899
THEEFFECTO F SOLUTES AND TEMPERATURE ON THE STRUCTURE OF WATER
+
(AFRO‘ = AFO‘ wp - wr in eq 2 and = AFo’ Wp - Wr in eq 23). w‘ is work required to bring reactants together to mean separation distance R; wp is the similar quantity for the products. Defined by eq 5. Compare also eq 25. Rate constants of the cross-reaction ( I c l z ) and of the exchange reactions ( k l l , Iczz). Value of AF* extrapolated, in a AF* us. AFO’ plot, to AFO‘ = 0. Potential-energy barrier of a gas-phase cross-reaction (7). Potential-energy barriers of gaseous exchange reactions (7) (with i = j ) . Average barrier for the two exchange reactions, as in eq 8c. Potential-energy change in the reaction. Bond energies of AIB and A2B single bonds. Bond orders of A1B and A2B. Exponents in bond energy os. bond order plots.
+
Potential energy in atom transfer (7) relative to initial potential energy. Intrinsic asymmetry defined by eq 13. in eq 14 or n* - l/z in eq 18. n2* Intrinsic barrier terms in eq 16. Degree-of-reaction parameter in eq 16. Value of n at barrier maximum. dgi/dn and d2gi/dn2at barrier maximum. Free-energy barriers in two exchange reactions. Work terms in two exchange reactions (Wii’
= w$).
Steric factors for forward and reverse reactions. Statistical factors for forward and reverse reactions. Contributions to AF* before (Wr) and after (- WP) the rearrangements, defined in eq 22. See eq 24b, paragraph before eq 26, and 29, respectively. Brpinsted slope. For its variation with AFO’, see eq 34 or 35.
The Effect of Solutes and Temperature on the Structure of Water
by 0. D. Bonner and G . B. Woolsey Department of Chemistry, Universitg of South Carolina, Columbia, South Carolina
29208
(Received August 14, 1967)
The spectrum of liquid water has been observed over the range 600-1800 mp by a differential method in which water a t 25” is compared either with an aqueous solution at the same temperature or water a t an elevated temperature. Five overtones have been observed, which may be identified with the same ones occurring in the vapor phase, and are believed to be due to the presence of nonbonded liquid water. The band at 958 mp was chosen for quantitative studies, and solvation numbers have been calculated for a series of simple electrolytes and also for several organic solutes. The numbers obtained for electrolytes differ only slightly from those which appear as parameters in certain equations, but the sequence for the alkali halides is not the same. Water-structure enhancement by organic solutes is experimentally confirmed. Temperatures studies show that the concentration of monomeric water increases approximately linearly with temperature and doubles over the range from 25 to 80”. The strength of the hydrogen bond, based upon this temperature dependence of the monomer concentration, is estimated to be 2.67 kcal/mol. A combination of these data with those from the literature yields a calculated value of the concentration of nonbonded water a t 25’ of 3.5 mol/l. or about 6%,
Introduction The structure of water has been the subject of numerous investigations and of much controversy for many years. Various techniques, such as infrared and Raman spectroscopy, nmr, X-ray diffraction, and dielectric re1ax:ktion measurements, have been used in these studies, which have also been extended to aqueous
solutions. An extensive bibliography on water structure will not be presented in this paper, since excellent ones are available in Kavanau’s monograph and in the book published by Pimentel and TciIcClellan.l Some of (1) (a) J. L. Kavanau, “Water and Solute-Water Interactions,” Holden-Day, San Francisco, Calif., 1964; (b) “The Hydrogen Bond,” G. C. Pimentel and A. L. McClellan, W. H. Freeman and Co., San Francisco, Calif., 1960.
volume 72, Number 3 March 1968
900 the models which are most successful in relating the structure of water to its properties are due to Forslind,Z Frank,3 and C l a ~ s s e n . ~ The degree of association of water has been the subject of much speculation, and evidence has been cited for both a mixture model and a continuum m0del.5 I n the first instance, water is postulated to consist of an equilibrium mixture of molecular species with different numbers of hydrogen bonds per molecule. The continuum model describes water as an essentially complete hydrogen-bonded system. Choppin and coworkers6%’have, for example, investigated the nearinfrared spectrum of water and have stated that “a ready explanation for the bands is found in their assignment to water molecules having different degrees of polymerization.” Falk and Ford,6 on the other hand, have examined the spectra of HDO in the same region and state that the spectra “are incompatible with the existence in water of any discrete molecular species differing in the extent of hydrogen bonding.” Although water molecules are known to be continuously making and breaking hydrogen bonds, infrared spectra represent an average structure, in that species having lifetimes of the order of sec may be detected and this experimental technique was used in the studies which are being reported.
