J Solution Chem (2008) 37: 1261–1270 DOI 10.1007/s10953-008-9301-3
Volumetric Properties of Dilute Solutions of Water in Acetone between 288.15 and 318.15 K Evgeniy V. Ivanov · Vladimir K. Abrosimov · Elena Y. Lebedeva
Received: 14 November 2007 / Accepted: 8 April 2008 / Published online: 15 July 2008 © Springer Science+Business Media, LLC 2008
Abstract Densities of dilute solutions of water in acetone, with solute mole fractions ranging up to 0.03, have been measured with an error of 8 ×10−6 g·cm−3 , at 288.15, 298.15, 308.15 and 318.15 K, using a precision vibrating-tube densimeter. The partial molar volumes of the solute water (down to infinite dilution) and solvent acetone, as well as the excess molar volumes of the specified mixtures, have been calculated. The effects of the solute concentration and temperature on the volume packing changes, caused by solvation of water in acetone, have been considered. Keywords Acetone · Dilute solutions of water · Partial and excess molar volumes · Solvation
1 Introduction The behavior of water present at very low concentrations in a non-aqueous medium, where the three-dimensional (3D) network of H bonds characteristic of the “pure” aqueous component is absent, remains poorly studied until now. The results of studies performed in this area during the last decade [1–5] show that the properties of water dissolved in an organic solvent substantially depend on the chemical nature (i.e., on the molecular structure and donor-accepting ability) of the latter component. Researchers are interested mainly in such a dissolving (solvating) medium, whose structural packing consists of molecules that do not form strong hydrogen bonds (due to the absence of proton-donating centers) but allows sufficiently strong specific interactions (via H-bonding) with molecules of an electron-accepting amphiprotic solute, which in this case is water.
E.V. Ivanov () · V.K. Abrosimov · E.Y. Lebedeva Laboratory of Thermodynamics of Solutions of Non-electrolytes and Biologically Active Substances, Institute of Solution Chemistry, Russian Academy of Sciences, 1 Akademicheskaya Street, 153045 Ivanovo, Russia e-mail:
[email protected]
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Acetone plays an important role among similar “aprotic dipolar” solvents.1 This is determined by the fact that acetone, being the starting unit of the homologous series of aliphatic ketones, is widely used in many fields of science and chemical technology. Water + acetone mixtures are one of the most studied liquid systems from the viewpoint of structural chemistry. Most research dealing with this subject analyzes the effect of the dissolved organic component on the spatially coordinated (by means of H-bonds) molecular packing of the surrounding aqueous medium [7–11]. Up to now, there are only a few works dedicated to the study of solvation and the structural state of water dissolved in acetone [8, 12, 13]. Therefore, questions about the forces resulting in formation of solvate complexes in dilute solutions (including infinite dilution) of water in acetone remain unanswered and, evidently, both experimental and theoretical methods are needed to solve this problem. Earlier [1, 5] we showed that useful information on structural effects induced by solvation (and other types of intermolecular interaction) can be obtained by using a “structurenon-perturbating” method such as precise densimetry. This method provides information about a range of volume characteristics that reflect structural (packing- and energy-related) rearrangements occurring during solvation. As far as we know, the volumetric properties of water dissolved in acetone have not been determined so far, with the exception of the limiting partial molar volume, V¯2∞ ∼ = 14.3 ± 0.1 cm3 ·mol−1 at 298.15 K [12]. At higher temperatures such data are absent, probably due to experimental difficulties caused by the low boiling point (T ∼ = 329.5 K [7, 14]) of acetone. Based on the above reasoning, we measured the densities of dilute solutions of water in acetone and computed the partial molar volumes (including their values at infinite dilution) of components, as well as the volumetric effects of their mixing, at 288.15, 298.15, 308.15, and 318.15 K.
