Thermal expansion and structure in water and aqueous solutions

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1 Thermal expansion and structure in water and aqueous solutions LOREN G. HEPLER Department of Chemistry, University of Lethbridge, Lethbridge, Alberta Received July 17, 1969 The thermodynamic equation (acp/bp), = -T(aZV/aT2), is used as a basis for relating thermal expansion to structure (at several temperatures and pressures) of water and "normal" liquids. Similar considerations lead to a relation between the sign of (aztzo/atz)p for solutions and classification of solutes as structure-making or structure-breaking. Canadian Journal of Chemistry, 47, 4613 (1969) A variety of evidence has led to the view that water is a partly "structured" liquid that can be loosely described as a sort of partly broken down ice. Possibly the simplest useful description of liquid water, is that in which the water is pictured as being a mixture of two species; one a bulky icelike species with relatively low density and the other a denser species that is formed by breaking (or bending) the hydrogen bonds that maintain the ice-likeness of the bulky species. Since both increasing temperature and increasing pressure would have the effect of increasing the fraction of the dense species at the expense of the bulky species, this simple model can account qualitatively for the maximum in density, the unusually high heat capacity, and several other properties of water. Some of the properties of aqueous solutions have also been interpreted in terms of the "structure-making" or "structure-breaking" characteristics of various solutes. This paper is concerned with the relation between these structural ideas and the thermal expansion of water and of aqueous solutions. Partial molal heat capacities of aqueous electrolytes are commonly negative. An early explanation (for example, Lewis and Randall (1)) that is consistent with other properties of aqueous electrolytes is that these solutes break up the bulky aggregates and thereby decrease the effective heat capacity of the water. Since increasing pressure would also break up the bulky aggregates, the same reasoning suggests that the heat capacity of pure water should decrease with increasing pressure. We therefore expect (acp/ ap), to be negative and use the thermodynamic equation in predicting that (a2 V/aT2), for water is positive. Because increasing temperature also breaks up the bulky aggregates, we expect that the magnitude of (ac,/bp), should decrease with increasing temperature, which requires that T(a2 V/aT2), should also decrease with increasing temperature. Similarly, we expect that T(a2 v/at2), should decrease with increasing pressure. Since a variety of evidence suggests that D20 is a more structured liquid than is H20, we also expect that the magnitude of (ac,/ap), and thence T(a2 v/at2), would be larger for D20 than for H20. Kell (2) has tabulated values of density (p) and coefficient of thermal expansion (a = (I/V)(aV/aT),) for H20(liquid) at 1 atm. over a range of temperatures. These values have been used with the equation in which M represents the molecular weight, to obtain values of (a2 V/aT2), and thence thevalues of T(a2 V/aT2), that are shown in Fig. 1. Densities of D20(liquid) tabulated by Kell (2) also lead to the (molar) values of T(a2V/aT2), that are shown in Fig. 1. Here it might be noted that small irregularities in (a2v/at2), for D20 in the ranges of and "C have been smoothed in constructing the figure. Specific volumes tabulated by Kell and Whalley (3) have been used in calculating the (slightly smoothed) values of T(a2 V/aT2), for H20(liquid) under pressures of 200 and 1000 bars as also shown in Fig. 1. The curves in Fig. 1 show the predicted differences in T(a2V/aT2), for H20 and D20 at 1 atm, and confirm the predicted effect of pressure on H20. At higher temperatures the values of T(a2V/aT2), increase very slightly

