IONIC INTERACTIONS
IN
4573
SOLUTION
problems in the electrostatic analysis of ionic interactions. However, a diminution of dielectric constant in the immediate vicinity of an ion seems physically reasonable for hydrogen-bonding solvents and a qualitative estimate of its effect on the association constant is provided with the naive model. Equation 9, which applies within q, has been used with an effective dielectric constant of 10 t o estimate values of KA as a function of a. The calculated values agree with the range of K A observed as given in Tabje IV when the reasonable a values between 8 and 14 A are employed. The same pattern is observed with the other alcohols. A reasonable value of Eeff can be found to reproduce the observed range of association constant. However, this explanation does not account for the dependence of K A upon the nature of the anion, whereas in the first
explanation this can be attributed to a specific solvention interaction. Two explanations based on the behavior of solvent molecules in the immediate vicinity of the ion pairs have thus been offered for the high association of tetraalkylammonium salts in alcohols, which cannot be explained by continuum models. Relaxation measurements and studies involving solvents with different hydrogenbonding characteristics are in progress. These should help elucidate the relative importance of multistep association processes and diminished dielectric constant on ionic association. Acknowledgment. We wish to thank Professor J, C. Justice for computing the results given in Table IV and for many helpful discussions. This work was supported by Contract No. 14-01-001-1281with the Office of Saline Water, U. 8. Department of the Interior.
Ionic Interactions in Solution. 11. Infrared Studies by R. P. Taylor' and I. D. Kuntz, Jr.* Frick Chemical Laboratory, Princeton Uniuersity, Princeton, N e w Jerseu
08540
(Received J u n e 16, 1970)
Hydrogen bonding between phenol and a number of anions is studied by infrared spectroscopy. Small anions have multiple solvation equilibria, and stepwise association constants are determined by measuring solvation numbers (phenolation numbers) as a function of anion and phenol concentration. Concomitant nmr studies indicate that low concentrations of phenol markedly influence ion association equilibria in low dielectric solvents. I n these solvents the evidence suggests that solvation of anions by phenol changes contact to solventseparated ion aggregates. The phenol-anion association constants appear to be independent of the type and degree of ion association.
Introduction A number of workers have shown that strong hydrogen bonds exist between alcohols and halide anions in solution.2 a , b Equilibrium constants for the formation of 1: 1 alcohol-halide anion complexes have been measured in CCl, solution.2b We have shown that this hydrogen bonding interaction can strongly influence ion association for halide salts in low dielectric solvents. In the present work we measure anion solvation numbers by investigating the effects of a variety of salts on the OH stretching frequency of phenol. We determine the effect of phenol on the ion association equilibrium by correlating these results with concomitant nmr studies.
Experimental Section Infrared spectra were recorded on a Beckman IR-12 spectrophotometer operating in the double beam ab-
sorption mode. Barnes liquid cells with potassium bromide windows and 0.5-mm Teflon spacers were used. Measured absorbances were usually between 0.20 and 0.80 absorbance unit and were in general reproducible t o hO.01 absorbance unit. We estimate the ambient temperature for the ir experiment as about 40". Nmr spectra were recorded on a Varian A-60-A spectrometer, and chemical shifts (relative to internal TATS, 1% v/v), accurate t o h 1 He, were measured by the usual methods. Ambient probe temperature was 40". Methylene chloride was distilled from P206 onto
* T o whom correspondence should be addressed. (1) NSF Predoctoral Fellow, 1969-1970. (2) (a) A. Allerhand and P. von R. Schleyer, J . A m e r . Chem. SOC., 85, 1223 (1963); (b) R. D. Green, J. S.Martin, TT'. B. McG. Cassie, and J. B. Hyne, C a n . J . Chem., 47, 1639 (1969). (3) R. P. Taylor and I. D. Kuntz, Jr., J . A m e r . Chem. Soc., 9 2 , 4813 (1970).
