J . Phys. Chem. 1991. 95, 1488-1493
1488 1.0
-
0.8
-
0.6
-
reactions dominate, and all sonochemically generated radicals are trapped by alkali-metal species. The change in the relative rates of these reactions leads to the observed saturation kinetics. The usual steady-state kinetics analysis yields eq 1 I , where d , e, and fare constants involving many separate reaction rate coefficients. The solid line in Figure 7 is the best fit to eq 11. Given the large number of participating reactions, further analysis of the relative values of these constants is not justified.
0.4 0.2
-
0 0
0.2
0.4
0.6
0.8
K+ Concentration (M) Figure 7. Potassium ion concentration dependence of sonoluminescence from KOCBHllsolutions in I-octanol: (m) experimental data; (-) f i t to steady-state kinetic expression, IsL = d [ M ' ] / ( e +AM+]). roborating evidence for this two-site model and the diffusion of radicals from the hot spot to the heated shell and bulk liquid. The proposed mechanistic scheme also explains the decrease in sonoluminescence intensity with decreasing cavitational temperature (i.e., increased solvent vapor pressure or sparge gas thermal conductivity). The rate of production of radicals (eq 4) decreases with decreased cavitational temperature, which decreases the rate of the subsequent reduction and chemiluminescent reactions (eqs 5 and 6). In addition, the volume of the surrounding heated fluid (and thus the number of alkali-metal atoms involved) also decreases as the temperature of the cavitation event decreases. Further evidence consistent with our mechanism is found with the sonoluminescence intensity as a function of K+ concentration, shown in Figure 7. The observed saturation kineticszz are a consequence of the secondary nature of the reactions that generate M*. The primary process is the formation of radicals by the high temperatures of the cavitation event. At low alkali-metal ion concentrations, the rate of the activation reactions (eqs 5-7) is slow compared to the rate of other radical-trapping reactions. At high alkali-metal ion concentrations, the rate of the activation (21) (a) Kondo, T.; Krishna, C. M.; Riesz, P. Inf. J . Rudiaf.B i d . 1988, 53, 891. (b) Kondo, T.; Krishna, C. M.; Riesz, P. Radial. Res. 1988, 116,
56. (22) In principle, this behavior could also arise from self-absorption. Self-absorption occurs in gas-phase atomic emission spectroscopy at high atomic concentrations and can be recognized by a decrease in the intensity in the center of an emission line. It can be ruled out in this case for three reasons: the emission lines are very broad, the emission lines do not change shape as the concentration is increased, and the atomic concentration of potassium atoms is very low.
The line width from potassium sonoluminescence in water is narrower than that from l-octanol (Figure 2). The width of the resonance line is a direct function of the lifetime of the excited state, which in turn in inversely related to the rate of the quenching reaction, eq 9. This reaction involves the conversion of electronic energy of the alkali-metal atom to vibrational energy of the solvent molecule. The triatomic water is less effective than the polyatomic I-alcohols in this, giving a longer excited-state lifetime and a narrower sonoluminescence line width, as observed.
Conclusions The major consequence of this study is that the use by Sehgal et aL3 of high-resolution sonoluminescence spectra of Na and K emission to calculate the temperature of the cavitation event is incorrect. The line widths and peak positions of these spectra are insensitive to experimental parameters that affect cavitational heating, such as total vapor pressure and the thermal conductivity of the sparge gas. Thus, alkali-metal sonoluminescence is not a valid probe of the conditions produced during acoustic cavitation. The considerable line broadening observed in these systems is ascribed to pressure broadening. As calculated from the line width of the resonance lines, the lifetime of the potassium excited state is unusually short, ~ 0 . 0 5ps. The source of the unusual line width is from collisional deactivation from solvent molecules in the rapidly heated fluid immediately surrounding the collapsing bubble. Radicals formed during the cavitation event are responsible for the formation of the excited-state alkali-metal atoms. Acknowledgment. Professor Alexander Scheeline is thanked for his many discussions and careful reading of the manuscript. The assistance of Dr. B. Barbieri of I.S.S.,Inc., and Dr. R. Bartolo in the calibration of the sonoluminescence spectrophotometer is gratefully acknowledged. Dr. T. P. McCarthy is thanked for the loan of the potassium hollow cathode lamp. This work was supported by the National Science Foundation. K.S.S.gratefully acknowledges an N.I.H. Research Career Development Award and a Sloan Foundation Research Fellowship. Registry No. Ar, 7440-37-1; He, 7440-59-7;Li', 17341-24-1; Na+, 17341-25-2; K', 24203-36-9; Rb', 22537-38-8.
