Howard L. Yeager and Henry Reid
850
From the recorded spectra, the absorbances of the NO2 Q-branches near 791, 807, and 823 cm-l were measured. Plots of the abscrbances as a function of sample gas pressure in both cells were made. Figure 4 shows absorbance plots for the 791-cm-l Q-branch through the 7.5-cm cell and the 39.5-cm cell. Using these plots and similar plots for the other Q-branch absorbances, a pair of pressures p1 and p2 can be determined for any chosen absorbance of a particular Q branch. From these pressures, values of the equilibrium constant were calculated using eq 9. A region of linear dependence of absorbance on pressure is not apparent in these plots because the independent variable is the total sample gas pressure, not the NO2 partial pressure. The absorbance values used to calculate the equilibrium constant were chosen to be sufficiently small to assure that we were well within the pressure limits defined by the validity of the Beer-Lambert law of both cells. Table I shows the results of these calculations for the three NO2 Q branches whith were studied. The average of the calculated equilibrium constants is 0.140 atm a t 296 f 1 K and is in good agreement with values reported previously.
V. Conclusions The results in Table I show that the two cell technique provides a reasonable method for the determination of the equilibrium constant for the N02-Nz04 system. Using the average value of the equilibrium constant determined by this technique, the partial pressure of NO2 can be evaluated. Plotting the absorbance of each Q branch vs. the product p ~ o &for both cells shows a linear dependence. The linear region extends well beyond the largest values of
absorbance used in Table I1 to evaluate Keq.This indicates that the data were recorded within the limits of the validity of the Beer-Lambert law. Figure 5 shows the dependence of the 791 Q-branch absorbance on the product PNO&. Error treatment suggests that a theoretical error of about 15%is expected with this technique. This error is based on an estimate of a 1% error in measuring the pressure. Thus, by this technique, we estimate the value of the equilibrium constant for the reactions N204 2N02 at room temperature to be 0.14 f 0.02 atm. Table I1 shows a comparison of this result with previously reported values. The value of Harris and Churney5 is their data taken closest to 296 K. This two cell technique provides a reasonably accurate method for determining the equilibrium constant of a two component system. A variation of this method would be to use a single multiple-traversal cell and record spectra of various concentrations of sample at several different path lengths. These data could be used with eq 9 to make the equilibrium determination.
Acknowledgment. The authors wish to thank W. M. Uselman for his discussion on this project. This work was supported by EPA Grant No. 803075. References and Notes (1) J-C. Fontanella, A. Girard, L. Gramont, and N . Louisnard, Appl. Opt., 14, 825 (1975). (2) S. Hurlock, K. Narahari Rao, L. A. Weller, and P. K. L. Yin, J. Mol. Spectrosc., 48, 372 (1973). (3) M. G. Dunn, K. Wark, Jr., and J. T. Agnew, J. Chem. Phys., 3, 2445 (1962). (4) A. J. Vosper, J. Chem. SOC.A, 625 (1970). (5) L. Harris and K. L. Churney, J. Chem. Phys., 47, 1703 (1967). (6)F . H. Verhoek and F . Daniels, J. Am. Chem. Soc., 55, 1250 (1931).
Spectroscopic Studies of Ionic Association in Propylene Carbonate Howard L. Yeager* and Henry Reid Department of Chemistry, The University of Calgary, C a g r y , Alberta, Canada T2N IN4 (Received July 13, 1975; Revised Manuscript Received January 13, 1976) Publication costs assisted by the National Research Council of Canada
Far-infrared and 19FNMR spectroscopic techniques have been used to study lithium, sodium, potassium, and rubidium trifluoroacetates in propylene carbonate solutions. NMR results indicate that simple ion pairing predominates for the potassium and rubidium salts but that ion aggregation occurs for the lithium and sodium salts. The far-infrared cation solvation bands for the alkali metal trifluoroacetates are shifted from the corresponding nitrate and perchlorate salt band positions, the lithium ion band to lower frequency, and the other bands to higher frequencies. Plots of integrated absorbance vs. concentration for the lithium and sodium salts are linear. Results of the two techniques are compared, and the utility of the far-infrared method as a tool for studying ion association is discussed.
