J . Chem. SOC., Faraday Trans. I , 1982, 78, 1633-1639 Critical Comments on the Interpretation of Heat Capacities of Activation and on the Experimental Evidence for other Recent Mechanistic Proposals for Solvolyses of t-Butyl Halides in Water and in Binary Aqueous Mixtures BY T. WILLIAM BENTLEY* AND GILLIAN E. CARTER Department of Chemistry, University College of Swansea, Singleton Park, Swansea SA2 8PP Receiued 3rd August, 1981 Kinetic data for solvolyses of t-butyl bromide in homogeneous solutions in water and in aqueous binary mixtures with acetone, methanol and ethanol at 25 O C are reported, illustrating the development of simple conductometric techniques for studying relatively fast solvolytic reactions of sparingly soluble solutes. Solvolyses of t-butyl chloride in water and in aqueous ethanol are re-examined.Experimental errors due to (a) equilibration of solute between liquid and vapour phases and (b) formation of hydrophobic aggregates which can be disrupted by ultrasonic irradiation are discussed. Four recent mechanistic proposals are critically reassessed. It is shown that: (1) the induction period observed at low solute concentrations for solvolyses of t-butyl chloride in water is due to the buffering action of absorbed carbon dioxide; (2) recent kinetic data on the effects of ultrasonic irradiation are unreliable; (3) deviations from first-order kinetics for solvolyses of t-butyl chloride in 40% ethanol + water mixtures are due to equilibration of solute between liquid and vapour phases. It is also argued that (4) the most recent interpretations of heat capacities of activation, suggesting partially reversible formation of an intermediate in hydrolysis of t-butyl chloride, do not take adequate account of alternative interpretations.Solvolyses of t-butyl halides, (CH,),CX, provide one of the cornerstones of homogeneous solution kinetics.' The reaction is first order and is believed to occur by rate-determining heterolysis of the carbon-halogen bond to give a contact ion pair. The role of solvent as nucleophile cannot be assessed from the first-order rate law, and it is likely that these reactions proceed with some bimolecular (S,2) character by rearside nucleophilic solvation of the developing positive charge on the a-carbon atom and/or on the P-hydrogen atom.2 Alternatively such reactions could be described as mainly dissociative with weak associative ~haracter.~ More complicated kinetics could arise if there were reaction between the strong acid (HX) produced during solvolysis and another component of the reaction mixture, e.g.isobutene (product) or alcohol (co~olvent)~ may react with HX, or HX may catalyse further reaction of t-butyl halide or of isobutene. Consequently it may be necessary to add a buffer (e.g. 2,6-lutidine, a sterically hindered weak base) to prevent these side reactions. Recently there have been four novel mechanistic proposals, which we now wish to evaluate critically: (1) that an induction period observed at low concentrations of t-butyl chloride in water is due to a requirement for acid catalysis;5 (2) that the effects of ultrasonic irradiation on solvolysis of t-butyl chloride in water and in aqueous ethanol are due to disruption of solvent structure;6 (3) that solvolyses of t-butyl chloride in 40 % ethanol + water mixtures show mechanistically significant deviations 16331634 SOLVOLYSIS OF t-BUTYL HALIDES from first-order kinetics;6 (4) that the negative heat capacities of activation observed for hydrolysis of t-butyl chloride are due to partially reversible formation of contact ion pairs (or of some other intermediate).' Our reassessment of the first three proposals is based largely on reinvestigation of the experimental evidence: accurate