Structure of Mixtures of Water and Methanol Derived from Their

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The Structure of Mixtures of Water and Methanol Derived from their Cohesive Energy Densities and Internal Pressures from Sub-ambient Temperatures to 473 K Yizhak Marcus J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b11061 • Publication Date (Web): 03 Jan 2017 Downloaded from http://pubs.acs.org on January 12, 2017

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The Journal of Physical Chemistry

The Structure of Mixtures of Water and Methanol Derived from their Cohesive Energy Densities and Internal Pressures from Sub-ambient Temperatures to 473 K Yizhak Marcus Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel. E-mail: [email protected]

Abstract The cohesive energy densities ced and the internal pressures Pint of aqueous methanol mixtures are calculated from literature data for the entire composition range over the temperature range from 273 to 473 K, at saturation pressures up to 373 K and at 7.0 MPa above this temperature. The ratios Pint/ced are measures of the ‘structuredness’ of the studied fluids, the small values noted signify ‘tight’ structures, due to the hydrogen bonding. The ‘tighter’ the structure, the larger is the surface tension of the mixtures (at 298.15 and 323.15 K). This structural feature diminishes in intensity as the temperature and the methanol contents are increased, except in cold (423 K) water-rich mixtures. Under such exceptional conditions the hydrogenbonded structure of the water is enhanced.

INTRODUCTION The structural properties of alcohol-water mixtures have been summarized long ago by Franks and Ives.1 Both water and methanol are associated liquids, the molecules of which are held together mainly by hydrogen bonds. The preferential solvation of the molecules in mixtures of these liquids from sub-ambient to elevated temperatures was reported by the author several years ago.2 Several thermophysical properties of the mixtures for sub- and supercritical conditions were reported by the author more recently.3 The structuredness of liquids in general has been given quantitative measures by the author.4,5 The present paper complements these reports by stressing those structural aspects of water and methanol mixtures that can be derived from their cohesive energy densities and internal pressures that have by now been ascertained. Bagley et al.6 and Dack7 discussed the difference between the cohesive energy density, ced, and the internal pressure, Pint, (both having the dimensions of pressure) of associated liquids. Whereas

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Pint reflects mainly the non-chemical interactions between the molecules, i.e., the repulsion and dispersion interactions, ced – Pint reflects the chemical interactions, i.e. the dipole-(eventually induced) dipole and hydrogen bonding ones.6,7 Such treatments have dealt so far with water and methanol separately but the mixtures have not been treated. The ratios Pint/ced of liquids of many kinds show the strengths of the interactions.8,9 If 0.8 < Pint/ced < 1.2, as is the case for non-associated molecular liquids and many ionic liquids, the interactions between their molecules or ions are mainly of the non-chemical dispersion and repulsion types and the structure may be termed as ‘loose’. However, if Pint/ced < 0.8, as it is for associated molecular liquids and certain ionic liquids, or < 0.3 as for liquid metals or < 0.1 as for most molten salts, then other interactions predominate, and the structure may be termed as ‘tight’. These epithets, ‘loose’ and ‘tight’ pertain to the structural aspect of ‘stiffness’ coined by Bennetto and Caldin,10 describing the work expended on creating a cavity in the liquid for the accommodation of another particle. Both water and methanol have ‘tight’ structures: for water at ambient conditions the Pint/ced ratio is 0.07, for methanol it is 0.35, values that express the hydrogen-bonded structures: a threedimensional network for water and short chains for methanol. As the temperature is raised, ced for both liquids diminishes, but Pint behaves differently. For methanol it diminishes too, rather moderately, as it does for normal liquids, but for water it increases and reaches a flat maximum near 470 K, see Fig. 1. Hence, the difference ced – Pint decreases and the ratio Pint/ced increases as the temperature is increased much more rapidly for water than for methanol. The question arises of how do these quantities relate to the structuredness of mixtures of water and methanol in a manner complementary to the notion of preferential solvation reported previously.2 This paper answers this question in the temperature range 273 to 473 K, at which sufficient data are available. Due to the discrepancies in the boiling points of the two components, the pressures at which the data are reported and being used need to be taken into account. Up to 373 K the saturation pressures p are being employed (0.101325 MPa for pure water and up to 0.3524 MPa for pure methanol and the mixtures11). At higher temperatures isobaric data at 7 MPa have been used. The cohesive energy, ce, of a liquid is obtained from its molar enthalpy of vaporization, ∆VH, corrected by deduction of pVg to change from enthalpy to energy, where p is the vapor pressure of


