Article pubs.acs.org/JPCB
Cite This: J. Phys. Chem. B XXXX, XXX, XXX−XXX
OH Stretching Dynamics in Hydroxide Aqueous Solutions Marco Sbroscia, Armida Sodo, Fabio Bruni, Tommaso Corridoni,† and Maria Antonietta Ricci* Dipartimento di Scienze, Universitá degli Studi Roma Tre, Via della Vasca Navale 84, 00146 Roma, Italy S Supporting Information *
ABSTRACT: The concept of ions being either water “structure makers” or water “breakers” seems to be inconsistent with the existence of a critical number of water molecules per ion dictating the properties of an aqueous solution, independent of the ion identity. To investigate this issue, Raman spectra of hydroxide aqueous solutions in the region of the OH stretching mode have been obtained under ambient conditions and at concentrations ranging from extreme dilution to the solubility limit. Spectra have been analyzed with a relatively model-free approach, in terms of a superposition of contributions due to the vibrations of the OH− ions, with two contributions due to the solvent. One of these latter contributions falls at wavenumbers very close to that of the OH− stretching band, sharing with it its concentration dependence of the full width at half maximum (FWHM). The other contribution due to the solvent is very broad, with increasing FWHM with increasing ion concentration. In the light of these observations, an interpretation of the Raman spectra, based on the possibility of distinguishing the self and distinct contributions, is proposed. The present analysis is supported by structural data on the same solutions and puts into evidence relevant structural and dynamical changes occurring when the number of water molecules available per solute is below ∼20, irrespective of the ion identity.
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INTRODUCTION A large number of physical, chemical, biological, and industrial processes are influenced or driven by the structural and dynamical properties of electrolyte aqueous solutions. Depending on the process, either the hydration and mobility of the solute itself, or the perturbation of the hydrogen bond (HB) network upon ion solvation may be crucial. In particular, since the early paper by Cox and Wolfenden,1 the literature dealing with the perturbation of bulk water structure and dynamics due to ions in solution is so rich that a full account is unfeasible here. The most common concept adopted in the literature to describe the perturbation brought by ions to bulk water structure is grouping ions into the categories of “structure-maker” or “structurebreaker”.2,3 However, it is not clear whether an ion that interacts with water “making” a quite stable and strong hydration shell, while determining significant distortions (“breaking”) of the HB network, has to be included in the first or second category.4 The concept of ions being structure making or breaking has been recently criticized by some researchers,4,5 based on the results of a series of neutron diffraction (ND) experiments. These demonstrate that all ions in solution determine a distortion of the HB network with respect to that of neat water, to an extent depending on the ion (along with its counterion) and concentration.5 It has been found that this distortion is similar to that caused by an external pressure applied to pure water.5−9 Indeed ND experiments can quantify this distortion in terms of the shift of the second peak of the water oxygen−oxygen radial distribution function to shorter distances. This shift is due to the collapse of the water second neighboring shell toward the first one, as observed when high pressures are applied to pure water.10 © XXXX American Chemical Society
This collapse is due to H-bond bending, not necessarily to bond breaking: thus, it does not affect the tetrahedral-like structure of water at distances on the order of the first neighbor shell, but it affects its longer range microscopic order. Therefore, and on the one hand, techniques that probe the short-range/time order, as for instance femtosecond pump−probe spectroscopy of the water rotational dynamics,11,12 may not be sensitive to the longrange modifications induced by ions to the water structure, at odds with techniques probing macroscopic properties, such as viscosity.13 On the other hand, the OH stretching band of the Raman spectrum of electrolytic solutions probes, as in the case of pure water, the vibrational dynamics well beyond the distances between the first neighbor.14 Consequently, it is expected that the line shape of the OH stretching band of electrolytic solutions undergoes strong modifications with increase in ion concentration, as it happens in pure water when the thermodynamic conditions change.15 In 2007, we had investigated by Raman spectroscopy the OH vibrational band of aqueous solutions of hydroxides, namely, LiOH, NaOH, and KOH, at concentrations ranging from high dilution to about saturation.16 The spectra show the wellresolved and sharp stretching contribution due to the OH− ion superimposed on the water broad band. At that time, only the stretching band of the hydroxyl ions, OH− band, was discussed. The concentration dependence of the Raman shift, ν̃OH−, and full width at half maximum (FWHM) were found to be the same for Received: January 31, 2018 Revised: March 13, 2018 Published: March 13, 2018 A
DOI: 10.1021/acs.jpcb.8b01094 J. Phys. Chem. B XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry B
Figure 1. (A) Isotropic Raman spectra of KOH in aqueous solutions at different concentrations. Raman spectra of the other investigated solutions are qualitatively similar. (B) Data (black points) and fit (red line) of the isotropic OH stretching band of pure water. The four Gaussian components used for the fit have been reported. (C, D) Data (black points) and fit (red line) of the Raman spectrum of KOH at the concentrations of 3 and 83 water molecules per potassium hydroxide molecule, respectively, obtained by 5 Gaussian components plus a linear background (dashed gray line). The Gaussian term labeled OH− accounts for the vibrational mode of OH− ions. Bands I−IV are needed to reproduce the whole stretching band. The value of the reduced χ2 is reported in the figure legend, as an example. The gray dots at the bottom of the spectrum are the fit residual. All fits are of the same quality as the example shown here.
