Chemical Physics Letters 479 (2009) 56–59

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Chemical Physics Letters

journal homepage: www.elsevier .com/locate /cplet t

Hydration entropy of polar, nonpolar and charged species

Giuseppe Graziano *

Dipartimento di Scienze Biologiche ed Ambientali, Università del Sannio, Via Port’Arsa 11, 82100 Benevento, Italy

a r t i c l e i n f o a b s t r a c t

Article history:Received 15 June 2009In final form 31 July 2009Available online 3 August 2009

0009-2614/$ - see front matter � 2009 Elsevier B.V. Adoi:10.1016/j.cplett.2009.07.101

* Fax: +39 0824 23013.E-mail address: graziano@unisannio.it

At room temperature and atmospheric pressure, the magnitude of the hydration entropy of neutral sol-utes increases with the molecular volume according to a trend that is largely insensitive to the polar nat-ure of the solute molecule. This general trend is well reproduced by the entropy change upon cavitycreation in water as calculated by means of classic scaled particle theory. In contrast, the magnitude ofthe hydration entropy of the 20 alkali halides decreases on increasing the size of the constituent ions,demonstrating that the strength of charge–water dipole interactions plays the dominant role.

� 2009 Elsevier B.V. All rights reserved.

1. Introduction

At room temperature and atmospheric pressure, hydrationleads to an entropy decrease for all types of solutes, nonpolar mol-ecules, polar non-charged molecules and ions [1]. In order to try toshed light on the molecular origin of such entropy decrease, it isnecessary to use the so-called Ben-Naim standard that refers tothe transfer from a fixed position in the ideal gas phase to a fixedposition in water, at constant temperature and pressure [1]. Thehydration entropy change defined according to the Ben-Naim stan-dard, DS�, accounts solely for the entropy change of water mole-cules, and for eventual changes in the accessibility of internaldegrees of freedom of the solute molecule upon phase transfer [2].

In a recent article Ben-Amotz and Underwood have shown thatthe DS� values at 25 �C of alkanes, cycloalkanes, water, n-alcohols,ethers, linear ketones and nitriles, when plotted as a function of thesolute van der Waals volume, prove to be close to each other and todefine a single curve [3]. They also claimed, from the analysis offour alkali halides, that the situation of ions should be similar.Ben-Amotz and Underwood analyzed their results on the basis ofa general dissection of the hydration process in a series of sequen-tial and reversible coupling steps: (a) creation of a cavity in watersuitable to host the solute molecule; (b) turning on solute–watervan der Waals interactions and (c) turning on solute–water H-bonding (or charge–dipole) interactions [4–6]. They showed thatthe insensitivity of the hydration entropy to the polar nature ofthe solute can be rationalized thanks to the Gibbs inequalities[7], and the validity of the linear response theory [8,9]. The latter,however, does not hold for the cavity creation process, holds forthe turning on of van der Waals interactions and, only in anapproximate way, for electrostatic coupling processes [3]. In addi-tion, the linear response theory is not a molecular-level approach,

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and so it cannot provide a really microscopic explanation of thenegative hydration entropies. These deficiencies prompted me toreconsider the matter.

In the present Letter I have analyzed a larger DS� data set, show-ing that the DS� values of non-charged solutes roughly occur on asingle curve and that the latter practically corresponds to the en-tropy change upon cavity creation calculated by means of classicscaled particle theory, SPT [10,11]. It is also unequivocally demon-strated that the DS� values of the 20 alkali halides show a com-pletely different size dependence, in line with the fundamentalrole played by the ion charge density for the reorganization ofthe H-bonded network of water [12].