Experimental Section All spectra were recorded using a Cary hIodel-14M spectrophotometer. The spectra in Figure 1 were recorded with mater or aqueous solution in a 2-cm cell and with an empty cell in the reference beam. All other absorbances were measured using a differential technique which was developed for the observation of charge-transfer complexes between N-methylacetamide and aromatic acceptors. For each measurement, water at 25” was used in one of the matched cells as a reference, and aqueous solutions or water at another temperature was placed in the other cell. Cells of 10 cm length were used for the spectral region 9001000 mp and, because of the increasingly stronger absorbance, progressively shorter cells were used for measurements further into the infrared region. This technique has the advantage of compensating to a great extent for the underlying absorption of water, which is not directly due to the monomer overtones which are of interest, and emphasizes the differences in water structure caused by a change in temperature or the presence of a solute. I n contrast with direct measurements, such as those in Figure 1, the observed bands are sharp and do not shift with temperature or with the concentration of solute.
Results and Discussion A . Vibrational Bands. The positions of the fundamental vibrational bands of water vapor and their overtones have been accurately determined.* These The Journal of Physical Chemistry
0. D. BONNER AND G. B. WOOLSEY
1 .o
: 8 s
0.5
0 1100
1050
loQl
950
SO0
WAVE LENGTH (mu)
Figure 1. Shifts in the absorbance maxima of water with temperature and added electrolyte: (a) saturated MgClz, peak at 986 r n p ; (B) water a t 2j0, peak a t 977 mp; (C) water at 80°, peak at 965 mp; and ( D ) postulated curve for liquid monomeric water, peak a t 958 mfi.
bands are known to arise from the three vibrational modes of monomeric water. The spectrum of liquid water is considerably complicated, however, by hydrogen bonding which broadens the bands and shifts them to longer wavelengths. This shift is accentuated as the temperature of the liquid water is lowered and is related to the increased hydrogen bonding. Waggener and coworkers9 have recorded the spectra of liquid water over the range of temperature from 2 to 250”. It may be noted that as the temperature is raised, the bands become sharper and shift toward the blue, so as to approach a constant wavelength asymptotically. I n the case of the 201 overtone, this value is approximately 960 mp and it is about 1150 mp for the 111 overtone. There is certainly some hydrogen bonding in liquid water at 250”) but since the wavelengths of the bands do not shift appreciably with temperature above 200°, this probably represents the positions of the 201 and 111 overtones of liquid monomeric water and the shift from the vapor-phase values of 942 and (2) E. Forslind, Acta Polytech., 115, 9 (1952). (3) H. S. Frank and A . S. Quist, J . Chem. Phys., 3 4 , 604 (1961). (4) W.F. Claussen, ibid., 19, 259, 662, 1425 (1951). (5) M. Falk and T. A. Ford, Can. J. Chem., 44, 1699 (1966). (6) K. Buijs and G. R. Choppin, J. Chem. Phys., 39, 2035 (1963). (7) G. R. Choppin and K. Buijs, {bid., 39, 2042 (1963). (8) G . Herzberg, “Molecular Spectra and Molecular Structure. 11. Infrared and Raman Spectra of Polyatomio Molecular,” D. Van Nostrand Co., Inc., Princeton, N. J., 1959, p 281. (9) W. C. Waggener, A. J. Weinberger, and R. W. Stoughton, Annual Progress Report ORNL-3832, UC-4-Chemistry, Oak Ridge, Tenn., May 1965, pp 76-81.
THEEFFECT OF SOLUTES AND TEMPERATURE ON THE STRUCTURE OF WATER
L
1000
900
8 00
90 1
7 00
WAVE LENGTH (mu)
Figure 2. Absorbance of water: (A) water us. 5 m LiCl solution in 10-cm cells; (B) water at 25" us. water at 58" in 10-cm cells.
