Quantitative Description of the Hydrophobic Effect - American

9298

J. Phys. Chem. B 2006, 110, 9298-9303

Quantitative Description of the Hydrophobic Effect: the Enthalpic Contribution Boris N. Solomonov* and Igor A. Sedov Chemical Institute, Kazan State UniVersity, Russia ReceiVed: March 16, 2006

A new method of experimental determination of the hydrophobic effect enthalpy is proposed. The method is based on regarding the hydration enthalpy as the sum of the nonspecific hydration enthalpy, specific hydration enthalpy, and the hydrophobic effect enthalpy. The hydrophobic effect enthalpies of noble and simple substance gases, alkanes, arenes, and normal aliphatic alcohols are determined. For the noble gases and alkanes, the hydrophobic effect enthalpy is found to be negative and independent of the size of molecule. For aromatic hydrocarbons, it is positive and grows up with the size of the hydrocarbon. The hydrophobic effect enthalpies of normal aliphatic alcohols are determined by assuming that the specific interaction enthalpies of alcohols in water and in methanol are equal. The hydrophobic effect enthalpy values for the aliphatic alcohols (-10.0 ( 0.9 kJ‚mol-1) were found to be close to the alkanes hydrophobic effect enthalpies (-10.7 ( 1.5 kJ‚mol-1).

Introduction It is well-known that apolar substances are poorly soluble in water. This fact is usually attributed to their hydrophobicity. The importance of hydrophobicity studies is widely recognized. Hydrophobic effects play a significant role in various phenomena in aqueous solutions. The stability of biological membranes, globular proteins, and micelles depends critically on the interactions between their apolar parts.1-8 Although hydrophobicity is a well-known and extensively studied phenomenon, it still is not thoroughly explained. In our opinion, the problem of quantitative determination of the hydrophobic effect thermodynamic parameters is still actual. Quantitative characteristics of the hydrophobic effect are usually the differences between thermodynamic functions of hydration and solvation in the reference solvent. The reference solvent is supposed to model water “in the absence of hydrophobicity”. Thermodynamic functions of transfer from liquid alkane to water are often called thermodynamic functions of the hydrophobic effect.1,9 Octanol-water two-phase system partition coefficients (log P) are commonly used too.10 Another example is the poly(dimethylsiloxane)-water system.11 These approaches assume that partial molar thermodynamic functions of nonspecific solvation in the reference solvent and in “water in the absence of hydrophobicity” are equal. No difference in solvation and solution thermodynamic functions for the same solute in different solvents is assumed when no specific interactions occur. Such assumption is not correct. For example, thermodynamic functions of alkanes solvation in different apolar solvents are significantly different.12-14 In a series of papers,15-17 Abraham showed that Gibbs energies and enthalpies of solvation of noble gases and alkanes in different solvents depend linearly on the optimized molecular radius R, which is a measure of molecular size. On the other hand, there is no universal linear dependence on R for the hydration thermodynamic functions. Abraham suggested that the hydrophobic effect contribution is absent in hydration thermodynamic functions of noble gases. The hydrophobic effect thermodynamic functions of alkanes are considered as the * Corresponding author. E-mail: [email protected].

differences between their experimental thermodynamic functions and thermodynamic functions of a hypothetic noble gas with the same R. The suggestion about zero values of these functions for noble gases was not proved. In recent works,18 Graziano showed that the difference in size dependence of the solubility of noble gases and alkanes is a result of an unusually rapid growth of cavity formation Gibbs energy in water with the solute size, while the solute-solvent interaction energy in water increases in magnitude with the solute size slower than in other solvents. Mastroianni et al.19 and Somsen et al.20 proposed another method of estimation of the hydrophobic effect thermodynamic parameters. According to this method, enthalpies of solution of the hydrophobic compounds in single-phase water-organic solvent binary mixtures satisfy the equation:

