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Donor properties of water in organic solvents derived from infrared spectra of HDO
Journal of Molecular Structure 643 (2002) 29–35 www.elsevier.com/locate/molstruc
Donor properties of water in organic solvents derived from infrared spectra of HDO Janusz Stangret* Department of Physical Chemistry, Gdan´sk University of Technology, ul Narutowicza 11/12, PL-80-952 Gdan´sk, Poland Received 12 March 2002; revised 3 May 2002; accepted 14 May 2002
Abstract The co-operativity of water hydrogen bonds has been discussed, as a key to the appropriate interpretation of water infrared spectra. In that respect, interaction energy values have been ascribed to some structural arrangements of water. A scale for water electron donor properties in aprotic solvents has been proposed, basing on Gutmann’s donor numbers. q 2002 Elsevier Science B.V. All rights reserved. Keywords: Water; H-bonds; Co-operativity; Infrared spectra; Donor numbers; Organic solvents
1. Introduction Natural environment for a water molecule are Lewis acids and bases, water itself can play both of these functions. The energy of interaction of water with electron donor and electron acceptor is not additive, however, the interaction with a donor depends on the polarisation power of an acceptor and vice versa. Frank and Wen [1] began to include the co-operativity of water hydrogen bonds in structural models of liquid water. The co-operativity of water interactions is already well recognised [2 – 9]. There are problems, however, in adequate accounting of the phenomenon in theoretical models of aqueous solutions or in interpretation of experimental thermodynamic data. As a result, water hydrogen bonds cooperativity is frequently underestimated. In this paper, some infrared spectroscopy data, thermodynamic * Fax: þ48-58-347-2694. E-mail address: [email protected] (J. Stangret).
data, as well as Gutmann’s donor numbers (DN) [10] have been correlated to enable more quantitative description of water H-bond co-operativity.
2. Relation between the interaction type and the OD band position of HDO Co-operativity of water hydrogen bonds appears not only in energetic effects of interactions, but also in spectral effects of infrared bands. Establishing corresponding energetic and spectral relationships allows building up a platform between the thermodynamic characteristics and the molecular description of aqueous systems. The Badger – Bauer rule [11 – 14], which correlates linearly the energy of hydrogen bonds and the vibrational band position, is insufficient to explain spectral data in terms of water molecules interactions. The illustration of this statement could be shown in Fig. 1, which correlates the energy of water evaporation from organic solvents and the band
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Fig. 1. Energy of transfer of H2O at infinite dilution in different solvents to the gas phase, DUtr(H2O), versus OD band position of HDO in these solvents, n0OD ; at 25 8C, †: DUtr ðH2 OÞ ¼ ½DHv ðH2 OÞ 2 RT 2 DUs ðH2 OÞ; where DHv(H2O) is the H2O evaporation enthalpy (44.01 kJ mol 21 [18]), DUs ðH2 OÞ ø DHs ðH2 OÞ; the enthalpy of solution at infinite dilution in a solvent, and RT the work of gas expansion for evaporation process. Values of DHs(H2O) and n0OD ; for solvents based, respectively, on: TEA [2, 19], DMSO [20,21], THF [22,23], AN [24,25], NM [2,19], tetrachloromethane [2,26]; data for n0OD ; from Refs. [2,19,26] originally determined for OH vibration of HDO and data from Ref. [19] at 30 8C have been converted to OD vibration on the basis of the correlation curve from Ref. [27]. Data for water as solvent, A (discussed in text): (1) OD band position in H2O, measured value: 2509 ^ 2 cm21; (2) hypothetical band position of OD without Hbonds through lone electron pairs, 2578 ^ 10 cm21; (3) OD band position in the situation with complete lack of water H-bonds (the only type of interactions are van der Waals interactions), 2649 ^ 10 cm21. The energetic state of cases (2) and (3) are illustrated by arrows from points A; DUww, energy of water Hbonds; DUvdW, the energy of water van der Waals interactions in water (14 kJ mol21, according to Luck [15]).
position of water vibration (OD group of HDO) in these solvents. A similar correlation can be found in the papers of Kleeberg [2] and Luck and co-workers [15,16], but shown in another aspect than herein. In this paper, the correlation serves to ascribe the OD band position to different types of water interactions.