Infrared Spectroscopic Studies of Concentrated Aqueous Electrolyte Solutions Olof Kristiansson*s+ and Jan Lindgren Institute of Chemistry, University of Uppsala, Box 531, S-751 21 Uppsala,Sweden (Received: July 23, 1990)
Infrared spectra of the OD stretching vibration of isotopically dilute HDO molecules in aqueous solutions of Ni(C10J2 and Mg(ClO.& are presented. For all concentrations,the spectra comprise four components; those corresponding to HDO molecules interacting with the anion, in the cation coordination sphere, in solvent-shared ion pairs, and in the bulk. Band parameters are given for these bands, as are quantitative estimates of the distribution of these species at all concentrations.
Introduction The stretching vibrations of the water molecule are, in principle, ideally suited as probes of ionic hydration in aqueous solutions.
'
Present address: Department of Chemistry, Swedish University of Agricultural Sciences, Box 701 5, S-75007Uppsala, Sweden.
These vibrations are highly sensitive to the extent of hydrogen bonding and thus to the local environment in the solution; also, the time scale of these vibrations makes possible the detection of species with lifetimes as short as IO-I's, which is shorter than most rearrangement processes occurring in solutions. However, the stretching vibration bands of liquid H 2 0 are extremely broad
0022-365419 112095- 1488$02.50/0 0 1991 American Chemical Society
IR Spectra of Concentrated Aqueous Electrolyte Solutions and intense and are also complicated by several types of vibrational interactions. The spectral features of O H and OD stretching vibrations of isotopically dilute HDO are considerably simpler,'-3 suggesting that information concerning ion-water interactions may be extracted more easily. The OD and O H stretching vibration bands of isotopically dilute HDO in liquid water at 25 OC are found at 2505 and 3420 cm-I, respectively. In aqueous electrolyte solutions, these bands are generally broad and single-peaked, resembling those of HDO in pure water.4 Some 20 years ago, however, it was found that these bands were split into two components in aqueous perchlorate salt solution^.^-^ A considerable number of investigations of this phenomenon have subsequently been made, and a number of other band splitting anions have been found (e.g., PF6-, BFC).~-I~The observations can be summarized as follows: (1) The high-frequency component (band A) increases in intensity, while the low-frequency component (band B) decreases as the salt concentration is increased. (2) The position of band A is determined mainly by the anion but is also slightly cation dependent. (3) The band width of band B increases with increasing salt concentrations. (4) A pseudo-isosbestic region is observed. For many years, the interpretation of these observations has been controversial. It has recently been shown that for dilute solutions, these spectra are composed of three components:I6 the high-frequency component was interpreted as originating from HDO molecules interacting with the anions, and band B as a superposition of the bands arising from HDO molecules in the cation Coordination sphere and in the bulk water. The different band positions of these two latter bands explain the observed band broadening of band B. This model does not provide any explanation of the slight cation dependence of band A, however, nor can it rationalize the observed intensity changes at high salt concentrations. Both contact (inner sphere) and solvent-shared ion pairs (outer sphere complexes) may exist in concentrated solutions. The perchlorate anion has a low tendency to coordinate cations;17inner sphere complexes are thus unlikely to occur in perchlorate solutions. This is strongly supported by the structures of the solid hexahydratesI8 and, in the case of Ni(C104)2, by the constancy of the UV-visible spectra. In an outer-sphere complex, a water molecule is influenced simultaneously by a cation and an anion. As suggested by many authors,sq'0*'2such a situation should result in the appearance of an additional absorption band at the expense of the bands originating from the fully hydrated ions. At high Waldron, R. D. J . Chem. Phys. 1957, 26, 809. Hornig, D. F. J. Chem. Phys. 1964, 40, 31 19. Falk, M.; Ford, T. A. Can. J . Chem. 1966, 44, 1699. Wyss, H. R.;Falk, M. Can. J . Chem. 1970, 48, 607. Hartman. K. A. J . Phys. Chem. 1966, 70, 270. Kecki, Z.; Witanowski, J.; Akst-Libszyk, K.; Minc, S.Rocr. Chem. 1966, 40, 919. (7) Thompson, W. K. Trans. Faraday SOC.1966, 62, 2667. (8) Brink, G.;Falk, M. Can. J . Chem. 1979, 48, 3019. (9) Walrafen, G.E. J . Phys. Chem. 1970,52,4176; 1971,55, 768. (IO) (a) Kecki, Z.; Dryjanski, P.; Kozlowska, E. Rocr. Chem. 1968, 42, 1749. (b) Kecki, Z.; Dryjanski, P. Rocr. Chem. 1969, 43, 1053; 1970, 44, 1141; J. Mol. Struct. 