J . Phys. Chem. 1985,89, 1193-1201 ppm, and the quadrupole relaxation rates are not strongly increased relative to variations with concentration for nonaqueous solutions. Apparently, even under conditions of forced association, contact ion pairing does not lead to a significant reduction in symmetry of the electric field gradient a t the 35Clnucleus. It is likely that solvent dipoles and nearby ions are rapidly reorienting during the transient ion-ion encounter so as to reduce the field gradient in the C104-ion and electrostatic attraction of the counterion. Thus, the 35C10; quadrupole relaxation rates are not generally sensitive to contact ion pairing with sodium in aqueous solution. Activation Energies of Relaxation. The Arrhenius activation energies for the W l relaxation process were determined from plots of the Arrhenius equation K = Ae-EaJkT where the relaxation rate K = l / T l , A is a temperature-independent factor, and E, is the Arrhenius activation energy. The activation energies thus obtained for 35Clrelaxation are plotted in Figure 5 which bears a striking resemblance to the chemical shift plot, Figure 1. Uncertainties of values from the three-point Arrhenius plots are about 1.5 kcal/mol.
1193
The Arrhenius activation parameters for relaxation shown in Figure 5 vary from -2 to -9 kcal/mol. Reimarsson et al.' point out that an Arrhenius barrier of about 2 kcal/mol can be associated with the energy of activation for dipole reoirentation of water in the hydration sphere of an ion at infinite dilution. The higher activation barriers observed here indicate greater energy barriers to rotational reorientation of large perchlorate-sodiumwater and/or perchloratewater clusters. Such reorientation of solvates containing dipoles next to 35C104-ions contributes a time dependence to electric field gradients and hence the quadrupolar relaxation rates. The much higher activation energies for relaxation in the NaC104-NaOH solutions suggest greater resistance to solvate cluster rotation and dipole reorientation than in the NaC104-H20 solutions. Therefore, the similarlity of Figure 5 to Figure 1 is such that the model invoked to explain Figure 1 should be used to explain Figure 5 . Acknowledgment. This work was prepared for the US.Department of Energy under Contract DE-AC06-77RL01030. Registry No. "Cl, 13981-72-1; NaC104, 7601-89-0; NaOH, 131013-2.
Vibrational Spectroscopic Studies of Sodlum Perchlorate Contact Ion Pair Formatlon in Aqueous Solutiont Allan G. Miller* Rockwell Hanford Operations, Richland, Washington 99352
and John W. Macklin* Department of Chemistry, University of Washington, Seattle, Washington 981 95 (Received: April 10, 1984)
A detailed study of the variations in the Raman spectrum of aqueous NaC10, and NaC104-NaOH mixtures with changing Na+ and NaClO, concentration and temperature is interpreted in terms of contact ion pair formation. Raman spectra of anhydrous and monohydrated crystalline solids and nonaqueous solutions of NaC104 are used comparatively to support the conclusions concerning aqueous solutions. Based upon resolution and assignment of components in the contours assigned to ul(Al) and v2(E) vibrations of the Td perchlorate ion, the equilibrium constant at 22 O C for contact ion association is 0.022 m. The associated value of hF0 is 2.22 kcal/mol.
Introduction
Contact ion pair association involving perchlorate ion was suggested by Geffeken in 1929.' Apparently due to the weakly interacting character of perchlorate ion in solution, contact pairing is difficult to detect. Recent applications of instrumental measurements in search of evidence for perchlorate contact association have led to mixed results. Conductivity measurements of aqueous NaC104 reported by D'Aprano2 and 35Clnuclear magnetic resonance (NMR) quadrupolar relaxation times reported by Reimarsson and Lindman3 were interpreted as indicating contact association between Na+ and C10, ions. Similar conclusions were reached by Eisenstadt and Friedman4 and Templeman and Van Geet5 based upon 23NaNMR relaxation times in aqueous NaC104 and by Greenberg and Popov6 based upon the interpretation of 23NaN M R chemical shifts. The latter report also includes Raman tPresented in parts to: the 177th National Meeting of the Amexan Chemical Society, Honolulu, HI, April 1979; the 35th Northwest Regional Meeting, the Joint 35th Northwest and 5th Rocky Mountain Regional Meeting of the American Chemical Society, Salt Lake City, UT, June 1980; the 181st National Meeting of the American Chemical Society, Atlanta, GA, March-April 1981; the 37th Northwest Meeting of the American Chemical Societv. Eugene. OR. June 1982. zC&enr address:' U.S.Testing Co., 2800 George Washington Way, Richland, WA 99352.