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the liquid and Vg is the molar volume of the vapor and, if applicable, by deduction of the cohesive energy of the vapor. If the vapor can be taken to be an ideal gas, as is the case at low vapor pressures, then pVg = pVgid = RT may be applied. Otherwise a correction for vapor non-ideality should be used and pVg = p(Vgid + B), where B is the second virial coefficient. Thus: ce = ∆VH – p(Vgid + B) – pB ≈ ∆VH – RT

(1)

The term – pB accounts approximately for the cohesive energy of the vapor. The second approximate equality is valid when B 298.15 K were taken from Machado and Streett,11 whereas the volumetric properties for sub-ambient temperatures were from Hruby et al..15 The enthalpy of vaporization at these temperatures were calculated via the ClausiusClapeyron expression from the vapor pressure expression reported by Gibbard and Creek,16 that were in accord with the calorimetric values reported by Fiock et al.,17 available up to 383 K. The second virial coefficients B were taken from Harvey and Lemmon18 for water and from Kudchadker and Eubank19 for methanol. For the aqueous methanol mixtures the excess volumes VE and enthalpies HE of mixing are from Westmeier20 for temperatures 273.15 < T/K < 373.15 at 10 K intervals. The values of HE at 323.15 K were taken from Tomaszkiewicz et al.21at saturation pressures and for 373.15, 423.15, and 473.15 K at 7.0 MPa from Simonson et al..22 The data in21 are of the wrong sign and for 298.15 K are about 5% lower than those in,22 but their negatives agree with the data of Lama and Lu.23 Since the data in21 were the only ones found for 323.15 K the negatives of the listed values were used here. The volumetric properties of the liquid mixtures were obtained at 0.1 MPa for 278.15, 288.15, 298.15, and 323.15 K from Easteal and Woolf,24 and for 288.15, 293.15, and 298.15 K from Benson and Kiyohara.25 The excess molar volumes for 373.15, 423.15, and 473.15 K at 7.0 MPa were taken from Simonson et al..22 The second virial coefficients pertain to a minor correction, and were therefore prorated from the values for the pure components according to the mixture composition. RESULTS The data from Section 2 were employed in eqs. (2) and (3) to obtain the cohesive energy density ced and the internal pressure Pint, their differences and ratios, shown in Table 1. The volumetric input data for the mixtures, in particular for the sub-ambient temperatures, had to be taken from the reports by several authors, leading to uncertainties of about 10 MPa in Pint. It should be noted that because of the negative expansibility of water below 277 K no significant internal pressures can be calculated for very cold water-rich mixtures. For methanol-rich mixtures at 273.15 K, the data of Easteal and Woolf25 for 278.15 and 288.15 K were extrapolated to 273.15 K to obtain Pint. Over the entire composition range from pure water to pure methanol and at all the temperatures ced exceeds Pint by more than 50 MPa, signifying ‘tight’ binding and association between the molecules.8,10 The ratios, Pint/ced present more detailed information: they increase from the very


