J . Phys. Chem. 1989, 93, 3799-3802 temperature that would reasonably populate the lowest host vibrations rather than the lowest guest contributions, the simulations presented in this study do not conclusively explain the falloff in C / R as the temperature approaches 300 K. To study this effect more quantitatively would require a series of simulations beginning with the one presented here and proceeding to ones near room temperature. The boundary conditions for such simulations should certainly include neighboring unit cells. In all the calculations, we have made an assumption that the observed motions of the trapped molecules do not depend on any correlation between the motions of molecules in neighboring cells. This assumption could have led to some disagreement between the calculated and observed properties but probably not to the extent demonstrated by the disagreement between the observed
3799
and calculated heat capacities. We are planning to include one or more extra cavities and cages into the system and study the effect of the explicit inclusion of the surroundings on the dynamical and thermodynamic difference properties of clathrate systems at a variety of temperatures. Acknowledgment. We thank the R. A. Welch Foundation for financial support of this work. Many of the calculations were carried out on the NSF Cray X/MP at San Diego on a grant from SDSC. We thank Dr. Jim Korp for help with the crystal coordinates and useful discussions. In addition we thank the referees for several interesting and insightful comments. Registry No. N2.12P-quinol, 119656-73-4;02-12P-quinol,11965674-5; CO.12P-quino1, 119656-75-6;NO-12P-quino1, 119656-76-7.
First Measurement of the Hydrogen Bond Basicity of Monomeric Water, Phenols, and Weakly Basic Alcohols Christian Laurence,* Michel Berthelot, Maryvonne Helbert, and Khadija Sraidi Laboratoire de Spectrochimie MolPculaire, FacultP des Sciences et des Techniques, UniversitP de Nantes, 44072 Nantes Cedex 03, France (Received: September 22, 1988)
Equilibrium constants have been measured for the formation of 1:1 complexes between 4-fluorophenol or 3,4-dinitrophenol and water, alcohols, and phenols as dilute CCl, or cyclohexanesolutions. The wavenumber displacements of the OH stretching vibration of methanol, 4-fluorophenol, or perfluoro-tert-butyl alcohol on H-bond formation provide other measures of the hydrogen bond basicity of an ROH compound. These data, together with thermodynamic and spectroscopic data from the literature, have been used to construct a thermodynamic hydrogen bond basicity scale ~ K Hby B means of a principal component analysis. The structural effects on pKHB have been analyzed in terms of field and polarizability effects, Youghly measured by the u* constant of the R group. The participation of steric effects is excluded since the basicity of alcohols becomes greater with increased branching of the alkyl moiety and also with increased length of the alkyl chain. The (3 scale of hydrogen bond basicity has been developed for ROH compounds (R = H, Alk, Ar).
Since the work of Taft et al.,] 4-fluorophenol has proved to be an excellent reference hydrogen bond donor for establishment of a hydrogen bond basicity scale for organic bases B. This scale, denoted by PKHB, is defined as the logarithm of the formation constant K of the 1:l complex 4-FC6H40H-B in CC14 at 25 OC. However, no pKHB values are available for compounds as fundamental as water, alcohols, and phenols. Additionally, no formation constant for the hydrogen-bonded complex between any hydrogen bond donor and water is available. Of course, this arises from the amphiprotic character of these molecules which consequently self-associate into dimer (ROH)2 and polymer (ROH); more basic than the monomer ROH.3 In order to measure the basicity of the monomer ROH alone, it is necessary to work with concentrations of R O H too dilute to obtain an accurately measurable concentration of the complex 4-FC6H40H--O(R)H, using, for example, the classical infrared m e t h ~ d . With ~ water another great difficulty is present: the very low water solubility in apolar solvents (8.7 X M in CC14 at 25 "C) makes the determination of the initial water concentration problematical. To obtain a greater quantity of complex, we can use a hydrogen bond donor stronger than 4-fluorophenol, as did Benizri and Bellon5 with 3-nitrophenol and 3,5-dichlorophenol and Abboud (1) (a) Gurka, D.; Taft, R. W. J . A m . Chem. SOC.1969, 91, 4794. (b) Taft, R. W.; Gurka, D.; Joris, L.; Schleyer, P. V. R.; Rakshys, J. W. J. A m . Chem. SOC.1969, 91, 4801. (2) Frange, B.; Abboud, J. L. M.; Benamou, C.; Bellon, L. J . Org. Chem. 1982, 47,
4553.
