J. Chem. Soc., Faraday Trans. I , 1982, 78, 881-886 Effects of Added Acetonitrile on the Heat Capacities of Activation for the Solvolysis of Simple Organic Esters in Water BY MICHAEL J. BLANDAMER,* JOHN BURGESS AND PHILIP P. DUCE Department of Chemistry, The University, Leicester LE1 7RH AND Ross E. ROBERTSON Department of Chemistry, University of Calgary, Calgary, Alberta, Canada AND JOHN W. M. SCOTT Department of Chemistry, Memorial University, St. John’s, Newfoundland, Canada Received 23rd April, 1981 Kinetic data for the solvolysis of a range of simple organic esters in water and in water + acetonitrile mixtures are examined in terms of the two-stage Albery-Robinson mechanism. The analysis is directed at understanding the dependence of previously reported heat capacities of activation on the composition of solvent.This dependence is shown to stem from a dependence on composition of the kinetic parameters describing the two-stage mechanism and on the variation of the temperature range over which the kinetic data were measured. For many years, Robertson1y2 has argued that the large negative heat capacities for the solvolysis of organic esters arise to a large extent from the enhanced water structure surrounding the hydrophobic initial state. It was also noted that addition of small amounts of monohydric alcohols or tetrahydrofuran produces a more negative value of AC$ for the solvolysis of t-butyl chloride, whereas addition of acetonitrile produces2 an increase in ACZ (i.e. less negative). The latter trend is consistent with the widely accepted hypothesis that added acetonitrile disrupts the hydrogen-bonded structure of waters3 Indeed this trend in AC$ with increase in mole fraction x, of acetonitrile has been used to identify the contribution to AC$ from reorganisation of water structure on activation from other solvolytic Although these generalisations rationalise the observed trends, there remain several problems which have often been overlooked.s Thus the rate constant and enthalpy of activation for t-butyl chloride decrease when all organic cosolvents are added. It is not therefore immediately apparent why the solvent dependence of AC$ is so discriminating between cosolvents.Various hypotheses may be advanced in this context. A more fundamental reassessment questions the significance of the heat capacity of activation for solvolysis in water, i.e.the starting point of the argument outlined above. More recent analyses of the kinetic data for this class of reactions7* * have prompted this reconsideration of the significance of the calculated ACZ. In particular, attention has been directed to the Albery-Robinson mechanism for the solvolysis of t-butyl chlorides [eqn (1)-(3)] : k, k, kp RX R+X- --+ products (1) 88 1882 SOLVOLYSIS OF ORGANIC ESTERS I N WATER where and k(obs) = kJ( 1 +a) a = k,/k3. If AH,Z and AH$ are independent of temperature, the dependence of k(obs) on temperature leads to an apparent heat capacity of activation AC,Z(app) which is relatedg to a and AAH# (= AH$ -AHt) by eqn (4): a (AAH#), (1+a), RT2 ' AC$(app) = -- (4) The ratio a, depending on the sign of AAHf, increases or decreases with increase in temperature, passing through unity at a temperature T,.However, AC$(app) is always negative and depends on temperature such that the final plot has an inverted bell shape with a minimum at a temperature near Ta. The foregoing mechanism and associated equations raise the question as to the possible re-interpretation of the effect of added acetonitrile on the kinetics of solvolysis. We have examined the data for six esters, and compared the outcome with a similar analysis for a range of different added solvents on the kinetics of solvolysis of t-butyl chloride.s ANALYSIS The kinetic data describing the dependence of rate constants on temperature have been fitteds to eqn (5) where a, is related to AHf and a, to AAHf : k = a,exp(-a,/T)/[l +a3exp(-a,/T)].( 5 ) The analysis used a modified Gauss-Newton technique based on explicit calculation of the relevant Hessian and Jacobian matrices.8 The computer program (FORTRAN) calculated the dependences of k,, a and ACg(app) on temperature. RESULTS The outcome of the analysis is summarised in table 1. In all cases eqn (5) satisfactorily fitted the data to within experimental error, a plot of the residuals { = 100 x [k(obs) - k(calc)]/k(calc)) against temperature showing a satisfactory scatter. Table 1 reports a number of quantities of interest. An important entry concerns the temperature range, TR, over which the kinetic data were measured. The temperature T, is an experimental temperature close to the mean temperature of the experimental range.Thus a(T,) is the calculated value of a at this