The correlation in Fig. 1 can be represented by two lines: (1) marked by points for water in the gas phase and for organic solvents like tetrachloromethane (CCl4), benzene (C6H6) and nitromethane (NM), as well as (2) marked by points for solvents like NM, acetonitrile (AN), tetrahydrofurane (THF), dimethylsulfoxide (DMSO) and triethylamine (TEA), referred further as electron donor solvents. Generally, solvents from the first group can interact with water by van der Waals forces, solvents from the second group can also form H-bonds with water. NM has an intermediate position in this classification. The correlation suggests that the extrapolated energy value for donor solvents at n0OD ¼ 2727 cm21 (the bond position for HDO in the gas phase) corresponds to the van der Waals interaction of water in an average solvent environment, as was also anticipated by Kleeberg [2]. It should be noticed, however, that the conditions of the extrapolation result in infinite distance between water and surrounding molecules, so the extrapolated energy value does not correspond to any physical state. As it can be seen, the n0OD value for HDO in H2O (point 1 in Fig. 1) is less than for HDO in DMSO, even so the energy of interaction in the second case is higher, this seemingly does not obey the Badger – Bauer rule. The explanation of this discrepancy depends on water H-bonds through lone electron pairs in aqueous environment, which result in additional polarisation of OD bonds of HDO when compared to the interactions in aprotic solvent medium. The horizontal line in Fig. 1, which corresponds to the energy of water evaporation, DUv ðH2 OÞ; enables estimation of the HDO band position in H2O in the case of lack of H-bonds via water lone electron pairs: n0OD ¼ 2578 ^ 10 cm21 : The value appears at the intersection of the horizontal line with the correlation line for electron donor solvents. All aprotic solvents for which the HDO bond position is less than 2578 cm21 form stronger H-bonds with water than water with water does. The determined frequency has been employed in the next chapter to construct a scale of donor properties of water in aprotic solvents. The extension of the more steep correlation line to the intersection with the horizontal line in Fig. 1 enables the estimation of the HDO band position in water in the case of complete lack of H-bonds
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formation (van der Waals forces are the only type of intermolecular interactions): n0OD ¼ 2649 ^ 10 cm21 : The energy level corresponding to the water evaporation, DUv ðH2 OÞ ¼ 41:53 kJ mol21 ; which has been used to obtain the characteristic n0OD values in water, corresponds to the same average intermolecular distance as in bulk water. Obviously, the molar evaporation energy in the case (2) and (3) in Fig. 1 must be less than 41.53 kJ mol21. In the case (3), it corresponds to van der Waals interactions of water in water, DUvdW ðH2 O; H2 OÞ; equal to 14 kJ mol21 [15]; a higher value has been also published by Luck [17], 17.6 kJ mol21. In the case (2), the energetic state of one mole of water is also hypothetical, formally, it corresponds to ½DUvdW ðH2 O; H2 OÞ þ 1=2DUww ðH2 O; H2 OÞ; where DUww ðH2 O; H2 OÞ indicates the energy of water H-bonds in bulk water; DUww ðH2 O; H2 OÞ þ DUvdW ðH2 O; H2 OÞ ¼ DUv ðH2 OÞ: Because of lack of corresponding data, this calculation method does not include the cooperativity of water interactions through OH groups and lone electron pairs, hidden in the DUww ðH2 O; H2 OÞ value. The energy for the case (2), which includes the co-operativity, should be less than calculated by the described way and shown in Fig. 1. The value of the OD bond position of HDO, which does not interact through lone electron pairs in water, obtained from the correlation in Fig. 1 is in good agreement with predictions drown on other bases: 1. It has been established by Glew and Rath [19] that data point for water does not obey the linear correlation of OH band position of HDO in aprotic solvents versus pKa of these solvents. From the linear relationship, the pKa for water should be 6.3 ^ 0.6, that is, 8.1 of pKa units higher than the value known for water. This value ðpKa ¼ 21:8Þ corresponds instead to n0OH ¼ 3503 cm21 ; which is a value 96 cm21 higher than observed for bulk water (n0OH for HDO in D2O equals 3407 cm21). The bond position converted to the OD vibration of HDO, on the basis of the correlation curve from Ref. [27], gives n0OD ¼ 2581 ^ 10 cm21 : 2. It has been established by Luck and co-workers [2 – 5,7] that the band shift of water co-ordinated to a metal cation (K) in ternary solutions: salt of K – water –aprotic solvent (B; in a huge excess),
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D n(K…water…B), linearly increases with respect to the band shift of water interacting with the solvent (B), Dn(water…B). The slopes of the correlation lines Dn(K…water…B) versus Dn(water…B) for different metal cations (K) in series of solvents (B), which differ in electron donor power, is a measure of co-operativity for interactions K…water…B. The extrapolated data at zero slope (lack of co-operativity) gain [5], after conversion to OD vibrations, n0OD ¼ 2589 ^ 15 cm21 : The contribution of water molecules, which do not form H-bonds via lone electron pairs in water is very small, less than 2% [2]. However, information about the band position of water in the considered state is very important for interpretation of water vibrational spectra. The published band position of HDO, which does not form any H-bonds in liquid water, spreads the range of 2630 – 2680 cm21 [26,28,29]. The most reliable value seems to be delivered by spectral studies of Lindner [30,31]. The band position is 2644 ^ 10 cm21, close to the value obtained from the correlation in Fig. 1.
