Kinetic and Thermodynamic Basicities of Anions in Mixed Solvents BY BRIAN G. Cox AND ALANGIBSON Department of Chemistry University of Stirling Stirling Scotland Received 1st May 1975 The rates and equilibria for reactions involving proton transfer between several nitroalkanes and fluoride acetate and hydroxide ions have been investigated in dimethylsulphoxide+ water and trifluoroethanol+ water mixtures. The results show that the effects of solvent variation on the rates are not simply related to the effects on the overall free energy changes occurring during the reactions. Recently observed anomalies in Bronsted /3 coefficients for reactions involving these substrates disappear as the fraction of water in the dimethylsulphoxide + water mixtures decreases. It is argued that the anomalous values in water result from specific hydration effects on the acidity constants.Much of the recent interest in proton transfer reactions (eqn (1)) SH+B-+ S-+BH (1) has centred on the relation between the reaction rates and kinetic hydrogen isotope effects and the overall free energy change occurring during the reacti0n.l. The effect of variations in the nature of both SH and B- have been extensively studied generally in aqueous media. It is becoming increasingly clear however that acid strengths are considerably influenced by the strong solvation which occurs in water. It is noticeable for example that within a series of related acids (e.g. benzoic acids carboxylic acids phenols) the pK,’s in dipolar aprotic solvents (polar solvents without acidic hydrogens) and in the gas phase are considerably more sensitive to the effect of substituents than they are in water.It has been suggested that a number of apparent anomalies in Bronsted p coefficients relating rates and equilibrium constants for proton transfer reactions may in fact have their origin in the variable contribution of hydration to the acidity constants (of SH and BH)? In the present paper we report a study of the effect of changing solvent on the rates equilibria and Bronsted p coefficient for reactions of the type shown in eqn (I). The substrates used include several substituted nitroalkanes and 1,l-dinitroethane. These substrates are sufficiently acidic to enable their pK,’s to be determined accur- ately.Also reactions involving these substrates in aqueous solution have in many cases shown anomalous Bronsted /3 coefficient^.^. It is of interest therefore to see the extent to which these anomalies are due to the effects of solvation in water. EXPERIMENTAL MATERIALS 2-Nitropropane was purified by spinning band distillation. G.l .c. and n.m.r. analysis showed it to be free from traces of 1-nitropropane and nitroethane. Nitroethane was dried (MgS04) and distilled. 1,l-Dinitroethane was prepared by reaction of nitroethane with silver nitrite in basic solution as previously described.* 1-Arylnitroethanes 1-(3’-107 ANION BASICITIES IN MIXED SOLVENTS methoxypheny1)-and 1-(4'-nitrophenyl)-l-nitroethane were prepared by oxidation of the oximes of the corresponding acetophenones as described by Bordwell et aIa9 Dimethylsulphoxide was purified by distillation under reduced pressure from calcium hydride ; trifluoroethanol was dried (Na2S04) and distilled ; inorganic chemicals were of Analar Grade.pK MEASUREMENTS pK,'s of the various acids in Me2SO+H20 and CF,CHzOH+H20 mixtures were determined by potentiometric measurements with glass electrodes. The electrodes were calibrated with dilute (ca. 10-'-10-3 M) perchloric acid solutions in the solvent mixtures. Values for acetic acid agree within 0.1 pK unit with values previously determined using conductance measurernents,l0 acid-base indicators and potentiometric measurements with hydrogen e1ectrodes.l2 In the determination of the pK of HF allowance