2 Experimental Guaranteed-HPLC-grade acetone (with a purity of no worse than 99.95 mol-%) was purchased from Chimmed Co. (Moscow, Russia) and used without further purification. The content of residual water, determined by the Karl Fisher titration method, was less than 0.008 wt-%. The density (ρ1 , see below) and refraction index (nD,1 , measured with a Pulfrich Refractometer) of the solvent were 0.784701 g·cm−3 and 1.3566, respectively (reliable data reported in literature are 0.78455 [15], 0.78486 [16], 0.78508 [17], and 0.78442 [18] for ρ1 and 1.3560 [14, 18] for nD,1 ) at 298.15 K.2 Water of natural isotope composition was deionized and twice distilled in an apparatus made of pyrex glass. The electrical conductivity of the resulting water was 1.3 ×10−5 S·m−1 . Solutions were prepared gravimetrically by diluting the degassed “mother” solvent with an accuracy of 2 ×10−5 units of csm,2 , where csm,2 is the solvomolality of the solute. The solvomolal concentration (solvomolality) csm,2 is a dimensionless rational parameter of the solution composition, which expresses the content of the solute in aqueous or non-aqueous 1 According to Kohlhoff-Parker’s classification [6, 7], aprotic dipolar solvents are solvents whose relative permittivity is ε1 > 15 (and dipole moment is μ1 > 8.3 × 10−30 C·m or 2.5 D in Debye units), and which
consist of molecules without “mobile” hydrogen atoms (here and below, quantities related to acetone are designated by the subscript 1, whereas those related to water are denoted by the subscript 2). 2 The scatter observed in the reported densities for acetone can be explained by the differences both in the
quality of the preparation of solvent samples and in details of the experimental procedure. In our case, the ρ1 value corresponds to the density of acetone with the above-mentioned content of residual water.
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media. Namely, csm,2 = 55.50843(n2 /n1 ) = 55.50843(x2 /x1 ), where n1 (x1 ) and n2 (x2 ) are the number of moles (mole fractions) of the solvent and solute, respectively [1, 19, 20]. The normalizing factor of 55.50843 (numerically equal to the number of H2 O moles in 1 kg of water) is introduced in order for csm,2 and molality mm,2 in aqueous solutions to coincide numerically. The use of this concentration scale reduces an error in the definition of the apparent molar volumes of the solute, Vφ,2 , at high dilutions [19]. The final concentration of water was no more than csm,2 = 1.73 units (or x2 ≤ 3.0 × 10−2 ). Densities of the solutions, ρ 1,2 , were measured under air-tight conditions using a digital vibrating-tube high-precision densimeter, whose design and specific features have been described in detail elsewhere [19, 21]. The measurements were performed by the static method (no flow of solution). During the measurements the cell temperature was maintained within ±0.002 K electronically by using a calibrated platinum resistance thermometer on the IPTS68 temperature scale. The apparatus was calibrated daily using the known densities of dry air and H2 O [22] at 288.15, 298.15, 308.15, and 318.15 K and p ∼ = 0.1 MPa. The reproducibility of the density measurements was ±5 × 10−6 g·cm−3 and the error of the measured ρ 1,2 (taking into account the influence of all possible factors) did not exceed 8 ×10−6 g·cm−3 . The experimental densities of dilute solutions of water in acetone along with the smoothed Vφ,2 values are listed in Table 1.
3 Results The regression analysis showed that the obtained concentration dependences of ρ 1,2 (Table 1) are adequately described by the linear equation ρ1,2 = a0 + a1 csm,2 .
