JOURNAL OF T H E AMERICAN CHEMICAL SOCIETY Registered i n U .S. Patent Ofice.
@ C o p v i g h l , 1964, by
VOLUME 86, NUMBER21
the American Chemical Society
NOVEMBER 5, 1964
PHYSICAL AND INORGANIC CHEMISTRY [CONTRIBUTION FROM
THE
BELLTELEPHONE LABORATORIES, INCORPORATED, MURRAYHILL, NEW
JERSEY]
Relative Strength of Picric, Acetic, and Trichloroacetic Acids in Various Environments. Dispersion Effects in Acid-Base Equilibria BY ERNESTGRUNWALD AND ELTON PRICE RECEIVED M A Y25, 1964 London dispersion interactions of a solute molecule with the surrounding medium are especially strong if some of the virtual electronic oscillators t h a t represent the solute molecule are delocalized. Thus, in acid dissociation, the dispersion energy contribution to AFO should be relatively large if either the acid or the conjugate base absorbs light in the visible, t h a t is, for one-color indicators. An example is picric acid. T h e visible color of picrate ion can be ascribed to delocalized dipole oscillators t h a t have one monopole located in t h e 0 - atom and the other in a nitro group. The relative acid strength, KO, of picric acid relative to acetic acid increases by almost two orders of magnitude in the solvent series HOH, CHIOH, C2HjOH, while t h a t of trichloroacetic acid remains nearly constant. These results are qualitatively consistent with a dispersion effect. The dominant dispersion term comes from the interaction of the delocalized oscillators of picrate ion with dispersion centers in nearby solvent molecules. T h e latter are localized, and their effective density increases in the sequence HOH < CHIOH < CzHjOH. A system permitting actual calculation of the dispersion energy is the reaction BH+.OA4c- = BH+.OPicHOAc. T h e relevant equilibrium constant, K B H ' , was measured in HOPic glacial acetic acid for BH = NHa+ and for B H = ( CH3)3i?JH+, KBH+increases by almost an order of magnitude as a result of the methyl substitution. T h e corresponding equilibrium constants for trichloroacetic acid are insensitive to the change in B H + . Electrostatic interactions within the ion pairs should largely cancel out in these comparisons. Calculation using a model in which BH' is hydrogen-bonded t o the 0 - atom in the ion pairs leads to an increment in dispersion energy of 1.6 kcal./mole, which is quite consistent with the observed increase in K B H - . The hypothesis of strong dispersion effects can also account for the well-known differences in the relative base strength of the aliphatic amines as obtained from measurements in dilute solution in water or with color indicators in solvents of low dielectric constant. I n mixed water-organic solvents, the dispersion effects oppose and sometimes overcome the preferential solvation of ions by water t h a t would result from purely electrostatic interactions.
+
+
+
+
Dispersion forces are van der Waals forces resulting from the interaction of the same virtual electronic oscillators that enter into the description of the optical dispersion of molecules.',* It is well known t h a t the dispersion forces make a major or even dominant contribution t o the van der Waals forces in Yet in the theory of medium effects on ionic organic reactions, emphasis is usually placed on the electrostatic interactions of permanent molecular charge distribution^,^ and i t is not unusual for dispersion effects to be neglected entirely. The assumption is, of course, t h a t dispersion interactions with solvent molecules are about the same for reactants and products and cancel each other in their effect on AF'. I t is difficult either to prove or to disprove this assumption. Although the calculation of dispersion energy quantities is understood in principle, actual calculations for neighboring complex organic molecules cannot be carried out exactly because the enormous amount of microscopic information that is needed is not available.