T h e Journal of Physical Chemistry, Vol. 74, No. 86, 1070
R. P. TAYLOR AND I. D. KUNTZ, JR.
4574 molecular sieves. Control experiments indicated that the traces of water (-0.1% by volume) which this solvent absorbs on exposure to air had no effect on the experimental results. Carbon tetrachloride (spectroscopic grade) was dried over PZOSand filtered before use. Nitromethane (spectroscopic grade) was used without further purification. Phenol was distilled under vacuum into a separatory funnel with a Teflon stopcock and stored in a desi~cator.~Solutions of known phenol Concentration were prepared gravimetrically by heating the separatory funnel and allowing the phenol to drip out into preweighed SO-ml volumetric flasks which were reweighed and filled t o mark with so1ventO4 Such stock solutions were then used to prepare solutions of the salts. The salts were purchased or prepared by standard techniques, recrystallized, and dried for a few hours at 80" under reduced pressure before they were used. Experimental Procedure. Mathematical Preliminaries. If we assume the existence of a number of mononuclear complexes between phenol molecules and a given anion, then the following equations hold.6
2.752.50
-
CI'
2.25-
Br-
2.00-
I .75
-
1.50-
I'
1.25-
Pic-
Ki
PhOH
+ X- _r (PhOH. . . X-) K2
PhOH
+ (PhOH. . ,X-) )r ((PhOH),. . .X-)
where (PT is the total concentration of phenol in solution, QF is the concentration of free phenol, and XT- is the formal anion concentration. The equations can be rearranged to give (for the case of n = 3)
+
+
a = - (PF[Kl 2KlK2QF 3K1KZK3'PF2] (3) 1 KIPF KXZQF' KIKZKS(OF'
+
+
The observed solvation number a should depend upon the stepwise association constants and the concentr at'ion of free phenol. QF is the only independent variable, as seen in eq 3. Plots of a vs. (OFmust superimpose for all values of XT- and (PT for each system studied. Results and Discussion Ir. The absorbance of the free OH peak of phenol (at 3585 em-l) in methylene chloride follows Beer's law behavior up to moderate phenol concentrations (-0.1 M ) . When a variety of salts are added to such solutions, the free phenol OH peak intensity decreases and a broad intense hydrogen bonded peak develops at lower frequency. (OF is measured directly from the ir experiment from the height of the free peak, and XT- and QT are known as they are simply the formal concentrations The Journal of Physical Chemistry,Vol. 74,No.$6,1070
6
(1)
The K,'s are the appropriate stepwise association constants. We define the anion's solvation number % (in this case phenolation number) as
+
4
2
8
IO
I
I
12
14
+T/XT
Figure 1. Average value plots, n us. phenol concentration/ salt concentration ((DT/XT-), for the interaction of phenol with the anions of a number of methyltriphenylphosphonium salts. The salt concentrations are varied, Ihe concentration of phenol is held fixed [0.118 M i 0.001 M I : I, C1-; 1, I-; I, Br-; U, Pic- (Picrate; 2,4,6-trinitrophenolate). The lines drawn through the experimental points were calculated based on the following parameters which were obtained from analysis of the data points for the methyltriphenylphosphonium salts [Other phenol concentrations were used, see Figure 21 : C1-, K1 = 400; K z = 26; K 3 = 26; Br-, K1 = 112; Kz = 19, Ka = 7 ; I-, K1 = 29; K z = 8; K 3 = 0; Pic-, K1 = 18; Kz = 5 ; K3 = 0.
of anion and phenol. Thus, a can be determined by eq 2. Plots of a os. (PTIXT-(Figure 1) for the interaction of halide and picrate anions with phenol in methylene chloride clearly indicate that there exist multiple solvation equilibria. As predicted in eq 3, a depends upon pf (see Figure 2). Stepwise association constants were calculated by fitting the data to eq 4 (see Table I). (PF
=
(PT
-
+
+ +
[XT-] [KlQF 2K1K2(pF2 3K1K2K3(PF3] (4) 1 Kl(PF f K1K'2(pF2 K1K2K3(oF3
+
The uncertainty in
clearly depends upon XT- and
QT
(4) L. Joris, Ph.D. Thesis, Princeton University, 1967
( 5 ) F. J. C. Rossotti and H. Rossotti, "The Determination of Stability Constants," McGraw-Hill Book Co., Ino., New York, N . y., 1961.