(1)
The ai coefficients (with standard deviations, σ0.95 ) are presented in Table 2. Values of ρ 1,2 (csm,2 ) approximated by the above equation were used for calculating the limiting values ∞ ≡ V¯2∞ (also see Table 2). Vφ,2 ∞ The values of Vφ,2 and Vφ,2 (≡ V¯2∞ ) were calculated using a rational procedure [19, 26]. This procedure is distinguished by an improved stability of the Vφ,2 (n2 ) values to the effects of uncertainties in solution densities and compositions in the highly dilute region. According to the method, the initial value of the solution volume, V s , was calculated (at n1 = 55.50843 and n2 = csm,2 , on the solvomolality scale) by the formula Vs = (55.50843M1 + csm,2 M2 )/ρ1,2 ,
(2)
where M1 and M2 are the molar masses of the components. Transforming the known formula [19, 27] for the calculation of Vφ,2 into the form n2 Vφ,2 = n1 M1 /ρ1,2 + n2 M2 /ρ1,2 − n1 M1 /ρ1 = Vs − n1 V1
(3)
and taking into account Eq. 2, one can obtain the expression Vs = 55.50843V1 + csm,2 Vφ,2 . Here, V1 = M 1 /ρ1 is the molar volume of the solvent. It follows from Eq. 4 that Vφ,2 = (Vs − 55.50843V1 )/csm,2
and
∞ Vφ,2 → Vφ,2 as csm,2 → 0.
(4)
–
14.073
14.079
14.083
14.087
14.091
14.095
14.099
14.104
14.109
14.112
14.113
14.115
14.117
14.118
14.118
–
–
–
1.7189
1.5022
1.3440
1.0924
0.89915
0.71636
0.55474
0.39991
0.26440
0.16282
0.094525
0.076062
0.048787
–
–
–
0.787529
0.787185
0.786912
0.786488
0.786183
0.785861
0.785595
0.785351
0.785114
0.784942
0.784838
0.784810
0.784752
0.784701
ρ1,2
–
–
–
14.199
14.205
14.210
14.218
14.223
14.229
14.234
14.238
14.242
14.246
14.248
14.248
14.249
14.250
Vφ,2
–
–
1.5579
1.4237
1.2905
1.1193
0.91194
0.74292
0.55847
0.41517
0.23830
0.14685
0.099221
0.084007
0.070933
0.048648
0.014318
csm,2 b
T = 308.15 K
–
–
0.775756
0.775523
0.775307
0.775034
0.774680
0.774398
0.774098
0.773872
0.773561
0.773418
0.773345
0.773311
0.773282
0.773263
0.773199
ρ1,2 c
–
–
14.333
14.338
14.342
14.347
14.353
14.359
14.364
14.368
14.374
14.376
14.378
14.378
14.379
14.379
14.380
Vφ,2
1.7302
1.6157
1.4098
1.1727
0.96390
0.78149
0.67996
0.54407
0.41044
0.26115
0.15398
0.12269
0.10825
0.090793
0.070926
0.047724
0.014318
csm,2 b
T = 318.15 K
0.764275
0.764068
0.763740
0.763339
0.763014
0.762705
0.762531
0.762307
0.762095
0.761838
0.761678
0.761619
0.761605
0.761562
0.761545
0.761490
0.761442
ρ1,2 c
a At each c sm,2 concentration studied, the reported experimental density value has been obtained by averaging from five to ten (at T = 318.15 K) ρ1,2 measured points b In the mole fraction scale, x = c 2 sm,2 /(55.50843 + csm,2 ) c For comparison, literature data for ρ at 308.15 K and 318.15 K are 0.77309 and 0.76141 g·cm−3 , respectively [16] 1
–
–
0.797354
0.87126
0.798552
0.797083
0.70601
1.5915
0.796811
0.55113
0.798250
0.796514
0.37709
0.797995
0.796340
0.26795
1.4044
0.796273
0.22234
1.2567
0.796139
0.15097
0.797533
0.796059
0.098458
0.797752
0.796012
0.066281
1.1143
0.795966
0.048772
0.98648
0.795916
0.014318
0.014318
csm,2 b
14.119
T = 298.15 K
csm,2 b
Vφ,2
ρ1,2
T = 288.15 K
14.456
14.460
14.466
14.474
14.480
14.486
14.489
14.493
14.497
14.502
14.505
14.506
14.507
14.507
14.508
14.509
14.510
Vφ,2