1972, 12, 219. ( I I ) (a) Adams, D. M.; Blandamer, M. J.; Symons, M. C. R.; Wadding ton, D. Trans. Faraday SOC.1971, 67, 61 1 . (b) Symons, M. C. R.; Waddington, D. J. Chem. Soc., Faraday Trans. 2 1975, 71, 22. (12) Gulierrez, L.; Mundy. W. C.; Spedding, F. H. J . Chem. Phys. 1974. 61, 1953. ( 1 3) McCabe, W. C.: Subramanian, S.;Fisher, H. F. J. Phys. Chem. 1970, 74, 4360. (14) (a) Schioberg, D. Eer. Bunsen-Ges Phys. Chem. 1981.85. 513. (b) Heinje, G.;Kammer, T.; Kleeberg, H.; Luck, W. A. P. In Interactions of Water in Ionic and Nonionic Hydrates; Kleeberg, H., Ed.; Springer-Verlag: Berlin, 1987; p 39. (IS) (a) Libus, Z.; Stangret, J. In Interactions o/ Water in Ionic and Nonionic Hydrates; Kleeberg, H.,Ed.; Springer-Verlag: Berlin, 1987: p 47. (b) Stangret, J.; Libus, Z. Spectrosc. Lett. 1988, 21, 397. (16) Kristiansson, 0.;Lindgren, J.; de Villepin, J. J. Phys. Chem. 1988, 92, 2680. ( I 7) Cotton, F. A.; Wilkinsson, G. Aduanced Inorganic Chemistry, 4th ed.; Wiley-lnterscience: New York, 1980. (18) West, C . D. Z . Kristallogr. 1935, A91. 480. (I) (2) (3) (4) (5) (6)
The Journal of Physical Chemistry, Vol. 95, No. 3, 1991 TABLE I: Band Positions of OD Stretching Vibrations of Molecules in NiKIO,), and MdClO,), Solutions#
I II
N i(C104)2
111
I II
Mg(C104)2
111
1489
HDO
15 I43 84 71 131 76
2630 2423 2619 263 1 2426 2620
1-111 refer to the different environments schematically shown in Figure 3.
salt concentrations, the spectra referred to above should thus be described in terms of four components: the three existing in dilute solutions and the one representing the solvent-shared ion pair. The aim of this work is to show how an extension of the model used for dilute solutions to include a component representing the solvent-shared ion pair successfully rationalizes the observed spectral features for all salt concentrations. Experimental spectra are presented and discussed for the OD stretching vibrations of isotopically dilute HDO molecules in aqueous solutions of Ni(C104)2and Mg(C104)2over a broad concentration range. Experimental Section Stock solutions of nickel(I1) perchlorate (GFSChemicals Co.) were prepared. Solutions of magnesium(I1) perchlorate were obtained by dissolving analytical grade MgO in HC104, and the pH was adjusted to 5.0. The D 2 0 (99.98%) was obtained from Studsvik AB. HDO solutions were prepared by adding a weighed amount of D,O to a weighed amount of stock solution. For each concentration, a minimum of three independent preparations was made; differences of no more than 0.5% in absorbance were obtained. The reference H 2 0 solutions were prepared by adding an equivalent amount of H 2 0 to the stock solutions. Concentrations of Ni2+and Mg2+were determined titrimetrically, using standard bases on the eluates of cation exchangers. Densities were determined with a pycnometer. Spectra were recorded on a Perkin-Elmer 580B spectrometer on line with the Perkin-Elmer Data Station 3500. A resolution of 10 cm-I was selected to minimize noise. Sixteen scans (60 min) were made in the 1800-2900-~m-~region, and the average was taken. The solutions were contained in a cell with CaF, windows and a Teflon spacer. The path length in the cell was 0.0455 (2) mm, as determined interferometrically. The cell was thermostatically controlled by circulating water through the mounting plates of the cell. The temperature used in the experiments was 20.0 OC, as measured by a thermocouple inserted in the solution in the cell. The solid hydrate Ni(C104)2.6H20 was prepared by recrystallization from a solution containing 5 mol % DzO. The composition of the crystals was verified by X-ray powder diffraction. Evaluation of the Spectra. Results Dilure Solutions. It has been shownI6 that, in dilute aqueous solutions, the OD stretching vibration spectra of isotopically dilute HDO molecules in aqueous solutions have three sources: HDO in the first coordination sphere of the cation, HDO interacting with the anion, and HDO molecules in the bulk water. A double difference technique is used to obtain the spectra of the OD oscillators interacting with the ions. The method has previously been described in detail;16only a brief outline is given here. The spectra of four solutions are recorded in the region 1800-2900 cm-l: A, x M salt and y mol 7% HDO in H20; B, x M salt in H20; C, y mol o/o HDO in H20; D, H,O. The difference (Aobs