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small value for pure water at 283.15 K, 0.018, as the methanol content increases at a given temperature and with the temperature up to 373.15 K at all compositions of the mixtures. It should be noted that as the pressure differs between the lower temperatures included in Table 1 and the three highest ones, the increase of Pint/ced with the temperature holds only for pure water and pure methanol for all the temperatures, but a maximum is reached for the mixtures. The values of Pint/ced are plotted in Fig. 2 against the compositions of the mixtures. For the two lower temperatures, 298.15 and 323.15 K the curves are smooth and can be expressed by a quadratic power series with the composition. At 373.15 K the ratio is appreciably larger but the curve is rather parallel to those at the lower temperatures up to xMeOH = 0.8, and then drops abruptly for neat methanol. At still higher temperatures the curves become more irregular (needing 4th power series to describe them) and show diminishing values at intermediate compositions. DISCUSSION The differences ced – Pint, were designated by Bagley et al.6 and by Dack7 as representing the chemical interactions between molecules in the liquid. These differences diminish regularly from the large value for pure water at ambient temperature as the methanol content and the temperature increase. (An exception is pure hot methanol at 373.15 and 423.15 K.) This means that the threedimensional hydrogen-bonded network present in cold pure water is gradually destroyed (except in cold water-rich mixtures, see below) at increasing temperatures and methanol contents and is partly replaced by short hydrogen-bonded chains or cycles involving both water and methanol molecules. This picture corroborates the more detailed one obtained from the preferential solvation study.2 The ratios Pint/ced are more instructive as Fig, 2 shows, particularly at the elevated temperatures. At the lower temperatures, even at 373.15 K at 7.0 MPa pressure, this ratio increases and reaches a flat maximum near xMeOH = 0.8. This indicates that the tightness of the structure diminishes gradually, an aspect that should be reflected in the gradual decrease of the surface tension. The latter quantity describes the work that needs to be done for the creation of a cavity in the liquid for the accommodation of a new particle. The products of the surface tensions, taken from Vazquez et al.,26 and the Pint/ced ratios for both 298.15 and 323.15 K are constant, 8.4+0.9, except in very water-rich regions, xMeOH < 0.1. This means that the tighter the structure of the aqueous methanol mixtures (the smaller Pint/ced), the larger is their surface tension. Up to 373 K the addition of



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methanol beyond 0.1 mole fraction (see below regarding very water-rich mixtures) serves to disrupt the hydrogen bonded network of the water, because water has 2 donor and 2 acceptor sites whereas methanol has only one of each. This disruption is reflected by the gradual increase of the Pint/ced ratio shown in Fig. 2. At 373 K, however, which is beyond the normal boiling point of methanol, the hydrogen bonding reaches a minimum at xMeOH = 0.8 and the Pint/ced ratio reaches a maximum. Beyond this composition the self-association of methanol, possibly to rings, predominates and Pint/ced ratio diminishes again. The curves at 423.15 and 473.15 K (at 7.0 MPa pressure), on the contrary, are more interesting. In water-rich mixtures, up to xMeOH = 0.4, the ratio Pint/ced at 423.15 K remains essentially constant and at 473.15 K even shows a pronounced minimum near xMeOH = 0.2. This means that although much of the three-dimensional hydrogen-bonded structure of water has been destroyed at these elevated temperatures, the presence of methanol serves to increase the structuredness of the liquid by promoting self-hydrogen bonding of the water, whereas the mutual interaction is suppressed, as is manifested in the preferential solvation curves.2 At lower temperatures the effect of methanol of enhancement of the water structure in water-rich aqueous methanol mixtures is manifested also by other quantities. This effect is shown by the positive excess partial molar volumes VWE 27 and heat capacities CpWE 28 of the water. As results from the positive CpWE values at low temperatures, 269 and 288 K, this enhancement is maximal near xMeOH = 0.22, it is near xMeOH = 0.285 at 298 K, but extends beyond xMeOH = 0.30 at 308 K.28 Acknowledgement No external funding was received for this study. The author declares no competing financial interests REFERENCES (1) Franks, F.; Ives, D. J. G. The structural properties of alcohol-water mixtures. Quart. Rev. 1966, 20, 1-44. (2) Marcus, Y. Preferential solvation in mixed solvents. Part 8. Aqueous methanol from sub-ambient to elevated temperatures. Phys. Chem. Chem. Phys. 1999, 1, 2975-2983. (3) Marcus, Y. Some Thermophysical Properties of Methanol and Aqueous Methanol