3. Donor number of water in aprotic solvents The popular method of characterising the electron donor properties of solvents by one parameter is DN, proposed by Gutmann [10]. It helps to consider the solute/ion – solvent interaction in the approach based on the idea of acid –base reactions. DN is defined as the negative enthalpy value (DH ), in kcal mol21 (determined calorimetrically), for the 1:1 adduct formation of the electron donor solvent with SbCl5, as electron acceptor, in a highly diluted solution of 1,2-dichloroethane:DN ; 2DHðdonor·SbCl5 Þ: The DN have been found to be related to various other empirical properties, so the DN scale has been also extended beyond the originally defined method of determination. Many other parameters have been proposed to determine solvating properties of solvents, they have been reviewed in papers [32 –34]. Critical opinions referring to the DN scale frequently concern DN values for water. According to Gutmann, DN for monomeric water, like in gas
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phase, equals to 18, whereas for liquid water < 33 [10]. The value given for liquid water usually seems to be too high and, for water diluted in different media, there are doubts which DN value should be used. Taking into account, the co-operativity of water Hbonds it is reasonable to expect different DN values in different systems. Data correlated in Fig. 2 give the possibility of obtaining DN values for water in different environments. Relationship between DN of aprotic solvents and the OD band position of HDO diluted in these solvents has been shown in Fig. 2. As it can be seen, DN values do not linearly change with n0OD : Construction of the diagram includes the assumption that DN values for pure solvents are the same as for solvents diluted in 1,2-dichloroethane, in which DN have been determined. This assumption, however, does not explain observed non-linear relationship in Fig. 2. A decrease of DN values could be rather expected for pure structured solvents and thus an increase of non-linear character of the relationship. The interesting observation is that for DN exceeding ca. 33 accompanying OD band shift is very small. This effect will require additional explanation. This is based indeed on one point only, corresponding to TEA, but there are circumstances to expect that the relationship suggested in Fig. 2 is qualitatively correct. Taking into account solvents which are stronger electron donors than pyridine (Py) and weaker than TEA, like: 2-methylpiridine ðn0OD ¼ 2512 cm21 Þ; 2,4,6-trimethylpyridine ðn0OD ¼ 21 2506 cm Þ; ethylamine ðDN ¼ 55:5Þ and t-butylamine ðDN ¼ 57:0Þ; for which either the band position of diluted water is known (the two first solvents; n0OD values have been calculated basing on n0OH values published [19], using the correlation given in Ref. [27]) or DN values are known (the two endmost solvents). Basing on the correlation in Fig. 2, DN for liquid water can be determined. The value equals to 26.7 as an ordinate which corresponds to n0OD ¼ 2578 cm21 (Section 2). If n0OD ¼ 2509 cm21 (the value measured for HDO in pure H2O) instead of n0OD ¼ 2578 cm21 has been used, the value of 30.8 has been obtained, which is close to the value given by Gutmann (< 33). The value of 30.8 is too high, however, because it corresponds to water molecules for which donor centres have been blocked by interaction with
surrounding molecules and includes additional polarisation of OD bonds caused by interaction via lone electron pairs. Relation of DN and n0OD from Fig. 2 enables to draw another correlation: between DN of water diluted in given solvent, DN(H2O), and DN of the solvent, DN. Determination of DN(H2O) values can be done by ascribing to points in Fig. 2 a new ordinate, basing on the unit of the new scale, DN(H2O). This unit is determined by the co-ordinates of positions: (2727; 0) and (2578; 26.7) for the DN and n0OD axis system. The first distinguished point corresponds to water in gas phase, for which Gutmann ascribed DN ¼ 18; thus DN(H2O,gas) ¼ 18. The second one corresponds to water molecules, which do not form Hbonds via lone electron pairs in water, DNðH2 O; H2 OÞ ¼ 26:7: Construction of the correlation of DN(H2O) versus DN is based on the assumption that electron donor ability of water changes proportionally to the electron donor ability of the solvent. This assumption is justified by Luck and co-workers’ spectroscopic studies [2 – 5,7] concerning water in molecular complexes of the [metal cation –water – aprotic solvent] and [water–aprotic solvent] types. The band position of water in the first instance is a measure of donor ability of water, in the second instance, donor ability of the solvent. Both DN and n0OD values are the measure of donor ability of solvent and (as it can be seen in Fig. 2) do not change linearly. Thus, the question arises: according to which scale (DN or n0OD ) should DN(H2O) values proportionally change as they depend on both DN and n0OD : In this context, two cases could be considered. (a) The case of linear dependence of DN(H2O) versus DN. Definition of the DN(H2O) scale, the right ordinate axis in Fig. 2(a), is based on direct projection of above-mentioned distinguished points for water and ascribing to them the 18 and 26.7 values. The method of reading DN(H2O) value in a given solvent has been shown in Fig. 2(a), for NM as an example. DN(H2O) values correlate linearly relative to DN, corresponding points have been marked in Fig. 3. In the discussed case, DN(H2O) values depend only indirectly on the n0OD scale, by the value DNðH2 O; H2 OÞ ¼ 26:7:
J. Stangret / Journal of Molecular Structure 643 (2002) 29–35
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Fig. 2. Relationship between Gutmann DN left axis, and the OD band position of HDO, n0OD ; in different aprotic solvents, †: data for DN based on Ref. [10], data for n0OD as in Fig. 1. Same relationship for water in solvents, DN(H2O) right axis: (a) assuming that DN(H2O) values correlate linearly with DN values and (b) assuming that DN(H2O) values correlate linearly with n0OD values (explanation in text). The point W corresponds to gas water or to liquid water at 25 8C (explanation in text); arrows illustrate the way of finding the DN(H2O) values.
(b) The case of linear dependence of DN(H2O) versus n0OD : Definition of the DN(H2O) scale, the right ordinate axis in Fig. 2(b), is based on direct projection of distinguished points for water on the line coming from the point (2727; 0); the slope of the line relative to the n0OD axis can be in the range 0 – 908. It is convenient to pass the line through the point corresponding to TEA: this solvent closes the
scale of Gutmann’s DN. Because this projection maintains unchanged n0OD values, obtained points correlate linearly in n0OD and DN(H2O) axis system by definition – corresponding points have been marked in Fig. 3. The method of reading the DN(H2O) value in a given solvent has been shown in Fig. 2(b), for NM as an example. In the discussed case, DN(H2O) values depend only indirectly on
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Fig. 3. Relationship between the DN of water in aprotic solvents, DN(H2O), and the DN of these solvents, DN: K corresponds to the assumption that DN(H2O) values correlate linearly with DN values (Fig. 2(a)); L corresponds to the assumption that DN(H2O) values correlate linearly with n0OD values (Fig. 2(b)); † corresponds to the average value of DN(H2O) arising from the values ascribed to K and L; and W corresponds to water in gas phase or in liquid at 25 8C.
the DN scale, by the values DN(H2O,gas) ¼ 18 and DNðH2 O; H2 OÞ ¼ 26:7: Fig. 3 shows the relationship between DN of water diluted in aprotic solvents, DN(H2O), and DN of these solvents, DN. As an appropriate representation of DN(H2O), in a given solvent, averages of values obtained basing on above considered assumptions have been accepted. The marked difference for DN(H2O), values in Fig. 3 can be considered as an error of estimation. The data correlated in this figure can help in estimating electron donor properties of water in different media.