kinetic studies of organic solutes in water are made difficult by their low solubility and/or high reactivity.Also, t-butyl chloride is partitioned between liquid and vapour phases, so it is necessary to minimise the vapour space above the solution.8 In this paper we report kinetic data for t-butyl chloride and bromide in water and in aqueous binary mixtures.These studies require a combination of techniques for assessing the reliability of kinetic data for reactions of sparingly soluble solutes, because it is necessary to check whether truly homogeneous solutions are formed rather than aggregates of small number of molecules. EXPERIMENTAL t-Butyl halides were distilled from anhydroLj sodium sulphate and their purity was checked by n.m.r. and refractive index. Acetone, ethanol and methanol were purified as described previouslyg and binary mixtures were prepared as stock solutions by weight or in smaller quantities using calibrated pipettes.Conductance techniques for rapid reactions were as described previously'* with the following modifications of method A. The conductance cell (capacity ca. 20 cm3) was fitted with a side-arm used for rapid injection of < 20 mm3 of a 0.25-5 % solution of the alkyl halide in acetone. Either a nitrogen driven stirrer was used throughout the kinetic run or the cell was shaken vigorously using a B and T shaker before recording the conductance data. Servoscibe Is or Phillips PM8041 recorders (maximum chart speeds 1 cm s-' and 2 cm s-l, respectively) were used, the latter with millimetre graph paper. After using the mechanical shaker the conductance reading was not steady for ca. 1 s, and the fastest reactions (t-butyl bromide in water at 25 "C) were followed from 80-90% reaction onwards.Low-temperature measurements (< 20 "C) were carried out using a Grant refrigerated thermostatic bath ( f 0.05 "C) and other measurements using Grant SP50 thermostatic baths. Slower kinetic runs (ti > 120 s) were monitored using a Wayne Kerr model B33 1 autobalance conductance bridge. RESULTS Included in this paper are kinetic data for solvolyses of t-butyl chloride in aqueous ethanol at 0.5 OC (table l), of t-butyl chloride and bromide in aqueous ethanol at 25 OC (table 2) and of t-butyl bromide in aqueous methanol and aqueous acetone at 25 O C (table 3). These results were obtained conductimetrically using < mol dm-3 solutions, assuming that the change in conductance is proportional to the extent of reaction." Where direct comparisons can be made, our results agree well with those obtained titrimetrically.8* l2 By combining our techniques for sparingly soluble solutess with those for relatively fast solvolytic reactions,lo we examined a wider range of solvolyses of t-butyl bromide than was possible titrimetri~al1y.l~ Our result for the fastest reaction examined at 25 O C , t-butyl bromide in water, is in agreement with the extrapolated value previously obtained conductometrically.14 Satisfactory bromide/ chloride (Br/Cl) rate ratios (tables 2 and 3) provide further evidence for the reliability of the results.Additional internal checks of the reliability of the kinetic runs were carried out; it was established that: (i) the rate constant calculated for 50% reaction was in satisfactory agreement with that for the full run (> 85% reaction); (ii) the precision of fit to first-order kinetics was high (usually better than 0.3%); (iii) there was generally insignificant 'drift' of the conductance of the solution even after ten half-lives.T.W. BENTLEY AND G. E. CARTER 1635 TABLE l.