spectroscopic indications of contact pairing in nonaqueous solvents. While the study of 35ClN M R relaxation times by Berman and Stengle' also showed evidence of perchlorate contact ion pairing with alkali metals in organic solvents, they found no indication of such association in aqueous solutions. Infrared spectroscopic studies afford convincing evidence of ion pair formation by perchlorate ion in solution. Perelygin and mworkers have interpreted infrared spectra of NaClO, in organic solvents as indicative of contact ion pairing based upon splitting of bands due to degenerate vibrations in Td symmetry and appearance of IR-forbidden features due to the vl(AI) and v2(E) Clod- vibrations.8 Devlin et al. conclude that splitting of the allowed degenerate bands in infrared spectra of matrix-isolated alkali-metal perchlorate systems is caused by contact ion asso(1) Geffeken, W. 2.Phys. Chem., Abz. B 1929, 5, 118. ( 2 ) D'Aprano, A. J. Phys. Chem. 1971, 75, 3290. ( 3 ) Reimamon, P.; Lindman, B. Inorg. Nucl. Chem. Lett. 19778 13,449. (4) Eisenstadt, M.; Friedman, H. L. J . Chem. Phys. 1966, 44, 1407. (5) Templeman, G. J.; Van Geet, A. L. J. Am. Chem. SOC.1972.94.5578. ( 6 ) Greenberg, M. S.; Popov, A. I. J. Solution Chem. 1976, 5 , 653. (7) Berman, H.A.; Stengle, T. R. J . Phys. Chem. 1975, 79, 1001. ( 8 ) (a) Perelygin, I. S.; Yamidanov, S.Y. Russ. J . Phys. Chem. 1978, 52, 741. (b) Perelygin, I. S.; Klimchuk, M. A. Russ. J. Phys. Chem. (Engl. Transl.) 1976,50, 1857. (c) Perelygin, I. S.; Klimchuk, M. A. Russ.J . Phys. Chem. (Engl. Transl.) 1975, 49, 79.
0022-3654/85/2089-1193%01.50/0 0 1985 American Chemical Society
1194 The Journal of Physical Chemistry, Vol. 89, No. 7, 1985
~ i a t i o n . ~Infrared spectra of aqueous solutions of NaC10, may show similar indicative characteristics. While most of the above reports favor Na+C104- contact associations in aqueous solution, Raman spectroscopic studies of various NaC104 solutions by a number of different research groups have notably yielded no evidence of contact ion pair formation.Ibl2 Since Raman spectroscopy is one of the most powerful tools for studying structure and interactions of oxyanions in aqueous solution, any indicative variations in the Raman spectrum of C10, dependent upon contact ion pairing with Na+ must be subtle and difficult to detect. This paper describes our extensive Raman studies of sodium perchlorate under various conditions in aqueous solution and in other solvents in order to define subtle differences in the various measurements that are most probably caused by contact ion pairing. The experiments are designed to detect, structurally characterize, and quantify sodium perchlorate contact ion pairing in solution. Experimental Section Preparation of Solutions. Anhydrous sodium perchlorate crystals from G. Frederick Smith Chemical Co. were dried at 105 OC and used to prepare two series of solutions. A NaC104 water series that contained 10% D 2 0 to provide an internal lock for N M R measurements was prepared from a saturated solution of NaC10, in 10% D20-H20. Aliquots of 3.5, 5.5, and 7.8 mL of this solution were each diluted to 10.0 mL with the 10% D20-H20 to obtain approximately 4, 7, and 11 m NaC104, respectively. Final concentrations are included in Tables I1 and 111. A 1.05 m NaC104 solution was prepared by dissolving 6.061 1 g of anhydrous NaC104 in 10% D20-H20 and diluting to 50 mL. A portion of this solution was diluted tenfold to make a 0.1 m NaC104 solution. A second series of solutions contained 1.OO M perchlorate and various concentrations of NaOH. These solutions were prepared by diluting 2 mL of 5.00 M NaCIO, and an appropriate aliquot of 50%, 19.26 M, NaOH to 10 mL to obtain total sodium concentrations of 3.16,6.48,9.70, 12.8, and 19.7 m. The 5.00 M NaC1O4 solution was prepared by dissolving 15.3057 g of NaC10, crystals in 10% D20-H20 and diluting to 25 mL. A solution with 26.0 m Na+ and 1.38 m C104-was prepared by dissolving 1.2234 g of NaC104 in a mixture containing 9 parts 50% NaOH and 1 part 40% NaOD, and a saturated solution of anhydrous NaC10, in the NaOH-NaOD mixture gave 28.2 m Na+ and 4.28 m C104-. Organic solutions were prepared by saturating reagent grade, untreated solvents with dried sodium perchlorate crystals. Methanol solutions were prepared from methanol dried over a Linde 4A molecular sieve. A dilute solution in methanol was prepared by a twofold dilution of the saturated solution with dry methanol. An additional solution containing sodium methoxide was prepared by reacting methanol with freshly cut sodium metal and then dissolving weighed NaC104 crystals to make 0.909 M NaC104. Analyses. The NaOH concentration of solutions in 50% NaOH was determined by reverse titration of excess standard nitric acid with standard NaOH. Sodium perchlorate concentrations in saturated aqueous solutions were determined by elution through strong cation-exchange resin, Bio-Rad 50W-W8, H+ form, and titration of the eluted acid with standard NaOH. Recoveries of seven standard NaCl aliquots were 98.5% 1.2% relative standard deviation. The resin was regenerated between elutions with 6 M HCI. Sodium methoxide was determined by the reverse titration with nitric acid, and sodium perchlorate in sodium methoxide free methanol was determined by evaporating an aliquot to dryness and weighing the residue. (9) (a) Ritzhaupt, G.; Devlin, J. P. J . Chem. Phys. 1975, 62, 1982. (b) Draeger, J.; Ritzhaupt, G.; Devlin, J. P. Inorg. Chem. 1979, 18, 1808. (10) Jones, M.M.;Jones, E. A.; Harmon, D. F.; Semmes, R. T. J . Am. Chem. SOC.1%1,83, 2038. (11) Glebovskii, D. N.; Latysheva, V. A.; Myund, L. A.; Tarosov, B. P. Mol. Fiz.Biofiz. Vodn. Sist. 1973, 1, 84. (12) Hester, R. E.; Plane, R. A. Inorg. Chem. 1964, 3, 769.