1136 mp may be ascribed to the proximity of nearest neighbors in the liquid.1° It has been observed that the presence of electrolyte shifts the water bands toward the red in a manner similar to hydrogen bonding. The spectra in Figure 1 were recorded to obtain quantitative shifts for the 201 overtone, which might be useful in the interpretation of the subsequent data. Curve A for a saturated solution of MgC12, in which it may be assumed that essentially all water molecules are polarized by Mg2+ ion, has a peak at the longest wavelength (986 mp). A similar curve was obtained for a saturated solution of Lacla. The band maximum is shifted to 977 mp for pure water at the same temperature. It appears at shorter wavelengths and increases in intensity as the temperature is increased. Curve D represents a postulated curve for liquid monomeric water. The position of this band and its intensity are estimated from the datag on liquid water at 250". Similar families of curves are experimentally obtainable for the other overtones of water. I n other studies, vibrational bands have been observed at five different wavelengths by the differential technique, described above, when solutions of LiCl are compared with pure water at 25'. The bands are sharp and their position is unchanged when electrolytes
other than LiCl are used. They also occur in the same position when pure water samples at two different temperatures are compared (Figures 2 and 3). These results are consistent with the vacant-lattice-point model,2depicting water as primarily a hydrogen-bonded structure with a small fraction of interstitial monomeric molecules. One might consider all of the experimentally observed spectra to be combinations of curves A and D of Figure 1, which represent the hydrogen bonded and monomeric forms, respectively. Any shift in equilibrium caused by the addition of electrolyte or a change in temperature would result in a maximum change in absorbance at the wavelengths of monomeric-water overtones, since these have much larger molar absorbances. Table I lists the positions of these vibrational bands in liquid water and also the positions of bands which have been observed in the vapor phase.* It is apparent that these band positions in the liquid phase do not correspond with those of Choppin,B which were obtained by the mathematical resolution of the water spectrum. It is believed that this differential method is more accurate in compensating for the absorbance caused by the shoulders of bands, which have (10) Reference 8, p 534.
Volume 76,Number 3 March 1068
0. D. BONNER AND G. B. WOOLSEY
902
1SOD
la0
1500
1300
1200
1100
a
~~~
~~~~~
~~
~~
Table I: Vibrational Bands of Water -Band Vapor
position, mp-Liquid
723 823 942 1136 1379
734 832 958 1148 1405
Band assignment
3Vi $2Yl 2vi Y1 Y1
+ + + + -I+ YI
Y2
Y8
ya
Y2
ya
YI
been shifted by hydrogen bonding or by polarization, due to the presence of an electrolyte, and more nearly represents the position of the band due to monomeric water in the liquid state. The correspondence of the values for the 201 and 111 overtones with the high temperature values of Waggenerg and the uniformity of the shift for all overtones in the liquid is further substantiation of the experimental method. It is interesting to note (Figures 2 and 3) that when water at a higher temperature is compared with water at 25", there is an absorption minimum which lies just to the red side of the bands listed in Table I. On the other hand, when water at 25" is compared with a solution of any electrolyte, there are broad absorption maxima which lie at approximately the same position. This might be expected, since electrolytes will decrease the concentration of all water and thus pure water would have more hydrogen-bonded water as well as The Journal of Physical Chemistry
more water monomer than solutions. I n water at 58", however, the concentration of the monomer species has been increased at the expense of the hydrogenbonded water. The fact that the absorption minima in this curve at 1030 and 1235 mp are reasonably sharp may substantiate, to some extent, the evidence presented by Choppine,' for water molecules containing one hydrogen bond, since the concentration of this specie should decrease as the temperature is elevated and the observed shift from the position of nonbonded band is reasonable. B. Solvation of Simple Electrolytes. Estimates of the extent of solvation of simple electrolytes in aqueous solutions are available. These have been primarily based on measurements of various properties of their aqueous solutions, such as conductance, heat of mixing, and activity coefficients. Stokes and Robinson" have calculated hydration numbers, which are parameters occurring in an extended Debye-Huckel type of equation, Glueckaufl* arrives at another set of numbers which are slightly smaller, by using a modified expression. I n contrast with solvation numbers, which are calculated so that certain observed properties of these solutions will fit a semitheoretical expression, it is (11) R. H.Stokes and R. A. Robinson, J . Am. Chem. SOC.,70, 1870 (1948). (12) E.Glueckauf, Trans. Faraday Soc., 51, 1235 (1955).