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Mixtures at Sub- and Supercritical Conditions. J. Mol. Liq. 2016, ahead of print, http://dx.doi.org/10.1016/j.molliq.2016.07.049. (4) Marcus, Y. The structuredness of solvents. J. Solution Chem. 1992, 21, 1217-1230. (5) Marcus, Y. The structuredness of solvents. 2. Data for ambient conditions. J. Solution Chem., 1996, 25, 455-469. (6) Bagley, E. A.; Nelson, T. P.; Scugliano J. M. Three-dimensional solubility parameters and their relationship to internal pressure measurements in polar and hydrogen bonded solvents. J. Paint Technol. 1971,43, 35-45. (7) Dack, M. R. J. The importance of solvent internal pressure and cohesiom in solution phenomena. Chem. Soc. Rev. 1975, 4, 211-229. (8) Marcus, Y. Internal pressure of liquids and solutions. Chem. Rev. 2013, 113, 6536-6551. (9) Marcus, Y. Internal pressure of neat liquids: a review. In T. Letcher, E. Wilhelm, eds., Enthalpy and Internal Energy: Liquids, Solutions and Vapours, 2016, RSC, Cambridge , Ch. 19, in press. (10) Bennetto, H. P.; Caldin, E. F. Solvent effects on the kinetics of the nickel(II) and cobalt(II) ions with 2,2'-bipyridyl and 2,2',2"-terpyridyl. J. Chem. Soc. A 1971, 21912198. (11) Machado, J. R. S.; Streett, W. B. Equation of state and thermodynamic properties of liquid methanol from 298 to 489 K and pressures to 1040 bar. J. Chem. Eng. Data 1983, 28, 218-223. (12) Kell, G. S. Precise representation of volume properties of water at one atmosphere. J. Chem. Eng. Data 1967, 12, 66-69. (13) Sato, H.; Uematsu, M.; Watanabe, K.; Saul, A.; Wagner, W. New international skeleton tables for the thermodynamic properties of ordinary water substance. J. Phys. Chem. Ref. Data 1989 17, 1439-1540. (14) Marcus, Y. The structuredness of water at elevated temperatures along the saturation line. J. Mol. Liquids 1999, 79, 151-165. (15) Hruby, J.; Klomfar, J.; Šifner, O. (T,p, ρ) relation of liquid methanol at temperatures from 205 K to 321 K and pressures up to 50 MPa. J. Chem. Thermodyn .1993, 25, 12291242. (16) Gibbard, H. F.; Creek, J. L. Vapor pressure of methanol from 288.15 to 337.65 K. J.