(3) Huyskens, P. L. J . Am. Chem. SOC.1977, 99, 2579. (4) Joesten, M. D.; Schaad, L. J. Hydrogen Bonding, Marcel Dekker: New York, 1974. ( 5 ) Benizri, R.; Bellon, L. Bull. SOC.Chim. Fr. 1978, 378.
0022-3654/89/2093-3799$01.50/0
et aL6 with 3,4-dinitrophenol, but it is then difficult to anchor these data to the pKHB scale.6 Other authors have defined spectroscopic hydrogen bond basicity scales for alcohols. For example, Aslam et al.' have used the wavenumber displacement of the O H stretching vibration of phenol at 361 1 cm-l in CC14 to define a scale Av(0H) = 361 1 - v(OH-.ORH). In the same vein, Legon et al.' have calculated a scale Av(FH) = 3958 - v(FH-.ORH) from investigations of gas-phase hydrogen-bonded complexes formed between hydrogen fluoride and alcohols. But as shown by Gramstad et al.,9 there is no general relationship between log K and AV that permits ready transformation of these spectroscopic scales into thermodynamic scales. For these reasons, and in spite of those difficulties mentioned above, we have decided to measure the pKHe values for water, a few alcohols, and one phenol. We think that this is now possible with the aid of a Fourier transform infrared spectrometer which allows more precise measurement of the lower concentrations of complexes 4-FC6H40H-.0(R)H than classical dispersive spectrometers. Fully aware, however, of some imprecision in the values so obtained, we have checked them by a principal component analysis bearing on the literature hydrogen bond basicity therr n ~ d y n a m i cand ~ . ~s p e c t r o s ~ o p i cscales ~ ~ ~ of alcohols and on three new spectroscopic scales measured in this work, namely, a Avl( 6 ) Abboud, J. L. M.; Sraidi, K.; Guiheneuf, G.; Negro, A,; Kamlet, M. J.; Taft, R. W. J . Org. Chem. 1985, SO, 2870. (7) Aslam, M. H.; Collier, G.; Shorter, J. J . Chem. SOC.,Perkin Trans. 2 1981. 1572. (8) Legon, A. C.; Millen, D. J.; Schrems, 0. J . Chem. SOC.,Faraday Trans. 1 1979, 592. (9) Gramstad, T. Spectrochim. Acta 1963, 19, 497.
0 1989 American Chemical Society
3800 The Journal of Physical Chemistry, Vol. 93, No. 9, 1989 (OH,methanol) scale, a Av3(0H,4-FC6H40H) scale, and a Av,(OH, perfluoro-tert-butyl alcohol) scale. This last scale with (CF,),COH (pFtB), which is a very strong hydrogen bond donor, allows for the first time an investigation of phenols and very weakly basic alcohols. This statistical analysis leads to a reliable PKHB thermodynamic scale for water, 20 alcohols, and 5 phenols, the hydrogen bond basicities of which embrace a large structural field from adamantan- 1-01 to hexafluoroisopropyl alcohol. The structural effects on the monomer basicities of ROH compounds can then be analyzed more securely.
Experimental Section Infrared measurements were made with a Bruker IFS45 WHR Fourier transform spectrometer by selecting 1-cm-' resolution and 256 accumulations. A 1-cm quartz infrasil cell was thermostated at 25 h 0.1 "C by the thermoelectric effect. Alcohols, phenols, and solvents were commercial compounds from Aldrich, Merck (CCI,), or 3M (FC 75, trade name of a perfluorinated butyltetrahydropyran). Adamantan- 1-01 and 4fluorophenol were purified by sublimation. Spectroscopic grade CC14 was dried with 4-A molecular sieves. Liquid alcohols were distilled. Their purity was checked by gas chromatography, and they were dried on basic alumina and/or 3- or 4-A molecular sieves. All solutions were prepared in a dry box. Equilibrium constants for 4-fluorophenol have been determined in CCI, by the Rose and Drago method,I0 from absorbance variations of the u(0H) band of complexed 4-fluorophenol. A direct method," from absorbance variations of the v(0H) band of free 4-fluorophenol (extinction coefficient 235 L mol-' cm-I) has been used both in the case of water and for self-association of 4-fluorophenol. The initial concentrations of 4-fluorophenol and of alcohols are known by weight. For the 4-fluorophenolwater complex, the initial water concentration in CC14is calculated from the absorbance of the v,(H20) band at 3707 cm-' (extinction coefficient 31 L mol-' cm-' 1 2 ) . Equilibrium constants with 3,4-dinitrophenoi were measured in cyclohexane at 23.3 "C with a Cary 219 UV-visible spectrometer by the method of Abboud.6