There are special cases, however, where we can predict qualitatively t h a t dispersion effects on A F o should be maximal even though we cannot calculate them quantitatively. These cases are of interest not only for their own sake, but also because they set a rough upper limit to the magnitude of dispersion effects on A F o in general. In this paper we shall be concerned with dispersion effects due to the solvent environment in acid-base reactions. Analysis of data for reactions in which such effects are expected to be relatively large reveals very substantial specific effects that vary with molecular structure in precisely the way expected qualitatively for a dispersion effect. New measurements are reported for the relative strength of picric, acetic, and trichloroacetic acid under conditions where enough is known about the molecular environments so t h a t the dispersion effects can be roughly calculated. The medium effects observed under these conditions are highly specific, yet agree both qualitatively and semi(1) F . London, Z . physik. Chem. (Leipzig), B l l , 222 (1930). quantitatively with the calculated dispersion effects. (2) F.London, J . Phys. Chem., 46, 305 (1942). Our conclusion is t h a t the contribution of the dispersion (3) B. Linder, J . Chem. P h y s . , 37, 963 (1962), B. Linder a n d D. Hoernschemeyer, ibid., 40, 622 (1964). effect to the medium effect on A F o can range up to (4) See. for example, C . K. Ingold, "Structure and Mechanism in Orseveral kilocalories per mole. ganic Chemistry," Cornell University Press, Ithaca, N . Y., 1953. pp. 345-350. 4317
4518
ERNESTG R U N W A LA D N D ELTON PRICE
Localized as. Delocalized Electronic Oscillators In this section we wish to obtain some macroscopic criteria for predicting the relative magnitude of the dispersion effects on A F o for acid dissociation. Our discussion will closely follow the methods for treating complex organic molecules that have been suggested by London,' but will not go beyond the approximation represented by second-order perturbation theory. A brief review of the basic ideas will be helpful. 1. Each optical transition of the molecule is represented as a virtual electronic oscillator, and the transition moment is identified with the dipole moment of the osci1lator.j The dispersion effect of the molecule is a sum of independent terms assignable to the individual oscillators. The effect of an individual oscillator depends on the properties of that oscillator and is proportional to the oscillator strength, f. LVeakly allowed transitions (f < 0.01, say), which are of considerable interest in spectroscopy and photochemistry, play only a minor role. 2 . If the electrons are localized in a given partstructure, the transition moment of any strongly allowed transition must also be localized in t h a t partstructure. Hence the monopoles, q , in the expression 1.1 = qr for the dipole moment of the corresponding oscillator are localized in the same region of space in which the electrons are localized. The proof of this important theorem is almost selfevident. When we say that an electron is localized in a given part-structure, we mean that its wave function in the ground state of the molecule is negligible except in t h a t part-structure. Hence, the transition moment integral for excitation of the electron to an electronic level k in an arbitrary direction x, x$k*dr, cannot be large unless x $ k * is large in the same region of space in which $0 is localized 3. The interaction of two adjacent molecules can be represented as a double sum of pairwise interaction terms, each virtual oscillator in one molecule interacting independently with every virtual oscillator in the other molecule. 4. Dispersion effects attenuate rapidly with the distance between the interacting oscillators. Let us now apply these concepts specifically to the dissociation of an oxygen acid (eq. 1). It is convenient
s$,.
ROH
=
RO-
+ H+
(1)
to subdivide the oscillators representing ROH and ROinto three sets, those t h a t are localized in R , those that are localized in OH or 0-, and those that are delocalized. The latter are oscillators t h a t have one monopole located in R and the other in OH or O-.6 Delocalization results in a marked increase of the dispersion energy. For definiteness, consider a solvent molecule adjacent to the 0- atom in RO-. Such a solvent molecule will interact relatively strongly with the electronic oscillators assignable to the 0- atom, but, because of the greater distance, only relatively weakly with those localized in R . \Ye shall neglect interaction with the latter in first approximation. ( 5 ) See, for example, W. Kauzmann, "Quantum Chemistry." Academic 1957. Press, S e w York, ?j Y., ( 6 ) T h e s t a t u s of oscillators representing the electron pair t h a t is localized in t h e R - 0 bond is ambiguous in this scheme b u t causes no problem in making predictions. We shall arbitrarily regard one electron as localized in 0, the other as localized in R
Vol.