2 4614 CANADIAN JOURNAL OF CHEMISTRY. VOL. 47, 1969 standing of structure-makinglbreaking by various solutes. We begin by differentiating the thermodynamic equation of state (BHIBP), = V - T(aV/aT), with respect to n2 (P, T, and n, constant) and then with respect to T (n,, 1z2, and P constant) to obtain FIG. 1. Thermal expansion data: A (D20, 1 atm); B (HzO, 1 atm); C (H20, 200 bars); D (HzO, 1000 bars). with increasing temperature, in contrast with the decrease observed at lower temperatures that was predicted earlier on the basis of structural arguments. This slight increase of T(a2V/aT2), at higher temperatures can be rationalized as follows. According to the structural model described earlier, water becomes more like a normal liquid as the temperature (or pressure) increases. In order to ascertain what constitutes "normal" variation of volume with temperature, density data for a number of liquids (n-heptane, diethylether, CCl,, ethanol, benzene, and mercury) have been used to obtain corresponding values of T(a2V/aT2), over a range of temperatures. Although the highest values (for ether and heptane) of T(a2V/aT2), are some 500 times the smallest values (for Hg), the temperature dependence of this quantity falls within the relatively narrow range of an increase of about 1-2% per degree. At 100 "C we find that T(a2 V/ at2), for water is increasing by only about 0.2% per degree, and even at 140 "C the increase is still less than 0.5% per degree. Thus we see that the volumetric behavior of water, even at high temperature, is still consistent with a structural model in which it is assumed that increasing temperature and pressure break down structure and cause water to approach "normal" behavior. Extension of the approach described here to aqueous solutions should contribute to under- Since present considerations are limited to consequences of solute-solvent interactions, we choose to apply eq. [3] to partial molal properties of the solute at infinite dilution as indicated subsequently by the superscript zero. As already mentioned, partial molal heat capacities of electrolytes are commonly negative. The common explanation (1) in terms of structure-breaking leads to the prediction that (acpo/ ap), should be positive. On the basis of this reasoning and eq. [3], it is seen that structurebreaking solutes should have negative (a2 VZ0/ at2),. Similar reasoning shows that positive (a2 VZo/aT2), should be associated with structuremaking solutes. Although interpretation of the experimental data is not entirely certain, a variety of evidence (4-6) suggests that alcohols (in dilute solutions) are structure-making solutes. On this basis and our reasoning concerning the sign of (ac,/ap),, we expect that (a2 VZ0/aT2), should be positive for aqueous alcohols. The most obvious confirmation of this expectation is the figure presented by Alexander (7) in which vz0 values for methanol, ethanol, i-propanol, i-butanol, and i-pentanol are plotted against temperature (O- 60 "C). Franks and Smith (4)' have obtained - VZ0 values for the four isomeric butanols at four temperatures ( "C), while Friedman and Scheraga (8) have reported VZ0 values for nine alcohols at four temperatures (1-50 "C). All of the VZ0 vs. temperature curves for alcohols (4,7, 8) are of the general shape illustrated in Fig. 2, with the positive (a2v20/at2)p expected for structure-makers. Dunn's measurements (9) have led to VZ0 values for NaCI, KBr, KC1, BaCl,, and CaC1, at eight temperatures from 0.5 to 65 "C. The general shape of graphs of vz0 against Tis shown 'References to earlier work, with particular emphasis on volumetric properties, are cited in this paper.

3 HEPLER: THERMAL EXPANSION AND STRUCTURE 4615 sistent with the idea that structure-making is in the form of "iceberg" formation about the hydrocarbon parts of these ions, with the extent of structure-making increasing as the amount of hydrocarbon increases. Millero and Drost- Hansen (15) have previously pointed out that volumetric properties of aqueous alcohols and tetraalkylammonium salts are similar, with both a 3 1 having volumetric properties different from i at2 Is those of most electrolytes. The V20 values for aqueous urea, given by Stokes (16), show that (a2 VZ0/aT2), is negative, which indicates that urea should be regarded as a structure-breaking solute. Masterton (17) has reported V20 data for benzene, methane, ethane, and propane in aqueous solution at several temperatures. For benzene, (a2 VZ0/aT2), is very close to zero. The T resulting conclusion that benzene is neither a FIG. 2. Typical thermal expansion data for aqueous structure-maker a strong structuresolutes: Curve A is associated with structure-making breaker may be explained in terms of a balance solutes and curve B with structure-breaking solutes. between iceberg formation and structure-breaking due to poor fit of planar benzene molecules in Fig. 2, with (a2 V20/aT2), negative as expected into the partly tetrahedral structure of water. for structure-breaking solutes. Bull and Breese Masterton's data (17) indicate that (a2 V20/a~'), (10) have recently published a graph of apparent values are.negztive for methane, ethane, and molal volume of KC1 (dilute solution) against propane. Thus the approach developed in this temperature that is in agreement with the paper leads to the conclusion that these solutes general shape of the curve in Fig. 2 based on are structure-breakers in aqueous solution. On Dunn's data (9). Data from Ellis (11, 12) for the basis of different reasoning, Masterton (17) LiCl, NaC1, KCl, CsCl, MgCl,, CaCl,, SrCl,, has previously suggested a "breaking down of and BaCl, up to 200 "C also lead to negative the cage-like structure of water molecules around (a2 VZ0/aT2),. Other data from Millero (13) the aliphatic hydrocarbon molecules". Thus confirm that (a2 V20/aT2), is negative for most both this paper and Masterton disagree with the aqueous salt solutions. Thus the volumetric comm'on idea that methane, ethane, and propane data indicate that these electrolytes should be are net structure-makers as a result of iceberg regarded as structure-breaking solutes in water. formation about the solute molecules. We also conclude from the high temperature Although classification of solutes as structuredata that water at temperatures well above the makers or -breakers has proven useful in several normal boiling point is still sufficiently structured connections, it must be recognized that the entire that structure-breaking solutes can "find" concept of structure in water and aqueous structure to break. solutions is only partly satisfactory (18). One Gopal and Siddiqi (14) have reported V20 problem is that we are unable to be entirely values for four tetraalkylammonium iodides specific about the structure that is being made or (methyl, ethyl, propyl, and butyl) at tempera- broken by various solutes or as a result of changes tures ranging from "C. Values of (a2 V20/ in temperature and pressure. A further difficulty at2), are positive, indicating that these solutes is that we have no unambiguous numerical are all net structure-makers, as previously measure of structure-makinglbreaking. Theresuggested on other grounds for some R,NX fore, it should not be surprising that there are compounds. The magnitude of (a2v20/i3t2), disagreements between conclusions based on increases in going from methyl to ethyl to propyl different approaches. A similar situation is to butyl compounds in this series. This is con- known in connection with the useful but poorly