for the formation of HFj was made using simultaneous measurements of pH and the fluoride ion activity (with a fluoride-ion-selective electrode) as described by Kresge and Chiang.l3 The pK of rn-methoxy phenylnitroethane in water was obtained from spectrophotometric measurements in tris( hydroxyme t hyl amino)met hane buffers. The acidity constants KA of the acids HA in solvent S are represented by eqn (2) where the y's are activity coefficients referred to infinite dilution in solvent S. The activity coefficients of ionic species were calculated from the Davies equation (3) l4 where A is the Debye-Huckel function dependent upon the solvent dielectric constant and temperature. The activity coefficients of AI+ -logy* =-0.3AI (3) l+P neutral species were assumed to be unity.All measurements were carried out at 25 (+0.1)"C. KINETIC MEASUREMENTS The proton-transfer reactions were followed either by direct spectrophotometric obser- vation of the substrate anion formed or by measuring spectrophotometrically the rates of iodination of the substrates. Iodination reactions were followed under conditions where the rate determining step in the iodination was the deprotonation of the substrate (SH). Thc particular method used for a given substrate-base reaction is included in the Results section. The reactions were followed with a Gilford 2400 spectrophotometer or a Durrum-Gibson stopped flow spectrophotometer depending upon the reaction rate. All measure- ments were made at 25 (kO.2)"C. RESULTS 2-NI TROPROPAN E The rates of deprotonation of 2-nitropropane (2-NP) were obtained from measured rates of iodination.15* l6 The reactions were carried out in solutions with [2-NP]ca.5 x 10-3-5x 10-2M [I-] = 0.01 M and initial iodine concentrations <10-4M. The rates were measured in Me,SO +H20 mixtures using acetate and fluoride buffers with anion concentrations in the range 2 x 10-2-10-'M. Fluoride buffers with [F-]/[HF] 21 40 (pH = 4.7 in water) were used to avoid complications arising from HF; formation. The iodination of 2-nitropropane is known to be reversible 16. l7 where either [I-] or [H+]is high but under the conditions used the rate law shown in eqn (4) and (5)was obeyed over -d[I;]/dt = -d[2-NP],dt = ke[2-NP] (4) B. G. COX AND A. GIBSON 109 where k = k,+k~[B] (5) at least 90 % of reaction.acetate or fluoride ions. In eqn (4) and (9,[I;] = [I2]+[I,] and B refers to either In solvent mixtures containing dimethylsulphoxide ko was negligible compared with kB[B] so that k = kB[B]. The results for the system are given in table 1. NITROETHANE Rates of proton transfer from nitroethane (NE) to acetate in Me2S0+H20 and CF3CH20H+H20 mixtures have been measured. Equilibrium constants have been obtained from measured pKa's. The experimental conditions and methods were the same as for 2-nitropropane except that nitroethane concentrations were ca. 0.15 M. The results are also listed in table 1. TABLEN RATES AND EQUILIBRIA FOR PROTON TRANSFER FROM NITROALKANES (SH) TO ACETATE AND FLUORIDE IONS IN SOLVENT MISTURES AT 25°C 1.2-Nitropropane in Me,SO+ HzO mixtures -PKHOA~6 10gkoAcb ~KSH XM~~SO~ ~KSH ~KSII -PKHF 7+hgFb 0.00 7.74c 3.0 0.43 4.6 0.42 0.21 9.5 3.7 1.41 4.6 1.95 0.38 11.0 3.9 2.25 4.3 3.16 0.51 12.1 4.1 2.74 3.9 3.89 0.70 -3.80 1.oo 16.2d 4.2 2. Nitroethane in Me2SO+Hz0 and CF3CH20H+ HzO mixtures Xnre2soa ~KSHPKsIi-pKHoAc 5+bgkOAcb XTFE' PKSH ~KSH -~KHOAC 5+logkOAC 0.00 8.8 4.1 0.51 0.00 8.8 4.1 0.51 0.21 10.2 4.2 1.63 0.20 10.2 4.4 0.22 0.38 11.7 4.5 2.47 0.32 -0.17 1.00 16.4d 4.4 -0.50 11.5 4.4 -0.07 (a) mole fraction of dimethylsulphoxide ; (6) kg dm3m01-'s-' are rate constants for proton transfer from SH to B ; (c) ref. (16) ; (d)ref. (19) ; (e)mole fraction of trifluoroethanol.TABLE 2.