Table 1 Experimental densities (ρ1,2 , g·cm−3 ) of water solutions in acetone (solvent) and smoothed apparent molar volumes (Vφ,2 , cm3 ·mol−1 ) of the solute at the studied solvomolal concentrations (csm,2 ) and temperatures (T )a
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Table 2 Parameters of the Eqs. 1 and 6 for dilute solutions of water in acetonea T /K
a0
103 × a1
V¯2∞ b
−V¯2E,∞ c
V¯2∞ /Vw,2 d
−bV
288.15
0.795892 (2.6×10−6 )
1.673 (3.3×10−3 )
14.12
3.91
1.24
0.029
298.15
0.784677 (2.8×10−6 )
1.663 (3.3×10−3 )
14.25
3.82
1.25
0.030
308.15
0.773175 (2.5×10−6 )
1.654 (3.1×10−3 )
14.38
3.74
1.26
0.030
318.15
0.761418 (2.6×10−6 )
1.645 (3.2×10−3 )
14.51
3.68
1.27
0.031
a Units: a , g·cm−3 ; V and b , cm3 ·mol−1 . (Because the value of c i V sm,2 is dimensionless, the units of a1 and bV are those of the density and volume, respectively.) The standard (root-mean-square) error of the parameter at the 95% confidence level (σ0.95 ) is given in parentheses b The error in V¯ ∞ determined by accounting for the standard deviations in the smoothed density data is no 2 more than ±0.05 cm3 ·mol−1
c The excess limiting partial molar volume or “volume effect of dissolution” of water in acetone, V¯ ∞ − V 2 2 [23, 24], where V2 is the molar volume of the solute [1, 22] dV 3 −1 at T = 298.15 K [25]; it is postulated that V ∼ w,2 = NA vw,2 = 11.4 cm ·mol w,2 is independent of T in
the temperature range under study
Substituting the dependence of V s versus csm,2 by the appropriate approximating monotonic function, we obtain an equation in which the coefficient of the linear term is ∞ (≡ V¯2∞ ). Regression analysis showed that this dependence for dilute solutions equal to Vφ,2 of water in acetone is adequately described by the second-order polynomial ∞ csm,2 + bV (csm,2 )2 . Vs = 55.50843V1 + Vφ,2
(5)
As numerical values of the parameter 55.50843V1 in Eq. 5 are known with high accuracy, the given equation can be rewritten in a more convenient form ∞ csm,2 + bV (csm,2 )2 . Vs − 55.50843V1 = Vφ,2
(6)
∞ The use of this procedure for the calculation of Vφ,2 has certain advantages over the usual extrapolation procedure, because the experimental Vφ,2 (csm,2 ) values, according to Eq. 5, lie in the narrow range of confidence intervals relative to the line intersecting the ordinate at the already known intercept (55.50843V1 ). This allows one to exclude the influence of the so-called “gramophone horn” effect caused by the dramatic increase in uncertainty of Vφ,2 as n2 → 0 [19, 26]. Based on the Vφ,2 values, the partial molar volumes of water, V¯2 , and acetone, V¯1 , as well E , were estimated in the composition and as the excess molar volumes of their mixtures, V1,2 temperature range of our studies. On the solvomolality scale, the Vφ,2 value is related to V¯2 by the formula [19]
V¯2 = Vφ,2 + csm,2 (∂Vφ,2 /∂csm,2 )T ,p,n1 =55.50843 .
(7)
Because the plot of Vφ,2 (sm,2 ) was found to be linear in the studied concentration region (see Eq. 6 and Table 1), the V¯2 values were computed from the equation V¯2 = Vφ,2 + bV csm,2 .
(8)
Proceeding from Gibbs-Duhem’s first equation [19, 27], we obtain V¯1 = (V1,2 − n2 V¯2 )/n1 = (Vs − csm,2 V¯2 )/55.50843.