X(j
According to the Kuhn-Thomas sum rule,; the total strength of all oscillators assignable to a structure is just equal to the number of electrons. Hence the total oscillator strength formally assignable to the 0 - atom is equal for all RO- species. 1L-e shall now compare two species. In i, all oscillators assignable to the 0atom are localized. In ii, one of the localized oscillators of species i becomes delocalized while the others remain localized. In Fig. 1 we depict the interaction of the oscillator that becomes delocalized with a fixed oscillator that is localized in the adjacent solvent molecule. The former is represented as a pair of monopoles fy located a t points P1 and P', the latter as an isotropically oscillating dipole, ,us, located a t P3. Let R1 denote the distance PlP3, Ra the distance P2P3,and cp the angle PlP3P2. The dispersion energy, according to London, is then given by eq. 2, where u and v S are the characteristic frequencies of the oscillators. In Fig. l a , which
represents species i, R1 = Rz and cos cp = 1. Hence, R I --t ~ Rz-4 = COS q)/R12Rz2,and &isp is the small difference of nearly equal quantities. In Fig. Ib, which represents ii, R2 >> Iil and %(cos p)/R12RX2' < R l P 4 . Hence, &isp is no longer the difference of nearly equal quantities and is therefore relatively large. Another way of putting i t is that Fig. l a represents essentially a dipole-dipole interaction, Fig. l b a charge-dipole interaction. If we recall that the effect of a dipole is the small difference between the nearly equal but opposing effects of the monopoles, then i t is obvious t h a t delocalization, that is, removal of one monopole to a great distance, will result in a great enhancement of the effect. Calculations reported in a later section for a particular model show t h a t the enhancement in the dispersion energy resulting from the delocalization of a given oscillator can easily amount to a full order of magnitude. Compared to this large increase, any effect t h a t the delocalization might have on the properties of the other oscillators, which remain localized, should be relatively insignificant. Of course. the other monopole of the delocalized oscillator, which is located in R (Fig. l b ) , will also interact strongly with any solvent molecule near it. Returning to the equilibrium shown in eq. 1, we therefore expect a large dispersion energy contribution to AFO if a substantial oscillator strength that is localized in ROH becomes delocalized in RO-, or vice versa. Since delocalization of electronic oscillators can be recognized by the appearance of absorption bands in the visible or near-ultraviolet, we predict t h a t dispersion effects on AFO will be relatively large if ROH is colorless while RO- is intensely colored, or vice versa; that is, if the system ROH-RO- is a one-color indicator. In this paper we use picric acid as a typical onecolor indicator for which dispersion effects on A F o should be relatively large. It is therefore instructive to analyze the relevant spectra. For picric acid and picrate ion we fise some recent data obtained in chloroform ~ o l u t i o n . ~For other phenols and phenoxide ions we cite data for aqueous solution.8 (7) G Briegleb. J Czekalla, and .4.Hauser, 2 . p h y s i k . Chem. ( F r a n k f u r t ) , 21, 99 (1959).
ACIDS RELATIVE STRENGTH OF PICRIC, ACETIC,AND TRICHLOROACETIC
Nov. 5 , 1964
In the region near 4000 A. where neither picric acid nor phenoxide ion shows strong absorption, picrate ion shows strong absorption with two maxima. From the published graph' we calculate the following wave lengths (Amax) and molar extinction coefficients (E,,,) for the band maxima: (1) 4200 A,, 1.2 X 1W; (2) X i 0 .i , 2.0 X 104 For comparison, 0 - and p-nitrophenoxide ions in water show fnalogous absorption a t A,, = -Ll(iCI (0) and 4025 A ( p ) , with emax = 0.5 X I O 4 ( 0 ) and 1.9 X 104( p ) ? The well-known interpretation of thes: facts is t h a t the characteristic absorption near 4000 A. is the result of electronic coupling between the 0-atom and an oor p-nitro group The coupling is often described in terms of resonance among valence-bond structures such as 1-111 for the picrate
I
NOz I
-J
"\
\o,
I1
+ \@-
I NO1
I11 (two structures)