temperature. AC,Z(app, T,) is the heat capacity of activation calculated using eqn (4) at T,, where the activation enthalpy AH# (app, T,) is the corresponding enthalpy of activation. Included in table 1 is the temperature at which a is unity [T(a = l)] and the temperature at which ACZ(app) is a minimum, together with this value of AC,Z(app). The dependence of AC$(app) on temperature is shown in fig. 1 for benzyl chloride in waterlo and in water + acetonitrile mixture where x, = 0.05. The plots for the other systems reported in table 1 are similar in their general appearance. DISCUSSION Before embarking on a detailed discussion of the results, we make two important points which clarify several features of the analysis.First, the values of AC,f reported by Robertson and coworkers were obtained1 by fitting the data to the three-constantTABLE EFFECT OF ADDED ACETONITRILE ON THE KINETIC PARAMETERS DESCRIBING THE SOLVOLYSIS OF VARIOUS SIMPLE ORGANIC ESTERS IN WATER A c t 290K) (app, Tm) A H # AC$ bPP9 AC$ number temp. AH? @PP, max) mole fraction of of data range T, k(obs, T , ) k,(T,) (298 K) AAH# T(a = 1) /J at T /J /J. (~PP, Tm) acetonitrile, x2 points /K /K s-' a(T,) /10-8 s-* /kJ mol-I /kJ mol-l /K mol-I K-l /K mol-1 K-' mol-l K-I /kJ mol-l t-butyl chloride8 0 20 274-293 0.05 40 273293 0.10 44 275-297 0.20 50 286-313 benzyl chloridelo- Is 0 51 288-338 0.048 44 315-335 0.177 40 324-346 0 39 324-344 0.084 45 316-345 0.084 34 321-337 pchlorobenzyl I4 p-methylbenzenesulphonyl c h l ~ r i d e ' ~ ~ l5 0 34 278-296 0.05 34 278-300 p-methoxybenzenesulphonyl I5 0 41 275-293 0.048 41 274-300 0 9 273291 0.2 (ethyl alcohol) 38 283-315 1 -adamantyl nitrate'" 284 283 287 300 41.45 19.98 12.96 9.542 0.13 02.27 0.10 8.33 4.68 6.55 1.43 8.90 104.6 109.4 89.1 117.1 -47.2 -28.9 -37.9 - 34.4 316.7 265.4 336.0 260.5 - 672 - 364 -391 - 531 315 210 330 255 -431 - 222 - 192 - 234 - 348 - 265 - 173 -150 99.2 89.3 85.7 86.4 365 220 340 280 - 56.7 -51.4 - 122 -691 - 120 -22.7 - 30.7 - 124.2 89.88 83.84 84.31 89.49 313 326 329 333 0.7663 0.8668 0.5334 0.1571 0.106 0.456 12.93 15.23 0.8413 1.197 0.0769 0.252 93.10 99.71 95.53 131.3 -33.71 - 17.09 - 35.86 -44.56 378.9 23 1.7 350.2 285.0 - 246 - 172 - 323 - 740 d fi m w 0 a m P 3.213 0.3269 0.089 0.220 0.350 0.398 91.12 95.64 - 51.25 -43.4 383.0 365.9 - 545 -431 375 360 -21.2 -61.4 -214 - 306 86.93 87.81 333 33 1 4 0 z m - 244 - 159 288 289 13.35 7.625 5.814 9.255 9.107 7.845 106.1 97.59 - 38.5 - 36.2 259.6 251.9 - 667 - 628 255 250 - 269 - 166 73.25 64.9 1 9.48 26.30 98.09 96.04 - 29.6 -31.6 250.0 227.0 -430 - 589 245 225 - 133 -357 - 171 -44.2 73.06 65.42 284 286 14.59 8.331 5.480 3 1.23 m 283 298 13.69 2.002 0.277 5.18 1.745 1.22 126.7 127.1 -41.9 -33.2 305 266 - 575 -477 300 260 - 524 - 270 -448 - 202 117.6 99.2 00 00 w884 SOLVOLYSIS OF ORGANIC ESTERS IN WATER 100 200 300 400 500 600 T/K I I I 1 I 100 200 300 400 SO0 600 TIK -20 - I -60 - 0 E a -100 h 1 h 4 I;p W 1L -140 FIG.1.-Calculated dependence of AC$(app) on temperature for solvolysis of benzyl chloride in (A) water and (B) water + acetonitrile, mole fraction = 0.048.Valentiner equation" which assumes at the outset that AC; is independent of temperature. Although this equation has, it is now realised,12 several unsatisfactory features, the dependence of AC; on composition forms the background of the problems discussed here. Consequently, we designate these previously reported values as AC$ (V). Secondly, it is convenient to examine the relationship between the range, TR, and the dependence of AC,Z on temperature required by eqn (5). This is illustrated in fig. 2 where, rather than indicating the range, we have indicated five possible values of T,. In a given investigation the range will extend to differing amounts about these mid-points.Part of our argument is that AC,f(V), as previously reported, is some averaged quantity over the sampled section of the dependence described by eqn (5). Suppose, therefore, that throughout a series of investigations TR remains the same. Although the temperature T* corresponding to the minimum in AC,f and the value of AC$ at the minimum depends on the solvent and substrate, we can consider what happens to AC$(V) as T* changes relative to Tm. Therefore, if by adding acetonitrile, T, moves from (a) to (b) or (c) (fig. 2), AC$(V) becomes more negative. Similarly, if Tm moves from (b) or ( d ) to (e), AC$ becomes less negative. Of course, a dramatic decrease in T* together with an increase in T, might lead to a small [i.e. ( d ) -+ (e)] or negligible [ie.(a) --* (e)] change in ACZ(V). With these points in mind, we turn to a consideration of the results in table 1. The pattern is set by the data for t-butyl chloride.