upon complexation are not yet fully understood. Our previous work was concerned with the measurements of osmotic coefficients, activity and activity coefficient properties Received: November 3, 2013 Revised: November 14, 2013

A

dx.doi.org/10.1021/jp410814w | J. Phys. Chem. B XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry B

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solutions containing KBr. All of these results are presented and discussed in the following pages.

of electrolytes and non-electrolytes as well as of surfactants in aqueous solutions of 18-crown-6 and also of aqueous cyclodextrin solutions.19−25 It has been shown with the help of NMR relaxation and diffusion data26,27 that the conformations of these host molecules, their H-bonding with water molecules in the cavities, as well as hydrophobic interaction along with the water structure-making effect govern equilibrium properties in the solution phase. The observed enthalpy−entropy compensation (EEC) effect22,28,29 and application of McMillan−Mayer theory for solution30−32 to obtain osmotic second virial coefficient values for the solute molecules have helped us to understand solute−solvent interactions and solute−solute association in such solutions. The EEC is a very important phenomenon for understanding the molecular interactions in the solution phase of the large numbers of systems ranging from small molecules (alcohols, amino acids, salts, etc.) to the enormous biomolecules (proteins, DNA, etc.).33−35 To yield useful valid data from the EEC effect, the separate experimental source of enthalpy and Gibbs free energy data are required. We have already reported the utility of activity and heat data for understanding the concentration dependent EEC effects and obtained the partial molar entropies of solute as well as of solvent for 18-crown-6, 15-crown-5, and amino acids in aqueous solutions.22,28,29 The main conclusion was that, to adopt a particular conformation and to stabilize guest molecules, along with the H-bonding, the electrostatic interactions, hydrophobic pairwise interactions are also important. The molecular dynamics study by Kowall and Geiger,36 ab initio studies,37 as well as the neutron diffraction experiments38 with the 18-crown-6 system indicate that the hydrophobic hydration of crown plays an important role in governing the conformational dynamics of 18-crown-6 in aqueous solutions which elucidates the importance of cooperative electrostatic interactions. The hydrophobic interaction,39,40 i.e., association of the non-polar moieties of the molecule in water, is thus important and even exists for small size molecules in water, for example, acetone, tertiary butanol, trimethyl-amine, and tetramethyl-urea, as shown by studies of the NMR-association parameter.41,42 Such studies have not yet been reported on the hydration and complexation for cryptands. Additionally, Ben-Naim has discussed solvent induced interactions in terms of hydrophobic and hydrophilic attraction phenomena.43,44 According to him, the hydrophilic interactions are more significant and are of more functionality in biochemical processes than hydrophobic interactions. In this context, 2,2,2-cryptand in water could be a good model system to study such solvent induced interactions which is due to topology and conformational states of the cryptand ligand and its hydration behavior especially in water. It is known that the free macrocyclic ligands and their complexes may exist in three forms: out−out (exo−exo), out−in (exo− endo), and in−in (endo−endo), differing by the orientation of the nitrogen bridgeheads toward the inside or the outside of the intramolecular cavity.45,46 Also, there are complications due to protonation of the nitrogens in aqueous solutions. Recently, we have shown successfully that if the density data of aqueous 2,2,2-cryptand solutions when corrected properly for hydrolysis yield results for volume changes due to ionization (negative volume change) and complexation with K+ ions (positive volume change) in conformity with each other as well gives the volume change due to addition of proton to the monoprotonated 2,2,2-cryptand.47 In the present work, we report the experimental osmotic data and analysis for binary aqueous 2,2,2-cryptand solutions and ternary aqueous 2,2,2-cryptand

2. EXPERIMENTAL SECTION 2.1. Materials. 2,2,2-Cryptand (purity 98%) was procured from Sigma-Aldrich and used without further purification. The molecular structure of the 2,2,2-cryptand is shown in Figure 1.

Figure 1. Molecular structure of the 2,2,2-cryptand.

The salt KBr of AR grade (Merck) was dried under a vacuum at 393 K for 24 h before use. All of the solutions were prepared on a molality basis using quartz doubly distilled water, and for every measurement, the solutions were prepared freshly. The weighing of the substance, required for solution preparation, was done by using a Shimadzu AUW220D high precision analytical balance having a readability of 0.01 mg. 2.2. Experimental Method. The osmotic coefficients for binary and water activity for the ternary system were measured using a Knauer Vapor Pressure Osmometer (model: K-7000) at 298.15 ± 0.001 K. The details about the calibration, measurements, and error analysis of the vapor pressure osmometer were described earlier.20,48,49 The density data for aqueous binary 2,2,2-cryptand solutions and ternary solutions (with a fixed 2,2,2-cryptand (∼0.1 mol·kg−1) and varying the KBr concentration) at 298.15 K were obtained by using an Anton Paar Digital Densitometer (DMA-5000), and the details are given in our earlier publication.47

3. RESULTS 3.1. Binary Aqueous 2,2,2-Cryptand Solutions. 3.1.1. Osmotic and Activity Coefficients. Earlier, we reported that the hydrolysis correction is essential for the 2,2,2-cryptand in aqueous solutions especially at low concentrations and hence molalities were corrected for hydrolysis and used subsequently for all the calculations. The monoprotonation is important for which the hydrolysis constant is 7.27 × 10−5. The diprotonation is being neglected, as the hydrolysis constant is of the order 10−7. Thus, if α is the degree of hydrolysis (the values are taken from our recent paper),47 then [(1 − α)mexp] is the molality of unhydrolyzed 2,2,2-cryptand, where mexp is the experimental molality. The experimental osmotic coefficient ϕ01 values of 2,2,2-cryptand in aqueous solutions were determined over the concentration range of ∼0.009 to ∼0.24 mol·kg−1 at 298.15 K using the following expression: Osmolality ϕ10 = v1m1 (1) where v1 is the number of ions produced on dissociation of 2,2,2-cryptand at infinite dilution and m1 is the molality of the 2,2,2-cryptand after hydrolysis correction in binary aqueous solutions [m1 = (1 − α)mexp]. According to the definition of B



