165.1 J . Org. rhPm.. Vol 44, No. I O , 1979
Capobianco, Magno, and Scorrano
L. Vander Jagt, ibid., 91, 6850 (1969); (i) E. N. Peters and H. C. Brown, ;bid., 96, 265 (1974); (j) H. C. Brown, S.Ikegami, K. T. Liu, and G. L. Tritle, ibid., 98, 2531 (1976); (k) F. Wilcox, M. Sexton, and M. F. Wilcox, J. Org. Chem., 28, 1079 (1963); (I) H. L. Goering and C. B. Schewene, J. Am. Chem. Soc.. 87, 3516 (1965). (13) We are indebted to Professor P. v. R. Schleyer for this suggestion and for preliminary calculations (with D. Khoury) on 2. (14) (a) Reviewed by V.F. Nowlan and T. T. Tidwell, Acc. Chem. Res., 10, 252 (1977); (b) see also D. S. Noyce, D. R. Harrter, and R. M. Pollack, J. Am. Chem. SOC.,90, 3971 (1968). (15) (a) The p + values for the dehydration of arylcarbinols are uniformly high, close to the carbonium ion value: 1,2diphenylethanol~,'~~ -4.3; &tolyldi-ter?-butylcarbinols,'6a -4.2 (anti), -3.9 (syn); phenyldi-tert-butylcarbinols,'6a -3.9. These data refute the recent suggestion'6c that the differences between t-BulMe ratios in alcohols and pnitrobenzoates are due to an early transition state in the former reaction. (b) The question of possible steric effects upon the preequilibrium,'6d though interesting, is not relevant to the EFF approach. (16) (a)J. S. Lomas and J-E Dubois, Tetrahedron, 34, 1597 (1978); (b) Tetrahedron Lett., 407 (1976);(c) R. C. Badger and J. L. Fry, J. Am. Chem. SOC., in press; (d) T. T. Tidwell, Tetrahedron, 34, 1855 (1978). (17) A good account of the hazards involved in trying to interpret solvolysis rates by strain energy calculations is given by N, L. Allinger and G. A. Lane, J. Am. Chem. Soc.. 96, 2937 (1974). (18) (a) N. L. Allinger. J. Am. Chem. Soc., 99, 8127(1977); (b)L. S.Bartell, bid., 99, 3279 (1977); (c) D. N. J. White and M. J. Bovill, J. Chem. Soc., Perkin Trans. 2, 1610 (1977). (19) N. L. Allinger and D. Y. Chung, J. Am. Chem. SOC.,98, 6798 (1976). (20) (a)E. M. Engler, M. Farcasiu, A. Sevin. J. M. Cense, and P. v. R. Schleyer, J. Am. Chem. Soc., 95, 5769 (1973); (b) T. M. Gund, P. v. R. Schleyer, P. H. Gund. and W. T. Wipke. ibid., 97, 743 (1975). (211 A possible reason for this anomaly lies in the fact that the carbonium ion of lowest energy, according to molecular mechanics, does not have the same conformation as the most stable hydrocarbon. Carbonium ion formation in this case may therefore require greater energy than is indicated by the strain energy calculation since a small additional rotational barrier has to be overcome. Nevertheless. the corresponding gnitrobenzoate is well-correlated (22) S Winstein, M. Shatavsky. C. Norton, and R. B. Woodward, J. Am. Chem. Soc., 77,4183 (1955); (b) S.Winstein. F. Gadient, E. T. Stafford. and P. E. Klinedinst. ibid.. 80, 5895 (1958); (c)P. v. R. Schleyer and R. D. Nicholas, ibid., 83, 182 (1961); (di P. G. Gassman and J. M. Pascone, ibid., 95, 7801 (1973). (23) See S. P. McManus and J. M. Harris, J. Org. Chem., 42, 1422 (1977). (24) H Tanida and T. Tsushima, J. Am. Chem. SOC.,92, 3397 (1970). (25) R. Hoffmann, F.D. Mollere, and E. Heilbronner, J. Am. Chem. SOC..95,4860 (1973j.