-sOLVOLYTIC RATE CONSTANTS ( k ) FOR t-BUTYL CHLORIDE IN AQUEOUS ETHANOL AT 0.5 "C solvent rate constant k/ lo4 s-' mole ethanol (%)" fraction ref. (6)b ref. (12)C3d this workbTe 10 0.033 6.06 5.15 5.2 k0.2f 20 0.072 4.05 3.44 3.49 f 0.069 30 0.117 2.43 1.99 1.96 f 0.019 40 0.171 1.24 0.62 0.62 f 0.019 a % v/v ethanol + water; determined conductometrically ; calculated from data at 0 and 25 "C; minimum vapour space above the solution; conductivity cell unstirred; f mean of four kinetic runs; one additional kinetic run with continuous stirring gave k = 5.0 x determined titrimetrically ; s-'.9 Mean of two kinetic runs, errors shown are average deviations. TABLE 2.-sOLVOLYTIC RATE CONSTANTS ( k ) FOR t-BUTYL BROMIDE AND CHLORIDE IN AQUEOUS ETHANOL AT 25 O C solvent rate constant k/s-' rate constant k/s-l ethanol (%)" (CH313CBr (CH3),C Cle (n)b Br/C1 (water)d (7.0 f0.2) x lo-' (5) (2.8 k 0 . l ) x (10) 25 10 (4.9 f 0.2) x lo-' ( 6 ) (1.83k0.04) x (4) 27 20 (2.7 k0.2) x lo-' (6) (1.10f0.04) x (7) 25 30 (1.26f0.05) x lo-' (5) (4.8 f0.1) x 10-3 (3) 26 40 (4.0 k0.2) x (6) (1.46f0.03) x (21) 27 a v/v ethanol+water. Number of kinetic runs; errors shown are average deviations.In Data at other temperatures: k/s-'; -0.08 "C; (1.67 t 0.08) x lO-l, 14.46 "C; errors shown are average devia- satisfactory agreement with data reported in ref. (8). (2.08 & 0.07) x tions of duplicate runs; activation parameters A S = 93 kJ mol-l, A S = + 62 J mol-l K-l. TABLE 3.-%LVOLYTIC RATE CONSTANTS (k) FOR t-BUTYL BROMIDE IN AQUEOUS METHANOL AND AQUEOUS ACETONE AT 25 "C rate constant k / s l rate constant k/s-l solvent (%)" me thanolb Br/CIC ace toneb Br/Clc ~ ~ ~~ ~ 10 (4.7 f0.2) x 10-1 27 (3.6 f0.3) x 10-l 23 20 (2.57f0.07) x lo-' 26 (2.01 f0.06) x 10-1 27 30 (1.34 f 0.05) x 10-1 26 (8.6 f0.2) x 31 50 (2.69 f 0.02) x 31 40 (6.51 f0.06) x 29 (3.07 f 0.05) x 35 80 (8.8 fO.l) x 39d " Volume % of organic solvent+water. Determined condtktometrically at least in duplicate; k calculated from data at an accurately determined temperature close ( f 0.2 "C) to 25 "C.Rate constant for bromide [ref. (13)] is 8.7 x Bromide/chloride rate ratios; kinetic data for chloride from ref. (8). s-l, in agreement with this work.1636 SOLVOLYSIS OF t-BUTYL HALIDES Anomalous results were initially obtained for solvolyses of ca. 0.0005 mol dm-3 t-butyl bromide in 80% (v/v) methanol + water solutions. Although t-butyl bromide dissolved rapidly at 25 OC, there was little change in the conductance of the solution for ca. 4 min after injection of the bromide. The induction period remained the same irrespective of how long or how vigorously the mixture was shaken, but disappeared when solutions free from carbon dioxide were used.Similarly we observed the previously reported5 induction period of up to 30 s for hydrolysis of t-butyl chloride (injected as an acetone solution) in water at 25 OC, but no induction period when freshly distilled water was used. DISCUSSION The induction period for solvolyses of low concentrations of t-butyl halides in aqueous media appears to be due to the buffering effect of dissolved carbon dioxide, which is known to affect the conductance of dilute solutions of HCl.15 Consequently there is no reliable evidence supporting the proposal5 that hydrolysis of t-butyl chloride is catalysed by HCl. Solvolyses of t-butyl chIoride in water at 25 OC did not give satisfactory infinity conductance values, unless the vapour space above the solution was minimised [see also ref.