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The data of water activity (aw), activity coefficient of water (γ00), and activity coefficient of solute (γ01) are collected in Table 2. The variation of the mean molal activity coefficient of 2,2,2cryptand (γ01) as a function of the square root of the molality of 2,2,2-cryptand in aqueous binary solutions ((m1)1/2) at 298.15 K is shown in Figure 3. The osmotic coefficient for 2,2,2-cryptand decreases drastically as a function of the concentration of cryptand, indicating that strong ion-pair formation must be occurring in this system. Hence, the osmotic coefficient data from this work are used to obtain the ion-pair dissociation constant for cryptate hydroxide in aqueous solution at 298.15 K for which the method reported by Masterton and Berka51 is used. In this method, the experimental osmotic coefficient (ϕ01) is related to the degree of dissociation of ion-pair (α′) as

osmotic coefficient (eq 1), if we plot the ratio of osmolality to molality as a function of molality, then extrapolating to infinite dilution (i.e., in the limit of zero concentration of solute) yields the value of v1 (=2), since the osmotic coefficient is unity in the limit of infinite dilution as per the standard state based upon Henry’s law. This means that the 2,2,2-cryptand exists in water as 1:1 electrolyte in the form of hydroxide [CrptH]+[OH−]. The osmotic coefficient can now be expressed using the following equation ϕ10 = 1 −

2.303 A γ m1 + 3

n

∑ Ai(m1)i/2 i=2

(2)

where Aγ is the Debye−Hückel limiting slope for aqueous solutions; Aγ is 0.5115 at 298.15 K for aqueous solutions. The coefficients Ai in eq 2 were estimated using the method of least-squares fit and are given in Table 1. The variation of

ϕ10 = α′ϕ1′ 0 +

Table 1. Coefficients Ai in eq 2

(5)

where ϕ1′ 0 and ϕ0′ are true osmotic coefficients for completely dissociated 1:1 electrolyte and completely associated, i.e., neutral ion-paired species, respectively. Under the approximation that the neutral species behave ideally (i.e., at least in the low concentration limit), ϕ′0 = 1, eq 5 becomes

−0.3927 −19.6029 74.9258 −76.7199

A1 A2 A3 A4

(1 − α′) ϕ0′ 2

experimental osmotic coefficient (ϕ01) as a function of the square root of the molality of 2,2,2-cryptand in aqueous binary solutions ((m1)1/2) at 298.15 K is shown in Figure 2.

ϕ10 = α′ϕ1′ 0 +

(1 − α′) 2

(6)

Masterton and Berka51 processed osmotic coefficient data for a large number of 1:1 as well as 2:1 electrolytes at 298.15 K, and averaging all of these, they obtained the data of osmotic coefficients for completely dissociated 1:1 and 2:1 electrolytes as a function of concentration, which can be substituted in eq 6 to calculate the degree of dissociation of ion-pair which in turn is used to estimate the ion-pair dissociation constant K with the help of following equilibrium and eq 7 [2,2,2‐cryptate][OH]aq ⇌ [2,2,2‐cryptate]aq + [OH]aq (1 − α′)m1 α′m1 α′m1

with equilibrium constant K given by K=

The solvent activities (aw) were calculated from the experimental osmotic coefficient (ϕ01) data by making use of the following equation

(3)

where x0 and x1 are the mole fractions of water and the electrolyte solute in the aqueous solutions, respectively. The mean molal activity coefficients of 2,2,2-cryptand (γ01) in binary aqueous solutions were estimated using the equation50 n

ln

γ10

= −2.303A γ m1 +

∑ i=2

(i + 2) Ai (m1)i /2 i

(7)

where γ1′ 0 is the mean molal activity coefficient of completely dissociated 1:1 electrolyte. Using the data for α′ and γ1′ 0 , the equilibrium constant K for ion-pair dissociation is calculated at different concentrations up to ∼0.1 mol·kg−1 and the average value is reported here. We have not considered the concentrations above ∼0.1 mol·kg−1, since the K values obtained are not constant and this is due to the serious assumption in the original method that completely associated ion-pair species are ideal. Thus, using the above method, the ion-pair dissociation constant (K) is found to be 1.19 × 10−2 mol·kg−1. The activity coefficient data obtained for both components have been used to obtain the free energy due to mixing (ΔGm) and excess free energy change (ΔGE) in solution by using eqs 8 and 9, respectively.

Figure 2. Variation of experimental osmotic coefficient (ϕ01) as a function of the square root of the molality of 2,2,2-cryptand in aqueous binary solutions ((m1)1/2) at 298.15 K.

⎛x ⎞ ln a w = −ϕ10⎜ 1 ⎟ ⎝ x0 ⎠

α′ 2m1 (γ ′ 0)2 1 − α′ 1

(4) C

ΔGm = v1RT (x0 ln a w + x1 ln a10)

(8)

ΔGE = v1RT (x0 ln γ0 + x1 ln γ10)

(9)


The uncertainty in ϕ01 values at the lowest concentration is of the order ±1 × 10−3. bThe uncertainty in the water activity (aw) and solvent activity coefficient (γ00) are of the order of ±1 × 10−4. cThe mean molal activity coefficients of solute (ϕ01) at the lowest concentration studied are accurate up to ±1 × 10−3. dThe errors in ΔGE, ΔGmix, and ΔHmix or ΔHE, TΔSmix, and TΔSE are estimated to be of the order of ±0.05 J·mol−1.

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Figure 3. Variation of the mean molal activity coefficient of 2,2,2cryptand (γ01) as a function of the square root of the molality of 2,2cryptand in aqueous binary solutions ((m1)1/2) at 298.15 K.

where xi is the mole fraction for the ith component (i = 0 for solvent and i = 1 for solute), R is the gas constant, T is the absolute temperature, and a01 is the activity of cryptand in binary aqueous solution. For Gibbs free energy change calculations, the activity coefficient data have been converted to mole fraction scale. 3.1.2. Enthalpy−Entropy Compensation and Partial Molal Entropies for Aqueous Solutions of 2,2,2-Cryptand. The virial expansion of excess enthalpy (HE) of solute in aqueous solutions can be represented by HE = ϕL = h2m1 + h3(m1)2 + ...