4. Summary The bond position of HDO diluted in H2O has been determined for two cases: (1) of complete lack of H-bonds and (2) of lack of H-bonds via water electron pairs. These positions, equal to 2649 ^ 10 and 2578 ^ 10 cm21, respectively (in a good agreement with data obtained from the other basis), are important for interpretation of water
infrared spectra in aqueous solutions. For the comparison purposes, the value for HDO in bulk equals to 2509 ^ 2 cm21 and for ice to 2420 cm21 [35]. Increasing energy of water intermolecular interactions accompanies the above quoted order of band positions, which confirms co-operativity of Hbonds in water. The result obtained evidences additional polarisation of OD/OH bonds of HDO caused by Hbonds via lone electron pairs. On the other hand, the energy of H-bonds via OD/OH groups determines electron donor properties of water molecule, which in turn depends on the electron donor properties of the water molecule environment. From the correlation of the band position of HDO diluted in different aprotic solvents and Gutmann’s DN of these solvents, the DN of water in water environment has been determined, as an ordinate which corresponds to the band position of 2578 cm21 (of HDO diluted in H2O in the case of lack of H-bonds via water electron pairs). This value, equals to 26.7, should be a better measure of water donor properties than the value given by Gutmann (< 33), because it
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corresponds to water molecules for which donor centres have not been blocked by interaction with surrounding molecules. Using the DN for water in water environment obtained ðDN ¼ 26:7Þ and the value for monomeric water determined by Gutmann ðDN ¼ 18Þ; the scale of DN for water in different aprotic solvents has been constructed.
References [1] H.S. Frank, W.-Y. Wen, Disc. Faraday Soc. 24 (1957) 133. [2] H. Kleeberg (Eds.), Interactions of Water in Ionic and Nonionic Hydrates, Springer, Berlin, 1987, p. 89. [3] H. Kleeberg, G. Heinje, W.A.P. Luck, J. Phys. Chem. 90 (1986) 4427. [4] H. Kleeberg, J. Mol. Struct. 237 (1990) 187. [5] G. Heinje, T. Kammer, H. Kleeberg, W.A.P. Luck, in: H. Kleeberg (Ed.), Interactions of Water in Ionic and Nonionic Hydrates, Springer, Berlin, 1987, p. 39. [6] H. Kleeberg, D. Klein, W.A.P. Luck, J. Phys. Chem. 91 (1987) 3200. [7] H. Kleeberg, W.A.P. Luck, Z. Phys. Chemie (Leipzig) 270 (1989) 613. [8] K. Hermansson, J. Lindgren, M.M. Probst, Chem. Phys. Lett. 233 (1995) 371. [9] P. Barnes, J.L. Finney, J.D. Nicholas, J.E. Quinn, Nature 282 (1979) 459. [10] V. Gutmann, Electrochim. Acta 21 (1976) 661. [11] R.M. Badger, S.H. Bauer, J. Chem. Phys. 5 (1937) 839. [12] R.S. Drago, N. O’Bryan, G.C. Vogel, J. Am. Chem. Soc. 92 (1970) 3924. [13] C.N. Rao, P.C. Dwivedi, H. Ratajczak, W.J. Orville Thomas, J. Chem. Soc., Faraday Trans. 2 5 (1975) 955.
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[14] W.A.P. Luck, T. Wess, Can. J. Chem. 69 (1991) 1819. [15] H. Kleeberg, O. Koc¸ak, W.A.P. Luck, J. Solution Chem. 11 (1982) 611. [16] W.A.P. Luck, J. Mol. Struct. 217 (1990) 282. [17] W.A.P. Luck, H.Y. Zheng, J. Chem. Soc., Faraday Trans. 2 80 (1984) 1253. [18] Y. Marcus, Ion Solvation, Wiley/Interscience, Chichester, 1985. [19] D.N. Glew, N.S. Rath, Can. J. Chem. 49 (1971) 837. [20] T.C. Chan, W.A. Van Hook, J. Solution Chem. 5 (1976) 107. [21] J. Stangret, E. Kamien´ska-Piotrowicz, Proceedings of Polish Chemical Society Conference, Gdan´sk, 22 –26 September 1997, S-5, P-35. [22] L.I. Katzin, D.M. Simon, J.R. Ferraro, J. Am. Chem. Soc. 74 (1952) 1191. [23] R. Nogalski, J. Stangret, Proceedings of Polish Chemical Society Conference, Poznan´, 23–26 September 1996, S-1, F30. [24] E. Kamien´ska-Piotrowicz, unpublished result, 1989. [25] D. Jamro´z, J. Stangret, J. Lindgren, J. Am. Chem. Soc. 115 (1993) 6165. [26] K.A. Hartman Jr., J. Phys. Chem. 70 (1966) 270. [27] B. Berglund, J. Lindgren, J. Tegenfeldt, J. Mol. Struct. 43 (1978) 169. [28] G.E. Walrafen, in: F. Franks (Ed.), Water. A Comprehensive Treatise, vol. 1, Plenum Press, New York, 1972, p. 151. [29] W.A.P. Luck (Eds.), Structure of Water and Aqueous Solutions, Chemie-Physik Verlag, Berlin, 1973, p. 221. [30] H. Lindner, Doctoral dissertation, University of Karlsruhe, 1970 (data have been shown and discussed in Ref. [31]). [31] G.E. Walrafen, in: F. Franks (Ed.), Water. A Comprehensive Treatise, vol. 1, Plenum Press, New York, 1972, pp. 184–187. [32] I. Persson, Pure Appl. Chem. 58 (1986) 1153. [33] M. Sandstro¨m, I. Petsson, P. Persson, Acta Chem. Scand. 44 (1990) 653. [34] Y. Marcus, Chem. Soc. Rev. (1993) 409. [35] M. Falk, Can. J. Chem. 49 (1971) 1137.