4575
IONIC INTERACTIONS IN SOLUTION Table I 2 50k
,--Solvent: K1 (l./mol)
Aniona 2.00L
c1Br-
IPic+ 1.25r
Anion
Solvent
Br-c
Carbon tetrachloride Methylene chloride Nitromethane
/
IO0
Br-a
D
75
50
Br-d
ii ,
01
02
03
OR
OS +f
06
07
OD
09
I
IO
methylene chlorideKz K8 (l,/xnol) (IJmoI)
4 0 0 k 120 1OOf30 30 k 9 20 i 6
25 f 10 20k 8 10 & 4 5 k 2
25 k 10 7323 0 0
1300 =t600
150 f 50
30 f 10
100i30
20i 8
7 k 3
30 k 10
3 f 2
0
a Methyltripheiiylphosphonium salt was used. * Pic-: Picrate anion (2,4,6-trinitrophenolate). c Tetrabutylammonium salt was used. Lower phenol concentrations were used (VF was always less than 0.02 M ) to minimize effects of phenol dimerization. d Tetrabutylammonium salt was used.
!m/l)
Figure 2 . n us. concentration of free phenol (vf)for the phenol-anion interactions. The lines drawn through the experimental points were calculated based on the K , values of Figure 1. Some of the data points of Figure 1 were omitted for clarity. C1- points: I,taken from Figure 1; 6, cation is CH3PfPh3 and phenol concentration = 0.1849 M ; cation is CH3AsfPh3 and phenol concentration = 0.0513 M ; A, cation is (C2H;)dN + and phenol concentration = 0.0873 144; V, cation is CHaP+Ph3 and phenol concentration = 0.0513 M ; 0 , cation is (C2H3)3N+Hand phenol concentration = 0.0873 M; Brpoints: I, taken from Figure 1; 8 , cation is CHIP+Pha and phenol concentration = 0.1849 M ; 9,cation is (n-CdH$)rN+ and phenol concentration = 0.118 M;Al cation is CHaPfPh3 and phenol concentration = 0.0513 M;W,cation is (CIH~)~I$+ and phenol concentration = 0.0873 M . I- points: a, taken from Figure 1; @, cation is CHsP+Ph3 and phenol concentration = 0.1849 M ; 0,cation is CHSP+Pha and phenol concentration = 0.0513 M . Pic- points: 0, taken from Figure 1 ) 0, cation is CHaAsfPhS and phenol concentration = 0.1849 M ; 0,cation is CHaP+Pha and phenol concentration = 0.1849 M ; A, cation is CHSPfPh3 and phenol concentration = 0.0513 M ; V, cation is CHaAstPh3 and phenol concentration = 0.0513 M .
but the experimental uncertainty in (PFis constant, and eq 4 was used to give equal weight to all data.6 Excellent fits were obtained; the average deviation between calculated and observed values of (PF was less than 0.002 M . We have also measured such multiple solvation equilibria in other solvents (Table I). For a variety of quaternary onium salts, differences in cation effects are small (Figure 2). Triethylammonium hydrochloride is clearly a special case as it falls far below the line for the other chloride salts (Figure 2). We believe that in this case hydrogen bonding between the cation and anion substantially reduces the phenolchloride interaction. A second possibility is that phenol acts as a base toward the cation.' Further ir studies could resolve this question. The relative magnitudes of the Kl's shalt. the expected dependence on anion charge densityS8 The fact that
the association constants for formation of the 2 : 1 and 3 : 1 complexes are substantially smaller t h m for the 1: 1 complexes suggests that there must be considerable distortion of the electron density of the anions on formation of the l : l hydrogen bonded complex. We emphasize that the K,'s are not absolute, but relative. Other equilibria may be important. Nitromethane and methylene chloride are certainly not inert; they may interact with the anions and can act as weak bases toward phenol. For example, we determined the equilibrium constant for formation of the hydrogen bond between phenol and nitromethane in carbon tetrachloride to be about 2 l./mol. In addition, the cations may compete with the phenol to achieve close proximity t o the anions; that is, the observed K,'s may be influenced by the effects of ion association. However, we believe this latter effect is unimportant (see below). Nmr. The a-methyl nmr frequencies of the methyltriphenylphosphonium salts dissolved in methylene chloride are nearly insensitive to salt concentration (Figure 3). However, in the presence of low concentrations of phenol the chemical shifts show marked salt concentration dependence (Figure 3). I n addition, for fixed salt concentrations, addition of small amounts of phenol significantly alters the cation chemical shifts (Table 11). These effects are more pronounced at lower temperature (Table 11). We offer the following interpretation of these nmr results. There should be extensive ion association in a low dielectric solvent such as methylene cfiloride. lo (6) W.F. Wentworth, J . Chem. Ed&., 42, 96 (1965). (7) H.B. Flora and W.12. Gilkerson, J . Amer. Chem. S o c , 92, 3273 (1970). (8) R. D. Green and J. S. Martin, ibid.,90, 3659 (1968). (9) J. T.Denison and J. B. Ramsey, ibid., 77, 2615 (1955). (10) R. M. Fuoss, ibid., 80, 5069 (1958). The Journal of Physical Chemistru, Vol. 74, N o . 26, 1970