(10)

where ϕL is the apparent molar relative enthalpy of the solution. Using the literature52 values of coefficients h2 and h3, the ϕL values for this system were calculated at the studied concentrations of 2,2,2-cryptand. The partial molar heat contents of solvent (L̅0) and solute (L̅ 1) were determined using the equations53 L̅ 0 = −

(m1)3/2 ⎛ ∂ϕL ⎞ ⎜⎜ ⎟⎟ 55.51v1 ⎝ ∂(m1)1/2 ⎠

T , P , n0

L1̅ = ϕL +

(m1)1/2 ⎛ ∂ϕL ⎞ ⎜⎜ ⎟⎟ v1 ⎝ ∂(m1)1/2 ⎠

T , P , n0

(11)

(12)

where n0 is the number of moles of solvent. The heat change due to mixing (ΔHmix) per mole of solution is calculated for different concentrations using the equation ΔHmix = x1(ϕL − L1) 55.51 + m1

(13)

where L1 is the relative partial molar heat content of the pure solute. The value of L1 is obtained by plotting L̅1 as a function of the ratio of the number of moles of solvent to the number moles of solute and extrapolating it to zero mole ratio. This extrapolated value is nothing but L1 (=15.37 kJ·mol−1), which is used in eq 13 for estimation of ΔHmix. Using the data of ΔHmix and ΔGmix, entropies of mixing (ΔSmix) have been calculated. Similarly, the excess entropies of solutions (ΔSE) were calculated from ΔGE and ΔHE values. The data of excess and mixing thermodynamic properties are collected in Table 2. The variations of ΔHmix, ΔGmix, and

a

−82.9 −76.4 −72.9 −71.2 −66.5 −62.9 −54.2 −48.8 −46.2 −42.4 −39.1 0.000 0.000 −0.001 −0.002 −0.004 −0.006 −0.016 −0.028 −0.036 −0.050 −0.060 0.00 −4.59 −8.02 −9.87 −14.78 −19.25 −32.05 −42.90 −48.48 −54.58 −55.78 0.00 9.80 16.19 19.69 31.13 41.41 78.49 113.63 134.77 165.65 190.98 0.0 141.7 248.1 308.3 501.5 684.8 1352.8 2019.0 2423.8 3002.6 3429.8 0.000 −0.011 −0.035 −0.054 −0.146 −0.275 −1.099 −2.490 −3.623 −5.631 −7.416 0.0 72.2 127.0 158.1 257.7 352.1 694.0 1031.5 1234.6 1522.5 1732.9 1.0000 0.6946 0.5747 0.5241 0.4106 0.3435 0.2318 0.1918 0.1773 0.1580 0.1415 1.0000 0.8371 0.7186 0.6740 0.6713 0.6118 0.5585 0.5232 0.5144 0.5005 0.5087 0.0000 0.0089 0.0160 0.0201 0.0333 0.0459 0.0926 0.1400 0.1691 0.2112 0.2426

1.00000 0.99973 0.99958 0.99951 0.99919 0.99898 0.99813 0.99734 0.99683 0.99614 0.99549

1.00000 1.00005 1.00016 1.00024 1.00039 1.00064 1.00148 1.00242 1.00298 1.00384 1.00434

0.00 −0.32 −0.78 −1.15 −3.33 −5.56 −16.75 −29.03 −37.10 −49.98 −62.36

0.0 −14.7 −25.0 −30.7 −49.2 −66.2 −127.3 −185.6 −220.3 −270.2 −309.1

0.00 −4.91 −8.80 −11.02 −18.11 −24.81 −48.80 −71.94 −85.58 −104.55 −118.14

TΔSE d (J·mol−1) TΔSmixd (J·mol−1) L̅1 (J·mol−1) L̅0 (J·mol−1) ΔHmix or ΔHE d (J·mol−1) ϕL (J·mol−1) ΔGmixd (J·mol−1) ΔGE d (J·mol−1) γ01 c γ00 b awb ϕ01 a m1 (mol·kg−1)

Table 2. Thermodynamic Data for Aqueous Binary Solutions of 2,2,2-Cryptand at 298.15 K

(S̅00 − S00)E (J·mol−1·K−1)

(S̅01 − S01)E (J·mol−1·K−1)


D



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Figure 4. Plot of the thermodynamic mixing parameters of aqueous 2,2,2-cryptand solutions as a function of the mole fraction of 2,2,2cryptand (x1) at 298.15 K: (●) ΔGmix; (▲) ΔHmix; (■) TΔSmix.

Figure 6. Correlation of the excess enthalpy (ΔHE) and excess entropy (ΔSE) for aqueous solutions of 2,2,2-cryptand at 298.15 K. The enthalpies and entropies of the solution are expressed as per mole of solution.

Figure 5. Plot of the excess thermodynamic properties of aqueous 2,2,2-cryptand solutions as a function of the mole fraction of 2,2,2cryptand (x1) at 298.15 K: (●) ΔGE; (▲) ΔHE; (■) TΔSE.

Figure 7. Correlation of the excess enthalpy (ΔHE) and excess entropy (ΔSE) for aqueous solutions of 2,2,2-cryptand at 298.15 K. The enthalpies and entropies of the solution are expressed as per mole of solute.

(S1̅ − S01)E as a function of the mole fraction of solute at 298.15 K is shown in Figure 8. 3.2. Ternary System: H2O + 0.1 m 2,2,2-Cryptand + KBr. 3.2.1. Calculations of Activity Coefficients of Solutes. Non-ideality in ternary aqueous solutions is defined using the experimental parameter Δ as

TΔSmix are shown in Figure 4, whereas those of ΔGE, ΔHE, and ΔSE are shown in Figure 5 as a function of the mole fraction of the solute. The enthalpy−entropy compensation phenomenon is also observed for the studied system, which is shown in Figures 6 and 7, respectively. In Figure 6, the values of ΔHE and ΔSE are expressed as per mole of solution, while, in Figure 7, they are expressed as per mole of solute. The excess partial molar entropies of solvent (S0̅ − S00)E and solute (S̅1 − S01)E were calculated using the equations53−56 (S0̅ − S00)E =

L̅0 − R ln γ0 T

Δ = −55.51 ln a w − v1m1ϕ10 − v2m2ϕ20

ϕ01

(16)