Introduction
A number of investigators have used far-infrared spectroscopy to study alkali metal ion solvation in a variety of s~lvents.l-~ The main features of this approach have been discussed by Edgell.6 Alkali metal ions in solution exhibit The Journal of Physical Chemistry, Vol. 80, No. 8, 1976
broad absorption bands in the far-infrared region corresponding to their vibration with adjacent solution species. Band positions depend upon the alkali metal ion and solvent used, but generally do not depend on the anion of the salt. However, for solvents which have poor donor properties or low dielectric constants, the band positions may also
85 1
Spectroscopic Studies of Ionic Association in Propylene Carbonate
show anion dependence. This behavior is explained by assuming that the anion penetrates into the inner solvation shell of the cation. In these cases, a general trend of decreasing band frequency with decreasing anion size (and presumably increasing association) for a given alkali metal ion is found. The variation of absorbance with concentration of these bands has also been measured in several solvents. Linear dependence is found in all cases, even those in which ion pairing is suggested, as for NaCo(C0)r in tetrahydrofuran.lb Edge11 concludes from the results of infrared and Raman studies6g7of this system that the salt exists as both contact and solvent-separated ion pairs in THF. Both of these species would exhibit far-infrared cation vibration bands, presumably of similar frequency. Since the relative amounts of the two types of ion pairs do not vary with concentration, the linear absorbance-concentration dependence is expected. The reason for band shifts to lower frequencies with increasing ion association is not well understood, however. Also, relative band positions for the same salts in different solvents are not always identical. For example, absorption frequencies for lithium salts in THFlb decrease in the order BPh4- > NOS- > C1- > Br- > I- while in acetonezc the order is BPh4- > NOS- > I- > Br- > C1-. We sought to explore these problems by studying a series of salts with widely differing extents of ion association, the alkali metal trifluoroacetates in the solvent propylene carbonate. Propylene carbonate (PC) has a high dielectric constant (64.92 at 25 oC)8but only moderate donor ability. Electrolytic conductance studies have shown that alkali metal perchlorates in dilute solution are unassociated while the corresponding trifluoroacetates all show ion ~ a i r i n g . ~AssoJ~ ciation constants for the trifluoroacetate salts in PC are: Li+, 1900; Na+, 190; K+, 42; Rb+, 26; and Cs+, 18 M-l.l0 Evidence of extensive ion aggregation for the lithium salt, even in dilute solution, was found. The possibility of slight ion aggregation for the sodium salt was also suspected. Thus, association constants vary by two orders of magnitude for this series of salts, providing a good opportunity for studying the influence of ion pairing and ion aggregation on the far-infrared cation solvation bands. Therefore the spectra of these salts in PC were measured and are compared to the results of similar measurements by Popov . and coworkers on the alkali metal perchlorates and nitrates in PC.2g In addition, the 19F NMR spectra of PC solutions of the trifluoroacetates were measured as a function of concentration in order to provide a complimentary spectroscopic probe of these solutions.
TABLE I: Frequencies of Cation Solvation Bands in Propylene Carbonate (cm-l)a
Cations ~~
Anions
Li+
c104-
398f4 (397f 4) (401f 6 )
Na+
K+
Rb+
Cs+
183f4 b b b (186f 4) Nos(188f4) (144f (115f (112f 6) 6) 6) CF3CO2367 f 3 196-+4 159f 118f b 6 8 Insufficient a The numbers in parentheses are those of ref 2g.
solubility.
150
400
350
300
cm-I Figure 1. Cation solvation bands in propylene carbonate: (A) LiC104: (B) LiCFSCO2.