(26) The steric energy components would be slightly different if a NewtonRaphson minimization procedure had been used: J. M. A. Baas, B. van de Graff, A. van Veen, and B. M. Wepster, Tetrahedron Lett., 819 (1978). (27) Internal angles are systematically smaller for t-Bu than for Me derivatives by 0.7-1.6' depending on the system. (28) MIND013 calculations err in the other direction, finding that the 7-norbornyl cation is 3.1 kcal mol-' more stable than the 2-cation: W. L Jorgensen, private communication quoted by P. v. R. Schleyer.'od (29) This approach avoids problems arising out of the eventual contribution of polar effects to the dehydration rates. Alkyl group polar effects are considered by some to be constant, whereas others maintain that Taft's ( T I scale expresses real differences in the abilities of alkyl groups to stabilize electrondeficient centers; see (a) M. Charton. J. Am. Chem. SOC.,99, 5687 (1977); (b) J. A. MacPhee and J.-E Dubois, Tetrahedron Lett., 2225 (1978). (30) C. A. Bunton, K. Khaleeluddin, and D. Whittaker, Tetrahedron Lett., 1825 (1963). For the corresponding pnitrobenzoates in 60% aqueous dioxane at 50 OC, the ratio is 565.3' That for 2-methyl-2-norbornyl pnitrobenzoates under the same conditions is given as 86, a value differing by a factor of 10 from the currently accepted value in 80% aqueous acetone at 25 OC. (31) H. C. Brown, F. J. Chloupek, and M. H. Rei, J. Am. Chem. SOC.,86, 1248 (1964). (32) The data given as "strain engeries" in ref 2j are "steric energies" according to the more recent definition'c and, as such, are underestimated Schleyer's customary force field was not, however, used in the 1972 publication. (33) H. C. Brown and M. Ravindranathan, J. Am. Chem. Soc., 100, 1865 (1978). (34) Details of these calculations are given in the supplementary material. (35) Alcohols which are neither new nor discussed below are described elsewhere: 2a, M. S.Newman, A. Arkell. and T. Fukunaga, J. Am. Chem. Soc.. 82, 2498 (1960); 2b, P. D. Bartlett and E. B. Lefferts, ibid., 77, 2804 (1955); 3a, E. Lunt and W. R. Wragg, J. Chem. Soc. C, 1845 (1970); 5, 6, 9, and 10, ref 8b and references therein; Ea, R. K. Bly and R. S.Bly, J. Org. Chem.. 28, 3165 (1963); l l a , W. Kraus and R. Dewald, Justus Liebigs Ann. Chem., 689, 21 (1965); 12a, M. L. Capmau, W. Chodkiewicz, and P. Cadiot, TetrahedronLett., 1619 (1965). (36) H. C. Brown and M. H. Rei, J. Org. Chem., 31, 1090 (1966). (37) H. Meerwein and K. van Emster, Chem. Ber., 53, 1815 (1920). (38)P. J. Pearce, D. H. Richards. and N. F. Scilly, J. Chem. SOC.,Perkin Trans. 7, 1655 (1972). (39) This compound has also been prepared by the addition of preformed 1-AdLi to ii-fer?-butyl ketone: G. Molle, J.-E. Dubois, and P. Bauer, Synth. Commun., 8, 39 (1978). (40) J. S. Lomas, P. K. Luong, and J.-E. Dubois, J. Org. Chem.. 42, 3394 (1977). (41) J. S.Lomas and J.-E. Dubois, J. Org. Chem.. 39, 1776 (1974).
Basicity Measurements in Aqueous-Organic Solvents. 1. The 20 o/o Ethanol-Aqueous Sulfuric Acid System Carlo Capobianco, Franco Magno, and Gianfranco Scorrano* Centrri ('"VR kfeccanismi di Reazioni Organiche, Istituto di Chimica Organics, 35100 Padooa, Itaiy, and Istituto d i Chimica Analitica, 35100 Padova, Italy Received December 3. 1978 T h e a c i d i t y functions Ho, H,,,,, Hdip,HGF.a n d H A have been compared in the solvent 20% ethanol-aqueous sulfuric acid. T h e y are a l l linearly related according t o t h e ( H x t log C H + ) = (1 - 4 e ) ( H o log C H + ) relationship. T h e
+
thermodynamic ~ K x H +values can be estimated for every base, even for those whose a c i d i t y f u n c t i o n i s u n k n o w n , by a p p l y i n g also in t h i s solvent the Runnett-Olsen equation. T h e p r o t o n a t i o n d a t a o f d i m e t h y l ether a n d d i m e t h y l sulfide show t h a t t h e P K X H t value is n o t sufficient t o define t h e p r o t o n a t i o n e q u i l i b r i u m o f weak bases. I n fact, t h e inversion of' basicity order t h a t occurs in going f r o m d i l u t e ( M e 2 0 > Me2S) t o more concentrated (MeZS > M e ? O ) acid solutions can be accounted for o n l y t h r o u g h t h e solvation parameter 4,. Comparison o f t h e values shows t h a t t h e d i f f e r e n t i a t i o n among a c i d i t y functions occurs because of differences in o n i u m i o n solvation energies, the n u m b e r of hydrogen b o n d i n g sites m a k i n g o n l y a second-order contribution. For t h e same compound, t h e protonamore positive) f r o m those t i o n parameters are in t h e m i x e d solvent o n l y slightly d i f f e r e n t (~KXHI m o r e negative, evaluated in aqueous acid solutions.