Miller and Macklin Spectroscopy. Raman spectra were taken at 25 f 3 OC with a Spex Industries Ramalog 5 Raman system equipped with 1800 grooves/mm holographic gratings and a photon counting system. The spectral band-pass for measurements in aqueous solution was 6 cm-l, unless otherwise noted, and the source was the 5145-A line of a Coherent Radiation CR-6 argon ion laser. Spectra of solutions of NaC104 in aprotic organic solvents were taken at 0.5 cm-' per increment and with a spectral band-pass of 2 cm-I. Spectra of solutions with low concentration of perchlorate are averages of multiple scans in order to obtain high signal-to-noise levels. Concentration-dependent variations of the integrated molar intensities of u1 and u2 were sought by comparison with those given by a 1.0 M solution of NaC104. Solvent spectral contributions were removed from sample spectra with a computer routine in which stored reference spectra of diatomic salt solutions were subtracted from sample spectra. Solutions were held in a temperature-controlled, water-jacketed cell for taking Raman spectra at nonambient temperatures. Infrared spectra were obtained on a Perkin-Elmer 83 spectrophotometer using Wilks AgCl minicells. Computer Resolution of Perchlorate Raman Bands. Spectral band resolutions were obtained on either a Raytheon or a Nicolet 1 180 computer using in-house resolution programs.I3 The Raman contours given by the vl(Al) stretching vibration and the v2(E) deformation motion of the C104- ion in water do not have features that clearly indicate the individual components of these composite bands. Resolution of these contours was based upon fitting their variations in spectra of solutions having different compositions. The resolutions are supported by analogy with spectra of nonaqueous solutions and crystalline NaCIO,. Each contour was fit by a systematic series of approximations beginning with manual adjustment of band parameters until contours in spectra of several different solutions were matched by changing only the height of the components and ending with computer refinement within the constraints of the established information. The quality of matching was visually judged by a display of the difference between the experimental and synthetic contours on a cathode ray tube. The band shapes were obtained from spectra of dilute solutions that contain primarily the unassociated C104- ion. The vl(Al) band at 932 cm-' in the spectrum of 0.1 m NaC104 and the v2(E) band at 460.5 cm-l in the spectrum of 1.05 m aqueous solutions were both fit by synthetic bands that had 40% Lorentzian and 60% Gaussian character. An additional broad band with similar shape was included at 924 cm-' in the vl(AI)region to accommodate weak intensity on the low-frequency side of the major peak. Synthetic bands with the same shape were used to fill additional intensity in spectra of the most concentrated solutions since a weak symmetry perturbation will not appreciably change the width or shape of the components in a given contour. This is an especially good approximation for the vl(Al) group of bands. The v2(E)contour in the spectrum of 28.2 m Na+-4.28 m C104solution is not fit by a single band with parameters obtained from the 1.05 m solution of NaC104. Attempts to resolve the contour with two bands also led to an unsatisfactory fit. A good fit of the v2(E) contour given by the 28.2 m solution requires two additional bands with similar shape on either side of the component established near 460 cm-I by the 1.05 m solution. The experimental justification of three bands in this contour is given below in the Discussion section. The matching was accomplished by manually varying the position, height, and width of the additional components along with the height of the central component with electromechanical controls. This procedure was repeated on spectra of the 16.9 m NaCIO, and 26.0 m Naf-1.38 m Clodsolutions until a good fit of the v,(E) contour in each spectrum was obtained by changing only the heights of the synthetic component peaks. Finally, the resolutions were refined by computer with band positions and shapes fixed. The component peak positions of the v2(E) envelope were found to be closer together in spectra of solutions containing sodium (13) Morrey, J. R.; Morgan, L. G.J . Chem. Phys. 1969, 51, 67.
Sodium Perchlorate Contact Ion Pair Formation
The Journal of Physical Chemistry, Vol. 89, No. 7, 1985 1195
413
434
490
462
504
W A V E NUMBER (cm l )
Figure 2. Perchlorate u2(E) Raman band as affected by increasing concentration.
M NaCIO,
WAVENUMBER i c m - l )
Figure 1. Variation of the perchlorate A, Raman band over a wide range of solution compositions: 0.1 m NaC104 in HzO; (---) 1 m NaC104, 6.5 m Na+; 1.2 m NaCIO.,, 12.8 m Na'; (-) 2.9 m NaC104, 28.2 m Na'.