4.0
3.0 W 0
z a
p
:m:
20
Q
Experimental Section
The preparation, purification, and analysis of the alkali metal trifluoroacetates have been described previously.1° The purification and analysis of propylene carbonate have also been d e ~ c r i b e d All . ~ solution preparation and transfer operations were performed in a glovebox under Nz atmosphere. Far-infrared spectra were recorded using a Digilab FTS16 Fourier transform spectrometer. Spectral measurements in the 600-200 and 450-80-cm-l ranges were made with 3 and 6-w mylar beam splitters, respectively. Standard demountable cells (Barnes Engineering) of 0.1-mm pathlength and polyethylene windows were used. With the instrument being operated in the single beam mode, a spectrum of the pure solvent was first recorded and stored in the computer and then subtracted from the spectrum of
1.c
0
CONCENTRATION (MI
Figure 2. Integrated absorbance vs. concentration of cation solvation bonds in propylene carbonate: (0)LiCF3C02;(A) NaCF3C02.
the solution. I9F NMR spectra were recorded using a modified Varian HA-100 spectrometer, with trifluoroacetic acid (Eastman Kodak) as external reference. The Journal of Physical Chemistry, Vol. 80, No. 8, 1976
Howard L. Yeager and Henry Reid
852
t
'0
1.0
2.0
Xf
220
-
0
01
0.2 0.3 0.4 CONCENTRATION ( M 1
C
Figure 3. I9F chemical shift vs. concentration for alkali metal trifluoroacetates in propylene carbonate: (0)LiCF3C02; (A)NaCF3C02; (0)KCF3C02; (V) RbCF3C02.
The Journal of Physical Chemistry, Vol. 80, No. 8, 1976
4.0
Figure 4. I9F NMR plots of eq 2 for lithium and rubidium trifluoroacetate in propylene carbonate. TABLE 11: Limiting 19FNMR Chemical Shifts of Trifluoroacetate Ion in Propylene Carbonate (Hz)"
Salt
6f
6,
LiCF3C02 397 246 388 242 NaCF3C02 KCF3C02 368 f 3 242 f 10 RbCF3C02 367 f 3 253 f 8 a Values are referenced to external trifluoroacetic acid. concentration dependences of the shifts, the data were analyzed using the equation
Results
The frequencies of solvation bands in PC for the alkali metal trifluoroacetates and lithium and sodium perchlorate are shown in Table I. Cesium trifluoroacetate had insufficient solubility for an accurate determination of its band position. Values in parentheses are those of Popov and coworkers.2g The nitrate and perchlorate salts are listed to show the alkali metal ion band positions for salts where contact ion pairing is expected to be minimal. The lithium trifluoroacetate peak shifts to lower frequency, the sodium and potassium bands shift to higher frequencies, and the rubidium band remains essentially unchanged in position from the corresponding nitrate and perchlorate bands. The trifluoroacetate band contours are broad and similar to those observed in other solvents, with the exception of the lithium salt. This band is noticeably narrower, as shown in Figure 1, in comparison to the lithium perchlorate band. Plots of integrated absorbance vs. concentration for lithium and sodium trifluoroacetate in PC are shown in Figure 2. The dependence is linear within experimental error in each case. A sharp band which can be assigned to a -CCFs out-ofplane rockll was observed in all spectra. The band position for lithium, sodium, potassium, and rubidium trifluoroacetate solutions was 279 f 2, 272 f 2, 267 f 2, and 266 f 2 cm-l, respectively. The results of I9F NMR concentration studies for these salts in PC are shown in Figure 3. Pronounced deshielding of fluorine in the trifluoroacetate ion with increasing concentration is observed for all salts. The relative magnitudes of shift are in the same order as the respective ion association constants, with the exception of lithium trifluoroacetate a t high concentrations. In order to test the ability of the ion association constants to quantitatively describe the
3.0
4
sobsd
= Xf6f -k
Xphp
(1)
where the observed chemical shift, &,bsd, is related to the chemical shifts of free and ion-paired trifluoroacetate ions, 6f and 6,, and the respective fractions of total trifluoroacetate present as each species, xf and x,. This equation assumes rapid exchange between the two ion environments compared to the NMR time scale and neglects the presence of ionic aggregates. Eq 1may be rearranged to aobsd -- -6fXf XP
+ 6,
(2)
XP
so that a plot of 6obsd/Xp vs. xf/xp yields 6f and 6, as the slope and intercept, respectively. The fractions were calculated using the ion association constants determined in ref 10; activity corrections were applied. The resulting plots for the lithium and rubidium salts are shown in Figure 4. Both the potassium and rubidium plots were linear throughout the concentration range studied, but the lithium and to a lesser extent the sodium plots showed curvature at higher concentrations. These deviations are probably due to ion aggregation and cast doubt on using eq 2 for the lithium and sodium salt data. Least-squares results for potassium and rubidium trifluoroacetate along with standard deviations for each parameter are listed in Table 11. The straight line portions of the lithium and sodium trifluoroacetate plots were used to graphically obtain values of 6f and 6,. These values are also listed in Table I1 for comparison. Discussion