The ground state is described largely by I, with small contributions from IT and 111. We expect two excited states of nearly equal energy, a para-quinoid state t h a t is described largely by 11, and an orthoquinoid state, with a statistical weight of 2 , t h a t is described largely by 111. By analogy with the mononitrophenoxide ions, band 1 of picrate ion can be assigned to the transition to the ortho-quinoid state, band 2 to that to the para-quinoid state. T h e properties of the virtual oscillators t h a t represent these transitions are listed in Table I. The oscillator strength and p 2 , the square of the transition moment, are derived from integrated band intensities by standard methods. The total oscillator strength of the two bands has the substantial value of 0.31. The valence-bond structures (1-111) suggest t h a t the separation, r , of the monopoles, p, in the expression = pr is very close to the distance, d , from the 0- atom to the center of mass of the two oxygen atoms in the 0- or p-nitro group. Values of d have been calculated from known interatomic distances10 and are listed in Table I. Assuming t h a t r = d , we then obtain values of p2 and of the fractional charge, p/e for each transition, as shown in Table I. Although this treatment is rather naive, its validity seems to be confirmed by the nearly identical values of p obtained for the monopoles located in the 0- and p-nitro groups. In any case, there is little doubt t h a t these oscillators are strongly delocalized. Another useful, though less visual, macroscopic criterion for delocalization of electronic oscillators is the change in the molar refraction on acid dissociation. As is well known, the molar refraction is given accurately by an atom- or bond-additivity (8) I>. D a u b a n d J . M. Vandenbelt, J . A m . Chem. Soc., 69, 2714 (1947); 71, 2414 (1949). (9) G . W. Wheland, "Resonance in Organic Chemistry," John Wiley and Sons, I n c . , S e w York, N . Y., 1955, p p . 288-294. (10) Based on d a t a in I>. Pauling, " N a t u r e of t h e Chemical Bond," 3rd E d . , Cornell University Press, I t h a c a , N. Y., 1960. (11) N. Bauer a n d K . F a j a n s in "Physical Methods of Organic Chemist r y , " A . Weissberger, E d . , Interscience Publishers, Inc., S e w York, N. Y., 1949, C h a p t e r 20. (12) K. G . Denbigh, Trans. F a r a d a y Soc., 36, 936 (1940).
4519
0 -9
R-0-
SOLVENT
Fig. 1.-Model for calculating the dispersion energy: ( a ) t h e and ( b ) the same oscillator is delocaloscillator is localized in 0-; ized. Monopole +q is located a t PI, monopole - q is located a t PPIand dipole p s is located at PB.
if the electronic oscillators representing the dispersion of the molecule are all localized in atoms or bonds. Delocalization of electronic oscillators produces exaltation of the molar refraction above the value given by the additivity scheme. As a result, if in eq. 1 all oscillators assignable to the OH or 0 - part-structures are localized, we expect a characteristic change of the molar refraction that is independent of R. The value of this change can be estimated as S1.34 cc. from molar refractions reported for the HOH-HO- system. l 3 TABLE I PROPERTIES OF VIRTUALOSCILLATORS DERIVEDFROM THE ABSORPTIONSPECTRUM OF PICRATE IONNEAR 4000 A. Property
A."
-----Position orrho (total)
of excited nitro group--ortho (per SO9 group)
4200 0 715 0.083 74 3.17 7.4
para
3670 vmax X 10-ls, sec.-l 0.818 Oscillator strength" 0.229 p z X 1086, e.s.u.acrn.2 179 d X lo8, cm.h 6.27 q z X 10z2, e.s.u.2 4.5 d e . . . 0.44 R1 X lo8, c m . h ... 3.3 3.3 Rz X lo8, c m . b ... 5.3 9 6 cos 'p , . . 0,831 1.000 E d isD, kcal.c 0 48 0.86 0.96 a Based on d a t a in ref. 7. Based on d a t a in ref. 10. c Equation 2. Amax,
4200 0.715 0.042 37 3.17 3.7 0.40
For comparison, the value obtained for the CH3COOHCH3COO- system, in which we shall be interested in the next section, is +1.36 cc.,I3or essentially the same as for HOH-HO-. Thus, by this criterion, the contribution of the dispersion effect to AFO for the dissociation of acetic acid should have a value characteristic of localized oscillators and should therefore be relatively small. Solvent Effects on Relative Acid Strength T h e relative strength of two acids, HY and H X , is measured by the equilibrium constant for reaction 3 and is equal to the ratio of the acid dissociation constants (eq. 4). If YH X are stronger centers of dispersion than H Y X-, then the equilibrium in eq. 3 will shift to the right as the solvent is changed so
+ +
(13) K . F a j a n s , Z. p h y s i k . Chem. (Leipzig), B24, 141 (1934); K . Fajans a n d G . Joos, Z.P h y s i k , 2S, 1 (1924).