∆solnH(M) ) (1 - xw)∆solnH(S) + xw∆solnH(W) + (xwn - xw)Hb(W) (1) where ∆solnH(M), ∆solnH(S), ∆solnH(W) are the enthalpies of solution in a binary mixture, organic solvent, and water, respectively, Hb(W) is the enthalpy of hydrophobic hydration, n is the number of water molecules hydrating per alkyl group, and xw is the molar fraction of water in a mixture. The linear dependence of solution enthalpy in binary mixtures of organic solvents from the molar fraction of one of the components is presumed. In fact, the solvation in binary mixtures can be preferential, i.e., the solvent shell near the solute molecule can have a composition other than the whole solvents mix. This leads to a nonlinear dependence of ∆solnH from the molar fraction of one of the components. Moreover, in systems studied by Somsen et al.,20 water can form hydrogen bonds with the second solvent (dimethylformamide). In a series of works,21-23 Jozwiak and Piekarski made an attempt to exclude these effects by adding a correction term ∆H*. An ideal behavior (∆H* ) 0) of DMF-water mixtures is still presumed. The correctness of this presumption is questionable. In a number of works,24,25 another attempt of the hydrophobic effect thermodynamic parameters evaluation was made. Thermodynamic functions of hydration (∆hydrGA, ∆hydrHA) for the

10.1021/jp061645+ CCC: $33.50 © 2006 American Chemical Society Published on Web 04/20/2006

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solutes A not interacting specifically with water are regarded as the sum of the nonspecific hydration thermodynamic functions (∆hydr(nonsp)GA, ∆hydr(nonsp)HA) and the hydrophobic effect thermodynamic functions (∆h.e.GA, ∆h.e.HA):

∆hydrGA ) ∆hydr(nonsp)GA + ∆h.e.GA

(2a)

∆hydrHA ) ∆hydr(nonsp)HA + ∆h.e.HA

(2b)

The values of ∆hydr (nonsp)GA and ∆hydr (nonsp)HA had been determined from a linear dependence between the Gibbs energy of solvation of A in a series of solvents and the corrected Hildebrand solubility parameter δHS*. It can be calculated similarly to the Hildebrand parameter δHS, but the difference between the solvent vaporization (∆vapHS) and self-association (∆assH) enthalpies is used in the numerator. Instead of

δHS )

x

∆vapHS - RT VMS

x

VMS

Methodology The following principles and definitions lie at the basis of our method. The enthalpy of solvation ∆solvHA/S is the enthalpy of isothermal transfer of solute A from the ideal gas state to an infinitely diluted solution in solvent S at 298.15 K and 0.1 MPa pressure. The solution enthalpy ∆solnHA/S is the enthalpy of transfer of solute A from its standard state (solid, liquid, or vapor) to an infinitely diluted solution in solvent S at 298.15 K and 0.1 MPa pressure. Solution and solvation enthalpies are interrelated through the equation:

∆solvH

) ∆solnH

A/S

- ∆vapH

A

(3)

where ∆vapHA is the standard molar vaporization enthalpy of A. If solvent S is water, the solvation enthalpy is called the hydration enthalpy ∆hydrHA:

∆hydrHA ) ∆hydnHA - ∆vapHA ∆hydnHA is the solution enthalpy of A in water.

(4)

where ∆cavHA/S is the cavity formation enthalpy and ∆intHA/S is the solute-solvent interaction enthalpy. The solute-solvent interactions can be of specific and nonspecific type. Specific interactions are usually considered as localized donor-acceptor interactions. The common examples of specific interactions are hydrogen bonding and charge transfers. The nonspecific interactions are related to dipolarity and polarizability of solute and solvent molecules. For a comprehensive discussion of this topic, interested readers can be referred to the book of Reichardt.26 So, ∆intHA/S can be given by:

(4a)

where ∆int(nonsp)HA/S and ∆int(sp)HA/S are, respectively, nonspecific and specific interaction enthalpies. The solvation enthalpy ∆solvHA/S can be regarded as the sum of nonspecific solvation ∆solv(nonsp)HA/S and specific interaction ∆int(sp)HA/S enthalpies:

∆vapHS - ∆assH - RT

Thermodynamic functions of solvation in water deviate from the universal linear correlation with δHS* observed for other solvents, including self-associated. The values of ∆h.e.GA and ∆h.e.HA are the differences (∆hydrGA - ∆hydr (nonsp)GA) and (∆hydrHA - ∆hydr (nonsp)HA), respectively. However, this method has two severe imperfections. First, there is no linear dependence between ∆solvGA/S (∆solvHA/S) and δHS* for many apolar compounds A. Second, a lot of experimental data are required to plot the correlation line. Below, we propose a new method to evaluate the contribution of the hydrophobic effect. It utilizes the same principle of division of the hydration enthalpy to nonspecific and specific contributions as the method24,25 considered above. Our method is free of the imperfections described above and can be applied to solutes interacting specifically with water (e.g., forming hydrogen bonds).

A/S

∆solvHA/S ) ∆cavHA/S + ∆intHA/S

∆intHA/S ) ∆int(nonsp)HA/S + ∆int(sp)HA/S

we have

δHS* )

The solvation process can be split into two steps: formation of a cavity with a suitable size to accommodate the solute molecule and insertion of the solute in the cavity, turning on the solute-solvent interactions. Thus, the solvation enthalpy can be given by:

(3a)

∆solvHA/S ) ∆solv(nonsp)HA/S + ∆int(sp)HA/S

(4b)

where ∆solv(nonsp)HA/S ) ∆cavHA/S + ∆int(nonsp)HA/S We suppose that the feature of liquid water in comparison with other solvents is the presence of the hydrophobic effect term in solvation (hydration) thermodynamic functions. As in other models, we suppose the additivity of the hydrophobic effect contribution:

∆hydrHA ) ∆hydr(nonsp)HA + ∆int(sp)HA/H2O + ∆h.e.HA (5) To determine ∆h.e.HA, we should know the hydration enthalpy and be able to estimate the nonspecific hydration enthalpy for systems without specific interactions and both nonspecific and specific hydration enthalpies for solutes interacting specifically with water. Previously27 we proposed a new simple method for estimation of the nonspecific solvation enthalpy. According to this method, ∆solv(nonsp)HA/S can be evaluated by the following equation:

∆solv(nonsp)HA/S ) (δcavhS - δcavhC6H12)‚VxA + ∆solvHA/C6H12 + (aR + bRxδcavhS) × [(∆solnHA/R - ∆solnHA/C6H12) -

(δcavhR - δcavhC6H12)‚VxA] (6)

Here ∆solnHA/R, ∆solnHA/C6H12 are the solution enthalpies of solute A in the standard solvent R and in cyclohexane, ∆solvHA/C6H12 is the solvation enthalpy of solute A in cyclohexane, VxA is the McGowan characteristic volume of solute A,28,29 and δcavhS, δcavhR, and δcavhC6H12 are the specific relative cavity formation enthalpies13,14 for each solvent. According to refs 13 and 14, the specific relative cavity formation enthalpy δcavhS is the enthalpy of transfer (the difference between the solution enthalpies) of an alkane from the imaginary solvent S0, where the solution enthalpy of an alkane is zero (∆solnHCnH2n+2/S0 ) 0),

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to solvent S, divided by the characteristic volume VxCnH2n+2 of an alkane. Hence, the δcavhS is given by:

δcavhS )

∆solnHCnH2n+2/S VxCnH2n+2

Discussion

(7)