Labram micro-Raman spectrometer (Dilor-Jobin Yvon), equipped with an Ar+ ion laser (λ = 514.5 nm). The illuminating and collecting optics of this system consist of a confocal microscope equipped with a 20× long working distance objective. The laser beam was focused just below the liquid meniscus and the power on the sample was kept at 1 mW. Isotropic spectra were extracted 4 according to the following definition:Iiso = IVV − 3 IVH .17
all hydroxide solutions investigated. In particular, we observed a softening of the vibration with increasing solute concentration and a sharp drop of FWHM at a solute concentration of about 1 solute per 20 water molecules. This result is particularly intriguing and not fully understood, as it provides evidence for a critical number of water molecules controlling the properties of aqueous solutions. For this reason, we thought that it could be of interest to reanalyze the 2007 data and to consider the water stretching band (not analyzed at that time) after subtraction of the OH− band contribution.
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RESULTS AND DISCUSSION It is well-known that phase transitions, and in general changes of the thermodynamic conditions, determine relevant modifications of the Raman shift and band profile of the OH stretching band of water.15,18 This band is, under all conditions, very broad, with a line shape that cannot be accounted for by considering the contributions of the symmetric and antisymmetric vibrations, intermolecular vibrational coupling, and Fermi resonance.15 Thus, an agreed theoretical framework for its interpretation is
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METHODS The experiment was performed on aqueous solutions of LiOH, NaOH, and KOH, at concentrations ranging from high dilution to about the solubility limit of the individual solutes. Samples were prepared by dilution, starting from concentrated commercial samples purchased from Sigma-Aldrich. Spectra were collected in both VV and VH configurations17 by using a B
DOI: 10.1021/acs.jpcb.8b01094 J. Phys. Chem. B XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry B
Figure 2. Full width at half maximum of the four bands fitting the water OH stretching band, as a function of the number, n, of water molecules per solute. Bands I−III (panels A−C) show a broadening at high concentration (low n values), at odds with band IV (panel D), for all hydroxide solutions. The FWHM transition is sharp and occurs at n ∼ 10−20 water molecules per solute. Blue symbols (diamonds) and lines refer to NaOH solutions, black symbols (circles) and lines refer to KOH solutions, and red symbols (triangles) and lines refer to LiOH solution.