Donor properties of water in organic solvents derived from infrared spectra of HDO Janusz Stangret* Department of Physical Chemistry, Gdan´sk University of Technology, ul Narutowicza 11/12, PL-80-952 Gdan´sk, Poland Received 12 March 2002; revised 3 May 2002; accepted 14 May 2002
Abstract The co-operativity of water hydrogen bonds has been discussed, as a key to the appropriate interpretation of water infrared spectra. In that respect, interaction energy values have been ascribed to some structural arrangements of water. A scale for water electron donor properties in aprotic solvents has been proposed, basing on Gutmann’s donor numbers. q 2002 Elsevier Science B.V. All rights reserved. Keywords: Water; H-bonds; Co-operativity; Infrared spectra; Donor numbers; Organic solvents
1. Introduction Natural environment for a water molecule are Lewis acids and bases, water itself can play both of these functions. The energy of interaction of water with electron donor and electron acceptor is not additive, however, the interaction with a donor depends on the polarisation power of an acceptor and vice versa. Frank and Wen [1] began to include the co-operativity of water hydrogen bonds in structural models of liquid water. The co-operativity of water interactions is already well recognised [2 – 9]. There are problems, however, in adequate accounting of the phenomenon in theoretical models of aqueous solutions or in interpretation of experimental thermodynamic data. As a result, water hydrogen bonds cooperativity is frequently underestimated. In this paper, some infrared spectroscopy data, thermodynamic * Fax: þ48-58-347-2694. E-mail address: [email protected] (J. Stangret).
data, as well as Gutmann’s donor numbers (DN) [10] have been correlated to enable more quantitative description of water H-bond co-operativity.
2. Relation between the interaction type and the OD band position of HDO Co-operativity of water hydrogen bonds appears not only in energetic effects of interactions, but also in spectral effects of infrared bands. Establishing corresponding energetic and spectral relationships allows building up a platform between the thermodynamic characteristics and the molecular description of aqueous systems. The Badger – Bauer rule [11 – 14], which correlates linearly the energy of hydrogen bonds and the vibrational band position, is insufficient to explain spectral data in terms of water molecules interactions. The illustration of this statement could be shown in Fig. 1, which correlates the energy of water evaporation from organic solvents and the band
0022-2860/02/$ - see front matter q 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 2 8 6 0 ( 0 2 ) 0 0 3 1 5 - 0
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Fig. 1. Energy of transfer of H2O at infinite dilution in different solvents to the gas phase, DUtr(H2O), versus OD band position of HDO in these solvents, n0OD ; at 25 8C, †: DUtr ðH2 OÞ ¼ ½DHv ðH2 OÞ 2 RT 2 DUs ðH2 OÞ; where DHv(H2O) is the H2O evaporation enthalpy (44.01 kJ mol 21 [18]), DUs ðH2 OÞ ø DHs ðH2 OÞ; the enthalpy of solution at infinite dilution in a solvent, and RT the work of gas expansion for evaporation process. Values of DHs(H2O) and n0OD ; for solvents based, respectively, on: TEA [2, 19], DMSO [20,21], THF [22,23], AN [24,25], NM [2,19], tetrachloromethane [2,26]; data for n0OD ; from Refs. [2,19,26] originally determined for OH vibration of HDO and data from Ref. [19] at 30 8C have been converted to OD vibration on the basis of the correlation curve from Ref. [27]. Data for water as solvent, A (discussed in text): (1) OD band position in H2O, measured value: 2509 ^ 2 cm21; (2) hypothetical band position of OD without Hbonds through lone electron pairs, 2578 ^ 10 cm21; (3) OD band position in the situation with complete lack of water H-bonds (the only type of interactions are van der Waals interactions), 2649 ^ 10 cm21. The energetic state of cases (2) and (3) are illustrated by arrows from points A; DUww, energy of water Hbonds; DUvdW, the energy of water van der Waals interactions in water (14 kJ mol21, according to Luck [15]).
position of water vibration (OD group of HDO) in these solvents. A similar correlation can be found in the papers of Kleeberg [2] and Luck and co-workers [15,16], but shown in another aspect than herein. In this paper, the correlation serves to ascribe the OD band position to different types of water interactions.
