Equilibrium and Kinetic Acidities of Carbon Acids BY F. G. BORDWELL Northwestern University Evanston Illinois U.S.A. Received 1st May 1975 Bnomalous Bronsted coefficients observed for nitroalkanes are rationalized in terms of a mechanism involving an intermediate anion. The results of measurements of equilibrium acidities of carbon acids in dimethyl sulphoxide (DMSO) solution are presented and compared with similar measurements made in solvents of low dielectric constant and in water. A linear correlation between gas-phase acidities and DMSO solution acidities for a series of ketones and for a series of nitriles is presented. Equilibrium measurements indicate the presence of a high degree of strain in the anion derived from trifluoromethylsulphonylcyclopropane.This result shows that the sulphur atom in the trifluoromethylsulphonyl group is entering into strong conjugation with the carbanion. Nitroalkanes are the only monofunctional carbon acids that are acidic enough to allow equilibrium measurements to be made in protic media. As such their proton transfer reactions have been subject to extensive study. Interest in nitroalkane substrates has been intensified recently by the observation that the Bronsted a coefficient relating the rates of deprotonation by a given base and the equilibrium constants for a series of nitroalkanes is usually anomalous in that a is often larger than 1.0 and is occasionally less than zero (i.e. negative). This observation raises doubts as to the suitability of the common practice of using the size of the Bronsted coefficient as an index of the extent of proton transfer in the transition state for the deprotonation of a carbon acid.The observation also makes dubious the common practice of using rates of deprotonation (" kinetic acidities ") as an index of carbanion stability since this requires an assumption to be made concerning the size of a. A number of interpretations of anomalous Brijnsted coefficients have been given. Our own working hypothesis is that deprotonations of nitroalkanes are not simple one- step proton transfer reactions but instead proceed by way of an intermediate or a "virtual '' intermediate anion.4 In the present paper several examples of anomalous Bronsted coefficients will be given and interpreted on the basis of this two-anion mechanism.A method for measuring equilibrium acidities of weak acids in dimethyl sulphoxide (DMSO) solution will then be presented and discussed. (Such measure- ments when coupled with rate studies in DMSO will in time provide additional information concerning the mechanisms of proton transfers). Finally the use of kinetic acidities as a measure of the stabilities of carbanions will be examined. ANOMALOUS BRONSTED COEFFICIENTS AND THE TWO-ANION MECHANISM The first examples of anomalous Bronsted coefficients to which attention was drawn were deprotonations of a-arylnitroalkanes and a-methylnitroalkanes. It was observed that the Bronsted a obtained on deprotonation of a-arylnitroalkanes such as ArCH2N02 by a given base (with changing m-and p-substituents) was larger than 1.0 and that a in the series CH3N02 MeCH,NO, Me,CHNO, for deproton- ation by hydroxide ion was negative2 To these examples we can now add the deprotonation of nitroalkanes of the type GCH2CH,CH,N02 by a given base.100 F. G. BORDWELL Using 8 G substituents a Bronsted plot of log k for deprotonation by lyate ion in 50% MeOH-H,O against equilibrium acidities in 50% MeOH-H20 showed that as in the ArCH2N02series the rates were more sensitive to substituent effects than the equilibria (a = 1.56).5 It is possible to rationalize this result as well as the previous results on the basis of the following two-anion mechanistic scheme I B-+H-C-NO~ ,+ BI....H I I.slow ,fast 3 2 Geometric and solvent reorganization The first (reversible) step is formation of a weak H-bonded complex (1) a step somewhat similar to the first step in the Eigen mechanism for proton transfer.6 The second rate-limiting step is formation of the "essentially pyramidal "nitro carbanion 2.Some rehybridization and solvent reorganization must occur in this step but the major changes of this type are assumed to occur in the next (fast) step where the strong BH-.C- H-bond is broken and replaced by strong H-bonding to the oxygen atoms of the planar nitronate ion (3). According to this scheme structural changes on the rate will be determined primarily in the step where 1 is converted to 2 whereas structural changes on the equilibrium will be determined primarily by their effect on the stability of the planar nitronate ion 3.It is not unreasonable then to expect that a structural change may have one effect on the transition state leading to anion 2 and a dzferent (smaller greater or opposite) effect