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Chem., Eng. Data 1974, 19, 308-310. (17) Fiock, E. F.; Ginnings, D. C.; Holton, W. B. Calorimetric determination of thermal properties of methyl alcohol, ethyl alcohol, and benzene. J. Res. Natl. Bur. Stand. 1931, 6, 881-900. (18) Harvey, A. H. ; Lemmon, E. W. Correlation for the second virial coefficient of water. J, Phys. Chem. Ref. Data 2004, 33, 369-376. (19) Kudchadker, A. P.; Eubank, P. T. Second virial coefficient of methanol. J. Chem. Thermodyn. 1970, 15, 7- 9. (20) Westmeier, S. Exzessenthalpie, freie exzessenthalpie, exzess volumen und viskosität von ausgewählten binären flüssigen mischungen. Chem. Techn. 1976, 28, 350-353. (21) Tomaszkiewicz, I.; Randzio, S. L.; Gierycz, P. Excess enthalpy in the methanol-water system at 278.15, 298.15, and 323.15 K under pressures of 0.1, 20, and 39 MPa. II. Experimental results and their analytical representation. Thermochim. Acta 1986, 103, 281-289. (22) Simonson, J. M.; Bradley, D. J.; Busey, R. H. Excess enthalpies and thermodynamics of (methanol + water) to 573 and 40 MPa. J. Chem. Thermodyn.1987, 19, 479-492. (23) Lama, R. F.; Lu, B. C. Y. Excess thermodynamic properties of aqueous methanol solutions. J. Chem. Eng. Data 1965, 10, 216-219. (24) Easteal, A. J.; Woolf, L. A. (p,Vm,T,x) measurements for {(1-x)H2O + xCH3OH} in the range 278 to 323 K and 0.1 to 280 MPa. J. Chem. Thermodyn. 1985, 17, 49-62. (25) Benson, G. C.; Kiyohara, O. Thermodynamics of aqueous mixtures of nonelectrolytes. I. Excess volumes of water-n-alcohol mixtures at several temperatures. J. Solution Chem. 1980, 9, 791-8001. (26) Vazquez, G.; Alvarez, E.; Navaza, J. M. Surface tension of alcohol + water from 20 to 50 ℃. J. Chem. Eng. Data 1995, 40, 611-614. (27) Marcus, Y. Water structure enhancement in water-rich binary solvent mixtures. J. Mol. Liq. 2011, 158, 23-26. (28) Marcus, Y. Water structure enhancement in water-rich binary solvent mixtures. Part II. The excess partial molar heat capacity of water. J. Mol. Liq. 2012, 166, 62-66.


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Table 1. The cohesive energy densities, ced, the internal pressures, Pint, their differences and their ratios for mixtures of water and methanol at several temperatures. The pressures at 273.15 up to 323.15 K are the saturation pressures and at 373.15, 423.15 and 473.15 K they are 7 MPa. T/K

xMeOH 0.0

0.2

0.4

0.6

0.8

1.0

ced/MPa 273.15

2374

2149

1757

1445

1198

916

283.15

2345

2120

1730

1418

1173

906

293.15

2314

2087

1699

1389

1147

895

298.15

2287

1782

1414

1143

969

840

323.15

2160

1708

1349

1085

915

798

373.15

1939

1486

1136

886

738

686

423.15

1695

1269

937

702

561

515

473.15

1471

1092

647

465

339

242

430

375

343

305

Pint/MPa 273.15 283.15

42

322

408

382

337

304

293.15

132

345

401

368

337

299

298.15

169

354

409

381

332

282

323.15

334

429

427

379

321

276

373.15

586

607

542

470

405

264

423.15

712

550

429

362

325

239

473.15

714

336

230

187

168

158

1327

1070

855

611

(ced – Pint)/MPa 273.05 283.15

2303

1798

1322

1036

836

602

293.15

2182

1742

1298

1021

810

596

298.15

2115

1428

1005

762

637

561

323.15

1826

1279

923

707

595

514

373.15

1353

880

595

417

334

427



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423.15

984

721

512

345

243

285

473.15

760

758

422

285

180

84

0.245

0.259

0.286

0.333

Pint/ced 273.15 283.15

0.018

0.152

0.236

0.269

0.287

0.336

293.15

0.057

0.165

0.236

0.265

0.294

0.334

298.15

0.075

0.199

0.289

0.333

0.343

0.336

323.15

0.155

0.251

0.317

0.349

0.351

0.350

373.15

0.303

0.408

0.478

0.531

0.550

0.384

423.15

0.421

0.435

0.458

0.514

0.575

0.460

473.15

0.485

0.308

0.356

0.402

0.496

0.653


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Fig. 1. The internal pressure, Pint (upright triangles), and cohesive energy densities, ced (inverted triangles) of water (empty) and methanol (filled) as functions of the temperature. The critical temperatures are shown as squares at the bottom, taken from [3], with permission.



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Fig 2. The ratios Pint/ced for mixtures of water and methanol at various temperatures: 298.15 K (), 323.15 K (), 373.15 K (), 423.15 K (), and 473.15 K ().


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Structure of Mixtures of Water and Methanol Derived from Their

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