in ref 16 and leaving free all other fitting parameters. Changes of the spectral characteristics of the OH− band have already been commented in ref 16; hence, here we focus on the evolution with ion concentration of the water contribution. First of all, we notice that the Gaussian term centered at the highest wavenumbers, namely, band IV, is present also in pure water (see Figure 1B−D); thus, it cannot be considered as a residual of the OH− band, not accounted for by the Gaussian shape used in the fitting procedure of the spectra of the hydroxide solutions. Moreover, by comparing the fits reported in Figure 1, we can establish a one-to-one correspondence between bands I and IV in the case of solutions and pure solvent, whatever is the dynamical origin and meaning of the individual bands. Clearly, the width of the OH stretching band reflects the large number of different environments explored by the water molecules. To ground this on a more quantitative basis, the FWHM of the four Gaussian components has been evaluated for all solutions investigated as a function of the number, n, of water molecules available per solute molecule. Their behavior is reported in Figure 2. For the sake of completeness, the position of these bands is given in the Supporting Information. We notice that data for the different solutes superimpose with each other to a large extent. Interestingly, the water band at the highest wavenumbers (band IV) is very close to the OH− stretching band (at ν̃OH− ∼ 3620 cm−1)16 and shares with this latter band a sharp transition of its FWHM, which almost doubles on going from high concentration (n ≤ 20) to low concentration (n ≥ 20), independent of the counterion (Figure 2D). At the same time, its Raman shift moves from ν̃ ∼ 3590 to ∼3560 cm−1. The opposite trend is observed for the other three bands, which broaden at high solute concentrations. Yet, a sharp transition of the FWHM occurs for all bands and solutes at the same concentration (n ∼ 20), as already observed for the OH− band.16 These observations suggest that as n goes below ∼20, the vibrational dynamics of
not available, although there is a wide consensus on the idea that the HB network of water and its modifications must be responsible for its complex line shape and relevant intensity redistribution with changing thermodynamic conditions. In this context, the OH stretching line shape has been fitted with four or five Gaussian lines, and the evolution of their Raman shift, intensity, and FWHM with the state parameters relevant to their investigation was followed to address questions regarding the vibrational dynamics of water. The literature on this topic is extremely abundant, and its inclusion here is out of the scope of this report. The assignment of each individual Gaussian to a particular vibration or overtone,19 to the stretching vibration of a particular kind of water molecules, as for instance non-hydrogen bonded or tetrahedrally bonded, in a high-density or in a lowdensity environment15,18 and so on, is more questionable, although sometimes useful, to rationalize the information hidden in the Raman spectra. As already stated, the OH stretching band of hydroxides in water is the superposition of the contribution due to the H2O vibrations with the additional stretching contribution due to the OH− ions (see Figure 1A), the latter being a sharp band at ν̃OH− between ∼3610 and ∼3640 cm−1, depending on the solute concentration.16 In all samples, we notice a trivial increase of the intensity of the sharp contribution at high wavenumbers (ascribed to the OH− stretching band) with increasing solute concentration. At the same time, spectra undergo changes of the relative intensity of the two maxima of the water stretching band at ν̃ ∼ 3200 and ∼3300 cm−1 and an overall broadening of the band with a significant increase of the intensity at the lowest wavenumbers, which could be rationalized as an overall softening of the vibrational modes. To fit these data, we have used five Gaussian lines as described in ref 16: four for the water contribution (see Figure 1B) and one for the OH− stretching band (see Figure 1C,D). All fits have been obtained by keeping the FWHM of the OH− band fixed at the value reported C
DOI: 10.1021/acs.jpcb.8b01094 J. Phys. Chem. B XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry B water is strongly affected by the presence of ions. This is not surprising, based on neutron diffraction data, which associate with these solutions at this concentration an equivalent pressure of ∼800 MPa9 and a significant reduction of the average size of the H-bonded water clusters.14 The question to be addressed now is why the three Gaussian lines at lower wavenumbers broaden at low n values, contrary to what was shown by band IV and the OH− stretching band. It is well-known that the Raman spectroscopy probes the rotovibrational dynamics of a molecular liquid through the correlation functions of the derivative of the molecular ←→ q⎯ l polarizability, αi , with respect to the normal mode of interest,→ C(→ q⎯ l , t ) =
∑ ij
=
∑ i
←→
←→
←→
←→
∂ αi (0) ∂ αj (t ) ∂→ ∂→ q⎯ l q⎯ l
←→
+
Figure 3. First momentum of the Raman band resulting from the superposition of bands I−III, the so-called “distinct band”, as a function of the solution concentration. Same symbols are used as in Figure 2.