* For solvolysis in water the experimental temperature range was just below T(a = 1) and T* [(b) in fig. 23 such that AC$(V) is large and negative. When acetonitrile is added x, = 0.05, T(a = 1) and T* move to below the experimental range [(d) in fig. 21 and so ACZ(V) increases (i.e. becomes less negative). The increase is marked because at the same time the value of AC #(app) at the maximum is almost halved, a consequence of a dramatic fall in AAH? As more acetonitrile is added, T(a = 1) and T* move above and then below the experimental range, but the minimum value of ACZ (app) increases. Consequently AC,Z(app) at Tm increases gradually.On the other hand, AC$(app) at a common temperature, 290 K, passes through a maximum. A similar trend is observed for benzyl chloride. For reaction in water, TR is slightly further away from T* and T(a = 1) than for t-butyl chloride. Since ACf(app, max) is not so negative, these two effects combine to yield a smaller value for lAC$(V)l.BLANDAMER, BURGESS, DUCE, ROBERTSON A N D SCOTT 885 When x, = 0.048, T, has increased but T* and T(a = 1) have dropped to below TR with the result that ACZ increases. With an increase in x,, T, increases but T* and T(a = 1) increase and then decrease although AC$(app, max) decreases. The result is a decrease and then increase in AC$(app) at T,. A similar complicated solvent dependence of T(a = l), T,, TR and AC$(app, max) for the other substrates accounts for the trends in AC,Z(app) at T, and hence in AC$(V).0 n a Ii- L!! Q \- FIG. 2.-Diagramatic representation of the relationship between the mean of the experimental temperature range and the dependence of AC,Z (app) on temperature. The data in table 1 also include the effect of added ethyl alcohol on the kinetic data for 1 -adamantyl nitrate. For reaction in water, ACZ(V) is strikingly more negative than that for t-butyl chloride. This is the result of the upper limit of TR being close to T(a = 1) and T*, even though IAC$(app)( at T* is not as large as that for t-butyl chloride. Ethyl alcohol at x, = 0.2 also exerts a structure-breaking influence on water.3 The dramatic decrease in ACf(app) at Tm [and hence AC$(V)] is attributed to a decrease in T(a = 1) and T*, which are now below the lower end of TR.The major conclusion which follows from this analysis is that the changes in AC$(V) with added acetonitrile are not as straightforward as hitherto discussed. The determining factors are the solvent sensitivity of the ratio a and the related enthalpy term AAHf:. There appears to be a general trend for a to increase with increase in mole fraction of acetonitrile, indicating that recombination becomes increasingly favoured as the kinetic fate of the intermediate. Unfortunately, a is the ratio of the two rate constants k , and k3 so we have no indication of their absolute changes. Similar problems emerge in understanding the solvent sensitivity of AAH # .It is possible to understand these trends by combining possible effects of the acetonitrile on the water structure and hence on the solvation characteristics together with the gradual change in dielectric properties of the solvent. However, these arguments turn out to be qualitative at best and sweeping rationalisations at worst. What is required is a more detailed examination of solvent effects along the lines indicated here for a wider range of substrates and some way of splitting a into the component rate constants, k , and k3. We thank the S.R.C. for a grant to P.P.D.886 SOLVOLYSIS OF ORGANIC ESTERS IN WATER R. E. Robertson, Prog. Phys. Org. Chem., 1967, 4, 213. M. J. Blandamer, Adv. Phys. Org. Chem., 1977, 14, 203. E. C. F. KO and R. E. Robertson, Can. J. Chem., 1972, 50,946. K. M. Koshy, R. K. Mohanty and R. E. Robertson, Can. J. Chem., 1977,55, 1314. M. J. Blandamer, R. E. Robertson, J. M. W. Scott and A. Vrielink, J. Am. Chem. SOC., 1980, 102, 2585. M. J. Blandamer, J. Burgess, R. E. Robertson and J. M. W. Scott, J. Chem. SOC., Faraday Trans. I , submitted for publication. * M. J. Blandamer, J. Burgess, P. P. Duce, R. E. Robertson and J. M. W. Scott, J. Chem. SOC., Faraday Trans. I , 1981, 77, 1999. W. H. Albery and B. H. Robinson, Trans. Faraday SOC., 1969, 65, 980. * R. E. Robertson and S. E. Sugamori, Can. J. Chem., 1972,50, 1353. lo R. E. Robertson and J. M. W. Scott, J. Chem. SOC., 1961, 1596. l1 S. Valentiner, Z. Phys. Chem., 1907, 44, 253. l2 M. J. Blandamer, R. E. Robertson and J. M. W. Scott, Can. J. Chem., 1980, 58, 772. l3 R. E. Robertson, unpublished data. l4 K. M. Koshy, R. E. Robertson and W. M. J. Strachan, Can. J. Chem., 1973, 51, 2958. R. E. Robertson and B. Rossall, Can. J. Chem., 1971,49, 1441. K. M. Koshy, R. K. Mohanty and R. E. Robertson, Can. J. Chem., 1977,55, 1314. (PAPER 1/654)