THEEFFECT OF SOLUTES AND TEMPERATURE ON THE STRUCTURE OF WATER possible to make a more direct measurement of the extent of solute-solvent interaction as a function of electrolyte concentration from observations of the intensities of the bands listed in Table I.13 Three of the bands (958, 1148, and 1405 mp) have intensities sufficiently large for quantitative measurements, and preliminary studies indicated that the concentration dependence of the intensities of these bands were identical when pure water at 25" was compared with solutions of either LiCl, KCl, or KI; ie., the ratios of the intensities of all three bands were the same when solutions of different concentrations were compared. The band at !358 mp was chosen for all of the quantitative measurements, since there is less interference from other overtones which occur when organic solutes are used. Band intensities were determined for a number of electrolytes at concentrations ranging from 0.4 to 5.0 m, with water serving as the reference. Concentration-dependent bands similar to that of Figure 2A were obtained for all electrolytes. The data were converted to molar absorbances to yield a series of numbers representing the effectiveness per mole of these electrolytes in reducing the concentration of the species giving rise to the 958-mp band. This number tended to decrease for a given electrolyte as the concentration increased, indicating that each ion was polarizing a smaller number of water molecules. These numbers, which are reproducible with a deviation of not more than 3%, repiresent the relative solvations of the ions. It was desiredl to estimate absolute solvation numbers, and absorbances of saturated solutions of LiCl, ;\'lgClz, and LaCla were, therefore, measured with water as a standard. It is felt that since these electrolytes are very highly solvated, it is probable that saturated solutions whilch contain comparable numbers of ions and water molecules will polarize all water in the solution. It was further recognized that even in the dilute solutions the concentration of water is not 55.5 mol/l., since a portion of the volume is occupied by the solute, and the following procedure was used to correct the absorbances of all solutions. The simplest assumption is that the absorbance at 958 mp may be represented as a sum of that due to the monomeric species (band D, Figure 1) and a second species whose concentration is proportional only to the volume fraction of water (band A, Figure l ) . 1 4 The absorbance in the pure reference water is Ar
+
= h[H~O] h[X]
presumed to have been removed. The observed absorbance in the differential experiment using the double-beam intrument is Aobsd
= Ar
-A
= k[HL)I
+ k ~ I 1- fJ[xI (3)
Data for the three saturated salt solutions having quite different volume fractions of water yield three equations for the solution of the two unknowns. A fourth equation results when one measures the absorption of pure water at 958 m p vs. air. The solution of the four equations for the two unknowns give values of 0.55 for kl [HzO]and 0.76 for kz[XI in pure water, with an average deviation of =!=2%. This remarkable agreement is highly suggestive of the validity of the assumptions which have been made. These data indicate that monomeric water molecules account for 42% of the absorbance of the liquid at 25", even though they represent only a small fraction of the total water. The value for kz[X] was then used in the solution of eq 3 for the more dilute solutions. The solvation numbers listed in Table I1 are the fractions of monomeric water molecules removed by a mole of electrolyte multiplied by 55.5 mol of water per 1000 g, i.e.