2. Methods

Experimental DS� data, at 25 �C and 1 atm, for alkanes (13points), cycloalkanes (3 points), benzene and alkylbenzenes (7points), n-alcohols (10 points), 2-alcohols (5 points) and linear ke-tones (11 points) come from the Organic Compound Hydration(ORCHYD) database [13]; those for water and primary amines (4points) come from the Ben-Naim and Marcus compilation [14];those for noble gases (6 points) are from [15], and those of halome-thanes (4 points) are from [16]. Experimental DS� data, at 25 �C and1 atm, for the 20 alkali halides come from Table 2.25 of the Ben-Naim’s book [1]. The hard-sphere volumes, Vhs, of all the non-charged solutes are calculated using the group additivity contribu-tions of Ben-Amotz and Willis [17], except those of noble gasesthat are calculated on the basis of the respective hard-spherediameters [15]. These Vhs values are close to the van der Waals vol-umes used by Ben-Amotz and Underwood [3]. For the alkali ha-lides, the anion radii are those fixed by Pauling [18], and thecation radii are calculated by subtracting the chloride radius,1.81 Å, to the M+Cl� distance observed in the crystals with the NaClstructure (as reported in Table 13-6 of Pauling’s book). These ionicradii were able to correctly reproduce the salting out of methane

G. Graziano / Chemical Physics Letters 479 (2009) 56–59 57

and benzene caused by alkali chlorides, at room temperature, usingclassic SPT [19,20]. Experimental hydration thermodynamic data at25 �C and 1 atm, together with the Vhs values, are listed in two Ta-bles in the Supplementary material.

The entropy change upon cavity creation has been calculated bymeans of classic SPT for spherical cavities [10,11], using the exper-imental values of the density and thermal expansion coefficient ofwater at 25 �C and 1 atm. [21]. The effective hard-sphere diameterof water molecules r(H2O) has been fixed to 2.80 Å [16], a valueclose to the location of the first peak in the O–O radial distributionfunction of water, as determined by means of X-ray diffraction andneutron scattering measurements [22], and to the O–O distance inice, 2.76 Å [23]. Moreover, this value allows a satisfactory descrip-tion using SPT formulas of the cavity size distribution function ofwater [24–26], and is exactly twice the radius usually assigned toa water molecule for calculating the water accessible surface area[27].

3. Results

I have tried to verify the insensitivity of the hydration entropy,DS�, at 25 �C and 1 atm, to the polar nature of the solute molecule.The following series of neutral solutes have been considered: noblegases, alkanes, cycloalkanes, benzene and alkylbenzenes, water, n-alcohols and 2-alcohols, linear ketones, primary amines and halo-methanes. The constructed plot of �DS� versus the hard-spherevolume of the solute molecules, Vhs, is shown in Fig. 1. The insen-sitivity is an actual phenomenon: the data occur on a single curve,even though there is some scatter, especially for alkylbenzenes andhalomethanes. It is important to underscore that the point for thesolvation of water (considered to be a sphere of 2.80 Å diameter tobe consistent) in water does not scatter, but is in line with those forthe hydration of n-alcohols. What may be surprising but interest-ing is the finding that the values of the entropy change upon cavitycreation, calculated by means of classic SPT, DSc(SPT), are in satis-factory agreement with the experimental data, as emphasized bythe thick black curve in Fig. 1. Note that, in performing SPT calcu-lations, the experimental values of the density and thermal expan-sion coefficient of water at 25 �C and 1 atm, have been used, and

0 50 100 150 200

50

100

150

200

Vhs (angstrom3)

- ΔS

(J

K-1

mol

-1)

Fig. 1. Values of minus the hydration entropy DS�, at 25 �C and 1 atm, as a functionof the hard-sphere volume Vhs for noble gases (magenta diamonds with a centerdot), alkanes and cycloalkanes (red filled circles), n-alcohols (blue filled squares;note that the first square is for the solvation of water in water), 2-alcohols (orangefilled diamonds), primary amines (green filled up triangles), linear ketones (cyanfilled down triangles), alkylbenzenes (olive squares with a center dot), halome-thanes (dark yellow circles with a center dot). The thick black curve represents thevalues of the entropy change associated with cavity creation, calculated by meansof classic SPT, using the experimental values of the density and thermal expansioncoefficient of water at 25 �C and 1 atm, and r(H2O) = 2.80 Å.

the effective hard-sphere diameter of water molecules r(H2O)has been fixed to 2.80 Å. The process of cavity creation in watercauses an entropy decrease that accounts, in a satisfactory manner,for the whole hydration entropy change, not only for nonpolar spe-cies, but also for polar non-charged solutes. This means that: (a)the entropy contribution due to the reorganization of water–waterH-bonds upon turning on the solute–water van der Waals interac-tions is a small quantity because the perturbation is weak in com-parison to the strength of water–water H-bonds and (b) theentropy contribution upon turning on the solute–water H-bondingpotential (i.e., as in the case of n-alcohols) is not a large quantitybecause there is an entropy loss for the water molecules blockedto form H-bonds with the solute, and an entropy gain for the con-sequent structural disorder in the H-bonded network of water (i.e.,two opposite terms that tend to cancel each other).