(S)]. The second mechanistic proposal is based on rate accelerations observed on ultrasonic irradiation of solutions of t-butyl chloride in aqueous ethanol at 0.5 0C.6 Unfortunately, the kinetic data reported6 in the absence of ultrasonic irradiation are not consistent with literature values,12 nor with our measurements (table 1). t-Butyl chloride does not dissolve readily in aqueous ethanol at 0 OC, so we prepared the solutions at ca. 10 "C before equilibrating to 0.5 OC. Consequently ca. 80% of the total reaction was studied (table 1). We observed lower rate constants if the vapour space above the solution was not minimised, and lower rate constants are usually obtained if molecular aggregates instead of truly homogeneous solutions are f ~ r m e d . ~ Therefore these sources of error do not explain why the recently reported6 rate constants in the absence of ultrasonic irradiation are too high (table I).A trivial explanation such as incorrect temperature or solvent composition appears to be required. We have found that ultrasonic irradiation disrupts the molecular aggregates of sparingly soluble solutes in aqueous media.9 This effect could explain the 50-100% increase in rate constants on ultrasonic irradiation of solutions of t-butyl chloride in aqueous ethanol. Alternatively these effects may be due to inadequate temperature control-we were unable to obtain satisfactory thermostatic control inside an unstirred conductivity cell placed in an ultrasonic bath containing iced water, as described by earlier workers.6 Despite the unreliability of the experimental evidence it is conceivable that there is a small residual rate enhancement (i.e.not explicable by the effects discussed above) on ultrasonic irradiation of solvolyses of t-butyl chloride in aqueous ethanol. For hydrolyses of various esters it has been proposed that intense localized pressure increases in collapsing bubbles account for the observed rate enhancements;16 it is known that solvolytic reactions are accelerated by increases in pressure. l7 Consequently, recent proposals6 that ultrasonics provides evidence for disruption of solvent structure around a reacting solute in low concentration, and 'new insights' into the mechanisms of direct displacement reactions at carbon seem highly questionable. The third mechanistic proposal is based on deviations from first-order kinetics observed beyond 70% reaction for solvolyses of t-butyl chloride in 40% ethanol + water solution at 25 0C.6 We have observed similar results on numerous occasions, but reproduceable first-order rate constants, in agreement with the literature valueT.W. BENTLEY AND G. E. CARTER 1637 obtained titrimetrically,s can be obtained from the first 70% of reaction. t-Butyl chloride dissolves readily in 40% ethanol c water solution at 25 O C , so poor solubility does not appear to be the cause of these deviations. We have found that high-precision results from < 10% to > 99% reaction can be obtained if the vapour space above the solution is minimised; duplicate runs gave k = (1.45 0.01) x l 0-3 s-l with correlation coefficients > 0.99997 and a precision of fit to first-order kinetics better than 0.1 %.Consequently the reported deviations from first-order kinetics are not mechanistically significant. I I I 1 I 1 0 0 e 0 0 e 0 I I I I I I 1 I I 1 -5 - 4 - 3 - 2 log k (CH,), CCl FIG. 1.-Plot of logarithms of solvolysis rates of t-butyl bromide against t-butyl chloride for water (e), ethanol +water (0; slope: 0.94; correlation coefficient: 0.9999), methanol + water (a; slope 0.94; correlation coefficient: 0.9998), and acetone + water (0 ; slope 0.90; correlation coefficient: 0.9999). Kinetic data from tables 2 and 3, and ref. (8), (1 3) and (18). The kinetic results for t-butyl bromide (tables 2 and 3) complete three series of data: ethanol + water; methanol +water and acetone + water; kinetic data for the less aqueous media have been reported by l8 These results give good linear plots (fig.1) for logarithms of rate constants for t-butyl bromide against t-butyl chloride (or Y value8), with a small dispersion of lines for different solvent pairs. A consistent pattern of solvent effects on reactivity and mechanism has