-cOMPARISON OF pKa'S AND RATES WITH ACETATE IONS FOR NITROETHANE AND 1,l-DINITROETHANE IN MezSO+HzO MIXTURES AT 25°C -l,t dinitroethane nitroethane 7-XMe2SOQ PKSH 5 fIogkOAc PKSH 5+lOgkoAcb 8' 0.00 5.24d 5.33d 8.8 0.51 1.34 0.21 3.3 7.15 10.2 1.63 1.12 0.38 5.3 8.55 11.7 2.47 0.95 1.oo 6.6' - 16.4' - - (a)mole fraction of Me,SO ; (6) ko~~/dm~mol-'s-' are rate constants for proton transfer from SH to QAc- ; (c) = [~O~~~~,(DNE)-~O~~~A,(NE)]/[~K(NE)-~K(DNE)] ; (d) ref. (7) ; (e) ref. (19). 1,l-DIN ITROET H A N E The reaction of 1,1 -dinitroethane (DNE) with acetate in Me2S0+H20 mixtures (eqn 6)) was followed by observing the appearance of the dinitroethane anion koAc-CH3* CH(N02)2 +OAC-+ CH,* C(NO2); +HOAC (6) kHoAc ANION BASICITIES IN MIXED SOLVENTS spectrophotometrically at 385 nm.DNE concentrations were ca. 5 x M and acetate concentrations were in the range 0.02 to 0.1 M with [OAc-] = 2[HOAc]. The observed rate law was of the form shown in eqn (7) and (8) where K = KDNE/KHOAc is the equilibrium constant for -d[DNE]/dt = k,[DNE] where k = kOAc[OAc-]{ 1 + [HOAc]/K,[OAc-]) reaction (6) and koAcis the rate constant for the forward reaction. Kinetic and thermodynamic data for the reaction between dinitroethane and acetate are given in table 2 together with the corresponding results for nitroethane. 1-ARY LNI TROETH A NES The rates of reaction of m-OMe- and p-NO2-phenylnitroethane with OH-were followed by spectrophotometric observation of the nitroalkane anion.* Nitro-alkane concentrations were < M and [OH-] ca. 10-3-2x M. The observed rate law was as shown in eqn (9) -d[nitroalkane]/dt = ko,[OH-][nitroalkane]. (9) TABLE 3.-pK,'s AND RATES WITH HYDROXIDE AND ACETATE IONS FOR 1-ARYLNITROETHANES YC6H4/CH(Me)N02,IN Me2SO+H20 MIXTURES AT 25°C (1) reaction with OH--Y = pNO2 Y = m-OMe xble2SOa 'pKsHfIb p&H logkOHb B" 0.00 6.63 1.70 7.40 0.93 1.12 0.21 7.40 3.15 8.93 1.93 0.80 0.51 8.64 5.13 10.94 3.63 0.64 (2) reactions with OAc-Y = P-NO~ Y = m-OMe -xMe2s0 ~KSH 10gkoAcb -0 PC 0.51 8.64 0.20 10.94 -1.38 0.69 (a) mole fraction of Me2S0 ; (b) kg/drn3mol-'s-' are rate constants for proton transfer from SH to B ; (c) /3 = [b&B (p-NO2)-logk~(rn-OMe)]/[pK(m-OMe)-pK(p-NO,)].The rates of reaction with acetate ions in 80 vol% Me2SO+H,0 were also measured the reaction of the p-NOz derivative being followed by observation of the nitroalkane anion and the rn-OMe derivative by iodination as described earlier. Kinetic and thermodynamic data for the reactions are listed in table 3. DISCUSSION For a proton transfer reaction such as that shown in eqn (l) the Bronsted fl coefficient relating the effect of variations in the nature of B-or SH on the rates and equilibria may be defined by eqn (lo) where k is the p = 6AG*/6AG0 = GlogkB/610gK (10) rate constant and K (= KSH/KBH) is the equilibrium constant for the reaction. A Bronsted exponent greater than unity then indicates a reaction in which the substituent B.G. COX AND A. GIBSON effect on AG* is greater than that on AGO which is contrary to the expectation that the effect of a substituent should vary monotonically with the extent of reaction. Examination of the results in table 1 shows that for the reactions studied the effects of solvent on the reactions do not vary monotonically with the extent of proton transfer during the reaction. The pK,’s of both the substrates and bases vary con- siderably with increasing amounts of Me,SO (or CF3CH20H) in the solvent but there is little change in the equilibrium constant for the reactions between the substrate and bases (expressed as pKsH -pKBH). The rates however increase rapidly with content of the organic component in Me,SO+H,O mixtures and decrease in CF,CH20H+H,0 mixtures.This behaviour can be readily explained in terms of the large difference in the interaction of water with anions of high charge density such as