Standard solvent R is defined as a certain nonalkane solvent that does not interact specifically with the solutes. The standard solvent R empirical parameters aR and bR were calculated using linear regression analysis.27 For tetrachloromethane, aR ) 0.34 and bR ) 0.61, for benzene aR ) 0.20 and bR ) 0.38.30 In most cases, tetrachloromethane can be used as the standard solvent. However, some electron-donor solutes (e.g., triethylamine, pyridine, and diethyl ether) are known to interact specifically with CCl4.31-33 For such solutes, benzene can be chosen as the standard. In a recent work,27 the nonspecific solvation enthalpies for 280 solute-solvent pairs had been successfully predicted using this equation. We need the data on the solvation enthalpies of A in cyclohexane and the standard solvent, the values of δcavhS for cyclohexane, standard solvent, and water, and the enthalpy of vaporization of A to evaluate ∆hydr(nonsp)HA by using eq 6. Because we use ∆hydr(nonsp)HA in eq 5, the solution enthalpies ∆solnHA/C6H12 and ∆hydnHA can be taken instead of the solvation enthalpies ∆solvHA/C6H12 and ∆hydrHA. The δcavhS values of cyclohexane, benzene, and tetrachloromethane (δcavhC6H12 ) 1.4 kJ‚cm-3‚102, δcavhC6H6 ) 5.0 kJ‚cm-3‚102, δcavhCCl4 ) 1.9 kJ‚cm-3‚102) were calculated previously27 from experimental data on the solution enthalpies of alkanes without any problems. But determination of the δcavhS value for water is quite a complicated task. The δcavhS parameter has a certain analogy with the Hildebrand solubility parameter δHS reflecting the solvent-solvent interactions.34 However, the Hildebrand parameter reflects both nonspecific and specific solvent-solvent interactions, while δcavhS seems to reflect only the nonspecific interactions. It had been confirmed not only with calorimetric,27 but also with IR spectroscopic data.35,36 The solvent influence on the stretching vibrations frequencies of different bonds of the solute was successfully described using this parameter. The solution enthalpies of liquid alkanes in water are close to zero or even negative (pentane).37 According eq 7, we receive a zero or negative value for δcavhS. It means water-water nonspecific interactions are even weaker than alkane-alkane interactions. It is easy to suppose that the solution enthalpy contains the hydrophobic effect contribution, and we should subtract the hydrophobic effect enthalpy of alkane from the solution enthalpy of alkane in the numerator: H2O

δcavh

)

∆solnHCnH2n+2/H2O - ∆h.e.HCnH2n+2 VxCnH2n+2

compounds as well as of the compounds forming hydrogen bonds with water.

(8)

We used ∆h.e.HCnH2n+2 obtained previously25 for calculation of δcavhH2O. We calculated δcavhH2O from the solution enthalpies of C5-C8 alkanes37 by using eq 8 and received an average value δcavhH2O ) (9.5 ( 1.0)‚102 kJ‚cm-3‚102. This value is close to the dimethylformamide and acetonitrile δcavhS values (8.6‚102 and 10.7‚102 kJ‚cm-3‚102, respectively27) and indicates the closeness of the nonspecific interaction parameters for water, dimethylformamide, and acetonitrile. Finally, we have all the necessary data to determine the nonspecific interaction enthalpies. Below, we use them in calculation of the hydrophobic effect enthalpies of apolar