/',
(-e)
I
,
3.33MNat
(-e-)
hydroxide than spectra of those that do not. Therefore, in order to resolve the v2 band in spectra of solutions containing intermediate sodium hydroxide concentrations, the positions of the two outer components were shifted linearly with sodium hydroxide concentration between component positions from the resolutions of the v2(E) contour given by the solution containing 28.2 m Na+ to those obtained in the resolution of the v2(E) band for the NaC10, solutions in H 2 0 . The contour given by the vl(Al) stretching vibration also cannot be fit by one band. Moreover, when the low-frequency edge of the v,(Al) envelope in spectra of concentrated solutions was fit by the 932-cm-I component obtained from the spectra of the 0.1 m solution and the high-frequency edge by a similar component, some residual intensity between the two bands must be filled by a third band with shape and width similar to that of the first two. After an iterative fitting procedure between spectra of several solutions to determine the positions and widths, the heights of the three bands could be varied independently to fit the contours given by several other concentrations. The final envelope fitting was again done by the computer with the shape and positions of the component bands fixed. Spectra of concentrated NaC10, solutions clearly include some additional broad, very weak bands on the low-frequency side of the ul(Al) envelope. This intensity was made up by two synthetic bands that were positioned by the computer. The spectra of NaC10, dissolved in organic solvents generally have contours with features that better define the number and positions of the component bands. These spectra could be resolved by the computer program without manual intervention. There is a very strong analogy between these resolutions and those of the measurements in aqueous solution with regard to the number, shapes, relative positions, and intensities of the component bands. Results The Raman spectrum of aqueous sodium perchlorate varies as the concentration is increased. The band at 932.6 cm-' in the Raman spectrum of 0.1 m NaClO,, assigned to the vl(Al) vibration of the tetrahedral perchlorate ion, is increased in frequency by about 8 cm-I and doubled in width in the spectrum of the 1.05 m C104- - 28.2 m Na' solution. There is an accompanying redistribution of intensity in the weak asymmetry on the lowfrequency side of this band such that the maximum of this weak intensity is lowered about 10-15 cm-' (Figure 1). Comparison of the band at 460.5 cm-' in the Raman spectrum of 1.05 m NaC104, assigned to the v2(E) vibration of the perchlorate ion, with the corresponding band in the spectrum of the 4.28 m C104--28.2 m Na+ solution shows less pronounced but distinct differences. The frequency of the intensity maximum of the latter band is decreased 2-3 cm-', its width is slightly narrowed, and
I
456.9
I
I
I
469 3
I
481.5
I
I
493.9
'
WAVENUMBER (cm 1
Figure 3. vz(E) contour of sodium perchlorate in methanol solutions. 906.7
938.5
980
940 cm.'
900 650
Figure 4. Infrared spectrum of a saturated solution of NaC104 in D20.
it is asymmetric on the high-frequency side relative to the former (Figure 2). The above changes appear to be linear between the extremes of sodium and perchlorate ion concentrations. The Raman bands assigned to the v3 and v4(F2)stretching and deformation vibrations, ca. 1100 and 625 cm-I, of the perchlorate ion narrow slightly with increasing concentration, and a very slight asymmetry is detectable in the ~3(F2)band only in the spectrum of a saturated solution of sodium perchlorate in water. Changes in the vj and ~q(F2)bands are too small to be analytically useful. Consequently, no analysis of these features is attempted. We found no other concentration-dependent variations in the Raman spectra of aqueous sodium perchlorate. The integrated molar intensities of the bands do not appear to vary significantly with change in concentration, nor do the depolarization ratios. The ul(Al) and u2(E) contours in spectra of NaC104 dissolved in aprotic solvents have shoulders and partially resolved peaks indicating their composition (see Figure 8E-H). Spectra of methanol solutions are directly analogous to those given by aqueous
1196 The Journal of Physical Chemistry, Vol. 89, No. 7, 1985
Miller and Macklin
TABLE I: Frequencies and Assignments for Resolved Components of Clod-vl(Al) and v2(E) Contours
~
NaC104 form crystalline (anhydrous) crystalline
deformation region, cm-I free associated c104 CI0,A, B2g E
442.4" 481.3 449.5' 472.9
region of symmetric stretching frequencies, cm-' contact-paired C10,
solvent-
separated fundamental pairs A, fundamental
overtone
overtone
885.0 (884.8)b 898.5 (899.0)
965.5 (962.6) 949.7 (945.8)
952.2' 952.8"
934.6 (936.6) 934.6 (937.6) 925.2d
927.7 926.4 934.4
free C104overtone
fundamental AI
908.9, 914.8 (915.0) 909.2, 915.7 (915.8) 912.6 (920.6) 917.6, 925.8 (921.0) 917.6, 925.8 (921.0) 917.6, 925.8 (921.0)
930.3' 930.4 930.9' 932.6" 932.6 932.6
(monohydrate) A, 2 M in DMF' 0.5 M in pyridine 2.93 M in methanol 0.1 M in water 16.86 m in water 1.38 m in 26 m Na',
water
A2
A1
452.4 452.7' 453.7
468.3 457.5' 468.8 457.9 467.5 460.3'
904.6 (904.4) 903.5 (907.4) 904.2 (907.4)
456.9 457.2'
467.5 460.5' 466.6 460.5
913.1 (913.8) 913.1 (914.4)
(935.0)e (933.2)e
941.7 941.7'
934.6 934.6
&y
'Denotes greatest height in respective spectral region. *Parentheses denote 2 times the frequency of corresponding fundamental. 'DMF is N,N-dimethylformamide. dDenotes uncertain assignment. 'Peak not detected. solutions, but the shoulders and asymmetry are more pronounced (Figure 3). The infrared spectrum of a saturated solution of sodium perchlorate in D 2 0 shows a weak band a t -938 cm-' (Figure 4). The intensity of this band relative to that of the IR-allowed band due to the ~q(F2)vibration does not change markedly in spectra of several more dilute solutions, to and including 1 m NaC10,. The frequency of the band is shifted to -933 cm-'in the spectrum of the 1 m solution. Increasing the temperature of concentrated sodium perchlorate solutions shifts the Raman band assigned to the vl(Al) vibration to lower frequency and decreases the asymmetry of the v2(E) band. The width of these bands is anomalously broad in the spectra of some solutions at elevated temperature. The ul(Al) band in the spectrum of saturated NaCIO,, 16.9 m, in water at 45 OC and in the spectra of saturated NaClO, in 50% NaOH, 28.2 m Na+, a t 64 "C is about 20% broader than in the spectra taken at other temperatures. The uZ(E)band in the former spectrum is also slightly broader than it is in the spectra taken at other temperatures. The frequencies along with corresponding assignments for resolved components of the ul(Al) and u2(E) contours are given in Table I.