ERNEST GRUNWALD AND ELTON PRICE
4520 HY
KO
+ X=
KO =
Y-
+ HX
KAHy/KAHX
(3)
(-1)
Vol. 86
TABLE I1 EQUILIBRIUM CONSTANTS, KO, FOR RELATIVE ACID STRENGTH AT 25" _ _ _ _ _ _ _ _ l
t h a t the solvent molecules become stronger centers of dispersion. An actual example, to be considered in this section, is the relative strength of picric acid and acetic acid ( H Y = HOPic, H X = HOAc). In this example, the dispersion effect on KO is dominated by the interaction of solvent molecules with those delocalized oscillators of picrate ion that are responsible for its color. Values of KO have been reported for the solvents HOH, CHsOH, CzHjOH, and n-C4H90H. These solvents have the property t h a t the electronic oscillators representing the solvent molecules are all localized in atoms or bonds. T o make a precise calculation of the dispersion energy of solvation for each solvent, we would have to know the geometry of the solvent shells around each solute species. This kind of information is simply not available for solutions of complex molecules. Fortunately, the information is not needed, because we can derive the relative effectiveness of these solvents as sources of dispersion energy by considering only (i) the density of localized oscillators in various solvent shells, and (ii) the short range of the dispersion effect. The basic idea in this analysis is t h a t matter can be packed more densely in the neighborhood of a solute molecule if the atoms in the adjacent solvent shell are separated by covalent bond distances rather than by van der Waals distances and if gaps corresponding to interstices between molecules are minimized. This means that a few large molecules will represent a higher density of oscillators around the solute molecule than will a larger number of smaller molecules. Consider, for example, the solvation shell around a solute molecule in liquid water. Much of the space in the solvation shell, and particularly the space between the first and the second hydration layer, is interstitial or is swept out by van der Waals radii, and the density of oscillators in that space is low, On the other hand, if n-butyl alcohol is substituted for wa:er, the space t h a t would have been near the boundary between the first and second hydration layer in water is now filled with CH2 groups, and the density of oscillators within i t is high. Of course, in n-butyl alcohol there is also a boundary between the first and the second solvation layer near which the density of oscillators is low However, this boundary is a t a greater distance from the solute molecule than it is in water, and if i t lies outside the effective range of the dispersion effect, its adverse effect on the dispersion enerqy of solvation will be negligible. Thus, in the series of solvents C,HZn+10H,we expect the strength of picric acid relative to acetic acid to increase with n for small n. Furthermore, we expect t h a t the effect will reach saturation when n is large enough so t h a t the boundary between the first and second solvation layer is outside the effective range of the dispersion effect. This saturation value of n cannot be predicted without some ad hoc assumptions about the geometry of the solvation shells. If we assume that the OH groups are directed toward, and the alkyl groups away from, the solute molecules, the saturation value of n should be about 2 or 3.
Solvent
H O P I ~ -ClaCC02HHOAc HOAc 10-lKO 10-4K0
kcid pair HOPicphenol 1O-IOKO
HOPic-2,4(NOdzGHaOH 10-4fp
2 6 ca. 5 0 47 0 47 (1 HOH CHIOH 78 6 0 3 1 3 17 2 10 T 3 c n . 20 1 2 c C2HjOH n-CaHyOH 170 0 9 d n-CIHsOH, 0 05 S LiCl 28 1 4 0 3 e CHjCOlH 1 7 i K.4 is known with good accuracy for picric acid,I4 acetic acid, phenol, and 2,4-dinitrophenol.'j K.k for trichloroacetic acid is taken as 0.9 on the basis of kinetic, conductance, and spectrophotometric data and is uncertain by about a factor of two.16 The p * u * relationship predicts a K.k value ( J f 1 . 1 for ClaCC02H.1S Kef. 15, 18-20. c Kef. 15, 21, and 22 PA-, for phenol is taken as 15.3 f 0.5 on t h e basis of data in ref. 20 and 23. Data in the latter reference were corrected to 100f3; ethanol. See ref. 24. e See ref. 25. KO = K,,,,,,!K.~""[HOAc]; data from ref. 26 and 2 i .
