J . Chem. Soc., Faraday Trans. 1, 1982, 78, 1 103-1 1 15 Analysis of the Dependence on Temperature of Kinetic Solvent Isotope Effects Application to Kinetic Data for the Solvolysis of Organic Halides and Carboxylic Acid Anhydrides BY MICHAEL J. BLANDAMER,* JOHN BURGESS, NICHOLAS P. CLARE, PHILIP P. DUCE AND ROBERT P. GRAY Department of Chemistry, The University, Leicester LE 1 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, Camda Received 22nd April, 198 1 The implications are explored of both a single- and a two-stage mechanism for solvolytic reactions on the observed kinetic solvent isotope effect, ksie ( = k[D,O]/k[H,O]). The analysis identifies three types of behaviour for the dependence of ksie on temperature. In the first class, ksie changes regularly with temperature towards a limiting value.In a second class, ksie passes through either a maximum or minimum, the nature of the extremum depending on the difference between the apparent heat capacities of activation for reaction in the two solvents at the temperature of the extremum, Finally, and in exceptional cases, both a maximum and a minimum may be observed if the plots showing the dependence of apparent enthalpies of activation on temperature in the two solvents cross in two places. This analysis is used in an examination of the kinetic data for the hydrolysis of several organic carboxylic acid anhydrides where the case for a two-stage mechanism is well established.A similar mechanism for the solvolysis of t-butyl chloride, 2-chlorobutan- 1-01, 2,2-dibromopropane and 2-bromo-2-chloropropane clarifies the trends in previously reported activation parameters. The analysis reveals that no simple relationship exists between ksie and the apparent heat capacity of activation for solvolysis in water. For many years, Robertson1*2 advanced the hypothesis that the magnitude of the heat capacity of activation, AC;, and the kinetic solvent isotope effect, ksie (= k[D,O]/k[H,O]), for solvolytic reactions are linked to the extent of solvent re-organisation accompanying the activation process. Nevertheless, considerable controversy surrounds claims to the relative importance of the solvent isotope effects on the initial and transition ~ t a t e s .~ - ~ In these argument~l-~ a common assumption is that the solvolytic reaction involves a single stage with one kinetically important activation barrier. By way of contrast, Albery and Robinson3 suggested that, in the case of t-butyl chloride, the solvolytic reaction is a two-stage process where the first stage is reversible. In this case, the heat capacity of activation calculated from the dependence of rate constant on temperature and assuming a single-stage mechanism is an artefact of the analysis. Recently6 we have used the two-stage mechanism3 to account for the dependence of this heat-capacity term on solvent composition for the solvolysis of t-butyl chloride in a range of water + organic co-solvent mixtures.An extension of this analysis to the dependence of ksie on temperature forms the basis of this paper. 11031104 KINETIC SOLVENT ISOTOPE EFFECTS Examination of both single- and two-stage mechanisms leads to the identification of the possible patterns of behaviour in the dependence of ksie on temperature. We then consider the kinetic data'~ for the solvolysis of organic carboxylic anhydrides in water and D,O. These substrates undergo hydrolysis via a BAc2 mechanism' where the two-stage reaction scheme is formally identical to that proposed by Albery and Robinson3 for the solvolysis of t-butyl chloride. The data were originally analysed'? * to yield the activation parameters describing a single-stage reaction. It is therefore possible to compare and contrast the conclusions drawn from both analytical methods.A similar comparison can also be made between parameters describing the solvolysis of t-butyl chloride in waterg and D,O1° based on the two mechanisms. Indeed the values of ACZ for solvolysis of acetic anhydride and t-butyl chloride are similar., In addition, there is an indication that, for t-butyl chloride, ksie passes through a maximum near 292 K. This conclusion is based on a ratio of measured rate constants at roughly equal temperature^;^? lo