Acids in ethanol-water or dioxane-water have often been used to evaluaie the basic properties of organic substrates sparingly soluble in purely aqueous media.1 The practical importance of these systems notwithstanding, very limited attempts have been made to apply _ _ - to mixed solvents the same unifying that have considerably simplified the interpretation of acid-base equilibria in water. There is a general a g r e e m e n F that. in water, the activity coefficients of the 0022-3263/79/1944-1654$01.00/0
species involved in the protonation equilibrium of two bases X and B are linked through the following linear free-energy relationship: Equation 1 is easily rearranged in a form amenable to direct experimental verification by combining it with the equilibrium constant for the protonation of the base X (XH+ z X + H+)
0 1979 American Chemical Society
Basicity Measurements in Aqueous-Organic Solvents
J . Org. Chem., Vol. 4 4 , "Vo. 10, 1979
(eq 2) and with the analogous relation for the base B. ~ K x H =:+ log ( C X H + / C X C H + ) log ( c X c H + / c X H + ) = (1
+ log ( ~ x H + / ~ x ~ H + ) ( 2 )
- d e ) 1% (CBCH+/CBH+)
+ (1 - d'e)PKBH+- PKXH+
(3)
The resulting linear relationship (eq 3) between the logarithms of the experimentally available protonation quotients for the two bases has heen verified in a number of cases by Bunnett and Olsen2 and others5 Equation 3 may also be used to evaluate the PKXHt's of any base on the same reference scale. If, as proposed by Bunnett and Olsen,2 we take as base B a nitroaniline whose protonation behavior is described by the Ho acidity function [Ho = -log(aH+fB/fBH+)]and with ~ K B H=+ 0.0, eq 3 may be rearranged into eq 4 which, upon addition of Ho log C H + to both sides, gives the Bunnett and Olsen equation2 now commonly used2,3-6to evaluate ~ K x H + ' sin water:
+
log
(CZ;H+/CX)
-- log C H +
=
(de - 1)(Ho+ log C H + ) + PKXH+ (4) log ( C X H + / C X ) + Ho = deWo + log C H + ) + ~ K x H + (5) Equation 1 may also be verified in a different way, as suggested by Hammett." It follows in fact from eq 1 that the acidity functions defined by the base X[Hx = -log ( a ~ + f x / f X H + ) ] and by the Hammett bases B (Ho)are linearly related according t o
Hx
+ log C H +
= (1-
@e)(Ho4- log C H + )
(6)
By combining t>q2 and 6 and rearranging, the same general eq 5 may be easily derived.3 I t is now well known that each weak base defines its own acidity function,6and that only in limited cases is it possible to define an average acidity function which represents the behavior of a family of structurally related bases in all the acidity range. These limitations notwithstanding, we believe that eq 6 is more useful than eq 3 because it allows the verification of the relationship of eq 1 over a wide range of acidity. I t is a common experience that log-log plots are prone to be linear, especially when examined over a short range, as, by necessity, must be done by applying eq 3. With these results in mind and with the aim to provide the simplest possible way to define the behavior of weak organic bases also in acid solutions containing an organic solvent, we have started an investigation covering several aqueous-organic solvents. The results obtained in the 20% ethanol-80% aqueous sulfuric acid solutions are discussed in this paper. Results The 2090 ethanolic aqueous sulfuric acid has been prepared by diluting, as suggested by Kresge and Chen,7 10 mL of 95% aqueous ethanol with enough aqueous sulfuric acid to give a final 50 mL volume. The problems connected with the esterification of ethanol by concentrated sulfuric acid8 have been dealt with following the suggestion reported in detail in the Kresge and Chen's paper.7 Four acidity functions have so far been defined in this solvent: Ho (based on nitroanilines),7 Ha,, (based on azoben~ e n e s ) Hdlp , ~ , ~(based on diphenylamines),'O and HGF(based on ferrocene).ll 'To compare the four sets of data we must refer them to the same reference state, which will be defined in this work as the infinitely dilute solution in 20% ethanol-80% water. The same reference state has been used by Kresge and Chen7 for the Ho and Ha,, acidity functions and their data need not be changed. The Hdlpand HGFacidity functions have been instead referred to water as the reference state. According to Kresge and Chen7 the change to the 20% ethanolic standard state can be made for the Hdlpacidity function by
1655