Hydrophobic Effect Enthalpies of Noble and Other Inert Gases, Alkanes, and Arenes. It was shown that dissolved noble gases and alkanes cannot form hydrogen bonds with water.38 There is some evidence that benzene can form hydrogen-bonded complexes with water.39-44 The estimated bond formation enthalpy is approximately -3 kJ‚mol-1.41 We can also estimate the specific interaction enthalpy of water in benzene solution by eqs 4b and 6. By using appropriate solution enthalpies data45 (∆solvHH2O/C6H12 ) 8.0 kJ‚mol-1, ∆solvHH2O/CCl4 ) 16.4 kJ‚mol-1, ∆solvHH2O/C6H6 ) 20.1 kJ‚mol-1), appropriate δcavhS values, and water McGowan volume28 (VxH2O ) 0.1673 cm3‚mol-1‚10-2) in eqs 4b and 6, we obtain ∆int(sp)HH2O/C6H6 ) -2 kJ‚mol-1, close to the estimated alcohols in benzene-specific interaction enthalpy values (-2 to -4 kJ‚mol-1).27 The ∆int(sp)HH2O/C6H6 magnitude relates to water in benzene solution. But what can we say about the specific interaction enthalpy of benzene in water solution? Liquid water is a mixture of hydrogen-bonded associates and monomer molecules.46,47 A proton-accepting molecule of benzene in water competes for the hydrogen atom of water with other water associates. It was shown48-51 that the hydrogen bonding energy between water molecules is approximately -14 ( 1 kJ‚mol-1 per bond. Benzene can form hydrogen bonds with water only if a large positive entropy change compensates the enthalpically unfavorable process of breaking water-water hydrogen bonds. Such compensation seems unlikely. Therefore, we suggest there is no contribution of benzene-water hydrogen bonding to the hydration enthalpy of benzene. In the absence of the specific interactions, eq 5 can be rewritten as:

∆h.e.HA ) ∆hydrHA - ∆hydr(nonsp)HA

(9)

∆hydr(nonsp)HA can be calculated by eq 6 as described above. According eq 3a, we can use solution enthalpies ∆hydnHA and∆solnHA/C6H12 instead of solvation enthalpies ∆hydrHA and ∆solvHA/C6H12 in eqs 6 and 9. Calculated hydrophobic effect enthalpy values are given in Table 1. All necessary data for calculation are provided as well. We used benzene as the standard solvent R because more experimental data were obtained52-55 on it than on tetrachloromethane. The negative hydrophobic effect enthalpies of alkanes and noble gases corresponds with the classic interpretation of the hydrophobic effect as the strengthening of the hydrogen bonds network around apolar molecules.1,56-59 The ∆h.e.HA values for noble gases are in agreement with the values obtained in ref 25: (∆h.e.H(He) ) -14.2 kJ‚mol-1, ∆h.e.H(Ne)) -16.0 kJ‚mol-1, ∆h.e.H(Kr) ) -14.5 kJ‚mol-1, ∆h.e.H(Xe) ) -13.4 kJ‚mol-1). We cannot compare the values obtained for alkanes with the data from ref 25. In eq 6, we use the δcavhH2O values calculated by eq 8, taking the hydrophobic effect enthalpies data from ref 25, and therefore, we always receive the same ∆h.e.HA values as in ref 25. Minor differences between the obtained values and ref 25 data are there because we used the average δcavhH2O value for several alkanes (C5-C8). The opposite sign of ∆h.e.HA for aromatic compounds should mean a different hydration mechanism. This difference was noted in a number of works.41,60 Some researchers have another point of view; they find no difference between hydration of alkanes and arenes.61-63 The weakening of the hydrogen bonds

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TABLE 1: Hydrophobic Effect Enthalpies ∆h.e.HA and Supplementary Data for ∆h.e.HA Calculation by Eqs 6 and 9 for a Set of Solutes A Forming No Hydrogen Bonds with Watera helium neon argon krypton xenon hydrogen nitrogen oxygen methane ethane propane n-butane n-pentane n-hexane n-heptane n-octane cyclohexane benzene naphthalene biphenyl anthracene

VxA 28

∆solnHA/C6H12

∆solnHA/C6H6

∆solnHA/H2O

∆h.e.HA

∆h.e.(AN)HA

0.0680 0.0850 0.1900 0.2460 0.3290 0.1086 0.2222 0.1830 0.2495 0.3904 0.5313 0.6722 0.8131 0.9540 1.0949 1.2358 0.8454 0.7164 1.0854 1.3242 1.4544

10.1b 6.1b -0.9b -3.6b -10.0b 5.2b 2.1b 0.3b -3.0b -11.1b -16.7b -21.1b 1.1d 1.3d 1.7d 1.9d 0 3.9f 23.0f 23.8f 29.7f