e.g. at 285, 291 and 293 K, ksie = 0.705, 0.745 and 0.741, respectively. We also extend the treatment to include the data for 2,2-dibromopropane1°~ l1 and 2-bromo-2-chloropropane10~ l1 on the grounds that these solutes were previously classed as undergoing solvolysis by an SN 1 mechanism, a conclusion prompted by the large negative values for ACg.We also include one system, 4-chlorobutan- 1 -o1,l29 l3 where there is a possibility of neighbouring group participation.12 The results of the analysis lead to the conclusion that the value of ksie at some arbitrary temperature is not tremendously informative. However, an analysis of the data using a two-stage mechanism pinpoints those features which may lead to extrema in kSie. ANALYSIS The experimental quantity is the first-order rate constant k at temperature T and ambient pressure. The mechanism for the reaction is described in terms of two models and related reaction schemes. We then consider the ratio k/ko, where ko is the rate constant for reaction in water and k the rate constant for reaction in D,O, i.e.ksie = k/ko. MODEL 1 The rate constant k characterises a single-stage reaction. Previously' the dependence (1) It follows1 that ACZ is calculated from the estimate Ci,, and AH# at temperature T from 6, and Ci,. Implicit in eqn (1) is the assumption that AC,Z is independent of temperature. In an application of eqn (1) to a set of data it is necessary to test the statistical significance of including the third term; if it is not significant, In k is simply expressed as a linear function of T-l to yield AH# as the slope. The dependence of In (kSie) on temperature is calculated from the two sets of parameters, ai and a: where i = 1, 2 and 3. According to eqn (l), In (ksie) has an extremum at one temperature: (2) of k on temperature was fitted to eqn (1) using a linear least-squares procedure: In k = a, +a, T-l+ a3 In T.T(kSi, = extremum) = (a, - a9/(a3 -a:). The solvent isotope effect on the derived activation hparameters is represented by the medium operator,14 6,; e.g. eqn (3) for the heat capacity terms Thus at the temperature given by eqn (2), 6 , A W = 0.BLANDAMER et al. 1105 MODEL 11 The two-stage mechanism for the reaction is written3 as shown in eqn (4) k, k3 reactant (intermediate) + product. k2 If a = k,/k3, the observed rate constant is related to k , and a by eqn ( 5 ) (4) k = kJ(1 -a). ( 5 ) It is assumed3? 6, l5 that both In k, and In a are linear functions of T-l. Previouslys we showed how the dependence of k on Tcan be fitted to eqn (6) using a non-linear least-squares technique : k = x, exp (x,/ T ) / [ 1 .O + x3 exp (x4/ T)]. Therefore AH? is calculated from x, and AAHZ (= AH$ -AH:), from x4.(Both AH? and AAH# are sufficiently large that we may overlook the small curvature in plots of In k , and In a against T-l required by classical transition-state theory in the event that AH? and AAHZ are independent of temperature.) Thus a positive value for AHf means that In k , increases with increase in temperature whereas a positive AAHZ means that a decreases. The kinetic solvent isotope effect is given by eqn (7) Thus ksie is dependent on the ratio of (1 +ao) to (1 +a) rather than ao to a. This is a source of complexity. By fittings the dependence of k(D20) on T and then k(H20) on T to eqn (6), it is possible to calculate (k,/ky) and (a/ao) together with the solvent isotope effects on AH? and AAH#.COMPARISON OF MODELS 1 A N D 11 Here we contrast the two models for the solvolysis reaction and examine those conditions which lead to a maximum and/or minimum in the ksie. We recall that such an extremum is observed for acetic anhydride.'* The starting point is the equation3. 