The results of our literature search are summarized in Table i I . A41though the data are taken from a variety of sources,1 4 ~ 2 7results reported from different laboratories are mostly consistent and the values of KO should be accurate to 30% or better, except where noted in the table. I t is seen t h a t the relative strength, KO, of picric acid relative to acetic acid increases sharply with n for small n. However, the effect reaches saturation a t about n = 2 ; further increase in the size of the alkyl group from ethyl to n-butyl produces no marked effect. This behavior is quite different from t h a t of the dielectric constant in this series of solvents. The increase in l i D is actually greater between ethanol and n-butyl alcohol than between methanol and ethanol. Another revealing result in Table I1 is the large decrease of KO for picric acid in n-butyl alcohol ( D = 17.4)25when 0.05 iV LiCl is added. Under these conditions, a substantial fraction of the acetate and picrate ions form ion pairs with lithium ions, which are outstandingly poor centers of dispersion. (The molar refraction of Lif = 0.20 cc.13) Thus solvent molecules, which are good centers of dispersion, are displaced from the vicinity of the 0-atoms, and the extra dispersion energy of picrate ion is partially lost ( 1 4 ) H. von Halban and M . Seiler, Hela. Chim.Acla, 21, 385 (1038); R G. Bates and G. Schwarzenbach, E x p e r i r n l i n , 10,482 (1054). (15) I,. J . Minnick a n d M. Kilpatrick, J . P h y s . Chem., 43, 259 (19391, C. M ,Judson and M . Kilpatrick. J . A m . Chem. Soc., '71, 3110 ( 1 9 4 9 ) , M. Kilpatrick a n d C . A . Arenberg, ibid., 76, 3812 (1053). (16) F. G. Ciapetta and 51. Kilpatrick, tbid , 7 0 , 639 (1948), G . H . Debus, Can. 3. Chem., 3 4 , 1358 (1956), J . E . B. Kandles and J . M . Tedder, J . Chem. Soc., 1218 (1955). K . N. Bascombe and I < . P. Bell, c b d . 1096 (1959). (17) R . W. T a f t , J r . , 3. A m . Chem. Soc., 76, 4231 (1053). (18) I . M . Kolthoff and I,. S. Guss, ibid.,60,2516 (19381, 61,330 (1939) (19) H . Goldschmidt and H. Aarflot, Z . p h r s i k . Chem (Leipzig). A117, 317 (1925). (20) B. D. England and D . A . House, 3 Chem. Soc., -1421 (1962). For p K a u t o we used t h e value 16.92, which is appropriate for molar concentration units. (21) E . Grunwald and B. J. Berkowitz. J A m Chem Soc., 73, 4939 (1951). (22) A. J . Deyrup, %bid , 66, 6 0 (1934). (23) G. Schwarzenbach and H . Rudin, Heiz'. Chim. A c l n , 22, 360 (1939). (24) K.B Mason a n d M . Kilpatrick, J A m . Chem. Soc , 69, 572 ( 1 9 3 7 ) . (25) I , , A. Wooten a n d I>. P. H a m m e t t , $bid.,67, 2289 (1935) (26) S . Bruckenstein a n d I . ?vi.Kolthoff, rbid , '78, 2974 (1956). (27) A. M. Shkodin and S . A . Izmailov, J . Gen. Chem. L;SSR, 2 0 , 39 (1950).