(9)
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It should be noted that the mean molar volume of the (acetone + water) mixture, V1,2 = (x1 M1 + x2 M2 )/ρ1,2 , differs from the V s value (see Eq. 2): V1,2 = Vs /(55.50843 + csm,2 ). E To estimate the V1,2 values, we used the following formula [4, 19] E = x2 (Vφ,2 − V2 ) = csm,2 (Vφ,2 − V2 )/(csm,2 + 55.50843). V1,2
(10)
4 Discussion From the data of Table 2 it can be seen that the value of V¯2∞ for water in acetone increases almost linearly with increasing temperature. Herewith, the limiting partial molar expansi∞ , calculated as the temperature derivative of V¯2∞ , and postulating bility of the solute, E¯ p,2 a linear relation between V¯2∞ and T , is equal to 0.0130 cm3 ·mol−1 ·K−1 . This quantity is greater by several fold than the molar expansibility of the pure solute, Ep,2 (H2 O) [1, 22], at ∞ exceeds Ep,2 by a factor of five at T ≈ 288 all studied temperatures. Suffice it say that E¯ p,2 K (but only by a factor of two near 318 K). A similar (in magnitude) slope of the temperature dependence of V¯2∞ was found earlier for water solutions in aprotic dipolar solvents such as acetonitrile (herein after, written as AN) [5, 28] and 1,4-dioxane (1,4-DO) [5, 29] that, like acetone, have lower electrondonating ability than that of an aqueous medium.3 However, unlike the specified solvents where the V¯2∞ and V2 values are close to each other (differing only by no more than 1.0 cm3 ·mol−1 ), for the present water-containing binary system V¯2∞ V2 . It should be noted here that the hypothetical state corresponding to an infinitely dilute solution suggests that water molecules exist as monomeric (i.e., are not bonded with each other) molecules surrounded by a solvation shell of solvent molecules. It stands to reason that the properties and mutual orientation of molecules in a solvation complex of this kind differ from the structural characteristics of molecular packing for both the pure bulk solute and solvent. From this viewpoint, when discussing the results, it is more reasonable to use values of the excess partial molar volume, V¯2E,∞ (see Table 2), which characterize the volume changes associated with the isothermal transfer of one mole of solute from its pure state to the solution at infinite dilution. In the considered system, as stated above, the V¯2E,∞ values are negative in sign. Such behavior is expected for systems where, besides van der Waals (mainly dispersion) forces between solute and solvent molecules, (strong or weak) hydrogen-bonding forces are also involved, making V2 much lower than V¯2∞ [24]. Assuming that both V¯2∞ and V2 consist of the van der Waals “molecular” volume of the solute, Vw,2 = NA vw,2 (where N A is the Avogadro number), plus a varying volume of empty space near the solute molecules [20, 24], one can conclude that the specified interactions are accompanied by the formation of a substantially more densely-packed structure surrounding a water molecule. Indeed, from the ratio of V¯2∞ to Vw,2 , which on the average is 1.25 ± 0.02 (see Table 2), it follows that the intermolecular empty space in a water-acetone solvation complex is substantially smaller than that present in a pure aqueous medium (where the V¯2∞ /Vw,2 ratio is ca. 1.59 at 298.15 K [1]), probably due to a substantial weakening of the hydrogen bonds. Another important peculiarity of dilute solutions of water in acetone lies in the fact that the negative value of bV (Table 2) is virtually independent of temperature. That is, the ap∞ parent molar expansibility of the solute, Ep,φ,2 (csm,2 ) = Ep,φ,2 + (∂bV /∂T )p csm,2 [19, 24], 3 According to Gutmann [6, 7], the electron-donating capability of acetone expressed as the “donator numbers” (DNSbCl5 ∼ = 71.1 kJ·mol−1 ) is close to that of water (∼ = 75.3 kJ·mol−1 ) although their electron-
accepting capabilities (expressed as the “acceptor numbers”, AN: 12.5 and 54.8, respectively) differ strongly from each other.