10.3b 10.5b 1.3b -1.9b -7.1b 6.4b 4.3b 1.7b -1.3b -8.4b -13.4b -17.4b 4.5d 5.1d 5.7d 6.0d 3.7d 0 17.7g 18.2g 24.7g

-0.7c -3.8c -12.0c -15.3c -19.0c -4.0c -10.4c -12.1c -13.1c -19.4c -22.9c -25.9c -2.1e 0.1e 0.5e 1.6e 0.0e 2.1h 27.4h 30.2h 47.2h

-11.3 -16.1 -14.7 -14.8 -14.0 -11.1 -16.2 -14.9 -13.3 -13.3 -12.4 -12.0 -10.4 -9.4 -10.1 -9.9 -7.7 1.3 8.2 9.9 19.8

-11.0 -9.8 -11.1 -11.8 -9.8 -0.5 5.2 8.8 19.3

a All enthalpies are in kJ‚mol-1 at 298 K. b Abraham data.15 c Values taken from Plyasunov and Shock database.37 d Values calculated from the solvation enthalpies data by Abraham15 and vaporization enthalpies from Plyasunov and Shock database.70 e Values calculated from solvation and vaporization enthalpies data from Plyasunov and Shock database.70 f Values taken from ref 52. g Values taken from ref 53. h Values obtained by Borisover et al.71

TABLE 2: Experimental and Evaluated by Eq 6 Solvation Enthalpies of Benzene, Naphthalene, Biphenyl, and Anthracene in Various Solventsa,b benzene 1,2-dichloroethane 1,4-dioxane acetone acetonitrile benzonitrile chlorobenzene ethyl acetate methanol pyridine tetrachloromethane toluene p-xylene a

naphthalene

biphenyl

anthracene

expt

eval

expt

eval

expt

eval

expt

eval

-33.3 -34.0 -33.2 -31.3 -33.7 -33.8 -33.6 -32.3 -34.1 -33.2 -33.6 -33.3

-33.3 -33.5 -33.5 -32.6 -34.3 -34.4 -34.0 -34.1 -33.8 -34.3 -34.4 -34.2

-55.1 -56.1 -54.0 -50.7 -54.6 -55.4 -55.1 -54.1 -55.6 -54.1 -55.5 -54.9

-54.3 -54.7 -54.6 -53.1 -55.9 -56.0 -55.3 -55.6 -55.1 -56.0 -56.0 -55.8

-64.0 -64.7 -62.3 -60.2 -64.6 -64.7 -64.4 -63.6 -64.6 -63.1 -65.2 -64.6

-62.0 -62.5 -62.5 -60.5 -64.3 -64.6 -63.4 -63.9 -63.0 -64.6 -64.6 -64.5

-77.2 -79.1 -76.1 -73.7 -76.1 -77.1 -76.6

-75.1 -75.7 -75.7 -73.2 -78.0 -78.6 -76.9

-78.2 -77.2 -76.9 -77.2

-76.4 -78.7 -78.5 -78.6

All enthalpies are in kJ‚mol-1 at 298 K. b Expt: experimental values taken from ref 53; eval: solvation enthalpies evaluated by eq 6.