I have also tried to verify what is the situation for the hydrationentropy of ions at 25 �C and 1 atm. I have taken the DS� data for the20 alkali halides reported by Ben-Naim [1], and I have calculatedVhs for a given salt in two ways: (a) by computing the volume ofthe sphere corresponding to the cation and the volume of thesphere corresponding to the anion and summing up the two valuesand (b) by computing the volume of the sphere having the radiusequal to the sum of the radii of the anion and cation. Clearly, thetwo sets of values are markedly different; for instance, in the caseof KCl, Vhs = 34.7 Å3 following the (a) way, and 129.7 Å3 followingthe (b) way (for the complete list, see Table S2 of Supplementarymaterial). The constructed plot of �DS� versus Vhs for the 20 alkalihalides is shown in Fig. 2: the two sets of points correspond to thetwo ways of calculating Vhs, and the thick black curve represents�DSc(SPT). It is evident that the trend of DS� data for the salts isvery different from that of non-charged solutes, regardless of theVhs choice. The fundamental difference is that the DS� magnitudedecreases on increasing the size of the two ions constituting thesalt, whereas it increases with the size of the non-charged mole-cule, regardless of its polarity. This trend emphasizes that: (a)the perturbation of water structure caused by the electric field ofions overwhelms or is comparable to that due to the process ofcavity creation and (b) ions with high charge density cause a largerstructural reorganization of the H-bonded network of water with

Vhs (angstrom3)0 50 100 150 200 250

50

100

150

200

- ΔS

(J

K-1

mol

-1)

Fig. 2. Values of minus the hydration entropy DS�, at 25 �C and 1 atm, as a functionof the hard-sphere volume Vhs calculated in two different ways (see text for details)for the 20 alkali halides. Alkali fluorides (red filled circles or red circles with a centerdot); alkali chlorides (blue filled squares or blue squares with a center dot); alkalibromides (green filled up triangles or green triangles with a center dot); alkaliiodides (magenta filled diamonds or magenta diamonds with a center dot). Thethick black curve represents the values of the entropy change associated with cavitycreation, calculated by means of classic SPT, using the experimental values of thedensity and thermal expansion coefficient of water at 25 �C and 1 atm, andr(H2O) = 2.80 Å.

58 G. Graziano / Chemical Physics Letters 479 (2009) 56–59

respect to ions with low charge density [12]. Finally, it is worthnoting that also the DS� values of the 20 alkali halides define,approximately, a single curve-trend, but the latter qualitativelycontrasts with that defined by neutral solutes.

4. Discussion

The experimental DS� values, at 25 �C and 1 atm, of nonpolarand polar non-charged solutes when plotted as a function of themolecular hard-sphere volume, Vhs, occur, more-or-less, on thesame curve. This finding confirms the rightness of the results byBen-Amotz and Underwood [3]. Moreover, it suggests that thereis a unique cause-mechanism determining the entropy decreaseupon the hydration of neutral solutes. The experimental DS� dataare reproduced quite well by the entropy loss associated withthe process of cavity creation in water, calculated by means of clas-sic SPT [10,11]. This is an important result because it implies that:(a) the unique cause-mechanism should be the process of cavitycreation in water; (b) the entropy loss due to the excluded volumeeffect for cavity creation is the dominant term in the DS� values ofnon-charged species, regardless of their polarity [28–30]; (c) this isbecause the excluded volume effect in water is exaggerated by thesmall size of water molecules [31,32]. In this respect, it has to beunderscored that r(H2O) = 2.80 Å, used in SPT calculations, is aphysically reliable value for the effective size of water molecules[22–27,33].