ϕ02

where and are the osmotic coefficients of 2,2,2-cryptand and of electrolyte (KBr) in binary aqueous solutions, respectively, whereas m1 and m2 are the corresponding molalities. v1 and v2 are the number of ions produced on dissociation of component 1 (2,2,2-cryptand) and component 2 (i.e., KBr), respectively, at infinite dilution in an aqueous ternary mixture. The data of osmotic coefficients for 2,2,2-cryptand (ϕ01) is used from our experimental data of 2,2,2-cryptand in aqueous binary solutions at 298.15 K (Table 2). The data of osmotic coefficients (ϕ02) for KBr in water at 298.15 K was used from the literature.50 It has been shown that the Δ parameter can be

(14)

(L1̅ − L1) − v1R ln γ10 (15) T 0 where S0 is the molar entropy of the pure liquid water and S01 is the molar entropy of the solute in a hypothetical ideal solution of unit mole fraction. The values of the parameters (S̅0 − S00)E and (S̅1 − S01)E are reported in Table 2, while the variation of (S1̅ − S10)E =

E



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Table 4. Water Activity (aw) for the Ternary System H2O + 0.1008 m 2,2,2-Cryptand + KBr at 298.15 K m2 (mol·kg−1)

aw

Δ/m1m2 (obsd)

Δ/m1m2 (calcd)

% error in aw

0.0000 0.0688 0.0906 0.1135 0.1354 0.1655

0.99812 0.99738 0.99706 0.99666 0.99606 0.99492

−12.60 −11.98 −11.23 −9.87 −7.53

−12.56 −12.07 −11.16 −9.89 −7.53

−0.0004 0.0015 −0.0015 0.0003 0.0002

containing 2,2,2-cryptand (γ2), as given by expressions 20 and 21, respectively ln γ1 = ln γ10 + Figure 8. Variation of the excess partial molar entropy of 2,2,2cryptand (S̅1 − S01)E as a function of the mole fraction of 2,2,2-cryptand (x1) at 298.15 K.

ln γ2 = ln γ20 +

γ01

1

(17)

2

where γ1 and γ2 are the mean molal activity coefficients of components 1 and 2, respectively. Since the molality (m1) of the 2,2,2-cryptand is fixed in a ternary system, Δ/m1m2 can be expressed in terms of only m2 using the following expression Δ = m1m2

n

∑ Bi m2i

(18)

i=0

The coefficients Bi were estimated using the least-squares fit method. The least-squares coefficients Bi in eq 18 are collected in Table 3. The values of Δ/m1m2 obtained from the

(20)

n

∑ Bi m2i

(21)

i=0

γ02

+ v1RTm1 ln m1 + m2μ20 + v2RTm2 ln m2

−11.6406 −40.6169 395.5844

+ G1EX (m13/2) + G2EX (m23/2) + 2v1v2m1m2g12 + 3v12v2m12m2g112 + 3v1v22m1m22g122 + ... (22)

least-squares fit method were used for the recalculation of water activity, and the reliability of the data is expressed in terms of the percentage relative difference given by20 % relative difference in a w =

m1 v2

i=0

Bi m2i + 1 i+1

G(m1 , m2) = Gw0 − RT (v1m1 − v2m2) + m1μ10

Table 3. Coefficients Bi in eq 18 B0 B1 B2

n

∑

where and are the mean molal activity coefficients for 2,2,2-cryptand and KBr, respectively, in corresponding aqueous binary solutions. The data of mean molal activity coefficients γ1 and γ2 are collected in Table 5; their variations with KBr concentration are shown in Figure 9. The activity data, which have been converted to the mole fraction scale, were used to calculate the excess Gibbs energy change (ΔGE) for the studied ternary system which has also been included in Table 5. 3.2.2. Transfer Free Energies and Thermodynamic Equilibrium Constant. The salting constant and thermodynamic equilibrium constant values were determined by applying the method based on application of the McMillan− Mayer theory of solutions.30 In this method, the total Gibbs energy of a solution containing 1 kg of water (W), m1 moles of electrolyte 1 which dissociates into ν1 ions, and m2 moles of electrolyte 2 which dissociates into ν2 ions is given by30,57

related to activity coefficients of solute components in ternary solutions using the Gibbs−Duhem equation50 ⎛ ∂ ln γ2 ⎞ ⎛ ∂ ln γ1 ⎞ Δ = ν1⎜ ⎟ ⎟ = ν2⎜ m1m2 ⎝ ∂m1 ⎠m ⎝ ∂m2 ⎠m

1 v1

G0w

μ01

where is the Gibbs energy of 1 kg of pure water, and μ 10 are the standard chemical potentials of electrolyte 1 (2,2,2-cryptand) and electrolyte 2 (KBr), respectively, 3/2 EX 3/2 GEX 1 (m1 ) and G2 (m2 ) are the excess Gibbs energies of the corresponding binary systems, and g12, g112, etc., are the pair, triplet, and higher order interaction parameters which take into account all sources of non-ideality in the ternary system. For example, g12 is a measure of the new interactions between 2,2,2-cryptand and KBr and of the corresponding decrease in the cryptand−water and KBr−water interactions. An equation for the binary systems G(m1) and G(m2) can readily be derived from eq 22 by setting m1 or m2 equal to zero. The Gibbs energies of transfer of cryptand from water to an aqueous KBr solution (ΔG1tr) are given by the difference between the chemical potentials of cryptand in KBr solutions and in water. At constant temperature and pressure, from eq 22,

a w (calcd) − a w (obsd) × 100 a w (obsd) (19)

where aw(calcd) is the water activity calculated by eq 19 using the values of Δcalcd. The observed and calculated values of Δ/ m1m2 along with the error in water activity, expressed as % relative difference, are given in Table 4. From the measured water activity, the activity coefficients of the solvent (water) in a ternary mixture (γ0) have been calculated. Substituting eq 18 into eq 17 and integrating it yields the equations for the mean molal activity coefficient of 2,2,2cryptand in a ternary mixture containing KBr (γ1) and the mean molal activity coefficient for KBr in a ternary mixture F