network around aromatic molecules may be a reason, but there is also a possibility that eq 6 cannot correctly predict the nonspecific solvation enthalpy. To check the correctness of eq 6, in Table 2 the solvation enthalpies of benzene, naphthalene, biphenyl, and anthracene in various solvents, including associated, evaluated by eq 6, are compared with the experimental data from ref 53. The solvation enthalpies in cyclohexane are taken from ref 52. Benzene was used as the standard solvent R (aR ) 0.20 and bR ) 0.38). Experimental values of the solvation enthalpies of benzene, naphthalene, biphenyl, and anthracene in benzene and other solvents are taken from ref 53 and VxA values from ref 27. The observed difference between the calculated and experimental values is significantly less than naphthalene, biphenyl, and anthracene hydrophobic effect enthalpies. So the positive hydrophobic effect enthalpies of arenes are probably not the results of poor work of eq 6. According eq 6, the nonspecific solvation enthalpies of solute A in solvents with close δcavhS values for the same solute will be close, too. Water has the δcavhS value 9.5‚102 kJ‚cm-3‚102, close to the acetonitrile δcavhS value27 10.7‚102 kJ‚cm-3‚102. If there is no specific interaction of solute A with water and acetonirile (AN), we can easily estimate the hydrophobic effect

enthalpy by using the following equation:

∆h.e.(AN)HA ) ∆hydnHA - ∆solnHA/AN

(10)

The hydrophobic effect enthalpy values ∆h.e.(AN)HA estimated using this equation are presented in the last column of Table 1. Enthalpies of solution in acetonitrile ∆solnHA/AN were taken from Trampe and Eckert64 and Krishnan and Friedman65 data. Evaluated hydrophobic effect enthalpies for noble and other simple substance gases and for alkanes do not depend on molecule size. However, it was shown24,25 that the hydrophobic effect Gibbs energy of alkanes depends linearly on molecule size (molar refraction MR was used as the measure of molecular volume). On the other hand, the hydrophobic effect enthalpies for aromatic hydrocarbons increase as the molecule size grows (see Table 1). Hydrophobic Effect Enthalpies of Aliphatic Alcohols. The hydrophobicity of aliphatic alcohols, especially of the lowest homologues, can seem nonsense. Indeed, they mix with water in any proportion. But the solution entropy of alcohols in water is largely negative,66 and the heat capacity of solution is largely positive.67 These anomalies allow us to speak about the

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TABLE 3: Hydrophobic Effect Enthalpies ∆h.e.HROH, Specific Interaction Enthalpies in Methanol ∆int(sp)HROH/CH3OH of C1-C8 normal Saturated Alcohols and Supplementary Data for ∆h.e.HROH Calculationa methanol ethanol 1-propanol 1-butanol 1-pentanol 1-hexanol 1-octanol

VxA 27

∆solnHROH/C6H12

∆solnHROH/CCl4b

∆hydnHROH

∆solnHROH/CH3OH

∆int(sp)HROH/CH3OH

∆h.e.HROH

∆h.e.(S)HROH 69

0.3082 0.4491 0.5900 0.7309 0.8718 1.0127 1.2945

24.3b 23.9b 23.6c 23.5c 24.1c 24.4b 24.6b

18.4 18.4 18.5 18.5 18.6 18.6 18.7

-7.3d -10.2d -10.5d -9.4d -8.1d -6.5e -3.2e

0 0.02f 0.43f 0.88g 1.59g 2.13f 3.47h

-15.1 -15.7 -15.4 -16.1 -15.5 -15.4 -14.7

-5.6 -9.3 -10.4 -10.8 -10.5 -10.0 -9.1

-8.1 -13.4 -16.4 -18.0 -19.3

a All enthalpies are in kJ‚mol-1 at 298 K. b Data from ref 30. c Trampe and Eckert data.64 d Pfeffer et al. data.72 e Abraham data.73 f Calculated from excess solution enthalpies data by Pflug et al.74 g Stephenson and Fuchs data.75 h Interpolated value from a plot of solution enthalpy against carbon number.