Laurence et al. best correlated (r = 0.9999) with the column Av,. A second 5 X 5 matrix is limited to columns Avl, Avj, Au4, log K (3,4-dinitrophenol), and log K(4-fluorophenol) but is extended to the adamantan-1-01 row. One factor explains 98.4% of the total variance and is still best correlated (r = 0.9997) to the column AU,. A third 5 X 4 matrix refers to columns Av3, Av4, Au5, and log K(4-fluorophenol) and to rows t-BuOH, i-PrOH, EtOH, MeOH, and CICH2CH20H. The variation of alcohol basicity is greatly enlarged in this matrix (ApKHB = 0.64 instead of 0.42 for the first matrix); however, one factor still explains 98.6% of the total variance and is always best correlated to the column Au,. If we add the row H 2 0 to this alcohol matrix, one creates a 6 X 4 matrix for which the first principal component explains only 94.8% of the total variance and one needs a second principal component for explaining 99.5% of the total variance. As indicated by correlations between spectroscopic and thermodynamic scales, water appears to be distinct from the alcohols. A last 7 X 3 matrix refers to columns Au3, Av,, and log K(4fluorophenol) and to rows adamantan- 1-01, t-BuOH, i-PrOH, EtOH, MeOH, CICH2CH20H,and 4-FC6H40H. One factor explains 99.8% of the total variance of this matrix where a phenol has been added to alcohols. As a first approximation, we may then consider that, with respect to hydrogen bond basicity, alcohols and phenols belong to the same family.
Discussion This principal component analysis shows that the thermodynamic and spectroscopic hydrogen bond basicity dependent properties of alcohols and phenols are correlated by means of one factor and that this factor is very well correlated with Au4(pFtB), the most comprehensive property of Table I. The experimental log K(4-FC6H40H)values (first column of the table) can therefore be refined, and new values, as yet unmeasured, or experimentally inaccessible, can be calculated from the following correlation between log K(4-FC6H40H) and Av,(pFtB): s = 0.03
r = 0.998
n=7
Results Equilibrium Constants. The decimal logarithms of the formation constants (L mol-I) of complexes between 4-fluorophenol and water, adamantan-1-01, tert-butyl alcohol, isopropyl alcohol, ethanol, methanol, 2-chloroethanol, and 4-fluorophenol (in this case we are concerned with the dimerization constant) in CCI, at 25 "C are reported in column 1 of Table I. In column 2, the decimal logarithms of the formation constants (L mol-') of complexes between 3,4-dinitrophenol and cyclohexanol, n-octyl alcohol, 2-phenylethanol, allylic alcohol, and trichloroethanol add to the results already obtained under the same conditions (cyclohexane, 23.3 "C) by Abboud et aL6 for other alcohols. Frequency Shifts. The displacements on H-bond formation Aul(OH) = 3644 - v(OH-ORH) of the methanol O H stretching vibration in CCI,, Au3(0H) = 3614 - u(OH-.ORH) of the 4fluorophenol O H stretching vibration in CCI,, and Au4(OH) = 361 8 - v(OH-.ORH) of the perfluoro-tert-butyl alcohol O H stretching vibration in FC75 are reported respectively in columns 6,8, and 9 of Table I. Phenols behave both as x and oxygen bases toward hydrogen bond donors; however, our shifts refer only to oxygen complexes. Principal Component Analysis. From Table I we have constructed several full data matrices, on each of which we have made a principal component analysis. A first 4 X 10 matrix is constituted by all the scales studied but is limited to the four rows t-BuOH, i-PrOH, EtOH, and MeOH. One factor explains 98.1% of the total variance. It is
(s is standard deviation, r is correlation coefficient, and n is number of data points). This correlation enables us to calculate a PKHB scale (pKHB = log KCa'd(4-FC6H40H)) for 25 alcohols and phenols. This scale is reported in the eleventh column of Table I. Water departs from this linear correlation by 0.60 logarithmic unit (20 times the standard deviation) and therefore does not belong to the family of alcohols and phenols, as already suggested by the principal component analysis. The experimental value of water, log K(4-FC6H40H) = 0.65 cannot therefore be refined and must be retained with an error of f0.09 corresponding to the standard deviation of six different experimental determinations. These PKHB values enable us to investigate the influence of R substituent on the hydrogen bond basicity of ROH compounds. Adamantan-1-01 and tert-butyl alcohol are the two most basic alcohols. Since the adamantyl and t-butyl groups possess the highest steric constants EsI3in our ROH series, it is clear that steric effect acts only slightly on the hydrogen bond basicity of alcohols. In this respect alcohols behave quite differently from ethers, for which the hydrogen bond basicity is known to depend partly on steric effect.', The steady increase of hydrogen bond basicity on chain lengthening (Me < Et < n-Pr < n-Bu < n-Oct) and branching (Me < Et < i-Pr < t-Bu) of the R chain is rather in favor of a polarizability effect of alkyl substituent^.'^ As already suggested by Abboud et a1.,6this "gas-phase-like" behavior is noticeable and partly attributable to the low dielectric constant of the medium (FC75, cyclohexane, CC14).