Nov. 5 , 1964
RELATIVE STRENGTH OF
PICRIC,
Other data in Table I1 serve as control experiments. Relative to acetic acid, the strength of trichloroacetic acid is quite insensitive to the solvent, in contrast to that of picric acid. This shows t h a t the latter effect is not due to some peculiarity characteristic of acetic acid. The strength of picric acid relative to phenol varies with the solvent qualitatively in much the same way as t h a t relative to acetic acid, showing t h a t the effect is not due to a specific property of the carboxyl group. The solvent effect largely disappears in the comparison of picric acid with 2,4-dinitrophenol, a closely related one-color indicator. Effect of Ion-Pair Formation with NH4+and (CH,),NH+ on Relative Acid Strength We have seen t h a t the very striking medium effects on KO for picric acid relative to acetic acid are qualitatively consistent with dispersion effects. T o complete the demonstration, we must also show t h a t the effects are of the correct magnitude for a dispersion effect. Attempts to calculate the dispersion energy among complex molecules in solution are always hampered by the incompleteness of our knowledge of the microscopic environments. At best, the introduction of arbitrary assumptions can be minimized-it can never be avoided entirely. In this section we report some measurements of relative acid strength under conditions where a good deal is known about the microscopic environments. Although some arbitrary assumptions are still needed to calculate the dispersion energy, we believe that they are mild enough so that a t least semiquantitative agreement with experiment can be expected. I t is possible to change selectively the microscopic environment of an ionic species while keeping the overall solvent constant by taking advantage of ion-pair formation in a solvent of low dielectric constant. Accordingly, we have measured the equilibrium constant, KBHC, for reaction 5 , where B H + = N H 4 + or (CH3)3NH+. The solvent is glacial acetic acid. As KBH+
HOPic
+ B H + , O A C - B~H + . O P i c - + HOAc
(5)
might be expected on the basis of the low dielectric constant (D = 6.2 a t 2 5 O ) , the association of the free ions to ion pairs is nearly complete a t the 0.01-0.1 M concentrations employed in these measurements.28 The measurements of K B H +were made by a kinetic method and are based on an analysis of the rate of proton exchange between B H + and the carboxyl group of the solvent.29 Details will be reported in the Experimental section, b u t we shall indicate here t h a t the rates of exchange are almost exactly proportional to the concentrations of BH +OAc- in the equilibrium mixtures. Results of our measurements are listed in Table 111. KB" is defined by eq. 6, where the brackets KBH+
[HOAc][BH +OPic-] - ~ ~ _
[HOPic][BH+OAc-]
_
(6)
denote molar concentrations. The table shows that there is a large increase in KBH' for picric acid when B H + is (CH3)3NH+ rather than N H 4 + . The table ( 2 8 ) See, for example, d a t a in ref. 26 a n d 29. (29) E. Grunwald a n d E. Price, J. A m . C h c m . Soc., 86, 2 0 6 5 , 2970 (1964).
ACETIC, A N D TRICHLOROACETIC ACIDS
4521
also lists our results for trichloroacetic acid, which serve as a control. T h e latter are quite insensitive t o the change in B H + , the small difference being barely outside of experimental error. This pattern of K B H t (a high sensitivity to alkyl substitution in the cation in the case of picric acid, and a low one in the case of trichloroacetic acid) is completely analogous to t h e effect of alkyl substitution in the solvent on KO for these acids (see Table 11). TABLE I11 K"", O F P I C R I C ACID AND TRICHLOROACETIC X C I D RELATIVE TO ACETICACID AT 25"" ACID STRESGTH,
10-3.
Acid
i w 3 K B H +kBH tOAc-!
BH *
sec
-1
kBH+X-:
sec. - 1
Picric 4" 0.69 6.08 30 f 30 (CH3)3NH 3.4 0.945 (o.3)d Picric 6.2 6.08 2 f 2 CliCCOzH SH, (CH3)3NH+ 7.7 0 945 (O,l)d C13CCOzH 0 With glacial acetic acid as solvent and calculations based on eq. 14. Taken from ref. 29. X - = OPic- or CId2CO2-. Calculated from data in columns 3 and 4 by means of the Brphsted relationship, assuming a = 1 ; see text following eq. 14. +
+
+
In analyzing the results, i t simplifies matters to consider the ratio of KB", which is the equilibrium con;iH4+OPic-
+ (CH3)3KH+OAc-
K7
XH4+OAc-
+ (CH3)3NH+OPic- (7)
stant for reaction 7. I t is our thesis t h a t the electrostatic free energy terms due to the interaction of t h e permanent charge distributions of the ions in t h e ion pairs nearly cancel in their effect on K7 and that the observed effect is largely a dispersion effect, resulting from the replacement of H by C H 3 in the ammonium ion. The structure of the ion pairs formed from aliphatic amines and excess acetic acid has been studied by infrared spectroscopic methods in carbon tetrachloride and in c h l o r ~ f o r m . ~The ~ data suggest t h a t the ion pairs produced in acetic acid probably have the hydrogen-bonded structure, AcO-.HNR3+, with the acetyl group being further solvated by molecules of acetic acid. Cyclic structures such as IV, which are impossible for (CH3)3NH+, appear to be unimportant even in the nonpolar solvent^.^^,^^ We shall therefore
IV
postulate t h a t the ion pairs in our systems are represented by the formulas AcO-.HNH3+, AcO-.HN(CH3)3+, PicO-.HNH3+, and P ~ c O - . H N ( C H ~ ) ~ + , which involve a single hydrogen bond between cation and anion. Molecular models then indicate t h a t steric strains due to nonbonded repulsions between cation and anion are negligible in all ion pairs. Hence, the _ length of the O-.HN hydrogen bond should not change when the cation is (CH3)3NH+ instead of N H 4 + . Since the ionic charge is formally located on the nitrogen (30) E . A . Yerger a n d G. M. Barrow, ibid., 7 7 , 4474, 6206 (1955). (31) On t h e other h a n d , Davis and Paabo infer from t h e values of equilibrium constants t h a t diphenylguanidinium benzoate in benzene has a cyclic structure analogous t o I\': M . M. Davis and M . Paabo, ibid., 83, 5081 (1960).