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Table 5. Activity Coefficient Data for Each Component, Excess Gibbs Free Energy for Mixture, and Transfer Gibbs Free Energies for Transfer of Solute from Binary to Ternary Mixture for the Ternary System H2O + 0.1008 m 2,2,2-Cryptand + KBr, at 298.15 K m2 (mol·kg−1) 0.0000 0.0688 0.0906 0.1135 0.1354 0.1655 a

γ0

γ1

1.00006 0.99834 0.99788 0.99747 0.99728 0.99735

0.2234 0.1457 0.1274 0.1115 0.0993 0.0871

γ2 0.5561 0.4591 0.4636 0.4794 0.5059 0.5630

a

ΔGE (J·mol−1)

ΔG1tr (J·mol−1)

ΔG2tr (J·mol−1)

−6.56 −17.46 −20.61 −23.41 −25.15 −25.75

0.0 −2108.2 −2775.8 −3435.9 −4010.6 −4662.9

−2908.9 −3139.3 −3016.9 −2787.8 −2470.2 −1882.2

The value represents the trace activity coefficient for the K+ ions in aqueous 2,2,2-cryptand solutions at 298.15 K.

At low concentrations of both components in ternary solution, 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 = 2v1v2g12

(26)

The salting constant is used to determine the thermodynamic equilibrium constant (K) by20 ks = − 2.303 log K

(27)

It is obvious from eq 27 that, at low concentrations, the change in Gibbs energy of a cryptand by KBr (salting-out or salting-in) is exactly equal to the change in Gibbs energy of KBr by cryptand. The transfer Gibbs free energy data (i.e., Gibbs free energy change on the transfer of 2,2,2-cryptand from water to an aqueous KBr solution (ΔG1tr) and Gibbs free energy change on the transfer of KBr from water to an aqueous 2,2,2-cryptand solution (ΔG2tr)) are given in Table 5. The variations of ΔG1tr and ΔG2tr as a function of KBr concentrations are shown in Figure 10. The data of ΔG1tr have been used to calculate pair and triplet interaction parameters using eq 24. The pair and triplet interaction parameters along with the corresponding salting constant (ks) value for the studied ternary system are collected in Table 6. The standard molar entropy for inclusion complex 2,2,2-cryptand:K+ is estimated using the standard

Figure 9. Variation of the mean molal activity coefficient of 0.1008 m 2,2,2-cryptand (γ1) in aqueous ternary solutions containing KBr and of the mean molal activity coefficient of KBr (γ2) in aqueous ternary solutions containing 0.1008 m 2,2,2-cryptand, as a function of the molality of KBr in the ternary mixture at 298.15 K: (○) γ1; (□) γ2.

ΔGtr1(W → W + KBr) = (∂G(m1 , m2)/∂m1)m2 − (∂G(m1)/∂m1)m2 = 0

i.e., ΔGtr1(W → W + KBr) = 2v1v2m2g12 + 6v12v2m1m2g112 + 3v1v22m22g122 + ... (23)

It immediately follows that ⎛ ∂ΔG1 (W → W + KBr) ⎞ tr ⎟ ⎜ ∂m2 ⎝ ⎠m

1

⎛ ∂ΔG 2 (W → W + cryptand) ⎞ tr ⎟ =⎜ ∂m1 ⎝ ⎠m

2

= 2v1v2g12 + 6v12v2m1g112 + 6v1v22m2g122 + ...

(24)

Hence, the Gibbs free energy for the transfer of KBr from water to aqueous 2,2,2-cryptand solution (ΔG2tr) is given by Figure 10. Variation of Gibbs free energies of transfer of 0.1008 m 2,2,2-cryptand from water to aqueous KBr solutions (ΔG1tr) and Gibbs free energies of transfer of KBr from water to 0.1008 m 2,2,2-cryptand solutions (ΔG2tr), as a function of the molality of KBr at 298.15 K: (□) ΔG1tr; (○) ΔG2tr.

ΔGtr2(W → W + cryptand) = 2v1v2m1g12 + 3v12v2m12g112 + 6v1v22m1m2g122 + ... (25) G



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Table 6. Data of Pair (g12) and Triplet (g112 and g122) Interaction Parameters, Salting Coefficient (ks), Thermodynamic Equilibrium Constant (log K) for the Ternary System H2O + 0.1008 m 2,2,2-Cryptand + KBr, and Standard Molar Thermodynamic Functions for the Potassium 2,2,2-Cryptate Complex at 298.15 K g12 (J·kg·mol−2)

g112 (J·kg2·mol−3)

g122 (J·kg2·mol−3)

ks (kg·mol−1)

log K

ΔG0 (kJ·mol−1)

ΔH0 (kJ·mol−1)

ΔS0 (J·mol−1·K−1)

−4143.3

−69.6

1284.3

−13.37

5.8

−4.36

−9.36

−16.78

molar Gibbs free energy obtained from the binding constant K (ΔG0 = −RT ln K) and the standard molar enthalpy (ΔH0) which is nothing but the difference between the standard molar enthalpy of solution (ΔH0 = −24.73 kJ·mol−1)16 for the ternary system wherein complexed species exist and binary aqueous cryptand solutions estimated in this work (ΔH0solution = −L1 = −15.37 kJ·mol−1). The values of standard thermodynamic parameters for the 2,2,2-cryptand:K+ host−guest complex are also included in Table 6.

enthalpy and entropy compensation is attributed to the structural property of solvent water.59−62 Taking into consideration the importance of EEC, either linear or non-linear ranging from small molecules to large biological macromolecules which has been reviewed excellently in the literature, we have analyzed our data of Gibbs free energy with the help of processed literature heat data to study the concentration dependent enthalpy−entropy compensation effect. A plot of ΔHE against ΔSE for different concentrations of 2,2,2-cryptand in water at 298.15 K is shown in Figure 6 (the values of ΔHE and ΔSE are expressed as per mole of solution). For concentration dependent enthalpy−entropy compensation, a linear relation, ΔHE = a + bΔSE, exists in which a has energy dimensions and b is the compensation temperature (Tcomp). This linear relationship of EEC is observed for many systems. However, in the present case, we observe a non-linear EEC as seen from Figure 6 which can be expressed in a similar way but with an additional term as given by the following expression