The correlation in Fig. 1 can be represented by two lines: (1) marked by points for water in the gas phase and for organic solvents like tetrachloromethane (CCl4), benzene (C6H6) and nitromethane (NM), as well as (2) marked by points for solvents like NM, acetonitrile (AN), tetrahydrofurane (THF), dimethylsulfoxide (DMSO) and triethylamine (TEA), referred further as electron donor solvents. Generally, solvents from the first group can interact with water by van der Waals forces, solvents from the second group can also form H-bonds with water. NM has an intermediate position in this classification. The correlation suggests that the extrapolated energy value for donor solvents at n0OD ¼ 2727 cm21 (the bond position for HDO in the gas phase) corresponds to the van der Waals interaction of water in an average solvent environment, as was also anticipated by Kleeberg [2]. It should be noticed, however, that the conditions of the extrapolation result in infinite distance between water and surrounding molecules, so the extrapolated energy value does not correspond to any physical state. As it can be seen, the n0OD value for HDO in H2O (point 1 in Fig. 1) is less than for HDO in DMSO, even so the energy of interaction in the second case is higher, this seemingly does not obey the Badger – Bauer rule. The explanation of this discrepancy depends on water H-bonds through lone electron pairs in aqueous environment, which result in additional polarisation of OD bonds of HDO when compared to the interactions in aprotic solvent medium. The horizontal line in Fig. 1, which corresponds to the energy of water evaporation, DUv ðH2 OÞ; enables estimation of the HDO band position in H2O in the case of lack of H-bonds via water lone electron pairs: n0OD ¼ 2578 ^ 10 cm21 : The value appears at the intersection of the horizontal line with the correlation line for electron donor solvents. All aprotic solvents for which the HDO bond position is less than 2578 cm21 form stronger H-bonds with water than water with water does. The determined frequency has been employed in the next chapter to construct a scale of donor properties of water in aprotic solvents. The extension of the more steep correlation line to the intersection with the horizontal line in Fig. 1 enables the estimation of the HDO band position in water in the case of complete lack of H-bonds
J. Stangret / Journal of Molecular Structure 643 (2002) 29–35
formation (van der Waals forces are the only type of intermolecular interactions): n0OD ¼ 2649 ^ 10 cm21 : The energy level corresponding to the water evaporation, DUv ðH2 OÞ ¼ 41:53 kJ mol21 ; which has been used to obtain the characteristic n0OD values in water, corresponds to the same average intermolecular distance as in bulk water. Obviously, the molar evaporation energy in the case (2) and (3) in Fig. 1 must be less than 41.53 kJ mol21. In the case (3), it corresponds to van der Waals interactions of water in water, DUvdW ðH2 O; H2 OÞ; equal to 14 kJ mol21 [15]; a higher value has been also published by Luck [17], 17.6 kJ mol21. In the case (2), the energetic state of one mole of water is also hypothetical, formally, it corresponds to ½DUvdW ðH2 O; H2 OÞ þ 1=2DUww ðH2 O; H2 OÞ; where DUww ðH2 O; H2 OÞ indicates the energy of water H-bonds in bulk water; DUww ðH2 O; H2 OÞ þ DUvdW ðH2 O; H2 OÞ ¼ DUv ðH2 OÞ: Because of lack of corresponding data, this calculation method does not include the cooperativity of water interactions through OH groups and lone electron pairs, hidden in the DUww ðH2 O; H2 OÞ value. The energy for the case (2), which includes the co-operativity, should be less than calculated by the described way and shown in Fig. 1. The value of the OD bond position of HDO, which does not interact through lone electron pairs in water, obtained from the correlation in Fig. 1 is in good agreement with predictions drown on other bases: 1. It has been established by Glew and Rath [19] that data point for water does not obey the linear correlation of OH band position of HDO in aprotic solvents versus pKa of these solvents. From the linear relationship, the pKa for water should be 6.3 ^ 0.6, that is, 8.1 of pKa units higher than the value known for water. This value ðpKa ¼ 21:8Þ corresponds instead to n0OH ¼ 3503 cm21 ; which is a value 96 cm21 higher than observed for bulk water (n0OH for HDO in D2O equals 3407 cm21). The bond position converted to the OD vibration of HDO, on the basis of the correlation curve from Ref. [27], gives n0OD ¼ 2581 ^ 10 cm21 : 2. It has been established by Luck and co-workers [2 – 5,7] that the band shift of water co-ordinated to a metal cation (K) in ternary solutions: salt of K – water –aprotic solvent (B; in a huge excess),
31
D n(K…water…B), linearly increases with respect to the band shift of water interacting with the solvent (B), Dn(water…B). The slopes of the correlation lines Dn(K…water…B) versus Dn(water…B) for different metal cations (K) in series of solvents (B), which differ in electron donor power, is a measure of co-operativity for interactions K…water…B. The extrapolated data at zero slope (lack of co-operativity) gain [5], after conversion to OD vibrations, n0OD ¼ 2589 ^ 15 cm21 : The contribution of water molecules, which do not form H-bonds via lone electron pairs in water is very small, less than 2% [2]. However, information about the band position of water in the considered state is very important for interpretation of water vibrational spectra. The published band position of HDO, which does not form any H-bonds in liquid water, spreads the range of 2630 – 2680 cm21 [26,28,29]. The most reliable value seems to be delivered by spectral studies of Lindner [30,31]. The band position is 2644 ^ 10 cm21, close to the value obtained from the correlation in Fig. 1.