Ikl[Hz0l),o1n/1kl[Hz0I},ur,
H ~ OX
55.5
(4)
Table I1 : Table of Spectroscopic Solvation Numbers Electrolyte
H C1 LiCl NaCl KC1 CSCl NHdC1 NaBr NaI
Solvation number
Electrolyte
9.0 5.2 2.1 2.3
KBr KI KNO,
4.6
MgCh
3.0 0.7
CaCl, BaCl, LaCla
0.6
Solvation number
1.4 0.8 N O
11.5 8.2 5.0
16.8
These numbers are those obtained by extrapolation of the molar absorbance to infinite dilution so that the equilibrium concentration of the species present, in water will not be shifted by the presence of electrolyte and thus the decrease in concentration of water monomer will be proportional to the total decrease in the fraction of water unaffected by ionic solvation. Inspection of these solvation numbers shows them to be of the same order of magnitude as those appearing
(1)
where kl and kz are the molar absorbances, [H20] is the concentration of monomer, and [XI is the concentration of the other absorbing species. When saturated LiC1, MgClZ,or Lac13 is used, the absorbance is
A = kZf[Xl
903
(2)
where f is the volume fraction of water in the solution. The term kl(HzO] disappears, since all monomer is
(13) It may be noted that Durst and Taylor have used the water band between 980 and 1020 mp to estimate the solvation of chromic salts: R. A. Durst and J . K. Taylor, J. Res. NatE. Bur. Std., 68A,625 (1964). (14) The second species is obviously the polarized and/or hydrogenbonded water. Since only a small fraction of liquid water is monomeric, the above assumption is valid. Water spectra in Figure 1 and ref 9, as well as the subsequent calculations, verify that the molar absorbance of polarized and hydrogen-bonded water, kz, a t this wavelength is quite small compared with that of monomeric water, k l , since this is far out on the shoulder of the band. Volume 72,Number 9 March 1968
904 as parameters in various equations,"*'* although there are significant differences in the trends which are exhibited. The alkali metal chlorides are observed to decrease in solvation from LiCl to NaCl and then to increase again to CsC1. This phenomenon is confirmed by the greater solvation of KBr than NaBr and KI than NaI. This is not in agreement with the order in usual tables of hydration numbers,15 which are calculated from measurements of colligative properties. I t is believed, however, that the usual hydration numbers represent both ion-solvent interaction and ion-ion interactions such as ion pairing, etc. Solvation as measured spectroscopically is, on the other hand, believed to represent only ion-solvent interactions. This solvation can be accomplished in either of two fashions. A small ion such as Li+ or a highly charged ion such as Mg2+or La+3can polarize large numbers of water molecules and thus decrease the absorption at 958 mp. A larger ion such as Csf can increase the hydrogen bonding around the ion by reinforcing the structure in a similar fashion to organic solutes. These findings are in qualitative agreement with those of Bergqvist and Forslind,16 who report that nmr shifts for solutions of Rbf and Cs+ indicate a stabilizing effect on the water lattice. I t is also interesting that the larger NH4+ ion is observed to be more highly solvated than the K+ ion, even though the activity coefficients of NH&l and KCI are quite similar. This appears to substantiate the separation of ion-solvent and ion-ion interactions by the spectroscopic technique. C. Solvation of Organic Solutes. The solvation of organic nonelectrolytes as well as that of large organic ions such as the tetraalkylammonium ions must be considered as a different phenomenon from the solvac tion of lithium chloride. The tetraalkylammonium salts, for example, form crystalline hydrates, and X-ray diffraction patterns indicate that the hydrocarbon tails are found to be located in clathrate cages.I7 Aqueous solutions of these salts have osmotic and activity coefficients which are indicative of extensive ion pairing, jn spite of the shielding of the positive charge of the cation by the organic groups. Diamond1*has introduced the concept of water-structure enforced ion pairing to explain these results. This concept is based upon the assumption that hydrophobic ions tighten the water structure around them and force the oppositely charged ions even closer together. A similar phenomenon has been observed for nonelectrolytes when inert gases or hydrocarbons are dissolved in water. Franklg has interpreted the entropy decrease on solution as being due to tightening of the waterstructure around the solute. The enhancement of the water structure by organic solutes, such as the above mentioned examples, should be experimentally observable by the same technique which was used in the case of the simple electrolytes. The term solvation as used for these solutes, however, The Journal of Physical Chemistry
0. D. BONNER AND G. B. WOOLSEY is related to the increase in solvent hydrogen bonding per mole, rather than to the polarization of the solvent. Solvation numbers of four typical organic solutes have been measured (Table 111) in the same manner as for the simple electrolytes. The 958-mp bands were again similar to those of Figure 2A, although there was interference in some instances in the observation of the 1148- and 1405-mp bands. Three of these solvation