4. DISCUSSION 4.1. Analysis of Binary Aqueous 2,2,2-Cryptand Solutions Data. 4.1.1. Osmotic and Activity Coefficients. Examination of the experimental osmotic coefficient (ϕ01) values from Table 2 and its variation with concentration as depicted in Figure 2 indicates that large negative deviation from Raoult’s law is observed, which further emphasizes that this is possible only when strong ion-pair formation exists in solution phase. As such a behavior is generally observed for electrolytes in non-aqueous media having low dielectric constant, where strong ion-pairs always exist. We calculated the ion-pair dissociation constant and found that the strong ion-pair formation occurs in aqueous solutions of 2,2,2-cryptand similar to that occurring generally in non-aqueous media. Thus, the main source of non-ideality in binary aqueous solutions of studied cryptand is the ion-pairing. This is also reflected in Figure 3, where it is seen that the mean molal activity coefficients of 2,2,2-cryptand (γ01) decrease rapidly as a function of concentration. This is in contrast with that of 18-crown-6 where the activity coefficient increases with concentration in water due to hydration of 18-crown-6 without any solute aggregation at low concentration; however, water mediated hydrophobic interactions are always there with dominance of hydrophobic hydration at low concentrations. Our data and analysis conclusively reveal the formation of electrolyte species [CrptH]+[OH−] through chemical equlibria of hydrolysis (water acting as a catalyst and a reactant). 4.1.2. Excess and Mixing Thermodynamic Properties, Enthalpy−Entropy Compensation, and Partial Molal Entropies for Aqueous Solutions of 2,2,2-Cryptand. Examination of Figure 4 points out that mixing of 2,2,2-cryptand with water is accompanied by negative ΔGmix and ΔHmix and positive TΔSmix values as a function of 2,2,2-cryptand concentration in water. However, the excess parameters, i.e., ΔGE, ΔHE, and TΔSE, are all negative and become more negative in magnitude as a function of concentration (Table 2). Further, the examination of Figure 5 shows that solution properties of aqueous cryptand solutions are enthalpy dominated. Lumry34,58 discussed the interpretations and limitations of thermodynamic data in a variety of processes occurring in aqueous and mixed aqueous solvent systems. He gives importance to two types of species, i.e., lower density L and higher density H, present in water and the relevant interactions with the solute molecule and discussed the use of the linear Gibbs energy and compensation relationship observed for thermodynamic properties. In biochemical and chemistry literature,

ΔHE = a + bΔS E + c(ΔS E)2

(28)

where a and b are the terms of linear EEC expression and the additional coefficient c introduces a small non-linear contribution to the EEC effect and is probably due to the heat capacity (Cp), since the solution properties are largely dominated by enthalpic contribution. These may introduce a non-linear effect to EEC through an indirect heat capacity effect (or the relaxation at heat capacity effect).63 For example, c may be equal to (T′/Cp), where T′ is a temperature but whether it is a compensation temperature or experimental temperature is a question of debate. Thus, straightforward expression for parameter c in expression 28 of non-linear EEC is difficult due to the concentration dependence of heat capacity as well of enthalpy. To make better advances, we need an analysis of the number of systems where the non-linear concentration dependent EEC effect is in existence. Hence, we do not offer a further explanation for the c-coefficient at this moment and will concentrate only on the a- and b-coefficients of EEC (eq 28). The recent work of Starikov and Nordén not only proved that the EEC is a real and valid phenomenon which can be explained in the framework of classical thermodynamics but also that it can be derived exactly using the statistical thermodynamics.64,65 We have successfully applied the Starikov and Nordén model of EEC for understanding the concentration dependent EEC effects for some model systems such as amino acids, amino acid ionic liquids, etc., in aqueous solutions.29,66 We concluded with critical analysis that the concentration dependent EEC analysis is only meaningful if the data of enthalpies and entropies of solutions are expressed per mole of solute instead of per mole of solution. Therefore, the data of enthalpy and entropy of solutions in the present work have been converted to per mole of solute, and the resultant compensation effect is studied in Figure 7, where a non-linearity is clearly observed. The compensation temperature (Tcomp) is found to be 206.04 K, whereas the energetic parameter a is of −10.107 kJ·mol−1, from which the entropic parameter (a/Tcomp) is calculated as −49.05 J·mol−1·K−1. These results H



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metal ions as well as for α-cyclodextrin with drug molecules, pnitrophenol, acetate ion, etc.20,22−25 The trends of observed activity coefficients of solute components in this aqueous KBr− cryptand ternary system are thus attributed to strong inclusion complex formation between cryptand and the potassium ion of KBr. The detailed information about the nature and strength of inclusion complex formation can be probed using transfer Gibbs free energy analysis as outlined below. 4.2.2. Transfer Free Energies and Thermodynamic Equilibrium Constant. The trends, as seen from Figure 10, of transfer Gibbs energies for transfer of 2,2,2-cryptand from water to aqueous KBr solutions (ΔG1tr) and that of KBr from water to aqueous cryptand solutions (ΔG2tr) are similar to those observed for corresponding activity coefficient variations of individual solute components in an aqueous ternary mixture and again support strong inclusion complex formation. The critical analysis of transfer Gibbs free energies has been made using application of the McMillan−Mayer theory of solutions with the help of which pair and triplet interaction parameters are estimated, and the values of these parameters are collected in Table 6. The sign and magnitude of pair and triplet interaction parameters probe strength and nature on interactions occurring between cryptand and KBr. The pair interaction parameter, g12, is highly negative in magnitude, indicating pairwise interactions between solute 1 (i.e., 2,2,2-cryptand) and solute 2 (i.e., KBr) are energetically favorable and such a large negative value is only possible when a strong complex is formed between cryptand and KBr. The pair interaction parameter is used to determine the salting coefficient (ks) which is found to be a large negative, meaning that the salting-in effect is observed, suggesting that the solubilization process of cryptand becomes energetically more feasible in the presence of KBr than that in the absence of KBr. Further, the pair interaction parameter and ks are used to obtain the thermodynamic equilibrium constant (K) for the following equilibrium process in aqueous solution.