4 461 6 CANADIAN JOURNAL OF CHEMISTRY. VOL. 47, 1969 defined concept of hydration number, where it is common for different approaches to lead to different numbers. Since the conclusion of this paper concerning classification of alcohols and the larger tetraalkylammonium ions as structure-makers is in agreement with several earlier workers, no detailed comments on these solutes are required. On the other hand, several earlier workers have concluded that (CH3),N+ and possibly (C2- H5),N+ ions are structure-breakers, in contrast to our conclusion that these ions are structuremakers. Similarly, the present conclusion that urea is a structure-breaker is contrary to conclusions of some earlier workers. First, we consider the reliability of the data (14) we have used for the R,N+ salts. Since the most dilute solutions investigated were about 0.05 M, the extrapolation to infinite dilution to obtain desired FZo values is of considerable importance. Gopal and Siddiqi (14) did these extrapolations "as required" by Masson's equation with empirical limiting slope based on their own data for solutions more concentrated than about 0.05 M. Redlich and Meyer (19) have shown the inadequacies of this extrapolation procedure and have also shown how such extrapolations should be done in accord with the Debye-Huckel theory. Accurate measurements on R,NX compounds (only at 25") reported by Conway, Verrall, and Desnoyers (20) show that Gopal and Siddiqi (14) used incorrect slopes (wrong sign for three of their four solutes!) for extrapolation to infinite dilution. Although we conclude that the accuracy of the reported (14) VZo values is not high, it is likely that these values do lead to the correct sign for (a2~20/at2), for the larger R,N+ ions. On the other hand, it is possible that the reported values lead to an incorrect sign for (a2 FZo/aT2), for aqueous (CH,),NI. Further measurements are reauired to settle this uncertainty. The conclusion in this paper [assuming that the available data lead to the correct sign for (a2 VZ0/ at2),] that (CH,),NI is a structure-maker is in disagreement with some earlier workers. For example, Gopal and Siddiqi (14) have concluded from the concentration dependence of their apparent molar volumes that this solute is a structure-breaker, but it is the present author's opinion that their interpretation should have given greater consideration to solute-solute interactions and may therefore be mistaken. Other evidence that (CH3),Nf ion is a structurebreaker comes from results of conductance (21) and viscosity (22) measurements, although a Referee has suggested that the viscosity data might also be interpreted to indicate that (CH,),N+ is a structure-maker. Conway and LalibertC (23) have reported FZo values for NaF, NaC1, NaBr, (C2H5),Br, and (C,H,),Br in both H20 and D20 at 25 "C. They concluded from their results that the first three salts are structure-breakers and the latter two salts are structure-makers, in agreement with conclusions of this paper. Similar accurate data for (CH,),N+ halides and also other electrolytes with charges greater than 5 1 will be useful. Earlier workers (24-28) are in poor agreement as to whether urea should be classed as a structure-maker or structure-breaker, although the most recent work (28) and some earlier workers are in agreement with our conclusion that urea is a structure-breaker. Further, the inadequate logic leading to an earlier suggestion (26) that urea is a structure-maker has been pointed out (18). A Referee has pointed out that Krishnan and Friedman (29) have found evidence for a "saturation" effect in structure-making by alcohols and R,N+ ions. That is, structuremaking does not increase without limit as hydrocarbon size increases. The same Referee has also suggested that diffusion data from Witherspoon and Sarat (30) can be interpreted to support the idea presented in this paper that the gaseous hydrocarbons are structure-breakers. Acknowledgments The author is grateful to Brian Dunford, Robert Goldberg, and Frank Millero for helpful discussions. 1. G. N. LEWIS and M. RANDALL. Thermodynamics. McGraw-Hill Book Co., Inc., New York G. S. KELL. J. Chem. Eng. Data, 12, 66 (1967). 3. G. S. KELL and E. WHALLEY. Phil. Trans. Roy. Soc. 258a, 565 (1965). 4. F. FRANKS and H. T. SMITH. Trans. Faraday Soc. 64, 2962 (1968). 5. E. M. ARNETT, W. G. BENTRUDE, J. J. BURKE, and P. McC. DUGGLEBY. J. Amer. Chem. Soc. 87, 1541 (1965). E. M. ARNETT and D. R. MCKELVEY. J. Amer. Chem. Soc. 87, 1393 (1965). 6. G. L. BERTRAND, F. J. MILLERO, C. H. WU, and L. G. HEPLER. J. Phys. Chem. 70, 699 (1966). 7. D. M. ALEXANDER. J. Chem. Eng. Data, 4, 252 (1959).