adding -0.15 (the difference in ~ K x Hvalues + of the reference base, diphenylamine, in water and 20% ethanol) to the published data.I0More complex operations are required to change the reference state for the H G F acidity function. This is based" upon the difference between the ferrocene half-wave potential, Ellz, and the glass electrode potential, E,. These potentials are defined as: E1/2 =
E"
+ (2.303RT/2F) log (DFec+/DFec) - (2.303RT/F) 1% ( f F e c / f F e c + )
E,
= E,"
+ (2.303RT/F) log U H +
(7) (8)
where f are the molar activity coefficients, D are the diffusion coefficients of ferrocene (Fec) and ferricenium ion (Fee+), and a H+ is the proton activity. By subtracting eq 8 from eq 7 we obtain:
E
= E112 - E , = K
+(~.~O~RT/F)HGF
(9)
where H G F= -log ( u H + ~ F ~ ~ / is, ~ Faccording ~ ~ + ) to the definition of the acidity function, the acidity function based on the single indicator ferrocene, and K = Eo -E: - (2.303RT/2F) log ( D F ~ ~ + / isD constant F ~ ~ ) at a given temperature.12To define the H G Ffunction one must evaluate a t several acid concentrations the E potential and, in a solution of known proton activity, the K constant. We have measured the E potential in 20% ethanol-aqueous sulfuric acid solutions in the range 0.04-5.9 M as follows. Cyclic voltammetric curves relative t o the Fec/Fec+ system were recorded a t a stationary mercury microelectrode. In this way one avoids the noise, arising in the measuring circuit from switching in the circuit controlling an electrode with periodical renewal of the diffusion layer, and the distance between anodic and catodic peaks (60 mV) gives immediately an indication of the measurement reliability. The cyclic voltammetry offers, in this way, a distinct advantage over the polarographic method used by Janata and Jansen," especially a t low acidities where the oxidation wave of ferrocene is relatively close t o the current background," thus making the polarographic values less reliable. The definition of the K constant is not directly feasible since, to the best of our knowledge, no buffer solution has been defined for the system 20% ethanol-aqueous sulfuric acid. We may, however, arrive a t a reliable value by two independent methods. By definition,3all acidity functions must converge to the same point as the solution becomes more dilute and, hence, approaches ideality. In fact, Ho, Ha,,, and Hdip all give the same 1.03 value at 0.082 M. If this is also true for the HGFfunction, as it should be, one may evaluate from eq 9, and with the aid of the experimental E value (-0.259) in the 0.082 M acid solution, a K constant of -0.320. The second approach used implies that, as for the Ha,, and Hdlpacidity functions, HGF also is related to Ho according to eq 6. By substituting the HGF value derived from this relationship into eq 9 and rearranging, one obtains eq 10:
E
+ (2.303RT/F)log C H + = K + ~ ( H+olog CH+) (10) is 2.303RT(1 - d e ) / F .The plot E + 0.059 logcH+ vs.
where cy Ho log C H + gives a straight line ( r = 0.9933) with intercept -0.3215. The two K values are within the experimental error and we have computed the HGFfunction by using K = -0.321. In Table I we have collected the E and HGFvalues determined for several 20% ethanol-aqueous sulfuric acid solutions. A smoothed HGFfunction is obtained by plotting the values of Table I against the acid concentration. This function differs from the one reported by Janata and Jansen," apart from minor differences in the more dilute acid solutions (see above), by a constant value, our data being 1.75 units more negative than the ones obtained1' by anchoring the acidity function t o the water solution. To extend the HC,Fscale up to C H + = 10 M,
+
1656 J . Org. Chem., Vol. 44, No. 10, 1979
Capobianco, Magno, and Scorrano
Table I. The HGFAcidity Function Evaluation in 20% Ethanol-Aqueous Sulfuric Acid a 0.04 0.082 0.150 0.240 0.390 0.500
0.530 0.590 0.845 1.020 1.460 2.000 2.505 3.100 3.600 4.150 4.590 5.050 5.900
-0.209 -0.259 -0.269 -0.294 -0.304 -0.319 -0.334 -0.339 -0.359 -0.349 -0.379 -0.404 -0.439 -0.464 -0.479 -0.504 -0.539 -0.554 -0.599
+1.898 +1.051 +0.881 +0.458 +0.288 +0.034 -0.220 -0.305 -0.644 -0.475 -0.983 -1.407 -2.000 -2.424 -2.678 -3.102 -3.695 -3.949 -4.711
-400
, -2
- H. Figure 1. The protonation curve for p-methoxybenzamidein 20%
ethanol-aqueous sulfuric acid.
a At 25 O C . This is the difference between the ferrocene half-wave potential and the glass electrode potential. Evaluated by using a K value of -0.321 (see text) and therefore referred to the infinitely dilute solution in 20% ethanol-water as reference state.
we have added -1.75 to the values reported by Janata and