Moreover, it is worth noting that the DSc(SPT) values containalso a positive contribution for the structural reorganization ofwater–water H-bonds upon cavity creation (i.e., the term propor-tional to the thermal expansion coefficient of the liquid in theSPT formula [10,28]). It appears that the turning on of van derWaals interactions and/or H-bonding potential does not producea further structural reorganization of water with a significant en-tropy change [6,34]. In the case of n-alcohols and primary aminesthe H-bonding potential is localized in a very small part of the mol-ecule, determining a weak perturbation of the surrounding watermolecules because a very small number of them can form H-bondswith the OH group or the NH2 group. The greatest deviations (eventhough not large) from the DSc(SPT) curve are for halomethanesand alkylbenzene: their DS� values are significantly smaller inmagnitude than those of DSc(SPT). This could be because: (a) theirstrong dipoles or quadrupoles, respectively, involve the wholemolecular structure, significantly affecting the reorganization ofsurrounding water molecules and (b) both classes of solutes formH-bonds with water molecules [5,16].

To analyze the situation for charged solutes, I have calculatedthe Vhs values of alkali halides in two different ways, showingunequivocally that the trend of �DS� versus Vhs for the salts isqualitatively different from that of nonpolar and polar non-chargedsolutes, and is not qualitatively reproduced by the DSc(SPT) curve.This result contrasts with the claim by Ben-Amotz and Underwoodthat ‘rare gas atoms and alkali halide ions have nearly identicalexperimental hydration entropies, despite the significant charge-induced reorganization of water molecules’ [3]. Actually, Ben-Amotz and Underwood compared the DS� values of only four alkalihalides, NaF, KCl, RbBr and CsI, with the DS� data of Ne, Ar, Kr andXe, respectively, because each salt has twice the number of elec-trons of the corresponding noble gas; they did not consider at allthe size of the salt ions [3]. I think that the procedure adopted byBen-Amotz and Underwood is not correct because it does not allowthe analysis of the role of ion size in determining the DS� magni-tude. In fact, their statement is not right. It is approximately correctif one compares, at 25 �C and 1 atm, the hydration entropy of Ar,�60.4 J K�1 mol�1, with half of the hydration entropy of KCl,�49.2 J K�1mol�1; however, the hydration entropy of Ne,

�41.9 J K�1mol�1, is largely different from half of the hydration en-tropy of NaF, �98.9 J K�1mol�1; similarly, the hydration entropy ofXe, �74.8 J K�1mol�1, is largely different from half of the hydrationentropy of CsI, �17.8 J K�1mol�1 (see Table S2 of the Supplemen-tary material). What is really important is the fact that the hydra-tion Gibbs energy change of alkali halides is largely dominated bythe strongly favourable charge–water dipole interactions [1]. Thisimplies that the water–water reorganization enthalpy change isnot compensated by the water–water reorganization entropy be-cause the perturbation due to the electric field of the ions has astrength at least comparable to that of water–water H-bonds [35].

It is worth noting that the DS� magnitude decrease on increas-ing the ion size is in line with the expectation from the Born modelfor the hydration thermodynamics of ions (i.e., the Born hydrationentropy is inversely proportional to the ion radius [36]). However,the Born model does not work well in quantitatively reproducingthe experimental DS� values for alkali halides, as already pointedout by several authors [37,38]. It is beyond the scope of this Letterto analyze the virtues and deficiencies of the Born model.

In conclusion, at room temperature, nonpolar solutes and polarnon-charged solutes, having the same hard-sphere volume, possesspractically the same negative DS� values. The latter are well repro-duced by the entropy change associated with the process of cavitycreation, as calculated by means of classic SPT. The DSc(SPT) termdominates the hydration entropy of non-charged species becausethe excluded volume effect is amplified in water by the small sizeof water molecules. The negative hydration entropy of salts, atroom temperature, decreases in magnitude on increasing the sizeof the ions, in contrast with the trend of DSc(SPT). This is becausethe DS� magnitude of salts depends on the strength of charge–water dipole interactions that, in turn, depend upon the chargedensity of ions.

Acknowledgements

I would like to express my gratitude to the two reviewers forthe useful comments and suggestions.

Appendix A. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at doi:10.1016/j.cplett.2009.07.101.

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