6* l5 relating the enthalpy of activation AH# defined by model I and the two enthalpy terms, ACg1 and AAH#, introduced in model 11: (8) AH# = AH? +[a/(l +a)]AAH#. Eqn (8) describes a sigmoidal c ~ r v e ~ ~ ~ with a point of inflexion near the temperature where a = 1.0. In the context of model 11, the shape of this curve plays an important r61e in determining the dependence of ksie on temperature. Complexities emerge because a non-zero value for AAH# requires that a is dependent on temperature. Therefore the heat capacity of activation according to model I is given,6* l5 in terms Consequently AC; is negative irrespective of the sign of A A H Z , the dependence of AC; on temperature forming an inverted bell-shaped plotsv l5 with a minimum close to the temperature where a = 1.0.According to model I, the condition for In (kSie) to show an extremum is given by1106 KINETIC SOLVENT ISOTOPE EFFECTS The extremum is observed at the temperature where AH# = AHo#. Clearly if these quantities differ and are independent of temperature, no extremum will be observed. However, in terms of model 11, a more complicated pattern emerges. The analogue of eqn (10) is given by eqn (1 1) If the term in braces on the right-hand side of eqn (1 1) is independent of temperature, then as the temperature increases, In (k/ko) will either increase to an asymptotic limit if the term is positive or decrease to a lower limit if this term is negative.If both a and ao 6 1 , the overall trend is determined by the difference between AH? and AH:#. If both cc and ao >> 1, the trend in ksie is determined by the relative signs and magnitudes of four enthalpy terms, AH?, AH:#, AAH# and AAH*#. However, further complications emerge when either a or ao or both are, in terms of magnitude, near unity. It is informative to differentiate eqn (1 1) with respect to temperature to obtain eqn (12): d2 In dT2 (ksie) = -L{[AHf RT3 + ( & ) A A H # ] - [ A H : # + ( ~ ) A A H o # ] ] 1 +ao +- RT2 (l+a0)2 RT2 1 Eqn (1 1) shows that an extremum in ksie will be observed at the temperature where the sigmoidal curves showing the dependence on temperature of AH# [cf.eqn (S)] intersect. (There is no a priori requirement that they do so; no intersection occurs if, at all temperatures, AH# > or < AHo#.) At the temperature of intersection, the second differential, eqn (12), can be written as shown in eqn (13) where we have incorporated eqn (10) : If, therefore, ACpZ < ACo# at the intersection of the enthalpy curves, ksie is a maximum; if AC,Z > ACF, ksie is a minimum. A point of inflexion occurs where the second differential, eqn (1 2), is zero. No simple relationship between activation parameters emerges under this condition, although such a feature will be favoured near the temperature at which the plots showing the dependences of ACZ and ACif on temperature [eqn (9)] intersect [cf.eqn (13)]. The essential features of the analysis are summarised diagrammatically in fig. 1. Here the dotted line represents the reference system, the enthalpy plots crossing at A and B and the heat-capacity plots crossing at C . It follows from the values of ACZ and AC;# at temperature A, that here ksie is a minimum whereas at temperature B, ksie is a minimum. A point of inflexion in the dependence of In (Itsie) on temperature will occur near temperature C. These features will only be observed if the experimental temperature range includes A, B and C. In certain systems only one extremum may be observed and in others none at all. In the latter case, this might arise if the experimental range does not include the temperatures A, B or C.In certain systems, a point of inflexion may occur in the absence of an extremum but ,near the temperature where the two enthalpy curves come close together without actually crossing [cf. eqn (1 3 1 -BLANDAMER et al. 1107 B temperature 1 temperature - FIG. 1.-Schematic diagram showing the dependence of enthalpies and heat capacities of activation on temperature for solvolysis in water (full line) and deuterium oxide (dotted line). CALCULATIONS Numerical analysis of the data was carried out using computer programs (FORTRAN) written for the CDC Cyber computer at the University of Leicester. The linear least-squares fitting of the kinetic data to eqn (1) used a statistical packagels (GLIM).The non-linear least-squares fitting of the kinetic data to eqn (6) used the technique previously described.s RESULTS In this section we comment in some detail on the analysis of the data for the solvolysis of acetic anhydride’ and t-butyl chloride.@? lo However, we draw attention to the results of the analysis for other systems. At better than a 95% confidence level (Student’s ?