emerged from many studies of solvent mixtures using free energy plots,1a* 2, 9 3 lo, 1 2 ~ l3 e.g. fig. 1 using log k or AGI, and this treatment can be extended to solvents of widely varying ionizing power and nucleophilicity.la9 lo Despite the complexity of solvation effects these studies suggest that there is an underlying simplicity in the mechanism of aliphatic nucleophilic substitution,la with accumulating gas-phase data indicating S , 1 reactivity under solvent-free conditiom2 Unfortunately dissection of AGt for solution reactions into Am, AS$, AC; and even dAC$/dT provides a much more complex view.l2? 1 9 7 2o Such studies have been described as a ‘fetish’;21 they may represent unnecessary attention to detail, given the1638 SOLVOLYSIS OF t-BUTYL HALIDES present lack of understanding of the activation process in solution and the tendency for changes in Am and TAS to compensate each other.However, as there is considerable current interest in mechanistic proposal (4), we comment here on interpretations of ACi. This differs from the previous three proposals (above) in that the experimental rate data are well-established.l’* 22 For most, if not all solvolyses, a plot of log k against 1 / T is non-linear. Such curved Arrhenius plots may imply a dependence of activation energy with temperature. Of the various ways of treating the experimental data, the simplest is a direct plot of A S (obtained by differential methods22) against T.The results fit eqn (1) Am = AH,S+ TACb (1) where ACJ is the heat capacity of a c t i v a t i ~ n . l ~ * ~ ~ Alternatively a large amount of data has been fitted to the empirical eqn (2) log k = A/T+B log T+C (2) B = (ACb/R)+ 1 . (3) from which eqn (3) can be obtained using transition-state theory if dACb/dT = 0 2 0 Accurate kinetic data and alternative equations now indicate that AC: is temperature dependent,’? 22 as anticipated by Kohnstam19 who included a fourth term (D7) in eqn (2).This additional complexity has led to proposals for major revisions7’ 23 of previous interpretations (see later), when minor refinement may have been more readily justifiable. Until recently it was argued that ACL [from eqn (2) and (3)] probed solvent reorganization,ll* 1 9 9 2o rather than the mechanism of reaction of solute. This is consistent with the large variation in A d p on addition of cosolvent to 24 when only minor mechanistic changes would occur. Also A b p is almost constant for solvolyses of arenesulphonates of widely varying showing insensitivity to mechanism. Furthermore the parallels between A c p + and Winstein-Grunwald rn value show the relationship between solvent reorganization and the extent of charge dispersion or charge development in the transition These arguments were undermined by the observation of AC,f values that appeared to be too large for the equilibrium (required by transition-state theory) between covalent solute and partially ionic transition state.26 However, Jencks has recently suggested that some reactive intermediates in solution may not be solvent eq~ilibrated,~’ and this proposal could be extended to transition states.The suggested major revisions7* 23 in the above interpretation are based on an earlier ‘hypothetical’ proposal that AC$ is ‘spurious’, and is due entirely to mechanistic complexity-a two-stage mechanism in which formation of an intermediate [e.g. an ion pair-see eqn (4)Iz2 is only partially rate-limiting. The revised two-stage inter- pretation leads to a four-parameter equation, consistent with the experimental data and superior to eqn (2):227 23 (4) k, k, k-i RX $ [intermediate] -+ product.However, the fit of the data to the extended (four-parameter) version of eqn (2) is also good.22 Even if the general argument for eqn (4) is accepted, consideration of specific examples leads to further difficulties. Anomalous Arrhenius behaviour is observed for hydrolysis of ethyl for which an ion-pair intermediate is firmly excluded.’