on the stability of anion 3. When the structural change causes a greater effect on the stability of anion 2 than anion 3 as is true for deprotonations of ArCH,NO or GCH2CH2CH2N02 systems a will be larger than 1.0. It is understandable that a change in Ar will have a large effect on the deprotonation rate in ArCH,NO since Ar is attached directly to the carbon atom bearing the charge in 2 and the transition state for deprotonation leading to 2 will be strongly influenced by changes in Ar. On the other hand in ArCH=NO (3) substituents will have a smaller effect since the negative charge is primarily on oxygen two atoms removed and is much less subject to the influence of Ar.A similar argument can be made for the GCH,CH,CH,NO system. It is reasonable then for kinetic acidities to be more sensitive to structural changes in Ar or G than are equilibrium acidities (a > 1.O). If structural changes cause opposite effects on the stabilities of anions 2 and 3 a negative a will result. For example there is good reason to believe that the increased equilibrium acidities with increased methyl substitution in the series CH3N02 MeCH,NO, Me,CHNO is caused by methyl stabilization of 3. It is entirely possible on the other hand that methyl substitutiou may destabilize anion 2 (e.g. by weakening the H-bond).The inverse Bronsted correlation can be rationalized in this way. The large (nearly maximum) kH/kDisotope effects observed for deprotonation of simple nitroalkanes such as nitromethane nitroethane etc. by hydroxide ion can ACIDITIES OF CARBON ACIDS also be rationalized nicely by the two-anion mechanism. In the overall sense these reactions are exoenergetic and the kH/kD isotope effect would be expected to be small. On the other hand if the conversion of 1 to 2 is considered to be rate limiting this conversion would not need to be exoenergetic and could have a near-maximum isotope effect. In discussing this mechanistic scheme the question has been raised as to whether or not the conversion of 2 to 3 requires an activation barrier.4 In this connection we may note that in a rather closely analogous reaction the deprotonation of 2,4,6-trinitrotoluene by EtO- in EtOH a careful analysis by Caldin indicates that solvent reorganization is the major factor contributing to the activation barrier.' Some solvent reorganization and bond rehybridization must occur in the conversion of 1 to 2 but it seems reasonable to suppose that an additional barrier must be surmounted in converting 2 to 3.The importance of the contributions from solvent and geometric reorganization to the activation barriers in proton transfers is indicated also by the work of Ritchie in DMSO solution.8 Solvent reorganization would be expected to be less in DMSO than in a protic solvent such as MeOH and indeed Ritchie finds ca.a 100-fold faster rate for a proton transfer in DMSO as compared to a reaction with a comparable change in free energy carried out in MeOH8 We anticipate that the two-anion mechanism for deprotonation will hold for other substrates where conversion to the final anion requires extensive geometric and solvent reorganization such as in the deprotonation of aldehydes and ketones. On the other hand for substrates where these factors are of less importance such as sulphones and nitriles a change in mechanism is indicated since these carbon acids behave "normally " in Bronsted correlations i.e. in a manner similar to oxygen and nitrogen acids. EQUILIBRIUM ACIDITIES IN DIMETHYL SULPHOXIDE (DMSO) If solvent reorganization presents less of an activation barrier in DMSO than in protic solvents as seems likely,8 the activation barrier between anions 2 and 3 will be less in DMSO and the mechanism of the deprotonation reaction should change.If the activation barrier disappears completely such nitroalkanes may give " normal " Bronsted correlations in DMSO. As the first step toward investigation of this matter we have examined the equilibrium acidities of nitroalkanes and many other types of TABLE1.-ABSOLUTEEQUILIBRIUM ACIDITIES FOR METHANE CARBON ACIDS CHSEWG IN DIMETHYL SULPHOXIDE SOLUTION name formula pKa nit romet hane CHJNO;! 