-
klBObs)
- k3(Cobs
-
k2D0bs)
(1)
is then calculated; Aoh, Bobs,Cobs,and Dabs are the spectra corresponding to the solutions A, B, C, and D, respectively. The scale factors k l and k 2 are determined stoichiometrically. The scale factor k , is determined by a band-shape analysis, as described previously.16 A small band at 2935 cm-l has been included, however, to describe the overtone of the bending vibration of the
Kristiansson and Lindgren
1490 The Journal of Physical Chemistry, Vol. 95, No. 3, 1991
M,,q+Xb(sqlb)-are m and n, respectively, then a0 = am
0
bi
w A
(3)
This method has been applied to 0.214 M Mg(C104)2and 0.249 M Ni(C104)* aqueous solutions. The a0values obtained were 9.4 and 10.3, respectively. The calculated and observed spectra are shown in Figures la and 2a. Two bands were obtained in each case. The high-wavenumber band is interpreted as originating from HDO molecules coordinated to the perchlorate anion (Figure 31) and the low-frequency component from HDO molecules in the cation coordination sphere (Figure 311). The band parameters are given in Table 1. Concentrated Solutions. It is found that Lambert-Beer's law is not valid for concentrated solutions. A number of effects are observed: (a) a slight shift of the maximum of the high-frequency band toward lower wavenumbers and an increase in band-width; (b) a decrease of the value of CY;(c) an increase in the ratio of the band areas of the high- and low-frequency components. These effects are due to additional types of interaction occurring in the concentrated solutions. Subtraction of a scaled low-concentration spectrum reveals a new band, slightly shifted to lower wavenumbers from the high-frequency band obtained for dilute solutions. This is interpreted as being of the same origin as the band observed in ref 11, Le., HDO molecules shared between the (2104-anion and the cation in solvent-shared ion pairs (Figure 3111). In the final band-shape analysis of the concentrated solutions, a model is thus used involving four types of water molecule environment: the three types in Figure 3 and bulk water. The two types of C104- hydration band are very similar with regard to both position and width. In a first step, they cannot be treated separately in the band-shape analysis, and a superposition must be used. After the analysis, a separation can be made as described below. Examples of difference spectra are shown in Figures 1 and 2 . Equation 2 is modified in this situation: when water molecules are shared between the anion and cation, the quantity a is introduced such that k j = (CH,o(B) - C(s)a)/55.41 (4)
a
0'25t
+ bn/2
cy
= a0 - y/2
(5)
where y is the average number of OH oscillators involved in solvent-shared ion pairs per salt unit. In Figure 4, CY is plotted versus salt concentration. Linear functions are fitted to the observed points to give the least-squares lines: a(Ni(C10,)2) = 10.5(2) - 0.77(5)c(s) (6) (~(Mg(C104)2)= 9.1(2) - 0 . 7 3 ( 9 ) ~ ( ~ ) 2900
1800 (cm-1)
Figure 2. Observed (crosses) and calculated (full line) difference spectra of aqucous solutions of (a) 0.249 M, (b) 1.385 M, and (c) 2.736 M Ni(C104)2. In d the spectrum is shown of Ni(CIO4),.6H20 (s) containing ca. ST) D 2 0 .
HDO molecules, to avoid any bias in the description of the other bands. k 3 is related to the number of ion-perturbed water molecules by k j = (CH,O(B)- C ( ~ ) ~ O ) / C H , O ( D )
(2)
where CH,(B,D) are the H 2 0 concentrations in solutions B and D (mol L") and C(s) is the salt concentration (mol L-I). I f the coordination numbers of a cation, M, and an anion, X, in a salt 0
H
Ii
(7)
where c(s) is the salt concentration (mol kg-I). The numbers in parentheses are the estimated standard deviations. The intercept with the ordinate gives cyo as defined by eq 3. For the lowest concentrations, ca. 2% shared water molecules are predicted. If these small quantities are neglected, it is possible to calculate the individual coordination numbers of the ions by using y and the deviation from Beer's law of the cation hydration band. The fraction of ion-shared water molecules coordinated to the cations, R, at a concentration C(s) is given by 1 - R = ( m - 7 / 2 ) / m = hCo/hoC (8) where M is the cation coordination number and h the band height of the cation hydration band; ho is the band height at the lowest U
0
Figure 3. Schematic drawings of fragments of aggregates existing in aqueous perchlorate salt solutions, showing hydration of a perchlorate ion (I), a metal ion (II), and a solvent-shared ion pair (Ill).