hydrophobicity of alcohols. According eq 5, we should know the specific alcohol-water interaction enthalpy as well as the nonspecific interaction enthalpy to estimate the hydrophobic effect contribution to the solution enthalpy of alcohols in water. Water is an associated solvent, an equilibrium mixture of hydrogen-bonded associates and monomer molecules.46,47 A solute molecule forming hydrogen bonds with water can shift this equilibrium. Experimental hydration thermodynamic parameters contain the contribution of water-water hydrogen bonds breaking energy due to this shift. A model describing the solute-induced shift of the associates equilibrium in various solvents qualitatively has been suggested.68 The specific solutesolvent interaction enthalpy in associated solvents differs from the solute-solvent hydrogen-bonding enthalpy by a value that depends on the number of lone pair electrons and acidic hydrogen atoms in solute and solvent molecules. There are two acidic hydrogens and two lone pair electrons in a water molecule. It means both proton acceptors and proton donors will affect the equilibrium of water associates, competing with water molecules for the acidic hydrogens or the lone pair electrons. An aliphatic alcohol molecule has both proton acceptor and proton donor functions. No competition takes place if there is no significant difference in proton accepting or donating ability between water and aliphatic alcohols. It was shown48-51 that the hydrogen-bonding energy of water in itself is approximately -14 ( 1 kJ‚mol-1 per bond. The hydrogen-bonding enthalpy of methanol in itself is -15.1 kJ‚mol-1.30 This gives us the ground to use the hydrogen-bonding enthalpies of alcohols in methanol to approximate the hydrogen-bonding enthalpies of alcohols in water. Because we assume ∆int(sp)HROH/H2O ) ∆int(sp)HROH/CH3OH, the hydrophobic effect enthalpy can be calculated by the following equation:

essential differences are there between Somsen values and our present work results. First, we obtained less exothermic values for aliphatic alcohols. Second, Somsen values show some dependence on alkyl chain length. It should be noted that although both methods are based on completely different presumptions, the results do not differ dramatically. The obvious advantage of our method is that significantly less experimental data is required to determine the hydrophobic effect enthalpy.

∆h.e.HROH ) ∆hydrHROH - ∆hydr(nonsp)HROH -

Acknowledgment. We would like to thank Dr. A. Stolov for reviewing this manuscript.

∆int(sp)HROH/CH3OH (11)

Conclusion In the current work, the hydrophobic effect enthalpy is considered as the quantitative measure of the “special” properties of water in comparison with the other solvents. In our opinion, the investigations of the hydrophobicity cannot be successful when no quantitative parameters of the hydrophobic effect are present. The main result of present work is the development of a new hydrophobic effect enthalpy evaluation method. It can be applied to the apolar compounds and aliphatic alcohols as well as to the other solutes forming hydrogen bonds with water. This method will allow the study of the influence of the solute molecule structure to the hydrophobic effect enthalpy for a large number of nonelectrolyte solutes. The application of this method to the nonpolar compounds has shown that the nature of solute can influence the sign of the hydrophobic effect enthalpy from negative for the alkanes and noble gases to positive for the arenes. The rough equality of the hydrophobic effect enthalpies for the aliphatic alcohols (-10.0 ( 0.9 kJ‚mol-1) and alkanes (-10.7 ( 1.5 kJ‚mol-1) is likely the evidence of the additivity of the hydrophobic effect contribution to the enthalpy of hydration.

References and Notes ∆int(sp)HROH/CH3OH and ∆hydr(nonsp)HROH were calculated by eqs 4 and 6. In Table 3 the hydrophobic effect enthalpies of C1C8 normal saturated alcohols and the data for calculation are given. Benzene is known to form hydrogen bonds with dissolved aliphatic alcohols,27 so tetrachloromethane was used as the standard solvent R. The δcavhS value for CH3OH is 5.1‚102 kJ‚cm-3‚102.27 The hydrophobic effect enthalpies of considered alcohols, except methanol, fall in the range -10.0 ( 0.9 kJ‚mol-1, while the alkanes hydrophobic effect enthalpies are in the range -10.7 ( 1.5 kJ‚mol-1. These results, in our mind, indirectly confirm the assumptions used in eq 11. Somsen et al.69 determined the hydrophobic effect enthalpies of aliphatic alcohols by using eq 1. The values obtained in the referenced work are given in the last column of Table 3. Two

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