( I O ) Rose, N. J.; Drago, R. S . J . Am. Chem. SOC.1962, 84, 2037. ( 1 I ) Arnett, E. M.; Joris, L.; Mitchell, E.; Murty, T. S . S . R.; Gorie, T. M.; Schleyer, P. V. R. J . Am. Chem. Soc. 1970, 92, 2365. ( 1 2) Mc Tigue, P.; Renowden, P. V. J . Chem. Soc., Faraday Trans 1 1975, 1784.
( 1 3) Taft, R. W. In Steric Effects in Organic Chemistry; Newman, M. S . , Ed.; Wiley: New York, 1956; Chapter 13. (14) Bellon, L.; Taft, R. W.; Abboud, J . L. M . J . Org. Chem. 1980, 45, 1166. (15) Taft, R . W.; Topsom, R. D. Prog. Phys. Org. Chem. 1987, 16, I .
Hydrogen Bond Basicity of ROH Compounds
The Journal of Physical Chemistry, Vol. 93, No. 9, 1989 3801
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3802
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On the other hand, the steady decrease of PKHB with increasing halogen content of the chain (FCH2CHz BrCHzCHz C1CH2CH2 > CCI,CH, > CF,CH, > (CF,),CH) shows the importance of inductive (fieldI5) effects. This blend of polarizability and inductive effects is satisfactorily measured by the Taft u* constant,13 as shown by PKHB = -1.055~*+ 0.93 s = 0.13
r = 0.976
(2)
n = 17 (ref 19)
In the phenol series, the hydrogen bond basicity is correlated with the u' Hammett constant16 of the ring substituent: PKHB = -0.650~' - 0.05 s = 0.02
r = 0.993
(3)
n =5
These PKHB values can be anchored to the empirical /3 scale of hydrogen bond basicity, an essential scale in the Kamlet-Taft linear solvation energy relationships," to yield the hitherto un(16) Exner, 0. In Correlation Analysis in Chemistry; Chapman, N. B., Shorter, J., Eds.; Plenum Press: New York, 1978; Chapter 10.
available fl parameters for monomeric water, phenols, and weakly basic alcohols. Equation 418enables one to transform the PKHB scale into a p scale normalized from 0 to 1 ( p = 1 is for hexamethylphosphortriamide): @ = (PKHB + 1.1)/4.636
This
(4)
0 scale constitutes the last column in Table I.
Registry No. pFtB, 2378-02-1; H 2 0 , 7732-18-5; 4-FC6H40H, 37141-5; 2-CIC6H40H, 107-07-3; M e O H , 67-56-1; t-BuOH, 75-65-0; iP r O H , 67-63-0; E t O H , 64-17-5; C C 1 3 C H 2 0 H , 115-20-8; 3,4( N 0 2 ) 2 C 6 H 3 0 H ,577-71-9; adamantan-1-01, 768-95-6; cyclohexanol, 108-93-0; n-octyl alcohol, I1 1-87-5; 2-phenylethanol, 60-12-8; allylic alcohol, 107-18-6. (17) Taft, R. W.; Abboud, J. L. M.; Kamlet, M. J.; Abraham, M. H. J . Solution Chem. 1985, 14, 153. (18) Abraham, M. H.; Grellier, P. L.; Prior, D. V.; Morris, J. J.; Laurence, C.; Berthelot, M. Manuscript in preparation. (19) The 17 R substituents for which a u* values (in parentheses) is available are t-Bu (-0.30), i-Pr (-0.19), cyclohexyl (-0.15), n-Bu (-0.13), n-Pr (-0.115), Et (-O.lO), Me (O.OO), PhCHzCH2(0.08), PhCH2 (0.215), HOCH2CH2(0.189), BrCHzCHz (0.34), CICHzCH2(0.385), FCH2CH2(0.374), H (0.49), CC13CH2(0.90),CF3CH2(0.92), and (CF&2H (1.84).