F- RCO, RNO; (capable of H-bond stabilisation) and large polarisable anions (such as the transition state anions) relative to dipolar aprotic solvents such as Me2S0.18 Trifluoroethanol being more acidic than water would be expected to stabilise even further the smaller anions relative to the transition state anions. Such behaviour is perhaps not unexpected as it has been known for some time that the rates of reactions shown in eqn (1 1) *X-+RX + RX* +X-(1 1) where X and *Xare isotopes are very sensitive to the nature of the solvent IS although the equilibrium constant for the reaction is clearly independent of the solvent.reaction coordinate FIG.1.-Bronsted coefficients and solvent effects. The relevance of these effects to the explanation of the origin of p values greater than unity in water can be seen from the results in tables 2 and 3. Considering for example the results in table 2 as the fraction of Me,SO in the solvent is increased the difference in pK of dinitroethane and nitroethane increases going from 3.6 pK units in water to 9.8 pK units in Me2S0.19 This reflects the loss in the higher hydration energy of the mononitroalkane anion relative to the dinitroalkane anion with its more highly dispersed charge. Similar effects do not operate in the transition states since for both reactions these have highly dispersed charges.Thus the B ANION BASICITIES IN MIXED SOLVENTS values decrease (and become normal) as the Me2S0 content of the solvent increases. The results in table 3 may be explained in an analogous manner. This explanation is shown schematically in the figure where curve I represents nitroethane (or nz-OMe-phenylnitroethane) and curve I1 represents dinitroethane (or p-NO2-phenylnitroethane). The full lines indicate the reaction in for example the gas phase and the dotted line in water. For simplicity the curves in the two phases have been moved relative to one another to align reactants and the solvent is shown as having no effect on the transition state. It is interesting to note that Jones and Patel 2o have recently found that comparison of the effects of increasing fluorine substitution in acetylacetones on the acidity and rates of detritiation leads to anomalous p values.This is attributed to the effects of hydrate formation of the fluorinated ketones on their measured pK,'s. This may be regarded as an extreme example of the effects of hydration operating specifically on the measured equilibrium constant and so not having a corresponding effect on the transition state energies. It has in fact been suggested many years ago 21 that hydration effects could simply explain " anonlalies " such as the observation of parallel but separate Bronsted plots for primary secondary and tertiary amines. We suggest that in addition because within a series of related acids increases in acidity caused by substituents frequently arise from increased delocalisation of the anion charge hydration can also alter the slopes of Bronsted plots.This will apply equally to results obtained from the variation of a series of substituted carboxylate anions with a constant substrate or from variations in the nature of the substrate with a constant base. Such a factor should be borne in mind when attempting to relate observed fl values to transition state structures etc. We thank the SRC for a studentship for A. G. and a research grant and Prof. R. P. Bell for discussion. R. P. Bell Chenr. SOC.Reu. 1974 3 513. A. J. Kresge Chem. SOC. Rec.. 1973 2 475. (a) I. M. Kolthoff and M. K. Chantooni J. Amer. Chem. SOC.,1971 93 3843 ; (6)B.G. COX Ann. Reports Chem. SOC. A 1973 249. K. Hiraska R. Yamdagni and P. Kebarle J. Amer. Chent. SOC.,1973 95 6833. e.g. F. G. Bordwell and W. J. Boyle J. Amer. Chem. 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