3. Donor number of water in aprotic solvents The popular method of characterising the electron donor properties of solvents by one parameter is DN, proposed by Gutmann [10]. It helps to consider the solute/ion – solvent interaction in the approach based on the idea of acid –base reactions. DN is defined as the negative enthalpy value (DH ), in kcal mol21 (determined calorimetrically), for the 1:1 adduct formation of the electron donor solvent with SbCl5, as electron acceptor, in a highly diluted solution of 1,2-dichloroethane:DN ; 2DHðdonor·SbCl5 Þ: The DN have been found to be related to various other empirical properties, so the DN scale has been also extended beyond the originally defined method of determination. Many other parameters have been proposed to determine solvating properties of solvents, they have been reviewed in papers [32 –34]. Critical opinions referring to the DN scale frequently concern DN values for water. According to Gutmann, DN for monomeric water, like in gas
32
J. Stangret / Journal of Molecular Structure 643 (2002) 29–35
phase, equals to 18, whereas for liquid water < 33 [10]. The value given for liquid water usually seems to be too high and, for water diluted in different media, there are doubts which DN value should be used. Taking into account, the co-operativity of water Hbonds it is reasonable to expect different DN values in different systems. Data correlated in Fig. 2 give the possibility of obtaining DN values for water in different environments. Relationship between DN of aprotic solvents and the OD band position of HDO diluted in these solvents has been shown in Fig. 2. As it can be seen, DN values do not linearly change with n0OD : Construction of the diagram includes the assumption that DN values for pure solvents are the same as for solvents diluted in 1,2-dichloroethane, in which DN have been determined. This assumption, however, does not explain observed non-linear relationship in Fig. 2. A decrease of DN values could be rather expected for pure structured solvents and thus an increase of non-linear character of the relationship. The interesting observation is that for DN exceeding ca. 33 accompanying OD band shift is very small. This effect will require additional explanation. This is based indeed on one point only, corresponding to TEA, but there are circumstances to expect that the relationship suggested in Fig. 2 is qualitatively correct. Taking into account solvents which are stronger electron donors than pyridine (Py) and weaker than TEA, like: 2-methylpiridine ðn0OD ¼ 2512 cm21 Þ; 2,4,6-trimethylpyridine ðn0OD ¼ 21 2506 cm Þ; ethylamine ðDN ¼ 55:5Þ and t-butylamine ðDN ¼ 57:0Þ; for which either the band position of diluted water is known (the two first solvents; n0OD values have been calculated basing on n0OH values published [19], using the correlation given in Ref. [27]) or DN values are known (the two endmost solvents). Basing on the correlation in Fig. 2, DN for liquid water can be determined. The value equals to 26.7 as an ordinate which corresponds to n0OD ¼ 2578 cm21 (Section 2). If n0OD ¼ 2509 cm21 (the value measured for HDO in pure H2O) instead of n0OD ¼ 2578 cm21 has been used, the value of 30.8 has been obtained, which is close to the value given by Gutmann (< 33). The value of 30.8 is too high, however, because it corresponds to water molecules for which donor centres have been blocked by interaction with
surrounding molecules and includes additional polarisation of OD bonds caused by interaction via lone electron pairs. Relation of DN and n0OD from Fig. 2 enables to draw another correlation: between DN of water diluted in given solvent, DN(H2O), and DN of the solvent, DN. Determination of DN(H2O) values can be done by ascribing to points in Fig. 2 a new ordinate, basing on the unit of the new scale, DN(H2O). This unit is determined by the co-ordinates of positions: (2727; 0) and (2578; 26.7) for the DN and n0OD axis system. The first distinguished point corresponds to water in gas phase, for which Gutmann ascribed DN ¼ 18; thus DN(H2O,gas) ¼ 18. The second one corresponds to water molecules, which do not form Hbonds via lone electron pairs in water, DNðH2 O; H2 OÞ ¼ 26:7: Construction of the correlation of DN(H2O) versus DN is based on the assumption that electron donor ability of water changes proportionally to the electron donor ability of the solvent. This assumption is justified by Luck and co-workers’ spectroscopic studies [2 – 5,7] concerning water in molecular complexes of the [metal cation –water – aprotic solvent] and [water–aprotic solvent] types. The band position of water in the first instance is a measure of donor ability of water, in the second instance, donor ability of the solvent. Both DN and n0OD values are the measure of donor ability of solvent and (as it can be seen in Fig. 2) do not change linearly. Thus, the question arises: according to which scale (DN or n0OD ) should DN(H2O) values proportionally change as they depend on both DN and n0OD : In this context, two cases could be considered. (a) The case of linear dependence of DN(H2O) versus DN. Definition of the DN(H2O) scale, the right ordinate axis in Fig. 2(a), is based on direct projection of above-mentioned distinguished points for water and ascribing to them the 18 and 26.7 values. The method of reading DN(H2O) value in a given solvent has been shown in Fig. 2(a), for NM as an example. DN(H2O) values correlate linearly relative to DN, corresponding points have been marked in Fig. 3. In the discussed case, DN(H2O) values depend only indirectly on the n0OD scale, by the value DNðH2 O; H2 OÞ ¼ 26:7:
J. Stangret / Journal of Molecular Structure 643 (2002) 29–35
33
Fig. 2. Relationship between Gutmann DN left axis, and the OD band position of HDO, n0OD ; in different aprotic solvents, †: data for DN based on Ref. [10], data for n0OD as in Fig. 1. Same relationship for water in solvents, DN(H2O) right axis: (a) assuming that DN(H2O) values correlate linearly with DN values and (b) assuming that DN(H2O) values correlate linearly with n0OD values (explanation in text). The point W corresponds to gas water or to liquid water at 25 8C (explanation in text); arrows illustrate the way of finding the DN(H2O) values.