∂ αi (0) ∂ αi (t ) ∂→ ∂→ q⎯ l q⎯ l
∑ i≠j
←→
∂ αi (0) ∂ αj (t ) ∂→ q⎯ l q⎯ l ∂→
these modulations decreases with concentration and the mean square fluctuations of the vibrational frequency are substantially constant, this effect accounts for the observed sharp transition of the FWHM. In support of this assignment, we can say that both the hydration shell of the OH− ions24 and the first neighboring shell of water molecules are quite stable and independent of concentration and identity of the solute.9 In the case of bands I−III, the increase of the FWHM is a signature of the overall disruption of the HB network of water with increasing ion concentration. Indeed, distortions and disruptions of the HB network lead to an increase of the variety of environments experienced by water molecules, with consequences on the distinct correlation function defined in eq 1.
(1)
This function can always be separated into a self and a distinct contribution. Therefore, an interpretation of the Raman OH stretching spectra in terms of a superposition of the polarizability self-correlation function and of its distinct contribution can be attempted. Although this latter contribution is more sensible to the long-range structural changes of the HB network, the first term reflects the single molecule behavior. In this framework, we propose to assign band IV to the selfcontribution of the correlation function, taking into account that its Raman shift is close to that of the stretching mode of an isolated water molecule (ν̃ = 3656.65 cm−1)20−22 and its FWHM dependence on n is very similar to that of the OH− band. As a matter of fact, the OH− ions are isolated enough from one another at all investigated concentrations, thus allowing their contribution to be labeled as a “self” one. At the same time, bands I−III have intrinsically a common origin, as demonstrated by the common behavior of the FWHM, and probe the interference of the vibrational mode of distinct molecules within the HB network, via the distinct contribution of the correlation function in eq 1. These bands can therefore be considered as a single spectral contribution without assigning each Gaussian contribution to a particular family of water molecules. Consequently, to evaluate the center of gravity of their combination, we have computed the first momentum of the linear superposition of bands I−III, as described by eq 2, where the density probability, ρ(ν̃), properly normalized to unity, is given as the sum of the normalized intensity of the three bands ν̃ =
∫0
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CONCLUSIONS Raman scattering spectra of three hydroxide solutions in water, collected at a range of concentrations, have allowed us to identify three main contributions to the broad OH stretching band. A very sharp peak above ν̃ = 3600 cm−1, ascribed to the stretching vibration of the OH− ions, plus a sharp and a broad contribution due to the OH stretching band of water, extends to smaller wavenumbers. The sharp OH stretching contribution has a similar Raman shift as that of the OH− stretching band and abruptly sharpens as the number of water molecules per solute goes below n ∼ 20. The broad contribution is centered at lower wavenumbers; it shows an overall softening and the opposite behavior of the FWHM with respect to the other two bands, as a function of n. Interestingly, the sharpening/broadening of the bands takes place quite abruptly at n values on the order of ∼20 water molecules per solute, independent of the specific counterion. These observations suggest that the same arguments used by Corridoni et al.16 to explain the OH− stretching behavior should be valid also to explain the origin of the sharp OH contribution discussed in the present report. In particular, its broadening should be due to inhomogeneous dephasing, arising from modulations from the surrounding liquid, with a characteristic time decreasing with concentration. It can be therefore ascribed to the self-contribution of the polarizability correlation function, given that the first neighboring shell around water molecules does not sensibly change with ion concentration, as it is also found for the hydration shell of the OH− ions.9 In this