IR Spectra of Concentrated Aqueous Electrolyte Solutions
The Journal of Physical Chemistry, Vol. 95, No. 3, 1991
1491
0.15
',
0.1
0
2
4
6
8
10
c(s) (moVkg) Figure 6. Height of the Ni2+hydration band as a function of salt con-
centration. proximation, from spectra of the most dilute solutions, and the band height of this band at a concentration C(s) will be given by h = C ( a - m)ho/CO(aO - m) (15) 0
3
2
1
4
clsl I m o i / k g l
Figure 4. Parameter cy as a function of salt concentration for (a) Niand (b) Mg(C104)2.The estimated errors are indicated by the
vertical bars.
0
1
2
3
L
c(sI l m o l / k g l
Figure 5. Proportion of anion-occupied sites (R)on the (a) Ni(H20),2+ and (b) Mg(H20)62+ cations as a function of salt concentration.
obtainable concentration Co. In Figure 5, the quantity R is plotted versus salt concentration. The plots are seen to be linear; the least-squares lines through the points are R(Ni(CIO,),) = [0.1 19 (I)]c(s) R(Mg(Cl04)z) = [0.121 (I)]c(s)
(9) (10)
Combining cqs 5, 6, 8, and 9 and eqs 5, 7, 8, and IO gives m(Ni2+) = 6.5 (4)
( 1 1)
m(Mg2+) = 6.0 (8) (12) These values substituted into eq 3 give n, the coordination numbers for the perchlorate anion: n(Ni(C104),) = 4.0 (4)
(13)
n(Mg(C104)2) = 3.1 (8) (14) Thc two typcs of C104- hydration bands (types I and I l l in Figure 3) are, as stated above, very similar both with regard to position and width. The superposition of these bands cannot therefore be decomposed uniquely unless additional constraints are imposed. The results given above show that the band parameters for the type l band are obtained, to a very good ap-
Band-shape analyses of the concentrated solutions, with the type I band constrained to the position and width obtained from the dilute solutions and the height given by eq 15, gave the band parameters for the type 111 band shown in Table I. The OD stretching spectrum of the solid hydrate Ni(CI04)2.6H20containing ca. 5 mol % HDO is shown in Figure 2d. The band is centered at 2585 cm-' with a half-width of 50 cm-I.
Discussion The OD stretching spectra of HDO molecules in dilute to very concentrated aqueous solutions of Ni(C104)2and Mg(C104)2are described by four components. These correspond to HDO molecules in the three types of environments shown schematically in Figure 3 and to HDO in bulk water. The band parameters of the three components arising from the ion-affected OD oscillators are given in Table I, and examples of difference spectra are shown in Figure I and 2. The band originating from the hydrated Clodion (type I) are, within the estimated standard deviations, identical in the different solutions. The bands from the solvent-shared ion pairs (type I l l ) are shifted slightly to lower wavenumbers and are somewhat broader than this first band. The bands from the hydrated Ni2+ and Mg2+cations (type 11) are centered at 2419 and 2426 cm-l respectively. In Figure 2, it is seen that the ratio of the heights of the Mg2+hydration band and the high-frequency band is decreased as the salt concentration is increased. This effect is due to a transfer of species from type I1 to type 111. The height of the Ni2+cation hand, h, as a function of the salt concentration actually passes through a maximum, as can be in Figure 6. This observation can be further illustrated by combining eqs 8 and 9 giving h = hoC(s)(l - 0.1 I~c(s))/CO(S) The first term is a Lambert-Beer term increasing linearly with the salt concentration C(s). The second term expresses the decrease in h as the solvent-shared ion pairs are formed. The quantity R, the fraction of hydrogen atoms of water molecules coordinated to the cations involved in a solvent-shared ion pair, is plotted versus salt concentration in Figure 5. The plots are seen to be linear, implying no specific preference for H 2 0 or Clod in the second coordination sphere of these cations, but rather a random distribution. A similar result has been obtained by NMR spectroscopy on Cr(H20)d+with CIOL and CI- as count e r i o n ~ . ' ~In a second-order neutron diffraction difference study on a 4.35 M NiC12 solution,20an average of 5.8 (0.3) anions were found in the second hydration sphere of the cation, Le., R = 0.48. This value is in good agreement with that predicted from the present results where, at this concentration, a value of 0.52 is obtained. Comparison with Solid Hydrates. The spectra of the aqueous solutions can be compared with those of the solid hydrates M(19) Andersson, C. F. L. Diss. Abstr. Int. B. 1974, 34a, 4264. (20) Neilson, G.E.; Enderby, J . E. Proc. R. Soc. London 1983, A393,353.