-test), it is significant to include the third term in eqn (1) with reference to the kinetic data for solvolysis of acetic anhydride in both water and D20. The corresponding values of AC$ (i.e. model I) are negative, being strikingly more negative in water than in D,O (table 1). The maximum in In ksie is predicted [eqn (2)] to occur at 288.7 K, which is within the experimental range [cf.table 2 of ref. @)I. The solvent isotope effect on AH# (e.g. at 290 K, d,AH# = 1.16 kJ mol-l) is small but the isotope effect on AC$ is dramatic; S,ACg = 127 J mol-l K-l (table 1). A similar endothermic change occurs for propionic anhydride together with an appreciable change in AC$ but, in this case, the latter is in the opposite direction; SmAC: = -200 J mol-l K-l. A similar comparison is unfortunately not possible for the remaining three anhydrides because, as shown in table 1, these include systems where it was not possible to estimate u3 and at to the required confidence level. It is, however, noteworthy that for both phthalic and benzoic anhydrides, AC$ for solvolysis in D20 is large and negative. The result of the analysis for t-butyl chloride (table 1) shows a similar endothermic1108 KINETIC SOLVENT ISOTOPE EFFECTS change in AH# on going from water to D20.A similar pattern emerges for the remaining three systems, as indeed is the change in ACZ to a more negative value, e.g. for t-butyl chloride, S,AC,Z = - 146 J mol-1 K-l. The data predict that In ksie is a maximum when T = 303.4 K, which is just above the experimental temperature range. Thus when T < 303.4 K, S,AHZ > 0 and when T > 303.4 K, &,AHf < 0. When T = 303.4 K, ksie = 0.7514. Note that for 2-bromo-2-chloropropane SmAC,f is essentially zero, bearing in mind standard errors on each ACZ term. TABLE 1 .-DERIVED ACTIVATION PARA METERS^ (MODEL I) FOR SOLVOLYSIS OF ACID ANHYDRIDES AND ORGANIC HALIDES IN WATER AND DEUTERIUM OXIDE solute A H z (298 K)/ -ACz/ solvent ref.kJ mol-l J mol-l K-l acetic anhydride propionic anhydride succinic anhydride phthalic anhydride benzoic anhydride t-butyl chloride 2,2-dibromopropane 2-bromo-2-chloropropane 4-chlorobutan- 1-01 7 7 7 7 8 8 8 8 8 8 9 0 1 0 1 0 2 3 40.24 (0.18) 41.40 (0.15) 39.68 (0.07) 40.29 (0.23) 55.12 (0.45) 55.24 (0.12) 59.35 (0.57) 53.65 (0.77) 46.45 (0.32) 47.43 (0.46) 94.37 (0.28) 95.13 (1.16) 112.73 (0.13) 1 16.53 (0.18) 108.54 (0.02) 11 1.37 (0.06) 101.12 (0.33) 105.78 (0.28) 311 (14) 184 (29) 144(11) 344 (44) b b b 207 (62) 219 (27) 348 (19) 348 (20) 453 (16) 394 (8) 419 (33) 172 (8) 249 (7) b 494 (94) a Shown in brackets are the standard errors on derived quantities; third term in eqn (1) not significant at the 95% confidence level (Student's t-test).The results in table 1 follow from application of eqn (1) to the data. In the five cases where both SmAC,Z and S,AHf could be estimated, the analysis is satisfactory as expressed by the closeness of the fit between observed and calculated rate constants. Nevertheless some features of the analysis were disturbing. In those cases where it was statistically acceptable to use three terms in eqn (1) the correlation coefficients between the estimates of ai quantities (calculated from the normalised variance-covariance matrix) were in all instances close to unity, i.e. 1 .OO. We have commented elsewhere" on the unsatisfactory features of eqn (1). Nonetheless the analysis does identify important features of the data when analysed on the basis of model I.Turning to the analysis based on model 11, the data for the solvolysis of acetic anhydride in both water and D20 can be satisfactorily fitted to eqn (6). For the 36 individual rate constants describing reaction in water, agreement between calculated and observed values of k was within +0.78%, a plot of the residuals against temperature showing a satisfactory random scatter. Consequently it would not be justified to extend eqn (6), thereby leading to calculation of the dependence of AH:TABLE 2.