∞
dν ̃ ρ(ν)̃ ν ̃
(2) −1
At low ion concentrations, this is constant at ν̃ ∼ 3290 cm , but at n values close to 10, it drops toward 3260 cm−1 (see Figure 3), suggesting a softening of the distinct contribution to the stretching vibrational mode. The sharp increase of the FWHM of band IV can be ascribed, as done in ref 16 for the stretching band of the OH− ions, to inhomogeneous dephasing23 due to the interaction with the surrounding solvent, which modulates the frequency of the individual oscillators. Assuming that the characteristic time of D
DOI: 10.1021/acs.jpcb.8b01094 J. Phys. Chem. B XXXX, XXX, XXX−XXX
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(3) Hribar, B.; Southall, N. T.; Vlachy, V.; Dill, K. A. How Ions Affect the Structure of Water. J. Am. Chem. Soc. 2002, 124, 12302−12311. (4) Mancinelli, R.; Botti, A.; Bruni, F.; Ricci, M. A.; Soper, A. K. Hydration of Sodium, Potassium, and Chloride Ions in Solution and the Concept of Structure Maker/Breaker. J. Phys. Chem. B 2007, 111, 13570−13577. (5) Mancinelli, R.; Botti, A.; Bruni, F.; Ricci, M. A.; Soper, A. K. Perturbation of Water Structure Due to Monovalent Ions in Solution. Phys. Chem. Chem. Phys. 2007, 9, 2959−2967. (6) Leberman, R.; Soper, A. K. Effect of High Salt Concentrations on Water Structure. Nature 1995, 378, 364−366. (7) Botti, A.; Bruni, F.; Imberti, S.; Ricci, M. A.; Soper, A. K. Ions in Water: The Microscopic Structure of Concentrated NaOH Solutions. J. Chem. Phys. 2004, 120, 10154−10162. (8) Botti, A.; Bruni, F.; Imberti, S.; Ricci, M. A.; Soper, A. K. Ions in Water: The Microscopic Structure of a Concentrated HCl Solution. J. Chem. Phys. 2004, 121, 7840−7848. (9) Imberti, S.; Botti, A.; Bruni, F.; Cappa, G.; Ricci, M. A.; Soper, A. K. Ions in Water: The Microscopic Structure of Concentrated Hydroxide Solutions. J. Chem. Phys. 2005, 122, No. 194509. (10) Soper, A. K.; Ricci, M. A. Structures of High-Density and LowDensity Water. Phys. Rev. Lett. 2000, 84, 2881−2884. (11) Omta, A. W.; Kropman, M. F.; Woutersen, S.; Bakker, H. Negligible Effect of Ions on the Hydrogen-Bond Structure in Liquid Water. Science 2003, 301, 347−349. (12) Omta, A. W.; Kropman, M. F.; Woutersen, S.; Bakker, H. Influence of Ions on the Hydrogen-Bond Structure in Liquid Water. J. Chem. Phys. 2003, 119, 12457−12461. (13) Wimby, J. M.; Berntsson, T. S. Viscosity and Density of Aqueous Solutions of Lithium Bromide, Lithium Chloride, Zinc Bromide, Calcium Chloride and Lithium Nitrate. 1. Single Salt Solutions. J. Chem. Eng. Data 1994, 39, 68−72. (14) Corridoni, T.; Mancinelli, R.; Ricci, M. A.; Bruni, F. Viscosity of Aqueous Solutions and Local Microscopic Structure. J. Phys. Chem. B 2011, 115, 14008−14013. (15) Hu, Q.; Zhao, H.; Ouyang, S. Understanding Water Structure from Raman Spectra of Isotopic Substitution H2O/D2O up to 573 K. Phys. Chem. Chem. Phys. 2017, 19, 21540−21547. (16) Corridoni, T.; Sodo, A.; Bruni, F.; Ricci, M.; Nardone, M. Probing Water Dynamics with OH−. Chem. Phys. 2007, 336, 183−187. (17) Berne, B.; Pecora, R. Dynamic Light Scattering: With Applications to Chemistry, Biology, and Physics; Dover Books on Physics Series; Dover Publications, 2000. (18) Mallamace, F.; Branca, C.; Broccio, M.; Corsaro, C.; Mou, C.-Y.; Chen, S.-H. The Anomalous Behavior of the Density of Water in the Range 30 K < T < 373 K. Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 18387− 18391. (19) Plastinin, I. V.; Burikov, S. A.; Dolenko, S. A.; Dolenko, T. A. Contribution of Fermi and Darling-Dennison Resonances to the Formation of Raman Spectra of Water and Water-Ethanol Solutions. J. Raman Spectrosc. 2017, 48, 1235−1242. (20) Ikushima, Y.; Hatakeda, K.; Saito, N.; Arai, M. An in Situ Raman Spectroscopy Study of Subcritical and Supercritical water: The Peculiarity of Hydrogen Bonding near the Critical Point. J. Chem. Phys. 1998, 108, 5855−5860. (21) Ricci, M. A.; Nardone, M.; Fontana, A.; Andreani, C.; Hahn, W. Light and Neutron Scattering Studies of the OH Stretching Band in Liquid and Supercritical Water. J. Chem. Phys. 1998, 108, 450−454. (22) Martí, J. Analysis of the hydrogen bonding and vibrational spectra of supercritical model water by molecular dynamics simulations. J. Chem. Phys. 1999, 110, 6876−6886. (23) Oxtoby, D. W. Dephasing of Molecular Vibrations in Liquids; Advances in Chemical Physics; John Wiley & Sons, Inc., 2007; Vol. 40, pp 1−48. (24) Botti, A.; Bruni, F.; Imberti, S.; Ricci, M. A.; Soper, A. K. Solvation of Hydroxyl Ions in Water. J. Chem. Phys. 2003, 119, 5001−5004. (25) Roux, A.; Perron, G.; Desnoyers, J. Capacites Calorifiques, Volumes, Expansibilites et Compressibilites des Solutions Aqueuses