The Journal of Physical Chemistry, Vol. 95, No. 3, 1991 0 I 0 I1
0 I11 A Bulk
c(s) (molkg)
Figure 7. Distribution of OH oscillators of H 2 0 molecules in aqueous solutions of Ni(C104)2as a function of salt concentration. 1. 11, and 111 refer to the categories shown schematically in Figure 3 .
(C104)2.6H20(s). The OD stretching spectra of Ni(C104)2.6H20, containing ca. 5% HDO, is shown in Figure 2d. One single band is observed, centered at 2585 cm-l with a half-width of 50 cm-I. The corresponding spectra of Mg(C104)2.6H20has been studied at various temperatures;21 at 291 K, one band was obtained centered at 2604 cm-l with a half-width of 50 cm-I. The rather large half-width, as observed for a solid hydrate, was taken as an indication of disorder in the structure. Since no other OD stretching bands are observed in these two cases, every water molecule of the M(H20)62+unit is hydrogen bonded to a perchlorate anion. The spectra are furthermore consistent with structures where all hydrogens are effectively equivalent. The solid hydrates thus resemble very concentrated aqueous solutions, corresponding to a molal concentration of 9.25 mol kg-I. In terms of the nomenclature used for solutions, we have in these cases cy = 6 and R = 1 . A large number of spectroscopic and structural data exist on solid hydrates containing O-.Odistances. These data can be used to calculate correlation curves which, in turn, allow the present band position to be converted to O-.O distances. Using the correlation function given in ref 22, we find that the distance between a perchlorate anion and its coordinated water molecule is 3.06 %r. I n the formation of the solvent-shared ion pair, this distance is slightly shortened to 3.04 A. The average distance between water molecules in the first and second coordination spheres of the Ni2+ and Mg2+ cations is 2.76 A. Combination of the various parameters obtained in this study provides a detailed picture of the distribution of the different types of O H oscillators in aqueous solutions at different salt concentrations. In Figure 7, this distribution is shown as a function of salt concentration for solutions of Ni(C104)2,extrapolated to the solid hydratc. The fraction of OH oscillators not perturbed by the ions, as observed by IR spectroscopy, decreases as the salt concentration increases. In the two most concentrated solutions, these constitute approximately half the total. The concentration of OH oscillators interacting with Clod- ions (type I) and those bound to Ni2+cations (type 11, Figure 3) increases initially, passes through a maximum, and decreases to zero at the limit of the solid hydrate. The maximum for the type I oscillators occurs at lower concentration than for type I I , due to the lower coordination number for Clod-compared to Ni2+. The concentration of OH oscillators involved in a solvent-shared ion pair (type 111) increases over the entire concentration range up to the solid hydrate, where no other type cxists. Cooperatiuity, Asymmetric Water Molecules, and Aspects of Bulk Water. The two bands from water molecules of type 1 and I I (Figure 3) are similar, as regards both position and width. The effect of the cations on the frequency of the HDO molecules interacting with the C104- anion is relatively small compared to this effect on an HDO molecule interacting with another water moleculc in the bulk. This result is in agreement with an earlier study of the influence of cations on the stretching frequency o f HDO in ternary mixtures (salt/water/aprotic solvent with H-bond acceptor B).23 A linear correlation was found between the (21) White, M. A.; Falk, M. J . Chem. Phys. 1986, 84, 3484; A38, 614. (22) Berglund, B.; Lindgren. J.; Tegenfeldt, J. J . Mol. Sfrucf. 1978, 3, 179.