(b) The case of linear dependence of DN(H2O) versus n0OD : Definition of the DN(H2O) scale, the right ordinate axis in Fig. 2(b), is based on direct projection of distinguished points for water on the line coming from the point (2727; 0); the slope of the line relative to the n0OD axis can be in the range 0 – 908. It is convenient to pass the line through the point corresponding to TEA: this solvent closes the
scale of Gutmann’s DN. Because this projection maintains unchanged n0OD values, obtained points correlate linearly in n0OD and DN(H2O) axis system by definition – corresponding points have been marked in Fig. 3. The method of reading the DN(H2O) value in a given solvent has been shown in Fig. 2(b), for NM as an example. In the discussed case, DN(H2O) values depend only indirectly on
34
J. Stangret / Journal of Molecular Structure 643 (2002) 29–35
Fig. 3. Relationship between the DN of water in aprotic solvents, DN(H2O), and the DN of these solvents, DN: K corresponds to the assumption that DN(H2O) values correlate linearly with DN values (Fig. 2(a)); L corresponds to the assumption that DN(H2O) values correlate linearly with n0OD values (Fig. 2(b)); † corresponds to the average value of DN(H2O) arising from the values ascribed to K and L; and W corresponds to water in gas phase or in liquid at 25 8C.
the DN scale, by the values DN(H2O,gas) ¼ 18 and DNðH2 O; H2 OÞ ¼ 26:7: Fig. 3 shows the relationship between DN of water diluted in aprotic solvents, DN(H2O), and DN of these solvents, DN. As an appropriate representation of DN(H2O), in a given solvent, averages of values obtained basing on above considered assumptions have been accepted. The marked difference for DN(H2O), values in Fig. 3 can be considered as an error of estimation. The data correlated in this figure can help in estimating electron donor properties of water in different media.
4. Summary The bond position of HDO diluted in H2O has been determined for two cases: (1) of complete lack of H-bonds and (2) of lack of H-bonds via water electron pairs. These positions, equal to 2649 ^ 10 and 2578 ^ 10 cm21, respectively (in a good agreement with data obtained from the other basis), are important for interpretation of water
infrared spectra in aqueous solutions. For the comparison purposes, the value for HDO in bulk equals to 2509 ^ 2 cm21 and for ice to 2420 cm21 [35]. Increasing energy of water intermolecular interactions accompanies the above quoted order of band positions, which confirms co-operativity of Hbonds in water. The result obtained evidences additional polarisation of OD/OH bonds of HDO caused by Hbonds via lone electron pairs. On the other hand, the energy of H-bonds via OD/OH groups determines electron donor properties of water molecule, which in turn depends on the electron donor properties of the water molecule environment. From the correlation of the band position of HDO diluted in different aprotic solvents and Gutmann’s DN of these solvents, the DN of water in water environment has been determined, as an ordinate which corresponds to the band position of 2578 cm21 (of HDO diluted in H2O in the case of lack of H-bonds via water electron pairs). This value, equals to 26.7, should be a better measure of water donor properties than the value given by Gutmann (< 33), because it
J. Stangret / Journal of Molecular Structure 643 (2002) 29–35
corresponds to water molecules for which donor centres have not been blocked by interaction with surrounding molecules. Using the DN for water in water environment obtained ðDN ¼ 26:7Þ and the value for monomeric water determined by Gutmann ðDN ¼ 18Þ; the scale of DN for water in different aprotic solvents has been constructed.
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[14] W.A.P. Luck, T. Wess, Can. J. Chem. 69 (1991) 1819. [15] H. Kleeberg, O. Koc¸ak, W.A.P. Luck, J. Solution Chem. 11 (1982) 611. [16] W.A.P. Luck, J. Mol. Struct. 217 (1990) 282. [17] W.A.P. Luck, H.Y. Zheng, J. Chem. Soc., Faraday Trans. 2 80 (1984) 1253. [18] Y. Marcus, Ion Solvation, Wiley/Interscience, Chichester, 1985. [19] D.N. Glew, N.S. Rath, Can. J. Chem. 49 (1971) 837. [20] T.C. Chan, W.A. Van Hook, J. Solution Chem. 5 (1976) 107. [21] J. Stangret, E. Kamien´ska-Piotrowicz, Proceedings of Polish Chemical Society Conference, Gdan´sk, 22 –26 September 1997, S-5, P-35. [22] L.I. Katzin, D.M. Simon, J.R. Ferraro, J. Am. Chem. Soc. 74 (1952) 1191. [23] R. Nogalski, J. Stangret, Proceedings of Polish Chemical Society Conference, Poznan´, 23–26 September 1996, S-1, F30. [24] E. Kamien´ska-Piotrowicz, unpublished result, 1989. [25] D. Jamro´z, J. Stangret, J. Lindgren, J. Am. Chem. Soc. 115 (1993) 6165. [26] K.A. Hartman Jr., J. Phys. Chem. 70 (1966) 270. [27] B. Berglund, J. Lindgren, J. Tegenfeldt, J. Mol. Struct. 43 (1978) 169. [28] G.E. Walrafen, in: F. Franks (Ed.), Water. A Comprehensive Treatise, vol. 1, Plenum Press, New York, 1972, p. 151. [29] W.A.P. Luck (Eds.), Structure of Water and Aqueous Solutions, Chemie-Physik Verlag, Berlin, 1973, p. 221. [30] H. Lindner, Doctoral dissertation, University of Karlsruhe, 1970 (data have been shown and discussed in Ref. [31]). [31] G.E. Walrafen, in: F. Franks (Ed.), Water. A Comprehensive Treatise, vol. 1, Plenum Press, New York, 1972, pp. 184–187. [32] I. Persson, Pure Appl. Chem. 58 (1986) 1153. [33] M. Sandstro¨m, I. Petsson, P. Persson, Acta Chem. Scand. 44 (1990) 653. [34] Y. Marcus, Chem. Soc. Rev. (1993) 409. [35] M. Falk, Can. J. Chem. 49 (1971) 1137.