In order to interpret the results of the far-infrared study, the prominent solution species for each salt must be identified. Dilute solution conductance measurementsl0 support
Spectroscopic Studies of tonic Association in Propylene Carbonate the I9F NMR results for potassium and rubidium trifluoroacetates, indicating that free ions and ion pairs are the only species present at concentrations up to 0.5 M. Extensive ion aggregation is indicated by both techniques for lithium trifluoroacetate. The sodium trifluoroacetate results suggest that although ion pairs predominate at low concentration, ion aggregation becomes important in the concentration region in which far-infrared measurements have been made. The deshielding of fluorine in trifluoroacetate a t high concentration is greater for sodium than for the lithium salt, perhaps indicating the relative extents of ion aggregation. The trifluoroacetate ion probably exists in large ion clusters with lithium ion but only in smaller clusters with sodium ion. The net deshielding of fluorine may be less pronounced in larger ionic aggregates, yielding the observed concentration dependence shown in Figure 3. Nevertheless, both lithium and sodium trifluoroacetate show evidence of ion aggregation at concentrations above 0.1 M. The 6f values obtained for each salt would be expected to be equal if eq 1 properly described each system. Also, 6 , values should shift to lower field with increasing charge density of alkali metal ion. Although these expectations are consistent with the potassium and rubidium results, there is no such consistency with the lithium and sodium values, again suggesting additional solution species for these systems. The far-infrared results also indicate association for each of the salts in PC. Edgell has concluded that when alkali metal ion solvation bands shift with the anion used, contact ion pairs are present in solution. (Solvent-separated ion pairs are expected to show the same absorption band as a free solvated cation.)6 Lithium, sodium, and potassium trifluoroacetate all show such shifts, reflecting anion-cation contact. However, neither the magnitudes nor the directions of the shifts can be simply related to the extent of association. The highly aggregated lithium trifluoroacetate shifts to lower frequency while the aggregated sodium salt, along with potassium trifluoroacetate, shift to higher frequency. The uncertainties in these band positions are due to their broadness, but we believe the shifts are real and reflect the cation environment in the associated species. When anion-induced shifts have been found for these alkali metal solvation bands in other solvents, they are to lower frequency and become larger with increasing anion charge density. Therefore the contact ion pair species is identified with a low-frequency component of the band. This may be due to an effective increase in the mass of the vibrating species, as would occur if the anion partially vibrates (or oscillates)12 in phase with the cation. Since a contact pair has no net charge, the force constant in this interaction would be predominately due to dipole-dipole rather than ion-dipole forces. Both of these factors would generate a low-frequency component to the cation solvation band. The shift to higher frequency for sodium and potassium trifluoroacetate in PC may be due to a different behavior of the anion in the associated species. The metal
853
ion would be expected to be in close contact with the carboxylate function of the trifluoroacetate ion. This carboxylate grouping may be able to induce a localized ion-ion vibration component to the band which is not present with anions of more spherically symmetrical charge density. This would give rise to an overall band shift to higher frequency. Lithium trifluoroacetate's shift to lower frequency contradicts this interpretation. However, lithium ion exists in large ion aggregates which may be quite different in their influence on the cation vibration than are ion pairs or even small aggregates. The narrower band contour of the lithium trifluoroacetate absorbance suggests that there is not as wide a range of cation environments in these ion aggregates as with the other salts studied. The absorbance-concentration plots of Figure 2 were performed in order to test the ability of this approach to reveal different solution species, using the most associated salts. The linearity suggests that all cation environments have about the same molar absorptivity, and that such plots are not an effective method for determining the number or-character of cation environments in solution. It appears that shifts in far-infrared cation solvation bands are a function not only of anion penetration into the cation solvation shell but also of the structure and charge distribution in the ion pair or ion aggregate. Studies with additional anions should help to identify the specific factors which determine these shifts.