? 28 Also there is little support for the implied requirement7$ 22 that a t-butyl ion pair undergoes return in water, and we have recently argued against ion-pair returnT. W. BENTLEY AND G. E. CARTER 1639 even for solvolyses in very weakly nucleophilic alcohols. lo Therefore it seems unlikely that ion pairs are the intermediates that would be required by eqn (4).Alternatively the intermediate may be a preassociation complex,27 but this proposal would be difficult to verify. Further serious doubts about the two-stage mechanism arise from the derived values of kJk2 [eqn (4)]. Numerous studies (see above discussion fig. 1) have established that solvolysis rate constants vary uniformly with change in solvent composition but, for hydrolysis of t-butyl chloride, calculated values of k_Jkz show no regular trends with addition of organic cosolvents. We conclude that deductions about non-linear Arrhenius behaviour based on eqn (4) remain ‘hypothetical’ for solvolyses of aliphatic substrates. We thank the S.R.C. for financial support, and M. J. Blandamer, J.Burgess, R. H. Davies, R. E. Robertson and J. M. W. Scott for helpful comments. For recent reviews of the background to this work see: (a) T. W. Bentley and P. v. R. Schleyer, Adv. Phys. Org. Chem., 1977, 14, 1; (b) W. J. Albery, Annu. Rev. Phys. Chem., 1980, 31, 227. T. W. Bentley, C. T. Bowen, W. Parker and C. I. F. Watt, J. Am. Chem. SOC., 1979, 101, 2486. J. 0. Edwards, Inorganic Reaction Mechanisms (Benjamin, New York, 1964), p. 100. P. v. R. Schleyer and R. D. Nicholas, J. Am. Chem. Soc., 1961, 83, 2700. P. A. Adams, J. G. Sheppard and E. R. Swart, J. Chem. SOC., Chem. Commun., 1973, 663. J. P. Lorimer and T. J. Mason, J. Chem. SOC., Chem. Commun., 1980, 1135. Commun., 1981, 13; J. Chem. Soc., Faraday Trans. 1, 1981, 77, 1999. T. W. Bentley, C. T. Bowen, H.C. Brown and F. J. Chloupek, J. Org. Chem., 1981, 46, 38. ’ M. J. Blandamer, J. Burgess, P. P. Duce, R. E. Robertson and J. M. W. Scott, J. Chem. SOC., Chem. * A. H. Fainberg and S. Winstein, J. Am. Chem. Soc., 1956, 78, 2770. lo T. W. Bentley, C. T. Bowen, W. Parker and C. I. F. Watt, J. Chem. SOC., Perkin Trans. 2, 1980, 1244. l 1 E. A. Moelwyn-Hughes, R. E. Robertson and S. Sugamori, J. Chem. Soc., 1965, 1965. l 2 S. Winstein and A. H. Fainberg, J. Am. Chem. SOC., 1957, 79, 5937. l3 A. H. Fainberg and S. Winstein, J. Am. Chem. SOC., 1957, 79, 1602. l 4 E. A. Moelwyn-Hughes, J. Chem. SOC., 1962, 4301. l5 R. H. Stokes, J. Phys. Chem., 1961, 65, 1242. l6 D. S. Kristol, H. Klotz and R. C. Parker, Tetrahedron Left., 1981, 907, and references cited therein. l7 T. Asano and W. J. LeNoble, Chem. Rev., 1978, 78, 407. l9 G. Kohnstam, Adv. Phys. Org. Chem., 1967, 5, 121. 2o R. E. Robertson, Prog. Phys. Org. Chem., 1967, 4, 213. 21 M. J. S. Dewar, The Molecular Orbital Theory of Organic Chemistry (McGraw Hill, New York, 1969), 22 W. J. Albery and B. H. Robinson, Trans. Faraday SOC., 1969, 65, 980. 23 M. J. Blandamer, R. E. Robertson, P. D. Golding, J. M. MacNeil and J. M. W. Scott, J. Am. Chem. 24 K. M. Koshy, R. K. Mohanty and R. E. Robertson, Can. J. Chem., 1977, 55, 1314. 25 R. K. Mohanty and R. E. Robertson, Can. J. Chem., 1977, 55, 1319. 26 M. J. Blandamer, R. E. Robertson, J. M. W. Scott and A. Vrielink, J. Am. Chem. SOC., 1980, 102, 27 W. P. Jencks, Ace. Chem. Res., 1980, 13, 161. 28 M. H. Abraham, J. Chem. SOC., Perkin Trans. 2, 1973, 1893. E. Tommila, kf. Tiilikainen and A. Voipio, Ann. Acad. Scient. Fenn., Ser. A2, 1955, 65, 3. p. 28?. SOC., 1981, 103, 2415. 2585. (PAPER 1/1221)