...... ...@
e*
STRUCTURE I c3v
n
STRUCTURE II
STRUCTURE 111
c3v
c2v
Figure 5. Some possible structures of Na'C104- contact ion pairs
Discussion Concentration-dependent variations in the Raman spectra of oxyanions are commonly interpreted in terms of symmetry perturbations due to contact ion pair f ~ r m a t i o n . ' The ~ number and magnitude of the spectral variations increase with the strength of the interaction. For example, appearance of the Raman-forbidden band due to the u2 deformation vibration and splitting of the degenerate Y, and v4(E) bands in the Raman spectrum of aqueous sodium nitrate indicate destruction of the D3h symmetry of the nitrate ion by clearly manifested contact ion pair association with sodium ions.15 The split u4(E) band is typically resolved and used to quantify the extent of asso~iation.'~J~In highly concentrated N a N 0 3 solutions, a feature due to the vl(Al) stretching vibration of contact associated nitrate is observed along with the band assigned to the unassociated ion. We interpret the analogous but less distinct spectral modifications observed for sodium perchlorate solutions as due to contact ion pair associations that are apparently less strongly manifested than the Na+NO< pairs. (14) Irish, D. E. "In Raman Spectroscopy"; Szymanski,H. A,, Ed.; Plenum Press: New York, 1967; Vol. 1. (1 5 ) Findlay, T. V.;Symons, M.C. R. J . Chem. Soc., Faraday Trans. I , 1976, 11, 820. (16) Chang, T. G.;Irish, D.E.J. Phys. Chem. 1973,77,52; Can. J . Chem. 1973, 51, 118. (17) Lemley, A. T. G.; Plane, R. A. J . Chem. Phys. 1972, 57, 1648.
Assuming that the C104- ion gives a discrete vibrational spectrum for each different solution environment, some details of the structure of the Na+C10; contact associations are available from our interpretation of the Raman spectrum. Association of one or three of the C104- oxygen atoms with Na' ion lowers the symmetry of the ion to C,,,as in Figure 5 , structures I or 11. The u2(E) band of the Td clod- ion remains degenerate in C,, symmetry, and only a shift in frequency from its position in the spectrum of the unassociated ion would be observed. The spectrum resulting from coexisting associated and unassociated C104- ions would then contain two bands in the v2(E) region. Association of a sodium ion to two of the C104-oxygen atoms reduces the symmetry to C,, structure I11 in Figure 5 , and splits the Td u2(E) degeneracy. Again, the magnitude of the separation or frequency shift depends upon the strength of the association. Consequently, the simultaneous existence of Na+ C104- contact ion pairs with C, symmetry and unassociated Clod- ions leads to three bands in the u2(E) region of the Td spectrum. Determination of the number of spectral components in this region and their frequency separation indicates the contact ion pair structure and relative strength of the association. The number of bands required to resolve the Td, u2(E) Raman contour given by aqueous NaClO, can be decided by close scrutiny of the variations in the envelope as a function of increasing Na+C104- concentration and temperature. The asymmetry on the high-frequency side of the band maximum becomes more
The Journal of Physical Chemistry, Vol. 89, No. 7, 1985 1197
Sodium Perchlorate Contact Ion Pair Formation
l
4350
4430
.
#
451 0
,
l
4590
l
l
4670
~
4750
l
l
4830
WAVENUMBER (cm 11
Figure 6. Effect of temperature on the v2(E) band of 16.9 m NaC1O4
pronounced with increasing concentration, while the frequency maximum moves away from the asymmetry (Figures 2 and 3). Normalized, nested measurements of the contour for a concentrated solution taken a t various temperatures (Figure 6 ) show common crossover points on the low-frequency side and near the frequency maximum. Explanation of these observations requires two additional peaks, ofle on either side of the Td,vz(E) feature given by unassociated ClO,-, that increase in intensity with increasing concentration and have smaller bandwidths. The less intense component at higher wavenumbers must be further separated from the maximum than the lower frequency component. The need of at least three components to resolve the Td, v2(E) contour is strong evidence of C, symmetry and bidentate contact association between sodium and perchlorate ions. The indications of C, symmetry and bidentate contact association are directly supported by Raman measurements of NaC10, in organic solvents that show higher concentrations of associated ions and sharper bands that are better resolved than spectra of aqueous solutions and of crystalline NaC10, and NaClO, monohydrate that have C10; in C, symmetry sites.'* The Td,v2(E) contour in spectra of solutions in methanol clearly shaws the concentratiori-dependent changes described above for aqueous solutions (Figure 3). A three-band contour is more clearly evident as well in spectra of solutions in pyridine (Figure 8G),acetonitrile, and N,N-dimethylformamide (Figure 8E). Solutions of NaC10, in tetrahydrofuran (THF) are indicated by Z3NaN M R to contain mostly associated ions.6 The major features in the vZ(E) region of the Raman spectrum of NaC10, In THF are a band at 450 cm-' and a weaker band at 470 cm-' in agreement with C, symmetry of the ion pair.6 Moreover, the intensity ratios of the two bands are not appreciably affected by changes of concentration, thus further supporting the C, symmetry of the associated Na+ C10; contact ions. Two bands with the same relative intensities are also found in this region of the spectrum of crystalline NaC10, that has ClO,- in C, symmetry sited8 (Figure 9). The frequency and intensity pattern of bands in resolved v2(E) contours assigned to the contact ion pair are always the same as that in the spectrum of THF solution6 and the crystalline solids. Moreover, the more intense, lower frequency band is separated about half as far from the v2(E) maximum as the higher frequency partner. We also note that the greatest separation between these two components is in spectra of the crystalline solids. The v2 separation for the various solvents continues in the order aprotic solvents > methanol > water. Interestingly, the v2(E) split is decreased from 39 cm-' in the spectrum of anhydrous crystalline NaC10, to 23 cm-' in the monohydrate crystal spectrum, indicating the strong influence of one water molecule on reducing the strength of the sodium ion contact perturbation. The structural conclusions are in agreement with those of Devlin et al. based upon matrix-isolated spectra of hydrated M+C104+'a and normal-coordinate analysis.9b They conclude that bidentate (18)
Zachariason, W. H.Z.Kristallogr. 1931, 73,
141.