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almost does not change (or decreases only slightly) with increasing concentration over the investigated concentration region. It is obvious that these observations point to structural features of acetone as a solvent. As has been suggested previously [7, 30, 31], because a (CH3 )2 CO molecule has no “labile” protons, the molecular packing of acetone is stabilized at the expense of van der Waals forces and weak C–H· · ·O contacts. Again, the spatial structure of this solvent is determined in many respects by repulsive intermolecular interactions and steric factors, whereas the electrostatic interactions affect only the mutual orientation of its molecules [31]. The high isothermal compressibility value (βT ,1 ≈ 12.5 × 10−12 Pa−1 at 298.15 K) and low molar enthalpy of vaporization (vap H1◦ ≈ 30.8 kJ·mol−1 ) of acetone [7, 14] confirm that the above-specified types of intermolecular interactions lead to a rather weakly associated and, on the whole, unstable structure. From this it follows that the formation of strong · · ·H–O–H· · · O = C< bonds between molecules of water and acetone is doubtful, because such interactions are predicted to be energetically unfavorable and/or sterically hindered in their molecular packing, not only for pure state but also for water-containing solvent [13, 31–33]. This is confirmed partly by a perceptible endothermic effect of dissolution of H2 O in acetone, sol H2∞ ∼ = 4.4 kJ·mol−1 (298.15 K) [32], which shows that the water-acetone interaction is weaker than the interaction between molecules in the individual aqueous medium. Actually, in an acetone-water solution, a short-lived H-bond with an energy of about −11 kJ·mol−1 can be formed between H2 O and (CH3 )2 CO molecules, whereas for the water-water bond the energy mean-weighted value is taken to be –15.5 kJ·mol−1 [1, 8, 32]. On the other hand, the higher electron accepting capability of the aqueous component (see footnote 2) testifies indirectly to the fact that the acetone-water molecular affinity in an infinite-diluted solution (relative to H2 O) is higher than the acetone-acetone affinity in the bulk solvent. Thus, because of the important role of steric (configurational) factors in the packing- and energy-related transformations of acetone media under the influence of the dissolved water and increasing temperature (volume expansion), the “structure compression” effect (V¯2E,∞ in Table 2) that decreases with temperature must be attributed to a specific solute-solvent interaction. Most interesting here is the fact that the values of V¯2E,∞ (T ) for the (acetone + H2 O) system are comparable to those for the {hexamethylphosphoric triamide (HMPT) + H2 O} system, where V¯2E,∞ ≈ −4.04 cm3 ·mol−1 at 298.15 K [1, 5]. This suggests a certain similarity in the mode of interaction of dissolved water with acetone and a high-electron-donating aprotic dipolar solvent such as HMPT. However, in the latter case, unlike the acetone solution of water, sol H2∞ (298.15K) ∼ = −7.40 kJ·mol−1 , which argues for existence of a strong HMPT-H2 O interaction via hydrogen-bonding (with an energy of about –19 kJ·mol−1 ) [8, 32]. Additional information on the structure-packing effects in the studied binary solutions can be obtained from analysis of their excess molar volumes as well as the partial molar volumes of each of components (water, V¯1 , and acetone, V¯2 ). The values of V¯i (sm,2 ) and E (csm,2 ) calculated using Eqs. 8 to 10 are plotted in Figs. 1 and 2 as linear functions of the V1,2 solute solvomolal concentration. Because both the V¯1 − csm,2 and V¯2 − csm,2 lines are found to vary similarly at all studied temperatures, we only illustrate (in Fig. 1) these quantities at T = 298.15 K. The concentration dependences given in Figs. 1 and 2 demonstrate some rather interesting features that are worthy of note. Firstly, increasing the water content in the binary solution does not change the value of V¯1 within the limits of experimental error. One can assume that, at least in the concentration range studied, incorporation of water molecules into the acetone medium does