-KINETIC SOLVENT ISOTOPE EFFECTS; ANALYSIS IN 'TERMS OF MODEL 11 acetic anhydride t-butyl chloride 2,2-dibromopropane 2-bromo-2-chloropropane 4-chlorobutan- 1-01 H 2 0 D20 H 2 0 D20 H2O D2O H2O D2O H2O D2O n data points T range/K k, (290 K)/10-2 s-l AHt/kJ mol-1 a (290 K) -AAH#/kJ mol-1 T(a = l.O)/K -AC,f (min)/J mol-' K-l T(ACpZ = min)/K -AC,Z (290 K/J mol-l K-I ksie (a/ao; 290 K) fit, A/% ksie (k,/k;; 290 K) 36 42 20 37 275-298 278-3 13 274-293 277-294 0.78 2.8 0.25 3.4 1.705 1.004 1.126 1.225 86.95 87.89 106.38 121.54 9.535 17.097 0.1525 0.691 46.46 45.66 51.98 51.43 259.6 252.2 317.7 295.1 961 994 813 914 255 250 315 290 265 156 444 914 0.589 1.088 1.79 4.53 1 43 35 13 48 293-3 18 295-323 283-308 2863 13 2.4 2.7 2.5 3.7 1.287 x loT3 0.903 x lop3 5.162 x 3.556 x 1 15.33 118.44 114.97 1 18.29 62.47 61.77 60.65 60.05 349.1 346.5 335.0 333.58 970 962 988 986 340 345 330 330 68 81 167 185 0.012 0.015 0.034 0.039 0.702 0.689 1.25 1.14 42 14 323-358 318-358 1.4 3.4 5.503 x 3.989 x lop3 98.26 100.61 2.92 x 5.087 x 70.14 68.89 402.66 394.7 920 922 400 390 2 3.5 0.725 1.7421110 KINETIC SOLVENT ISOTOPE EFFECTS and AAH# on temperature. A similar state of affairs exists for the data describing the solvolysis of acetic anhydride in D,O, agreement between observed and calculated rate constants being within f 1.7%.From both sets of derived parameter [eqn (6)], the related kinetic parameters have been calculated (table 2) together with the dependences of AH#, AHo#, ACZ and AC;# on temperature [eqn (8) and (911; fig. 2. The minimum in AC,Z for solvolysis in D,O is at a slightly lower temperature 30- 3 50 250 300 TI K FIG. 2.-Solvolysis of acetic anhydride in water (full line) and D,O (dotted line). than for solvolysis in water. The minimum is also marginally more intense.The curves showing the dependence of AH# and AHof on temperature cross when T = 291 K. At this temperature (fig. 2), AC;# < AC$, a feature reflected in the corresponding minimum in In kSie. In the high-temperature limit, AH# c AHo# and so In ksie increases with increase in temperature. For comparison we have selected a common temperature, 290 K, and calculated the isotope effects on k,, a, AH? and AAH#, table 2. In this system, the separate kinetic and activation parameters for the two- stage process in each solvent combine to yield a minimum in In ksie within the measured temperature range [fig. 2(c)]. The analysis of the data for the remaining anhydrides was less satisfactory. The 40 data points for the solvolysis of propionic anhydride in water were satisfactorily fitted to eqn (6) but such was not the case for the 24 data points for solvolysis in D20.Despite repeated attempts to locate a minimum in the least-squares analysis, agreement between observed and calculated rate constants was in some cases no better than + 6%. This failure was disappointing because In ksie passes through a maximum, thereby contrasting propionic and acetic anhydrides. The kinetic data for phthalic and benzoic anhydrides in D,O were satisfactorily fitted to eqn (6), but such was not the case for the data describing solvolysis in water and for the kinetic data for succinic anhydride in both water and D20. The results of the analysis using eqn (6) for t-butyl chlorideQ* lo are summarised in table 2. For solvolysis in water agreement between observed and calculated rateBLANDAMER et ai.1111 -200 -400 - k I L E -600 - --- iF. Q - 800 1 2 0 k 2 60 - 300 T/K 1.C 0 n 0 -Y 2 -1-0 v c - -2.0 2 - 3 50 TI K FIG. 3.-Solvolysis of t-butyl chloride in water (full line) and D,O (dotted line). -1000 300 350 TIK I 3 50 1 TIK 260 300 3b0 TI K FIG. 4.-Solvolysis of 2-bromo-2-chloropropane in water (full line) and D,O (dotted line).1112 0.2 0 - -0.2 5 0 - --. -Y - G - - 0.4 -0.6 KINETIC SOLVENT ISOTOPE EFFECTS I 1 1 1 280 300 320 340 31 TIK ( C ) 0 1 I I 2 80 300 320 340 3f TIK FIG. 5.-Dependence of (A) In (k,/k:) and (B) In (ala") on temperature for (a) acetic anhydride, (b) t-butyl chloride, (c) 2-bromo-2chloropropane, ( d ) 2,2-dibromopropane and (e) Cchlorobutan- 1-01.BLANDAMER et al. 1113 constants was within +0.25% for 20 data points while for solvolysis in D20 the agreement was within & 3.0% for 37 data points.The calculated dependences of A H #, AHo#, AC:, AC$# and In ksie on temperature are shown in fig. 3. For this system there is a dramatic solvent effect on the temperature corresponding to the minimum in AC,Z [fig. 3 (a)]. The two curves cross at 307 K, whereas the curves for the enthalpy terms cross at 292 and 321 K, features producing a maximum and a minimum, respectively, for In