17.2 methyl trifluoromethyl sulphone acetophenone acetone CH3 SOiCFj CH3COPh CH3COCH3 18.8 24.7 26.5 methyl phenyl sulphone dimethyl sulphone acetoni trile CH3S02Ph CH3SOZCH3 CH3CN 29.0 31.1 31.3 dimethyl sulphoxide CH3SOCH3 35.1 a not statistically corrected.carbon acids in DMSO solution. A method has been developed which allows absolute pK's reproducible to k0.05unit to be determined over a pK range from about 5 to 32.1° Acidity measurements on over 350 compounds have been made to date. Included in this survey are many of the common methane carbon acids of the type CH3EWG (EWG = Electron-Withdrawing Group; see table 1). Equilibrium F. G. BORDWELL data free of ion association effects have not been available hitherto for most of these weak acids. It will be observed that the acidities of CH3EWG range over 18 powers of ten; nitromethane is more acidic than the parent hydrocarbon methane by over 40 pK units.The major factor in determining the size of these enormous acidifying effects is believed to be the ability of EWG to delocalize the charge in the anion and thus to stabilize the anion i.e. CH,-EWG -+ CH,=EWG-. SOLVENT EFFECTS ON EQUILIBRIUM ACIDITIES OF CARBON ACIDS As might be anticipated from their wide range of acidities the acid strengths of carbon acids are highly solvent dependent. DMSO has a high dielectric constant (49 at 20°) a high dipole moment and a high degree of polarizability. As a con- sequence equilibrium acidities measured at low concentrations in this solvent are not complicated by ion association effects.1° Acidities in DMSO cannot be compared directly with those in solvents of low dielectric constant such as benzene ether or cyclohexylamine (CHA) since the latter are ion-pair acidities and cannot be placed on an absolute scale.When a series of hydrocarbons of similar structural types are compared such as fluorenes xanthenes triphenylrnethane diphenylmethane etc. relative acidities in DMSO and CHA are found to agree to within a pK unit or less. This agreement is fortuitous however apparently being a consequence of the extent of ion pairing in CHA remaining essentially constant throughout the series. This becomes evident once a carbon acid giving a localized anion such as phenylacetylene is included in the series. Now the apparent difference in ion pair acidities in CHA between fluorene and phenylacetylene is only 0.3 pK unit whereas the absolute difference as determined in DMSO is 5.9 pK units.Similarly in a (low dielectric constant) polyether solvent acetophenone appears to be more acidic than fluorene by ca. 4 pK units whereas absolute measurements in DMSO show that it is less acidic than fluorene by 2.3 pK units. This reversal is probably caused by ion pairing effects in the polyether solvent. Direct comparisons of absolute equilibrium acidities in DMSO and in water are possible (table 2). TABLE 2.-cOMPARISON OF EQUILIBRIUM ACIDITIES IN DMSO AND IN WATER acid pK (DMSO)a pK(H20)b benzoic 11.0 4.2 ni tromethane 17.2 10.2 acetone 26.5 20 9-cyanofluorene 8.3 11.2c malononitrile 11.1 11.0 bis(met hylsulphony1)met hane 15.O 12.7 a data from our laboratory unless otherwise noted. b ref (l) unless otherwise noted.C in 50 % MeOH + H20. Examination of table 2 shows that for acids in which the charge in the anion resides primarily on oxygen such as benzoic acid nitromethane and acetone the acidities are about 7 pK units greater in water than in DMSO. This is a consequence of the strong stabilization of oxide ions by H-bonding in water as compared to very weak stabilization by H-bonding in DMSO. On the other hand €€-bonding is a minor factor in stabilizing an anion in which the charge is delocalized over a carbon framework as in the anion derived from 9-cyanofluorene; here the acidity is some- what greater in DMSO than in water. Finally in acids where delocalization of the ACIDITIES OF CARBON ACIDS charge to the EWG function is relatively small such as malononitrile or bis(methy1- sulphonyl)methane the acidities in DMSO and water do not differ greatly.The stabilizing effect on an anion provided by solvation is enormous ranging from ca. 60-80 kcal/mol for the transformation from the gas phase to DMSO for ions such as ClO and C1-. It is not surprising then to find that the stabilizing effect of substituents is often far greater in the gas phase than in DMSO. For example p for equilibrium acidities of rn-andp-substituted benzoic acids is ca. 2.5 in DMSO,I1 as compared to ca. 10 in the gas phase.12 What is surprising is to find that examples exist where structural changes cause changes in DMSO solution acidities that approach those in the gas phase in size. Thus plots of DMSO solution acidities against gas- phase acidities l3 for a series of nitriles and for a series of ketones are linear with slopes of ca.1.1 and 1.3 respectively (fig. l).14 It would appear that when the 1210 14 '6> 18 22 26 30 34 38 42 46 50 equilibrium acidities in DMSO/kcal mol-' FIG.1.