0
10
30
20
CONCENTRATION mNa
+
Figure 7. Concentration dependence of Raman band components attributed to ion-paired perchlorate: (A,V) the 937-cm-' component for solvent-separated ion pairs in NaC104-H20 and NaC104-NaOH-H20 0)components of the v 2 ( E ) band attributed solutions, respectively; (0, to contact ion pairs in NaC104-H20 and NaC104-NaOH-H20 solutions, respectively. Solid symbols denote the 941.7-cm-I component of the vl(Al) band.
association is retained at all hydration levels of contact-paired Na'C10; in the matrix-isolated condition. Assignment of Spectra. Assignment of the corresponding individual components in the v2(E) and v,(A,) envelopes of all the spectra is based upon comparisons of the various measurements and consideration of their similarities and differences. The spectrum of crystalline NaClO,, shown in Figure 9, indicates the effect of lowering the symmetry of C104-to C, by contact with Na+ ions and gives a relatively large perturbation. The v2(E) band is split into a more intense lower energy feature at 442 cm-' and a less intense band a t 481 cm-I. The former is assignable to an A, deformation vibration in the crystal with DZhsymmetry and the latter to a vibration with BZgsymmetry. The vibration corresponding to the vl(Al) stretching motion of the Td clo4-ion has A, symmetry in the crystal. The band assigned to this vibration is 21 cm-' higher in frequency in the crystal spectrum relative to the spectrum of the C10; ion in 0.1 m solution. The two components that maintain a constant intensity ratio in the resolved vz(E) contour in spectra of solutions with various concentrations are by analogy assigned to the corresponding AI and A2 deformation vibrations of C10; ions that have C, symmetry due to contact association with sodium. This assignment is supported and easily followed in spectra of all of the solutions since the narrower, more intense component is always about half as far from the central feature as the broader, less intense band is on the other side. The counterpart in the resolved vl(Al) envelope is assigned to the component at 942 cm-'. The third band, at 938 cm-I, in the vl(Al) group increases in relative insensity to a concentration of about 8-12 m and then decreases a s the concentration is further increased (Figure 8). We believe that this component is best assigned as due to solventseparated ion pairs. The intensity of this third band decreases in spectra of solutions with concentrations that have H 2 0 / N a + mole ratios8
52.9 14.8 8 . 4
3.3
5.1
2.8
2.1 1.9
u)
0 8
5
I z
c
06
442.2
a 0.4 600
400
800
1,000
1,200
WAVENUMBERS Icm-'~
\ \
0.2 1953.2 0
0
5
10
15
CONCENTRATION,
20
25
30
Na+
Figure 10. Fraction, a,of unpaired (free) perchloratevs. concentration: ( O ) , NaClO,-H,O
solutions; ( O ) , NaC104-NaOH-H20 solutions.
in which I,, and I, are the intensities given by unassociated and total C104- ions, respectively. The molal concentration of contact ion pairs, mA, is given by mA = (1 - a)mCIo,-
1
1472.9
1
Now, the concentration quotient, Qc,for the contact ion pair equilibrium in the aqueous sodium perchlorate solutions can be written in terms of (Y and total molal sodium perchlorate concentration, m, as
949.7
600
800
1.000
1.200
Qc
WAVENUMBERS (cm-11
Figure 9. Raman spectra of (A) crystalline NaC104 and (B) NaCl04-H20. The spectral band-pass is 2 cm-'.
concentration of the scattering species, the resolved Raman spectra assigned to associated and unassociated perchlorate ions allow a quantitative approximation of the extent of contact ion pair formation and subsequent calculation of the equilibrium constant and related thermodynamic parameters. The only previously reported thermodynamic information for sodium and perchlorate ion contact association is based on infrared spectroscopic measurements of organic solutions by Perelygin and co-workerssb*cand ion-exchange measurements on acetic acid-water solutions by Rodriguez and Poitrenaud.21 The molar intensities of the vl(Al) and v2(E) envelopes in the Raman s&m of C l o y do not vary with changing concentration and temperature. It is consequently assumed that the molar intensities of resolved components assigned to contact associated and unassociated C10, ions are equal. The integrated intensities of Raman bands due to perchlorate ions in the equilibrium Na+ + C104-
Na+C104-
(1)
can then be used directly to represent concentrations in equilibrium computations. Note that while there are likely a number of contact structures in the more concentrated solutions, the calculations here refer primarily to the direct bidentate association that leads to the strongest spectral perturbation and that is dominant in spectra of all of the solutions. Taking the approach given by Riddell,zz the fraction of unassociated perchlorate ions, a,is defined as CY
= Iu/I,
(2)
(21) Rodriguez, A. R.;Poitrenaud, C . Anal. Chim. Acta 1976.87, 141. (22) Riddell, J. D.; Lockwood, D.J.; Irish, D.E. Can. J. Chem. 1972,50, 2951.