ksie; fig. 3(c). However, the overall trend is for In ksie to increase with increase in temperature. A similar trend is observed for 2-bromo-2-chloropropane (fig. 4). However, for this system the corresponding enthalpy plots do not intersect so there is no extremum in In ksie although there is a point of inflexion near the temperature where the heat-capacity curves intersect (fig.4). This pattern is also followed by 2,2-dibromopropane. The corresponding plots for 4-chlorobutan- 1-01 resemble those for t-butyl chloride (fig. 3) except that the enthalpy plots intersect at 357 (where In ksie is a maximum) and the heat-capacity plots intersect at 397 K. The most important set of results are summarised in fig. 5, where we show the calculated dependence on temperature of the kinetic isotope effects for k , and a, i.e. In (k,/ky) and In (a/ao), over the experimental temperature ranges. DISCUSSION The established two-stage mechanism for the solvolysis of acetic anhydride provides a sound basis for analysis of the kinetic solvent isotope effect using model 11.Further, it is possible to identify the relationships between the thermodynamic activation parameters calculated from models I and I1 for the same set of kinetic data. For example, the increase in AC,Z for acetic anhydride on going from water to D20 (table 1) is according to model I1 misleading. It is not, for example, indicative of a dramatic difference in solute-solvent interactions in water and D20. According to model 11, there is only a slight change in this now apparent AC,f at the minimum (fig. 2). However, when this is combined with a modest shift in the temperature at this minimum (table 2), there is a more marked effect on some averaged AC,Z quantity calculated using eqn (1). If this interpretation of the trends in previously reported AC$ parameters is correct, then the information yielded by changes in A C g on going from water to D20 is not straightforward because AC,Z is a function of AAH# and a [eqn (9)].Indeed no simple relationship exists, according to model 11, between AC,Z for solvolysis in water and either the solvent isotope effect at one temperature [cf. eqn (7)] or the dependence of ksie on temperature [cf. eqn (1 l)]. Thus in terms of model 11, In ksie and its temperature dependence is a complex quantity reflecting the solvent isotope effect and temperature dependence of k , and a; fig. 5. Consequently the extremum in In ksie for acetic anhydride has no particular significance, except in so far as the experimental temperature range includes the temperatures where a and ao are most sensitive to temperature.Problems emerge as shown for other systems (cf. table 2), where following a fitting of the data for solvolysis in water and D20 separately to eqn (6), the analysis predicts extrema and points of inflexion in ksie outside the experimental range. However, we would argue that from inspection of the curves given, for example, in fig. 2-4 drawn over an extended temperature range, it is possible to identify those features which contribute to the dependence of In ksie over the measured temperature range. For example, in the case of acetic anhydride in either water or D20, AAH# is negative and so a and ao increase with increase in temperature. Therefore, the high-temperature limit of A H # (model I) is AH? - IAAH 21.On going from water to D20, the high-temperature limit of A H # is displaced vertically since d,AH,' > d,AAHZ > 0 (table 2). If all other quantities were unaffected by the1114 KINETIC SOLVENT ISOTOPE EFFECTS change in solvent of if T(a = 1) has also increased, no extremum in ksie would be observed. However, the temperature T(a = 1) decreases, resulting in an intersection of the enthalpy plots (fig. 2). The rather poor analytical results for propionic anhydride indicate that similar small changes in AH? and AAH # can produce a maximum in Inksie. For the other anhydrides (table 1) the kinetic data cover too small a temperature range to allow calculation of the trends in ksie based on model 11. If, however, for benzoic and phthalic anhydride in water, AH# is independent of temperature, the corresponding dependence (model 11) for AH # in D20 intersects this line producing extrema as previously