-Plot of gas-phase acidities (ref. (13) against DMSO solution acidities (ref. (14)). charge on the anion is highly delocalized the solvent effect remains essentially constant throughout the series and the effect of structural changes on the solution acidities gives a good measure of the relative intrinsic acidities of the compounds as revealed by gas-phase acidities. It is of interest to note that cyclopentadiene in which the charge on the anion is symmetrically distributed is more acidic in DMSO than in the gas phase judging from its position in fig.1 with respect to the lines for the nitrile and ketone families. THE EFFECT OF STRUCTURAL CHANGES ON EQUILIBRIUM AND KINETIC ACIDITIES For weak uncharged acids the effect of a structural change on the equilibrium acidity will generally give a good measure of the effect of structural change on anion stability. Since equilibrium acidity measurements for most types of carbon acids have not been available hitherto however it has become common practice to use kinetic acidities as an index of carbanion stabilities in order to obtain answers to F. G. BORDWELL such important questions as the effects of aromaticity antiaromaticity homoaro- maticity heteroatom substitution and s-character on relative carbanion stabilities.Some of the problems associated with the use of kinetic acidities as a means of judging carbanion stabilities have been outlined recently and several examples of misleading information relative to carbanion stabilities given by kinetic acidities with respect to a-hetero atom effects have been presented.l5 It appears likely that kinetic acidities have also given misleading information with respect to the effect of strain on the stability of substituted cyclopropane and cyclopropene anions.16 The kinetic acidities of such compounds have been used as an index of the presence of antiaromaticity in cyclopropene anions. For example the relative rates of base-initiated deuterium exchange for two phenylsulplionylcyclopropanes a phenylsulphonylcyclopropene and a corresponding open-chain compound are indicated under the formulas 4-7.Ph Ph Ph 4 5 6 7 Rel. rate 12 (1.0) Rel. rate 310 (1.0) The conclusion has been drawn that the faster rate for 4 relative to 5 indicates the absence of strain as a factor in determining the stability of the anion derived from 4 and that the lo3 slower rate for 7 compared to 6 can be attributed to antiaromaticity in the anion derived from 7.” Measurement of equilibrium acidities in DMSO for a number of cyclopropanes bearing EWG substituents i.e. c-PrEWG show however that the carbanions are highly strained relative to open-chain models (table 3). TABLE3.-EQUILIBRIUMACIDITIES OF CARBON ACIDS MEASURED IN DIMETHYL SULPHOXIDE SOLUTION EWG pK(CH3EWG) pK(i-PrEWG) pK(c-PrEWG) ApKa NO2 17.20+ 0.01 16.89+ 0.02 -27 -9 SOZCF 18.76+ 0.03 21.SO+ 0.03 26.60f0.03 7.3 COPh 24.70f 0.02 26.26+ 0.02 28.18+ 0.02 3.O SOzPh 29.04k0.05 >32 >32 >2.5 a pK(c-PrEWG)-pK(CH3EWG) statistically corrected.b rapid decomposition. Examination of table 3 shows that the c-PrEWG acids are less acidic than CH3EWG acids by factors ranging from ca. 3-9 pK units. This would correspond to an increased strain in the c-PrEWG- anion relative to the CH2EWG- anion amounting to 4 to 12 kcal/mol. The size of the estimated strain will depend of course on the open-chain model chosen. Use of the i-PrEWG model would decrease the size of the estimated strain but the conclusions would remain the same. In cyclopropane itself the high degree of s-character in the C-H bond is expected to cause an increase in acidity relative to open-chain alkanes.The EWG groups NO2 S02CF, CQPh and SO,Ph are all apparently imposing a high degree of p-character on the carbanion leading to large strain effects in the anion which completely over- shadow an intrinsically greater acidity caused by a higher degree of s-character in the C-H bond in the undissociated acid. The results show that strain effects in c-PrEWG- anions are large which indicates that strains in the corresponding cyclo- ACIDITIES OF CARBON ACIDS propene anions will also be large and must be considered in assessing their anti- aromaticity. The results also indicate a strong conjugation of sulphur in the S02CF3 and S02Ph groups with the carbanion the order being S02CF3> S0,Ph.This is the order predicted by Craig with respect to the change in the ability of d-orbitals on sulphur to participate in conjugation on introduction of a strong EWG (CF3 for Ph in the present instance). Recent theoretical analyses suggest however that d-orbital conjugation may not be significant.lg It is possible therefore that orbitals other than d-orbitals may be involved but there can be no escaping the fact that the conjugative ability of sulphur in sulphonyl groups towards a-carbanions is strong. Financial support by the National Science Foundation (MPS 74-12665) is grate- fully acknowledged. The author also wishes to express his appreciation to the University of Wales for a Visiting Professorship during the tenure of which this paper was written.R. P. Bell The Proton in Chemistry (Cornell University Press 2nd edn. 1973). ’F. G. Bordwell W. J. 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