(3)
1-Cr a2m
=-
(4)
The expression for the series of solutions containing sodium iiydroxide must include the molal concentrations of unassociated Na+ and C104- separately and is written
The values given by eq 2 are the integrated areas of the component(s) assigned to nonpaired species as a fraction of the total spectral envelope. These values obtained from the v2(E) band resolutions are plotted in Figure 10. The plot appears to be linear, indicating that Na+C104- contact ion pairing increases linearly with molality. Similarly derived values for the vl(Al) band are plotted in Figure 7 as (1 - a),the fraction of the band assigned to paired perchlorate. Table I1 lists the fractions of perchlorate in the contact-paired state as estimated from the total integrated areas of band components so assigned. The concentration equilibrium quotients given by eq 4 and 5 are plotted in Figure 11. The plot includes points given by smoothed values that are taken from the straight line in Figure 10 and several interpolated concentrations. The resulting quotients are extrapolated to zero concentration to estimate the thermodynamic equilibrium constant, Kk A value of 0.022 m-' is obtained for KA from the zero intercept of curves given by both series of solutions. The uncertainty extremes of the a values were obtained by propagation of the error given by the computer-generated uncertainties in the band areas for each resolution. The uncertainty in KA is estimated from these extremes to be f20%. No previous report of the thermodynamic equilibrium constant for inner-sphere Na+C104- contact association in aqueous solution with which to compare our value could be found. D'Aprano2 has determined a KA value of 0.19 m-l from conductivity measurements. This value is expected to be higher than that obtained from Raman measurements since conductance does not differentiate
Miller and Macklin
1200 The Journal of Physical Chemistry, Vol. 89, No. 7, 1985 TABLE 11: Fractions of Perchiorate in Contact Ion Pairs: Estimates from vl(Al) and q ( E ) Bands Yz( 1 - a)".' Vl(l - a ) a , b solvent solution exptl exptl smoothed Organic 0.227 at 927 cm-' pyridine 0.324 at 934.6 cm-I 0.609 0.631
DMF~
0.157 at 927 cm-l
0.104 at 934.6 cm-I
methanol
0.261
0.414
0.342
0.432
Aqueous 1.05 m NaC104 3.74 m NaC104 6.6 m NaC104 10.8 m NaC104 16.9 m NaC104 3.16 m Na', 1.06 m ClO46.5 m Na', 1.08 m ClO49.7 m Na', 1.12 m C1Oc 12.8 m Na', 1.16 m CIO; 19.7 m Na', 1.28 m C10; 26.0 m Na', 1.38 m CIO; 28.2 m Na', 4.28 m ClO4-
0.051 0.085 0.173 0.236 0.409 0.070 0.110 0.223 0.314 0.506 0.580 0.656
0.037 0.125 0.545 0.122 0.432 0.762 0.744
0.023 0.085 0.149 0.250 0.409 0.071 0.147 0.223 0.296 0.457 0.607 0.657
OLY is the fraction of perchlorate in the "free" or unassociated state plus any solvent-separated species. b ( l - a) represents the fractional area of the vI region bands assigned to the contact ion pair. '(1 - a) represents the area of the resolution excluding the component near 460 cm-I that has been assigned to "free" CIO;. dDMF is N,N-dimethylformamide.
/
CONCENTRATION
Na
TABLE III: Effective Activity Coemcients for NaCIO, in Aqueous Solutions
( Y d 2 = (y*)sT2a-2 m,mol/kg
R-S"
16.9 10.8 6.6 3.74 2.00d 1.05 0.50d 0.10d 0.07d 0.05d 0.02d 0.01d 0.001 0.00
5.8OC 1 .53' 0.928' 0.461 0.406 0.412 0.456 0.604
26.0 19.7 12.8 9.7 6.5 3.16
calcdb 24.6' 2.88' 0.765' 0.506 0.414 0.414 0.455 0.602 0.638 0.671 0.757 0.8 13 1.oo 1 .oo
Ya
R-S" 1.85 0.829 0.478 0.378 0.370 0.393 0.445 0.601
calcdb 7.85 1.56 0.658 0.415 0.377 0.395 0.445 0.601 0.669 0.756 0.814 1.oo 1.oo
9800'~~ 786c*e 44.2'1~ 9.44'3' 3.16' O.86Oe
a Values derived from data in ref 23. Values calculated from Pitzer's equations.24 'Extrapolated values. dInterpolated concentrations. CValuescalculated from Pitzer's equations.zs
This relationship is used to determine K A at various temperatures. Experimental values of stoichiometric activity coefficients, (y+)sT2,for 0.1-6.0 m sodium perchlorate reported by Robinson and Stokesz3as well as values calculated from equations derived by Pitzer et al.24*z5 have been used to calculate Q7. Robinson and Stokesz6point out that the stoichiometric activity coefficients of ions are generally measured assuming full dissociation of the ions and must be modified if the ions are involved in an ion-pairing equilibrium, so that (Y+)ST = (y(yf') (7) The activity coefficients for the NaC104-NaOH solut'ions were estimated from equations developed by Pitzer and Kimzsfor several mixed salt solutions, but not including NaC104-NaOH. Therefore, the appropriate computation parameters were approximated for this mixture by comparing values for salts having common ions with sodium hydroxide and sodium perchlorate. The activity coefficient of the ion pair, ya, was computed by using the Robinson and Stokesz3experimental values for ( y + ) s T z in the relationship
+
RCP8103 1 2 2
e",
Figure 11. K,/y and concentration quotients extrapolated to zero concentration: Qt a, NaC104-H20 series; NaC104-NaOH-H20 series. Solid symbols are experimental points.