Table I11 : Solvation Numbers of Organic Solutes Solute
Solvation number
Sucrose Dextrose Urea ( CHahNCl
21.0 10.0 2.5 13.8
numbers are quite large when compared with those of simple 1-1 electrolytes. It is of interest that the nonelectrolytes, dextrose and sucrose, which have osmotic coefficients greater than unity, are also solvated to a much greater extent than urea, for which the osmotic coefficient decreases rapidly from unity with increasing concentration. There is further correlation of solvation numbers and osmotic coefficients in that the quantity (4 - 1) is about twice as large for sucrose solutions as for dextrose solutions of the same concentration. D. Efect of Temperature on the Structure of Water and the Strength of the Hydrogen Bonds. Intensities of the 958-mp band have been measured as a function of temperature over the range from 25 to 8 5 O , with water at 25" being used as a reference in each instance. The absorbances are shown in Figure 4. This plot indicates that the absorbance increases almost linearly with increasing temperature. The value of ICl [€120 ], which is proportional to the concentration of monomeric water increases by a factor of 2 over the temperature at 25 to 80". It may be shown that these data also yield values for the strengths of the hydrogen bonds which are quite reasonable, If one makes the simplest approximation of the existence of two species in water, a monomer and a hydrogen-bonded polymer,20 and (15) H. S. Harned and B. B. Owen, "The Physical Chemistry of Electrolytic Solutions," Reinhold Publishing Corp., New York, N. Y., 1957,P 525. (16) ,M.S,Bergqvist and E. Forslind, Acta Chem. Scand., 16, 2069 (1962). (17) P. T. Buerskens and G. A. Jeffrey, J . Chem. Phys., 40, 906 (1964). (18) R. hl. Diamond, J . Phys. Chem., 67, 2513 (1963). (19) H. S. Frank and M . W. Evans, J . Chem. Phys., 13, 507 (1945). (20) This assumption is identical with that which was assumed earlier in the calculation of solvation numbers and is essentially an interpretation of the data using the vacant-lattice-point model (ref 2).
THEEFFECT OF SOLUTES AND TEMPERATURE ON THE STRUCTURE OF WATER
1 .a5
.96
s
-
.85
I I
."
.75
TEMPERATURE ( ' C )
Figure 4. Concentration of monomeric water as a function of temperature.
further assumes that the first monomer molecule to be freed, as the temperature is elevated, is one which is held by only one bond, one may write the equilibrium expression
(5)
(Hz0)B = HzO
or ~~(H,o)E
where (H20)B represents a molecule of hydrogenbonded water. The resulting van't Hoff equation
may be easily solved since, because of the small fraction of water existing as a monomer, the term involving (H20)B is relatively unaffected by the formation of one molecule oE free water. The integrated expression is then ] n -K2 = l n - - - -QIH,O(Z)
KI
ffHzO(1)
-
AH R
[
7'2
TITzT1]
(8)
905
One may now calculate a value of AH = 2.67 kcal, based upon the evidence that the concentration of water monomer, and thus the activity, approximately doubles over the temperature range from 25 to 80". This value may be compared with 2.8 kcal, as calculated by Wa1rafen,21and 3.41 kcal, as calculated by Scatchard.22 E . Concentration of Monomeric Water at 25". Although the above data yield relative values for the degree of association of water as a function of temperature, they give no indication of the absolute concentration of nonbonded water. Molar absorptivities, unfortunately, cannot be determined, since the concentration of the absorbing species in the liquid giving rise to the 958-mp band are unknown at any temperature. It is possible, however, that an approximate answer can be obtained from the data of Waggener, et aL9 These data indicate that the absorbance of the liquid at 25' is approximately 7.4 times that of the vapor at 250". From the calculations which were made in an earlier section of this paper, it is known that 42% of the absorbance of the liquid at 25" is due to water monomer. If one assumes that all of the absorbance in the vapor is due to monomer and that the molar absorptivities of this species are the same2* at 25 and 250", the concentration of nonhydrogenbonded water at 25" may be calculated to be 3.5 mol/l., or about 6%. This may be compared with the calculated value of 19.3 % interstitial water molecules at 20" using the vacant-lattice-point model. 24 The lower experimental value could result for a distortion of the hydrogen bonds in the matrix water with the consequent decrease in the number of vacant lattice sites.
(21) G. E. Walrafen, J. Chem. Phys., 44, 1546 (1966). (22) G. Scatchard, G. M. Kavanaugh, and L. B. Ticknor, J. Am. Chem. Soc., 74, 3715 (1952). (23) It is realized that this assumption may introduce an error of the order of 10%. (24) Reference l a , p 12.
Volume 78,Number S March 1968