R. P. TAYLOR AND I. D. KUNTZ, JR.
4576
Pic-,l+OH1=0.0 m/l 175
m/l
Cl;[+OH1=0.0
I95 I I
Table I1 : Effect of Phenol on the a-Methyl Proton Magnetic Resonance Frequencies of Some Methyltripheiiylphosphonium Salts in Methylene Chloriden
T Salt
CHsP +PhsClCHIP ‘PhJ CHIP+Ph~l’ic-
196.8 185.6 173.8
CHIP fPh3ClCHIP +Phd CHIP +Ph~l’ica
= 0 . 2 6 M-Av
167.4 170.9 162.9
29.4 14.6 10.9
-44O
=
[PhOHl = 0.0 M Salt
r-[PhOH] -V
--Y
T
+
= 40’
[PhOH] = 0.0M
--Y
c--[PhOH]
= 0.25
--Y
193.1 185 0 177.2 I
The fact that relatively low concentrations of phenol can significantly affect the cation chemical shifts suggests that the hydrogen bonding interaction between phenol and the anions must be at least competitive with the electrostatic effects which favor formation of contact species in methylene chloride. 9,10 More importantly, we shall show below that the observed trend of the K,’s in different solvents indicates that the phenol-anion equilibria are in fact independent of the degree of ion association. Intuitively we would expect the effects of ion association would be greatest in carbon tetrachloride (dielectric constant = 2.2), reduced somewhat in methylene chloride (dielectric constant = 8), and almost negligible in nitromethane (dielectric constant = 34.2).l 2 Continuum theoryg,l0would predict that the ion association equilibrium constants in carbon tetrachloride and nitromethane would differ by more than 15 orders of magnitude. If we assume that anions paired with cations have a weaker hydrogen bonding interaction with phenol than do “free” anions, then the K,’s should be smallest in carbon tetrachloride and largest in nitromethane. In fact, we observe just the opposite trend in the K,’s (Table I). Part of the decrease in the K,’s is due to hydrogen bonding between phenol and the two higher dielectric solvents. In nitromethane (-15 M ) the concentration of free phenol (that is, phenol not hydrogen KX) 1/ bonded to nitromethane) would be -1/(1 31 as large as the concentration of free phenol in carbon tetrachloride ( K = 2 l./mol, and 8 = nitromethane concentration).13 The K , values are in agreement with this prediction (Table I). It is clear that the K,’s do not decrease in lower dielectric solvents as expected from the effects of ion association. The trend we observe can be explained by interaction of phenol with the various solvents. We conclude that the association of halide anions with quaternary onium cations does not affect the strength of the phenol-anion hydrogen bonds. It should be recalled that our nmr results indicate that the concentration of contact species is significantly reduced when phenol-anion hydrogen bonds are formed. Whether phenol acts by forming free solvated ions or solvent-separated ion pairs14 is open to question, but there is strong evidence that solvent-separated ion pairs are the predominant species for salts in low dielectric
157.6 162.4 156.6
M--
A”
35.5 22.6 20.6
Salt concentrations are 0.05 M .
We assume that ion association significantly affects the cation chemical shifts only when contact species are f ~ r m e d . There ~ is also evidence that, for the anions under consideration, ion association (involving contact species) causes the cation chemical shifts to be displaced d o ~ n f i e l d . ~If we accept the above, then we conclude from the nmr and ir results that phenol coordinates to the anions through hydrogen bonding and thus considerably reduces the concentration of contact species. The temperature dependence of this effect is consistent with the negative enthalpy which characterizes hydrogen bond formation. l1 The Journal of Phulsical Chemistry, Vol. 74, N o . $6, 1970
-
(11) G. C. Pimentel and A. L. McClellan, “The Hydrogen Bond,” Freeman and Co., San Francisco, Calif., 1960. (12) Dielectric constants at 40°, estimated from the data in A . A. Maryott and F. A. Smith, “Table of Dielectric Constants of Pure Liquids,” National Bureau of Standards Circular S o . 514, U. 8 . Government Printing Ofiice, Washington, D. C., issued August, 1961. (13) I. D. Kuntz, F. P. Gasparro, M.D. Johnson, and It. P. Taylor, J. Amer. Chem. Soc., 90,4778 (1968). (14) Associated species of higher stoichiometry probably exist in CCL and CHzC12, but the same arguments apply.