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Fig. 1 Concentration dependent changes in the partial molar volumes of water (solid line) and acetone (dashed line) at 298.15 K
Fig. 2 Dependences of the excess molar volumes of dilute acetone solution of water against the solvomolal concentration of the solute at 288.15 K (solid line) and at 318.15 K (dashed line)
not noticeably change the solvent structure, which is characterized by the low stability of its molecular associates (see above). This is supported by the results of Chen, Koga et al. [34], which demonstrate that the thermodynamic interaction functions of acetone, E E = n2 (∂Y1E /∂n1 )T ,p where Y1E = (∂Y1,2 /∂n1 )T ,p,n2 and Y ≡ H, T S or V , are close to Y1−1 zero in the acetone-rich mixtures with water. Secondly, the V¯2 values slightly decrease with increasing concentration of the solute. In our opinion, that when both (∂ V¯2 /∂csm,2 )T ,p,n1 < 0 and (∂ V¯1 /∂csm,2 )T ,p,n2 ≈ 0, this is most likely due to the superposition of several (opposite in sign) volumetric effects that are mainly caused by the destruction of the initial molecular packing of acetone under the influence of
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water additives, and the strengthening of solvent-solute as well as solute–solute interactions. This explains in many respects why the values of bV in Table 2 are negative. Thirdly, the above-discussed peculiarities of intermolecular interactions in the studied binary system manifest themselves also in the close-to-linear concentration dependences of E presented in Fig. 2. It is seen that increasing the water content in acetone media results V1,2 E (csm,2 ) behave in the formation of more closely packed structures. Hence, the values of V1,2 ¯ similarly to those of V2 (csm,2 ) as seen in Fig. 1. Finally, it is interesting to also note that according to Eqs. 4 to 6, the positive sign of ∞ ∞ (≡ Ep,φ,2 ) is determined by the inequality (∂Vs /∂T )p > (55.50843)(∂V1 /∂T )p , i.e., in E¯ p,2 the presence of added water, the acetone medium as a whole has a greater molar expansibility. In this sense, the system considered here is somewhat typical, because a similar effect is characteristic for solutions of water in AN, 1,4-DO and some other aprotic dipolar solvents [1]. However, the molecular aspects of this phenomenon, as well as the strong “structure compression” effect (V¯2E,∞ in Table 2) and concentration-dependent behavior of V¯2 (Fig. 1) for water dissolved in acetone, remain poorly understood. In conclusion, it should be noted that, as was shown earlier by de Visser et al. [35], all aprotic dipolar solvents (except for sulfolane [1]) shift the “bulk water to denser water” equilibrium towards “dense water” (smaller volume). Hence, if the isolated water molecules and the solvent molecules in bulk water are considered as being almost hard spheres, then the dependence of V¯2∞ versus V1 should be very regular and many of solvents in question “obey” the same relationship. When the volumes of the hard-sphere solvent molecules are large, a dissolved water molecule fits more or less well in the holes between these spheres and the corresponding V¯2∞ value is small. As the V1 value decreases, the size of the holes decreases too, so that V¯2∞ increases until the value of V1 is so small that the water molecules do not fit into the solvent’s holes. Proceeding from this relationship, the value of V¯2∞ for water in acetone (V1 ∼ = 74.0 cm3 ·mol−1 ) should be about 15.7 cm3 ·mol−1 at 298.15 K, whereas the experimentally obtained value is only ca. 14.3 cm3 ·mol−1 (see Table 2). On the one hand, these circumstances confirm the above speculations about some distinctions between the structural state of water in an acetone medium as compared to that in several other aprotic dipolar solvents. On the other hand, the given hard-sphere interpretation is, strictly speaking, an over simplification and we cannot as yet offer a reasonable explanation for the unusual behavior of the binary system investigated in the present work. Acknowledgement ric studies.
We wish to thank Drs. A.G. Ramazanova and V.V. Korolev for help with the densimet-
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