5 HEPLER: THERMAL EXPANSION AND STRUCTURE M. E. FRIEDMAN and H. A. SCHERAGA. J. Phys. 21. R. L. KAY and D. F. EVANS. J. Phys. Chern. 70, Chern. 69, 3795 (1965) (1966). 9. L. A. DUNN. Trans. Faraday Soc. 64, 2951 (1968). 22. R. L. KAY, T. VITUCCIO, C. ZAWOYSKI, -and D. F. 10. H. B. BULL and K. BREESE. J. Phys. Chern. 72, EVANS. J. Phys. Chern (1966) ). 23. B. E. C O N W ~ and L. H. LAL~BER;~. J. Phys. 11. k-j. ELLIS J. Chern. Soc. A, 660 (1966). Chern. 72, 4317 (1968). 12. A. J. ELLIS. J. Chern. Soc. A, 1579 (1966). 24. J. A. RUPLEY. J. Phys. Chern. 68, 2002 (1964). 13. F. J. MILLERO. Private communication. 25. J. M. TSANGARIS and R. B. MARTIN. Arch. Bio- 14. R. GOPAL and M. A. SIDDIQI. J. Phys. Chern. 72, chern. Biophys. 112, 267 (1965) (1968). 26. M. ABU-HAMDIYYAH. J. Phys. Chern. 69, F. J. MILLERO and W. DROST--HANSEN. J. Phvs. (1965). Chern ). 16. R. H. --- STOKES., 27. G. G. HAMMES and R. SCHIMMEL. J. Arner. Chern ~ i t J. : Chern. 20, 2087 (1967). SOC. 89, 442 (1967). 17. W. L. MASTERTON. J. Chem. Phys. 22, 1830 (1954). 28. H. S. FRANK and F. FRANKS. J. Chern. Phys. 48, 18. A. HOLTZER and M. F. EMERSON. J. Phys. Chen~ (1968). 73, 26 (1969). 29. C. V. KRISHNAN and H. L. FRIEDMAN. J. Phys REDLICH and D. M. MEYER. Chenl. Rev. 64. Chern. 73, 1572 (1969). 221 (1964). 30. P. A. WITHERSPOON and D. N. SARAT. J. Phys. 20. B. E. CONWAY, R. E. VERRALL, and J. E. DESNOYERS. Chem. 69, 3752 (1965). Trans. Faraday Soc. 62, 1 (1966).

Apparent molar volume of sodium chloride in mixed solvent at different temperatures

Ultra Chemistry Vol. 8(2), 205-210 (2012). Apparent molar volume of sodium chloride in mixed solvent at different temperatures C.K. RATH 1, N.C. ROUT 2, S.P. DAS 3 and P.K. MISHRA 4 1 Department of Chemistry,