can be viewed in the framework of the Starikov and Nordén model of EEC according to which EEC is a statistically significant and physically nontrivial correlation; the “hidden/ imaginary Carnot process” may be represented by a set of microscopic heat engines, depending on the relation between the experimental temperature (T) and the compensation temperature, Tcomp; namely, Tcomp > T (“heat pump”) and Tcomp < T (“refrigerator”). Thus, the present system behaves like a “microscopic refrigerator” and further the nonzero a parameter indicates existence of microphases in equilibrium with each other, leading to a cyclic sequence of reversible phase transitions. A similar effect was also observed for aqueous solutions of amino acids as well as for aqueous solutions of amino acid ionic liquids.29,66 The large negative value of the entropic parameter (a/Tcomp) is also called the “pertinent entropy difference”, suggesting that the dissolution of 2,2,2-cryptand leads to a kosmotropic effect, i.e., the water structure making effect as also evidenced from a decrease in the partial molal entropy of water which decreases with an increase in the concentration of cryptand. This observation is further supported by the negative values of the partial molar entropy of solute which increases with an increase in concentration (Figure 8), showing the existence of hydrophobic interactions which are governed by the conformational dynamics of the 2,2,2-cryptand (in−in, out−in, and out−out conformations). Thus, along with the dominant electrostatic interactions responsible for ion-pairing as observed through the ion-pairing dissociation constant estimated using the osmotic and activity coefficient data above, the hydrophobic effect and solute−solvent interactions via Hbonding are responsible for the observed compensation effect. Our above analysis is consistent with the results of the simulation studies made by Auffinger and Wipff67 on the hydration of the 2,2,2-cryptand. Therefore, 2,2,2-cryptand in water can definitely be viewed as a model system to gain insight about the interactions in more complicated biological systems involving supramolecules and enzymes. 4.2. Analysis of Ternary System: H2O + 0.1 m 2,2,2Cryptand + KBr. 4.2.1. Activity and Activity Coefficient Data. The activity coefficient of solvent water (γ0) decreases with an increase in concentration of KBr in ternary aqueous solutions containing 2,2,2-cryptand (see Table 5) which is completely reversed to that in binary aqueous KBr solutions where the solvent activity coefficient increases with an increase in KBr concentration over the studied concentration range. The activity coefficient of water (γ0) is closely related to the translational motion of the hydrated sheath of an ion according to which the enhancement of translation motion must lead to the increase of the activity coefficient of water, whereas weakening of translation motion leads to a decrease in the activity coefficient of water.68,69 Thus, in this context, the decrease of the activity coefficient of water as a function KBr in aqueous solutions containing 2,2,2-cryptand can be attributed to breakdown of the hydration sheath around a potassium ion due to encapsulation of it in the 2,2,2-cryptand cavity, forming an inclusion complex. A similar effect can be seen from the variation of the activity coefficient of 2,2,2-cryptand (γ1) and that of KBr (γ2) as a function of KBr concentration, as depicted in Figure 9. It is observed that the activity coefficient of 2,2,2cryptand (γ1) decreases with concentration while the activity coefficient of KBr (γ2) goes through a minimum at a stoichiometric concentration. This observation is similar to that observed in the case of many inclusion complexes of macrocyclic ligands like 18-crown-6 with alkali and alkaline earth

{[2,2,2‐cryptand:H]+ }aq + {[OH]− }aq + {K+}aq + {Br −}aq ⇄ {[2,2,2‐cryptand:K]+ }aq + {Br −}aq + H 2O

The estimated thermodynamic equilibrium constant for the above process is nothing but the binding constant for the 2,2,2cryptand:K+ inclusion complex in aqueous solution and is found to be 6.40 × 105 kg·mol−1, which is written in Table 6 in the form log K. This value of binding constant confirms strong inclusion complex formation. The analysis of triplet interaction parameters g112 and g122 through their sign and magnitude shows that cryptand−cryptand interactions mediated by KBr are slightly favorable (since g112 is small negative in magnitude, see Table 6) which might be through the hydrophobic effect due to interaction of surface −CH2 groups of uncomplexed cryptand molecules and the cryptand:K+ inclusion complex; however, KBr−KBr interactions are ruled out or are of repulsive type due to comparative large positive values of g122 triplet interaction parameter (see Table 6). Our results demonstrate the utility of activity and transfer Gibbs free energy data for probing and understanding the host−guest type inclusion complexes through study of the model system of 2,2,2-cryptand in aqueous and aqueous KBr solutions, quite satisfactorily.

5. CONCLUSIONS The 2,2,2-cryptand−water−KBr system provided us with a versatile platform to investigate the factors governing recognition I