Kristiansson and Lindgren magnitude of the shift due to the cation and the shift due to the OH-B H bond in the binary (salt/solvent) mixtures. Hence, the effects of the donors and acceptors are not additive but rather of a cooperative nature. In the present study, the additional shift due to the cations is ca. 10 cm-' for HDO interacting with the C104- anion, whereas a shift of ca. 85 cm-I is observed for HDO molecules bound to water molecules in the bulk. The model used in the evaluation of these spectra gives a good spectroscopic description for all salt concentration. Two spectroscopic features merit some comment, however, since they might appear somewhat surprising. If we consider a water molecule in a solvent-shared ion pair, the most common situation at the concentrations used is one in which one O H group is bound to the anion and the other to a water molecule in the bulk. This situation requires that the force constants for these OH bonds are very different, since the OD stretching vibrations for the two situations differ by about 200 cm-I. This situation is quite possible, however, as shown for water molecules bound in HOH-Acomplexes in CH2C12.24 For F anions, a difference in the OH stretching frequency of 300 cm-l was observed. This corresponds to ca. 230 cm-l in the OD stretching region, which is actually larger than that required in the present case. Other examples of highly asymmetric water molecules are found in solid hydrates.25 This ability of the two OH bonds in a water molecule to be quite different has also been illustrated recently in a series of ab initio SCF calculations,26where the electron rearrangements for water molecules in different environments were studied. The case in which one water hydrogen is involved in a strong H bond to a hydroxide ion and the other not involved in any bond is particularly interesting. A large difference in the electron density of the two O H bonds was observed, where the one bound to the hydroxide ion is strongly polarized whereas the other is almost unaffected. The asymmetry of a water molecular may actually be so large that the vibrational coupling between the two O H bonds disappears, and the bonds vibrate quite independently.25v27 A second feature worthy of comment is that the shape of the bulk-water band in dilute solutions is identical with that of the most concentrated. In a 3.9 molal Ni(C104)2solution, for example, there are 14 water molecules/salt unit, and it would seem difficult to envisage the existence of any bulk water at all. To understand this, we shall consider spectroscopicresults obtained on small water clusters formed in a molecular beam.28 It was found that the stretching vibration spectra of clusters, containing three or more water molecules, absorb over the same frequency range as liquid water and also showed a pronounced similarity with that of the liquid. The spectra were interpreted in terms of the clusters having ring structures, with one hydrogen per water molecule participating in a hydrogen bond with a neighboring water. In a theoretical calculation of the vibrational frequencies of similar small clusters, it was possible to reproduce both the O H stretching frequency shifts and the shapes of the bands obtained in the experiment^.^^ Models for deformable water molecules were used in the calculations; the frequency shifts were the results of the new equilibrium distances produced. The width of the bands resulted when the configurations from a Monte Carlo simulation were used. Another interesting example of this behavior is given for molten (CH3)3N.10.25H20.30 The OD stretching spectrum of the melt is strikingly similar to that of HDO in pure water, even though the number of water molecules per trimethylamine is small. Comparison with Other Spectroscopic Studies of Solutions. The present study is, in some respects, a quantitative extension of the work of Brink and Falk.8 A similar approach was used and (23) Kleeberg, H.; Heinje, G . ; Luck, W. A. P. J . Phys. Chem. 1986, 90, 4427. (24) Schioberg, D.;Luck, W. A . P. Ado. Mol. Relax. Inferact. Processes 1979, 14, 217. ( 2 5 ) Lutz. H . D. Sfruct. Bonding 1988, 69, 97. (26) Hermansson, K. Acta Crystallogr. 1985, 841, 161. (27) Schiffer, J.; Hornig, D. J . Chem. Phys. 1968, 49, 4150. (28) Vernon, M. F.; Krajnovich, D. J.; Kwok, H . S.; Lisy, J . M.;Shen, Y. R.; Lee, Y. T. J . Chem. Phys. 1982, 77, 47. (29) Reimers. J . R.; Watts, R. 0. Chem. Phys. 1984, 85, 83. (30) Falk, M . Can. J . Chem. 1971, 49, 1137.
IR Spectra of Concentrated Aqueous Electrolyte Solutions similar conclusions reached by Symons et al.," where the coordination number of the perchlorate ion was also estimated. The values obtained (3.5-4.7) are in agreement with those found in this work. In a Raman study of a number of rare-earth perchlorates, spectral features were obtained using a differential analysis technique.I2 Absorption was assigned to hydrated rare-earth metal ions and to perchlorate ions. For high molalities, absorption was detected that could be assigned to water molecules in solvent-shared ion pairs at frequencies similar to those obtained in this study. Our concept of the physical phenomena occurring in solutions, along with their spectroscopic manifestations, is essentially the same as that given by these authors. However, in none of these studies was a characterization of specific absorption band positions and their widths possible. In refs 5 . 6 , or 9, it can be seen that the OD stretching spectra of the perchlorate solutions contain a region at 2560-2580 cm-l in which the absorbance is approximately constant as the salt concentration varies. This region has been referred to by some authors9 as a pseudoisosbestic point. Infrared spectra of HDO in pure H 2 0 at temperatures from 29 to 87 OC similarly exhibit an isosbestic point at 2575 c ~ - ' . ~ I It has been stated that the existence of such points and corresponding points in the O H stretching region 'demands the conclusion that the effects of temperature rise and of perchlorate addition are virtually equivalent with regard to changes between H-bonded and nonH-bonded OD an O H groups in solution^".^ The present results indicate that the interpretation of the spectral changes as a two-state equilibrium is an oversimplification. It has here been shown that the spectra of the perchlorate solutions consist of four components whose relative proportions are shown in Figure 7. The pseudoisosbestic point is a result of the band positions and their relative intensities. That temperature and concentration isosbestic points coincide is thus accidental. I n a recent paper of Stangret and Libus,Isb spectra were presented of the O D stretching vibration as well as the 2u1,3+ u2 band of H 2 0 in aqueous solutions of M(C104)2(M = Mg2+, Mn2+,Zn2+). The spectra obtained in the OD stretching region are similar in many ways to those obtained in this work, although no explicit band parameters were given to allow a detailed comparison of the data. In particular, the number of ion-affected water molecules ( N in their nomenclature corresponding to a in this work) is in good agreement for low salt concentrations. However, the authors interpret these values in terms of the perchlorate ions being coordinated to two water molecules, each symmetrically oriented with both their hydrogen atoms directed toward the anion. Both from entropy considerations and by analogy with neutron diffraction studies on the CI-anion,29we believe that this configuration is unlikely, and we favor a model whereby each perchlorate ion coordinates to four water molecules, each interacting via one hydrogen atom with the anion and one with a water molecule in the bulk. It must be noted, however, that the spectral data alone permits both interpretations. In ref 12, it is assumed that N is constant in the concentration range investigated. Here we show this assumption to be incorrect. The consequence of this (31) Senior, W. A.; Verral, R. E. J . Phys. Chem. 1969,73,4242. (32) Cummings, S.; Enderby, J. E.; Neilson, G . W.; Newsome, J. R.; Howe, R . A.; Howells, W. S.;Soper, A. K. Narure 1980,287,714.