4522
ERNESTGRUNWALD A N D ELTOKPRICE
atom in both species, and since the dipole moment of the permanent charge distribution is zero for one and very small for the other, h-H4+ and ( C H 3 ) & H t are nearly identical electrostatic systems. And because of the equal O-,HN bond lengths. the electrostatic free energies of interaction of NH,+ and (CH:I):INH+ with a given anion should be almost exactly the same. Moreover, whatever small differences do exist should tend to cancel out in the comparison of electrostatic interactions with two anions. as in eq. 7 . On this basis, the considerable deviation of K7 from unity could be largely a dispersion effect. T o support this assignment, we shall now make a semiquantitative calculation of the dispersion energy and show that it is of the same magnitude as - 112' In Ki. Our model is essentially t h a t shown in Fig. 1. The difference in the dispersion effect between HN(CH3)3' and HNH3' will be represented as a single oscillator, equivalent to the dispersion effect of three C H 2 groups and located a t the center of mass of the three carbon atoms. We shall assume that this oscillator is isotropic. The difference in the dispersion effect between picrate ion and acetate ion will be attributed to the delocalization in picrate ion of a certain fraction of the oscillator strength that is formally assignable to the 0- atom The properties of the oscillators that are delocalized in picrate ion have already been listed in Table I . The dispersion energy of these oscillators with the (CH,), equivalent oscillator can be calculated from eq. 2. The required value of p s y can be obtained from eq. 8, where v, is the characteristic frequency and a , the
polarizability. London assumed that hu, is equal to the ionization energy.' CY:! is equal to 3 a c ~ ? which , in turn is roughly equal to ~ ( ~ R & ' ~ T J V where O , RCH? is the additive contribution of a CHg group to the molar refraction and is Avogadro's number. LVe shall use ~ C = H 1.82 ~ X 10-?4 cm.3,11and us = 2 , 4 X 101j set.-' (10 e.v.). Values of XI,RS,and cos p were calculated from known interatomic distances'O for each delocalized transition. R1 is the distance from the (CH& equivalent oscillator to the 0- a t o m ; R2 is the distance to the KO2 group. R:!was calculated on the assumption that the O-"N bond lies on the twofold axis of the picrate ion. v was taken as v,,. Numerical values, including those of the dispersion energy for each transition, are listed in Table I . The total disFersion energy for the two ortho- and the para-delocalized oscillators is - 1.82 kcal. mole. These delocalized transitions represent a total oscillator strength of 0,31. To be subtracted from this result is the dispersion energy ascribable to an equal oscillator strength that is localized on the 0 - atom of acetate ion. We shall treat the localized oscillators as dipoles and obtain the relevant value of p 2 from the polarizability (which is based on molar refraction data) and the ionization potential, as previously stated. The polarizability of acetate ion can be represented formally as the sum of the polarizability of the uncharged acetate group (which we deduce from that of acetic acid), and an additional term, CY, clue to the electron that is transferred to
Vol S(i
the acetate group on ionization. Using molar and atomic refractions, 6a is given by eq. 9. The value of 6a = : 3 ( ~ ~ . &-~ -RHO.