GRAVITATIONAL STABILITY IN ISOTHERMAL DIFFUSIONEXPERIMENTS solvents which contain low concentrations of “coordinating solvent.”16r16 The discussion that follows, however, is unaltered if free ions are formed instead of solvent-separated species. If we assume that the addition of phenol leads to the formation of solvent-separated ion pairs in carbon tetrachloride (dielectric constant = 2.2) and methylene chloride (dielectric constant = KO), then our results indicate that the diflerence in free energy between contact and solvent-separated species is the same in both solvents. This effect may be explained in either of two ways.” (a) The short-range properties of ions in solution are independent of the dielectric constant of the medium. (b) Alternatively, the free energies of the two species vary from solvent to solvent, but they do so in parallel. While our experiments do not allow us t o distinguish between these two possibilities, we note that the results are in opposition to continuum theories, 9, lo which would predict that the difference in free energies between contact and solvent-separated species should increase as the dielectric constant of the solvent is lowered. We conclude that the magnitude of the contact interionic interactions in solution must be considerably less than would be expected on the basis of continuum theory, and, as previously mentioned, must be no stronger than specific short-range effects such as hydrogen bonding or ion-dipole interactions. We can imagine certain instances in which these contact interactions would be considerably stronger. Direct hydrogen bonding between cation and anion would
4577
be one case; the formation of a covalent bond between cation and anion would be a second example. l8 Lastly, small cations (e.g., Li+) or multiply charged species might show cation effects on the hydrogen bonding ability of anions. Our results can be readily generalized to include other protic systems. Multiple solvation equilibria should be possible for anions of high charge density in most alcohols and water. Whereas the total amount of ion association will (to first approximation) depend upon the solvent’s dielectric c o n ~ t a n t ,it~ !is~likely ~ that the nature of the associated species mill be strongly influenced by the relative strength of the solvent-anion hydrogen bond. Evans and Gardamlg reached a similar conclusion in their investigation of the conductance of the tetraalkylammonium salts in the straight-chain alcohols. Their results are most consistent with a two-state association model which allows for the existence of both contact and solvent-separated ion pairs. (15) E.D.Hughes, C. K. Ingold, S. Patai, and Y. Packer, J . Chem. Soc., 1206 (1957). (16) See, for example, the work of Smid and coworkers on systems involving ion-dipole interactions: L. L. Chan and J. Smid, J . Amer. Chem. Soc., 90, 4654 (1968),and earlier papers. (17) We thank Professor Spiro for some helpful suggestions regarding this discussion. (18) Some heavy metal halides exhibit this behavior. See G. E. Coates, “Organa-Metallic Compounds,” Wiley, New York, N. Y., 1956,p 151. (19) D.F.Evans and P. Gardam, J . Phys. Chem., 73, 158 (1969).
Gravitational Stability in Isothermal Diffusion Experiments of
Four-Component Liquid Systems’ by Hyoungman Kim Institute for Enzyme Research, University of Wisconsin, Madison, Wisconsin 63706 (Received July 7 , 1Q70)
The conditions for gravitational stability in free diffusion and the diaphragm cell method of studying diffusion in four-component systems are obtained. For each boundary condition, three criteria should be satisfied in order to definitely avoid convective mixing during the diffusion experiments.
Introduction In any diffusion experiment, it is imperative to have gravitatioIla1 stability everywhere in the column of diffusing liquid during the entire duration of the experiment, for otherwise, convective mixing will render meaningless the diffusion coefficients obtained from the
experiment. In the study of diffusion of a two-component system, initial stability at the time of boundary formation will ensure that there is density stability (1) This investigation was supported in part by Public Health Service Research Grant AM-05177 from the National Institute of Arthritis and Metabolic Diseases. The Journal of Physical Chemistry, Vol. 74, No. 26, 1970