The Journal of Physical Chemistry, Vol. 95, No. 3, 1991 1493
is that the spectra for high salt concentrations contain contributions from the bulk water and thus force the authors to conclude that no perchlorate ions exist in the second coordination sphere of the cations for any salt concentration. Conclusions The interpretation of the OD stretching spectra of HDO molecules in aqueous perchlorate solutions has been the subject of much discussion over recent years. It has here been shown that the spectra of dilute to very concentrated solutions consist of four components arising from HDO molecules interacting directly with the anion, within the cation coordination sphere, in solvent-shared ion pairs, and in the bulk. As the salt concentration is increased, there occurs a monotonic decrease in the bulk water component and an increase in the component representing the solvent shared ion pair. At the limit of the solid hydrate, all water molecules are essentially involved in an outer-sphere ion pair (Figure 7). The components due to the hydrated cations and anion increase initially and pass through a maximum at intermediate concentrations. The present results allow us to add to the already rather detailed picture of the structures of Ni(C104)2and Mg(C104)2aqueous solution^.^^-^^ The Ni2+ and Mg2+ cations are thus hexacoordinated to water molecules. These are sufficiently polarized by the cations to induce a significant strengthening of the H bonds formed to their neighboring water molecules, as implied by the shift in their OD stretching vibrations to lower frequencies. Correlation curves obtained from studies of solid hydrates allow these frequencies to be converted to 0-0 distances; the average distance between the first and second hydration sphere is 2.76 A for these cations. The perchlorate anion coordinates to four water molecules a t an average distance of 3.06 A. Only those water molecules that interact directly with the ions are sufficiently perturbed to produce a shift in the OH force constant. As the salt concentration is increased, water molecules in the second coordination sphere of the cations are replaced by perchlorate anions, forming solvent-shared ion pairs. The proportions of these increase linearly with salt concentration, implying a random distribution of perchlorate ions and water molecules. Acknowledgment. This work has k e n supported by grants from the Swedish Natural Science Research Council and the Knut and Alice Wallenberg Foundation, which are hereby gratefully acknowledged. We thank Dr. Magnus Sandstrom for his many valuable suggestions and interesting discussions and Prof. Josh Thomas for linguistic corrections and X-ray powder diffraction measurements. We are also grateful to the Central Analytical Laboratory of the Institute and to Mr. J. Broberg for his skilled experimental work. (33) Swift, T. J.; Connick, R. E. J . Chem. Phys. 1962,37,307. (34) Newsome, J. R.; Sandstrom, M.; Neilson, G . W.; Enderby, J. E. Chem. Phys. Lerr. 1981,82,399. (35) Neilson. G . W.; Schioberg, D.; Luck, W. A. P. Chem. Phys. Lerr. 1985, 122,475. (36) Hewish, N . A.; Enderby, J. E.; Howells, W. S. J . Phys. 1983,Cl6, 756. (37) Heinje, G.;Luck, W. A. P.; Heinzinger, K. J . Phys. Chem. 1987, 91, 331. (38) Kanno, H . J . Raman Specrrosc. 1987, 18, 301. (39) Irish, D. E.; Jarv, T. Chem. Soc. Faraday Discuss. 1978,64,95. (40) Skipper, N . T.; Cummings, S.;Neilson, G . W.; Enderby, J. E. Nature 1986,321,52.