between contact and solvent-separated ion pairs and both are included in the paired fraction. Analysis of the vl(A,) contour in spectra of aqueous sodium perchlorates gives separate bands that are attributable to contact and solvent-separated ion pairs; thus, the intensities can be used to obtain an equilibrium constant that includes both contact and solvent-separated ion pairs and one that includes only contact ion pairs. A value of 0.14 m-' is obtained for the former and 0.028 m-l for the latter. These values are in close agreement respectively with that obtained by D'ApranoZ based on conductivity, 0.19 m-I, and the value for contact pairs obtained from our analysis of the vz(E) contour, 0.022 m-l. The small value of K A at 22 OC is in agreement with the weak tendency toward contact ion pairing by sodium and perchlorate ions in aqueous solution. The thermodynamic equilibrium constant can also be estimated as a product of the concentration quotient and the corresponding quotient of activity coefficients
based on eq 6 above. The stoichiometric activity coefficients obtained for both solution series are plotted vs. concentration in Figure 12, and the effective activity coefficients are listed in Table 111. The coefficients for the NaC104-NaOH solution series appear to extrapolate to an intersection of the aqueous NaClO, solution curve at zero-added NaOH concentration, which is 1.OS m NaC10,. Agreement between the experimental and calculated activity coefficients is good for concentrations below 2 m NaC10, but becomes progressively worse as the concentration is increased. The activity coefficients given by Robinson and Stokesz3have been extrapolated to 16.86 m on linear graph paper with a Bruning ship curve for comparison with calculated values based on Pitzer's equationsz that are also meant to be used for concentrations below 6 m. These extensions are indicated by dashed lines in Figure 12. Note that the activity coefficients for the ion pair, ya, are only slightly smaller than the squared stoichiometric activity (23) Robinson, R. A.; Stokes, R. H. "Elecrrolyre Solurionr", 1st ed.; Butterworths: London, 1955; p 477. (24) Pitzer, K. S.; Mayorga, G. J . Phys. Chem. 1973, 77, 2300. (25) Pitzer, K. S.;Kim, J. J. J . Am. Chem. SOC.1974, 96, 5701. (26) Reference 23, p 379
The Journal of Physical Chemistry, Vol. 89, No. 7, 1985 1201
Sodium Perchlorate Contact Ion Pair Formation
TABLE I V Equilibrium Constants as a Function of Temperature and Corresponding Thermodynamic Parameters for NaC104 Association in Aqueous Solution'
Q-,. 16.9 m NaC10, 26.0 m Na+, 1.38 m CIO;
0.9 14az 0.948aS
KA = 275
K
0.031
295
K
0.22 0.22
/ /I
-
coefficients from which they were calculated. The difference increases slightly with increasing concentration. Resolutions of spectra of the most concentrated solutions in each of the two solution series provide the basis for investigation of thermodynamic parameters for the Na+C104- association equilibrium in two different environments. The Q, values obtained from spectra of the 16.86 m NaC104 solution and the NaOHNaC104 solutions containing 26.0 m Na+ measured at temperatures ranging from 2 to 64 OC were multiplied by the appropriate Q, to obtain a KA for the two solutions a t each temperature. Having noted that ya/(y+)sT2is nearly independent of concentration, it is also assumed to be independent of the change in temperature. The Q, varies only as a function of a* with temperature, (eq 8). Assuming further that the heat capacity at constant pressure is invariant in the temperature range studied, the integrated form of the van't Hoff equation is AHo ASo In KA = -(9) RT R
+-
A plot of In K , vs. 1 / T has slope equal to -AHo/R and intercept a t ASo/R. The slopes were determined by a linear least-squares fit of the plot, and ASOIR was obtained as the mean of values calculated at each temperature by using the van't Hoff equation. The resulting values of KA and subsequent AHo and ASo de-
AH,
QTQc
As,
AF (22 "C),
318 K
337 K
kcal/mol
cal/(deg.mol)
kcal/mol
0.18 0.17
0.015 0.015
-1.75 -2.24
-13.5 -15.1
2.23 2.21
association for the two solutions at 22 OC is 2.23 and 2.21
spec'Ja. Note: A recent article2' by Frost et al. describes work on perchlorate ionic interactions in aqueous solutions of alkali perchlorates. Their conclusions were based on time correlation functions and computer band resolutions of only the perchlorate u1(A1)Raman band. The results and assignments derived from their resolutions are quite similar to those which we are reporting for the more intense portion of the u1 band. The concentration quotients reported by Frost et al. are, however, up to 4 times larger than ours. In addition, the assignment of the low-frequency assymetry on the vi band reported by Frost et al. cannot be reconciled with the evidence reported in our paper. Acknowledgment. The contributions of Steve W. Dodd to this work in the form of preparation of most of the aqueous solutions, the taking of many Raman spectra, and writing some helpful computer programs are acknowledged with great appreciation. We thank Dr. J. R. Morrey for instructing A.G.M. in the use of the computer for curve resolutions. This work was prepared for the US. Department of Energy under Contract DE-AC0677RL01030. Registry No. NaC104, 7601-89-0; NaOH, 1310-73-2. (27) Frost, R. L.; James,D. W.; Appleby, R.; Mayes, R. E. J. Phys. Chem. 1982, 86, 3840.