Acknowledgment. The authors wish to thank Dr. R. Kydd for valuable advice and assistance in performing the far-infrared measurements. Financial assistance by the National Research Council of Canada and the University of Calgary is gratefully acknowledged. References and Notes (1) (a) W. F. Edgell, A. T. Watts, J. Lyford, IV, and W. Risen, Jr., J. Am. Chem. Soc., 88, 1815 (1966);(b) W. F. Edgell, J. Lyford. IV, R. Wright, W. Risen, Jr., and A. Watts, hid., 92, 2240 (1970). (2) (a) B. W. Maxey and A. I. Popov, J. Am. Chem. Soc., 89, 2230 (1967); 91,20 (1969);(b) J. L. Wuepper and A. I. Popov, ibid., 91, 4352 (1969); 92, 1493 (1970);(c) M. K. Wong, W. J. McKinney, and A. I. Popov, J. fhys. Chem., 75, 56 (1971);(d) W. J. McKinney and A. I. Popov, ibid., 74, 535 (1970);(e) M. K. Wong and A. I. Popov. J. lnorg. Nucl. Chem., 33, 1203 (1971);(f) P. R. Handy and A. I. Popov, Spectrochirn. Acta, Sect. A, 28, 1545 (1972);(g) M. S. Greenberg, 0.M. Weid, and A. I. Popov, ibid., 29, 1927 (1973). (3)(a) A. T. Tsatsas and W. M. Risen, Jr., J. Am. Chem. Soc., 92, 1789 (1970);(b) A. T. Tsatsas, R. W. Stearns, and W. M. Risen, Jr., ibid., 94,
5247 (1972). (4) T. L. Buxton and J. A. Caruso, J. fhys. Chem., 77, 1882 (1973). (5) (a) A. Regis and J. Corset, J. Chim. fhys. fhysiochem. Bioh, 69, 1508 (1972);(b) Can. J. Chern., 51,3577 (1973). (6)W. F. Edgell in "Ions and Ion Pairs in Organic Reactions", Vol. 1, M. Szwarc, Ed., Wiley, New York, N.Y., 1972,Chapter 4. (7)(a) W. F. Edgell, M. T. Yang, and N. Koizumi, J. Am. Chem. Soc., 87, 2563 (1965);(b) W. F. Edgell, J. Lyford, IV, A. Barbetta, and C. I. Jose, ibid., 93, 6403 (1971);(c) W. F. Edgell and J. Lyford, IV, ibid., 93, 6407
(1971). (8)R. Payne and I. E. Theodorou, J. fhys. Chem., 76,2892(1972). (9) M. L. Jansen and H. L. Yeager, J. fhys. Chem., 77,3089(1973). 10) M. L. Jansen and H. L. Yeager, J. fhys. Chem., 78, 1380 (1974). 11) M. J. Baillie. D. H. Brown, K. C. Moss, and 0.W. A. Sharp, J. Chem. Soc. A, 3 1 10 ( 1968). 12) W. F. Edgell and A. Barbetta, J. Am. Chem. Soc., 96,415 (1974).
The Journal of Physical Chemistry, Vol. 80,No. 8, 1976