reported.8 In a similar fashion to that for the acetic anhydrides, it is apparent that the analysis in terms of model I1 resolves many of the problemslO in interpreting the solvent isotope effects for the solvolysis of organic halides using model I.Thus the dramatic effect on ACZ for t-butyl chloride (table 1) is a combination of a decrease in AC$ at the minimum combined with an increase in the temperature at the minimum. In contrast, the small change in AC$ (model I) for 2-bromo-2-chloropropane is a consequence of a less dramatic solvent effect on AC$ (min) and the temperature corresponding to this minimum.Indeed, in contradiction to the claimed generalisation,1° AH # is not necessarily larger for solvolysis in D20 than in H20. Even if eqn (1) is retained, it was not previously recognized that the derived parameters, ai in eqn (l), predict that In ksie passes through a maximum. Certainly, in terms of model I1 there are indications of a more clear-cut set of generalisations. As shown in fig. 5, k/ko for five substrates increases with increase in temperature whereas a/ao decreases; the latter more gradually. Significantly the limiting high-temperature limit for both ratios is not unity.3 In all systems the temperature where a = 1.0 increases on going from water to D20, but there is not dramatic change in A A H f . The latter shows that the differences in the two enthalpies of activation governing the fate of the intermediate [eqn (4)] is insensitive to the change in solvent.It is, however, not unexpected that S,AH,Z > 0. Thus if the formation of the transition state involves charge-separation, we would anticipate that the partial molar enthalpy of the transition state increases on going from water to D,O because enthalpies of transfer of salts are, with the expection of large alkylammonium salts, generally positive.18 This trend combined with a decrease in the partial molar enthalpy of a hydrophobic initial state19 produces a positive value 6 , A H t . The fact that the derived parameters for 4-chlorobutan-1-01 fall into the same general pattern (table 2) is in agreement with the previous conclusion12 that the extent of neighbouring-group participation in the activation processes is small.Further, the overall self-consistency between the solvent isotope effects on the parameters based on model I1 lends support to the proposal made by Albery and Robinson3 concerning the operation of a two-stage mechanism. Nevertheless, we must conclude that the ksie for a given reaction at one temperature is not a useful guide to the mechanism of reaction. We thank the S.R.C. for a maintenance grant to P.P.D. We thank the Royal Society for a travel grant to M.J.B. 3 4 1 2 R. E. Robertson, Prog. Phys. Org. Chem., 1967, 4, 213. P. M. Laughton and R. E. Robertson, Solute-Soluent Interactions, ed. J. F. Coetzee and C . D. Ritchie (M. Dekker, New York, 1969), chap. 7. W. J. Albery and B. H. Robinson, Trans. Faraday SOC., 1969, 65, 980; 1623. C. G. Swain and E. R. Thornton, J. Am. Chem. SOC., 1962, 84, 822. P. M. Laughton and R. E. Robertson, Can. J. Chem., 1965, 43, 154. 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.BLANDAMER et at. 1115 R. E. Robertson, B. Rossall and W. A. Redmond, Can. J. Chem., 1971, 49, 3665. B. Rossall and R. E. Robertson, Can. J. Chem., 1975, 53, 869. E. A. Moelwyn-Hughes, R. E. Robertson and S. E. Sugamori, J. Chem. Soc., 1965, 1965. A. Queen and R. E. Robertson, J. Am. Chem. Soc., 1966,88, 1363. lo L. Treindl, R. E. Robertson and S. E. Sugamori, Can. J. Chem., 1969,47, 3397. l2 M. J. Blandamer, H. S. Golinkin and R. E. Robertson, J. Am. Chem. Soc., 1969, 91, 2678. l3 H. S. Golinkin and R. E. Robertson, unpublished data. l4 J. E. Leffler and E. Grunwald, Rates and Equilibria of Organic Reactions (Wiley, New York, 1963). Is J. M. W. Scott and R. E. Robertson, Can. J. Chem., 1972,50, 167. l7 M. J. Blandamer, J. M. W. Scott and R. E. Robertson, Can. J , Chem., 1980, 58, 772. l8 H. L. Friedman and C. V. Krishnan, in Water: A Comprehensive Treatise, ed. F. Franks (Plenum l9 G. C. Kresheck, H. Schneider and H. A. Scherago, J. Phys. Chem., 1965,69, 3132. GLZM (Royal Statistical Society, London, 1977). Press, New York, 1973), chap. 1. (PAPER 1/648)