framework, the other term of the Raman band is linked to the distinct term of the correlation function of the water polarizability, related to the long-range correlations, hence directly probing the connectivity of the HB network through the vibrational dynamics. As a matter of fact, this spectral contribution broadens as the ion concentration increases, suggesting increased dynamical disorder consequent to the structural modifications of the HB network of water.9,14 The evidence for a quite sharp change of the spectral parameters for all of the components fitting the Raman spectra of the solutions investigated in this work suggests that a number of water molecules below ∼20 must represent a turning point for macroscopic properties of these hydroxide solutions. Interestingly, in this concentration range, the apparent heat capacity changes sign,25,26 the vapor pressure reaches a plateau,27−29 and the specific conductance is maximum.30 Additionally, from a microscopic point of view, clear changes of the H-bond connectivity are expected, as shown by the changing size of the percolating HB network.16 The observed lack of ion-specific effect on water dynamics is not consistent with the textbook concept of ions being either structure makers or breakers. Finally, we want to mention that a similar approach, based on a separation between self and distinct contributions of the OH stretching band of pure water, has never been attempted, although being less factitious than just using an arbitrary number of Gaussian lines. On the basis of the evidences shown in the present work, such an approach would contrast with the assignment of the Raman scattering at lower wavenumbers to low-density, or icelike, patches of water molecules.18
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.8b01094. Position of the five Gaussian components used to fit the OH stretching band (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Maria Antonietta Ricci: 0000-0002-6904-6686 Present Address †
SUPSI-DFA, Piazza S. Francesco 19, and Liceo Cantonale, Via F. Chiesa 19, 6600 Locarno, Switzerland (T.C.). Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work has been supported by funding from Universitá Roma Tre. M.A.R. dedicates this paper to the dear memory of Vittorio Mazzacurati. The Grant of Excellence Departments, MIUR (ARTICOLO 1, COMMI 314−337 LEGGE 232/2016), is gratefully acknowledged.
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REFERENCES
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DOI: 10.1021/acs.jpcb.8b01094 J. Phys. Chem. B XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry B Concentrees de LiOH, NaOH et KOH. Can. J. Chem. 1984, 62, 878− 885. (26) Sipos, P. M.; Hefter, G.; May, P. M. Viscosities and Densities of Highly Concentrated Aqueous MOH Solutions (M+ = Na+, K+, Li+, Cs +, (CH3)4N+) at 25.0 °C. J. Chem. Eng. Data 2000, 45, 613−617. (27) Hayward, A. M.; Perman, E. P. Vapour Pressure and Heat of Dilution.-Part VII. Vapour Pressures of Aqueous Solutions of Sodium Hydroxide and of Alcoholic Solutions of Calcium Chloride. Trans. Faraday Soc. 1931, 27, 59−69. (28) Monnin, C.; Dubois, M. Thermodynamics of the LiOH + H2O System. J. Chem. Eng. Data 2005, 50, 1109−1113. (29) Nasirzadeh, K.; Neueder, R.; Kunz, W. Vapor Pressures and Osmotic Coefficients of Aqueous LiOH Solutions at Temperatures Ranging from 298.15 to 363.15 K. Ind. Eng. Chem. Res. 2005, 44, 3807− 3814. (30) Lown, D. A.; Thirsk, H. R. Proton Transfer Conductance in Aqueous Solution. Part 2.-Effect of Pressure on the Electrical Conductivity of Concentrated Orthophosphoric Acid in Water at 25°C. Trans. Faraday Soc. 1971, 67, 149−152.
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