Partial Molar Volume of Apolar Gases in Aqueous Solutions from Room Temperature to Supercritical Conditions Roberto Fernindez-Prini* and Maria Laura Japas Departamento Quimica de Reactores. ComisiBn Nacional de Energia AtBmica, Av Libertador 8250, 1429 Buenos Aires, Argentina (Received: January 21, 1988)
Measurements of the apparent molar volume of apolar gases dissolved in water over a very wide temperature range have been reported recently. The observed partial molar volumes of Ar and Xe in water may be accounted for successfully from room temperature to supercritical conditions with a perturbation method employed previously for calculating the solute's standard chemical potential and its temperature derivatives. These results, together with those obtained previously in this laboratory, show that the temperature and pressure derivatives of the standard chemical potential of nonpolar gases dissolved in water may be well described over wide p , T ranges by employing a simple perturbation procedure.
Introduction Recently Biggerstaff and Wood' reported precise values of the partial molar volume of apolar gases dissolved in water over a wide temperature range. They have measured the isobaric apparent molar volume of Ar, Xe, and C2H4in water from ambient temperature to temperatures above the critical temperature of water, Tcl. As the solution approached T,,, the apparent molar volumes of the dissolved gases were observed to increase sharply, the effect starting at lower temperature when p was closer to the saturation vapor pressure of the solvent. Since the solutions employed were very dilute (mole fraction smaller than 0.002), the measured apparent molar volume may be taken equal to V2-, the partial m o l a r volume of the gases at infinite dilution. The studies of the behavior of dilute solutions close to the critical point of the sol~ e n t have ~ - ~established that Vz" diverges as T T,, and p p c l ,where pcl is the solvent's critical pressure, a fact that has also been observed for dilute solutions in nonaqueous solvent^.^ At room temperature the partial molar volumes of apolar gases dissolved in aqueous solutions are significantly smaller than in nonaqueous solvents.68 This is considered one of the characteristic features distinguishing the behavior of nonpolar solutes in water from that exhibited in nonaqueous media. Various models have been proposed to explain these differences between aqueous and nonaqueous solvents. Close to room temperature the partial molar
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'To whom correspondence should be sent.
0022-3654/89/2093-3802$01.50/0
volumes of apolar gases in different liquids have been described by scaled particle theory'JI and by perturbation methods.* On the other hand, it is becoming increasingly recognized that, in order to validate the models which pretend to describe the behavior of solutes in aqueous solutions, their ability to predict the observed behavior should be tested over a wide temperature rangegqE0 and not just close to room temperature. Our studies of the solubility of apolar gases in aqueous solutions over a wide temperature range10J2J3led us to propose a procedure for the calculation of the thermodynamic properties of dissolution of nonpolar gases in water which very successfully accounts for ( 1 ) Biggerstaff, D. R.; Wood, R. H. J . Phys. Chem. 1988, 92, 1988. (2) Wheeler, J. C. Ber. Bunsen-Ges. Phys. Chem. 1972, 76, 308. (3) Rozen, A. M. Russ. J . Phys. Chem. 1976, 50, 837. (4) Chang, R.F.; Levelt Sengers, J. M. H. J . Phys. Chem. 1986,90,5921. ( 5 ) Eckert, C. A.; Zieger, D. H.; Johnston, K. P.; Kim, S. J . Phys. Chem. 1986, 90, 2738. (6) Eley, D. D. Trans. Faraday SOC.1939, 35, 1421. (7) Pierotti, R. A. Chem. Rev. 1976, 7 6 , 717. (8) Tiepel, E. W.; Gubbins, K. E. J . Phys. Chem. 1972, 7 6 , 3044. (9) FernHndez-Prini, R.; Japas, M. L. J . Phys. Chem. 1986, 90, 1385. (10) Ferngndez-Prini, R.;Crovetto, R.; Japas, M. L.; Laria, D. Acc. Chem. Res. 1985, 18, 207. (11) Lee, B. Biopolymers 1985, 24, 813. (12) Crovetto, R.;Fernindez-Prini, R.; Japas, M. L. Ber. Bunsen-Ges. Phys. Chem. 1984,88,484. (1 3) Fernbndez-Prini, R.;Alvarez, J.; Crovetto, R.; De Biasi, M. M.; Japas, M. L. In Chemistry in High Temperature Aqueous Solutions; Paine, J. P.
N., Ed.; Provo, in press.
0 1989 American Chemical Society