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(4) Lehn, J. M. Supramolecular Chemistry-Scope and Perspectives Molecules, Supermolecules, and Molecular Devices (Nobel Lecture). Angew. Chem., Int. Ed. 1988, 27, 89−112. (5) Cram, D. J. The Design of Molecular Hosts, Guests, and Their Complexes (Nobel Lecture). Angew. Chem., Int. Ed. 1988, 27, 1009− 1020. (6) Lehn, J. M. Design of Organic Complexing Agents Strategies towards Properties. Struct. Bonding (Berlin, Ger.) 1973, 16, 1−69. (7) Lehn, J. M.; Sauvage, J. P. [2]-Cryptates: Stability and Selectivity of Alkali and Alkaline- Earth Macrobicyclic Complexes. J. Am. Chem. Soc. 1975, 97, 6700−6707. (8) Kauffmann, E.; Lehn, J. M.; Sauvage, J. P. Enthalpy and Entropy of Formation of Alkali and Alkaline-Earth Macrobicyclic Cryptate Complexes [1]. Helv. Chim. Acta 1976, 59, 1099−1111. (9) Lehn, J. M.; Montavon, F. Cryptates. XXV. Stability and Selectivity of Cation Inclusion Complexes of Polyaza-Macrobicyclic Ligands. Selective Complexation of Toxic Heavy Metal Cations. Helv. Chim. Acta 1978, 61, 67−82. (10) Yee, E. L.; Tabib, J.; Weaver, M. J. The Thallium (I)/Thallium Amalgam Couple as an Electrochemical Probe of Cryptate Thermodynamics in Non-Aqueous Solvents. J. Electroanal. Chem. 1979, 96, 241−244. (11) Cox, B. G.; Schneider, H.; Stroka, J. Kinetics of Alkali Metal Complex Formation with Cryptands in Methanol. J. Am. Chem. Soc. 1978, 100, 4746−4749. (12) Mei, E.; Liu, L.; Dye, J. L.; Popov, A. I. Determination of Stability Constants of Cesium [2]-Cryptand Complexes in Nonaqueous Solvents by Cesium-133 NMR. J. Solution Chem. 1977, 6, 771−778. (13) Cox, B. G.; Schneider, H. The Acid Catalyzed Dissociation of Metal Cryptate Complexes. J. Am. Chem. Soc. 1977, 99, 2809−2811. (14) Boileau, S.; Hemery, P.; Justice, J. C. Conductance of Some Tetraphenylborides with Cryptates as Counter-Ions in Tetrahydrofuran. J. Solution Chem. 1975, 4, 873−891. (15) Ceraso, J. P.; Smith, P. B.; Landers, J. S.; Dye, J. L. A Sodium-23 Nuclear Magnetic Resonance Study of the Exchange Kinetics of Sodium(1+) Ion with 2,2,2-Cryptate Complexes in Water, Ethylenediamine, Tetrahydrofuran, and Pyridine. J. Phys. Chem. 1977, 81, 760−766. (16) Abraham, M. H.; Danil De Namor, A. F.; Schulz, R. A. Thermodynamic Studies of Cryptand 222 and Cryptates in Water and Methanol. J. Chem. Soc., Faraday Trans. 1 1980, 76, 869−884. (17) Morel-Desrosiers, N.; Morel, J. P. Volumes of Complexation of Cryptands with Mono- and Divalent Cations in Water and in Methanol. J. Am. Chem. Soc. 1981, 103, 4743−4746. (18) Morel-Desrosiers, N.; Morel, J. P. Heat Capacities and Volumes of Monoprotonation and Diprotonation of Cryptand 222 in Water at 298.15 K. J. Phys. Chem. 1984, 88, 1023−1027. (19) Patil, K.; Pawar, R.; Dagade, D. Studies of Osmotic and Activity Coefficients in Aqueous and CCl4 Solutions of 18-Crown-6 at 25 °C. J. Phys. Chem. A 2002, 106, 9606−9611. (20) Patil, K.; Dagade, D. Studies of Activity Coefficients for Ternary Systems: Water + 18-Crown-6 + Alkali Chlorides at 298.15 K. J. Solution Chem. 2003, 32, 951−966. (21) Dagade, D. H.; Kolhapurkar, R. R.; Patil, K. J. Studies of Osmotic Coefficients and Volumetric Behaviour on Aqueous Solutions of β−cyclodextrin at 298.15 K. Indian J. Chem. 2004, 43A, 2073−2080. (22) Dagade, D. H.; Kolhapurkar, R. R.; Terdale, S. S.; Patil, K. J. Thermodynamics of Aqueous Solutions of 18-Crown-6 at 298.15 K: Enthalpy and Entropy Effects. J. Solution Chem. 2005, 34, 415−426. (23) Terdale, S. S.; Dagade, D. H.; Patil, K. J. Thermodynamic Studies of Drug-α-Cyclodextrin Interactions in Water at 298.15 K: Promazine Hydrochloride/Chlorpromazine Hydrochloride + α-Cyclodextrin + H2O Systems. J. Phys. Chem. B 2007, 111, 13645−13652. (24) Terdale, S. S.; Dagade, D. H.; Patil, K. J. Activity and Activity Coefficient Studies of Aqueous Binary and Ternary Solutions of 4Nitrophenol, Sodium Salt of 4-Nitrophenol, Hydroquinone and α− Cyclodextrin at 298.15 K. J. Mol. Liq. 2008, 139, 61−71.

and encapsulation. The most common driving force for receptor−ligand binding is typically a result of specific preorganized interactions between the molecules, as exemplified in many enzymatic systems. In the case of binary aqueous solutions of 2,2,2-cryptand, our data on the activity and activity coefficients of the solvent and cryptand revealed that, along with the hydrolysis at the nitrogen charged centers, the hydrophobic interactions between the cryptand molecules are also of importance. Our data signifies that 2,2,2-cryptand in aqueous solutions exists as cryptand−H2O, i.e., [CrptH]+[OH−] species which acts as a 1:1 electrolyte. Further, the hydrated species exist as an ion-pair having a dissociation constant equal to 1.19 × 10−2 mol·kg−1. With the help of the developed hydrolysis correction procedure, we have obtained the excess properties for free energy and entropy changes. The partial molar entropy variation with 2,2,2-cryptand indicated the presence of the water structure making effect as well as the cryptand−cryptand hydrophobic interaction effect. The enthalpy−entropy compensation effect is tested, and the found compensation temperature (lower than the experimental temperature used) establishes that solvation and the structural interaction often play a critical role in guest encapsulation. The hydrogen bond arrangement in water as well the H-bonding with the polar groups and the nitrogen charged centers (in the limiting concentration range), i.e., hydrophilic interaction coupled with the presence of (preorganization) hydrophobic interaction between the cryptand molecules, seem to govern the formation of the appropriate conformation so that the proper guest can be accommodated. Further, our studies on transfer free energies in ternary solutions containing a guest K+(Br−) in aqueous 2,2,2-cryptand solutions revealed that along with the pairwise (2,2,2-cryptand−K+) and triplet (2,2,2-cryptand− 2,2,2-cryptand−K+), i.e., hydrophobic interactions impart the necessary stability for complexed species in solution phase. The results can be viewed in terms of the geometric fit for the 2,2,2-cryptand cations in a properly sized conformer of 2,2,2cryptand as a host and solvent water where both solute−solvent (hydrophilic) and cation−cation hydrophobic interaction effects are approximately adjusted (because of the structure and interaction forces) or manipulated to have stable host−guest type species in solution phase.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +91 8975012226. Fax: +91 257 2257432. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS V.R.S. acknowledges the University Grants Commission, New Delhi (India), for providing the financial assistance through Maulana Azad National Fellowship (MANF) for Minority Students.

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REFERENCES

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Thermodynamic Studies of Aqueous Solutions of 2,2,2-Cryptand at

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