Calculated Third Order Rate Constants for Interpreting the Mechanisms of Hydrolyses of Chloroformates, Carboxylic Acid Halides, Sulfonyl Chlorides and Phosphorochloridates

Hydrolyses of acid derivatives (e.g., carboxylic acid chlorides and fluorides, fluoro- and chloroformates, sulfonyl chlorides, phosphorochloridates, anhydrides) exhibit pseudo-first order kinetics. Reaction mechanisms vary from those involving a cationic intermediate (SN1) to concerted SN2 processes, and further to third order reactions, in which one solvent molecule acts as the attacking nucleophile and a second molecule acts as a general base catalyst. A unified framework is discussed, in which there are two reaction channels—an SN1-SN2 spectrum and an SN2-SN3 spectrum. Third order rate constants (k3) are calculated for solvolytic reactions in a wide range of compositions of acetone-water mixtures, and are shown to be either approximately constant or correlated with the Grunwald-Winstein Y parameter. These data and kinetic solvent isotope effects, provide the experimental evidence for the SN2-SN3 spectrum (e.g., for chloro- and fluoroformates, chloroacetyl chloride, p-nitrobenzoyl p-toluenesulfonate, sulfonyl chlorides). Deviations from linearity lead to U- or V-shaped plots, which assist in the identification of the point at which the reaction channel changes from SN2-SN3 to SN1-SN2 (e.g., for benzoyl chloride).


Introduction
Solvolyses involve reactions of a solvent nucleophile (e.g., water or alcohol) with a suitable substrate (e.g., of general formula RX, where R is an alkyl residue and X is an electronegative group) [1]. To aid OPEN ACCESS the solubility of RX in water, an organic cosolvent (e.g., acetone) is often added. An understanding of the factors influencing the reactivity of RX can be gained by studying the dependence of logarithms of observed pseudo-first order rate constant (log kobs) on empirical parameters for substituent and/or solvent effects [2]. These are examples of linear free energy relationships (LFER), from which reaction mechanisms can be proposed and effects of changing reaction conditions (e.g., cosolvents) could be predicted [3,4].
A useful concept is the idea that solvolyses proceed via a spectrum of reaction mechanisms. An SN1-SN2 spectrum of mechanisms is well established for many solvolyses (e.g., solvolyses of secondary alkyl sulfonates [5]). Density functional (DFT) calculations for benzoyl chlorides [6] were consistent with concerted SN2 reactions, with "loose" (cationic) transition states for electron-donating substituents and "tight" (associative) transitions states for electron withdrawing substituents ( Figure 1). Very recent DFT calculations [7] further illustrated the SN1-SN2 spectrum (e.g., for benzyl halides), but also provided support for the proposal [8] that there was also an SN2-SN3 spectrum of mechanisms for solvolyses of aromatic sulfonyl chlorides (2). Electrophilic solvation of the developing chloride anion and general solvation are excluded from the assessment of molecularity, and are not shown in Figure 1. At the SN1 extreme of the SN1-SN2 spectrum, there may be evidence for a cationic intermediate and reactions are unimolecular (e.g., solvolyses of p-dimethylaminobenzoyl fluoride (3, Z = NMe2) show common ion rate depression [9]).
The key feature of the SN3 mechanism is that the reactions are termolecular: a solvent nucleophile attacks the substrate (e.g., RX or p-Z-substituted benzoyl chlorides as in Figure 1b), and a second solvent molecule assists by partially deprotonating the nucleophile (three molecules undergo covalency change, but they could be preassembled by hydrogen bonding).
Although the kinetic order is usually first order (rate constant kobs), it has proved useful in some cases to calculate various third order rate constants (k3); as shown below, values of log k3 may be approximately constant or may give good linear plots vs. solvent polarity parameters for solvolyses of acid derivatives. Furthermore, deviations from linearity provide some of the clearest evidence for the relatively subtle change in mechanism from the end of the SN1-SN2 spectrum to the beginning of the SN2-SN3 spectrum.

Choice of Equation for Correlating Solvolysis Rates
The simplest (but not reliable) equation for obtaining the kinetic order of a pseudo-first order solvolysis is Equation (1), where n is the kinetic order, kn is the nth order rate constant and [water] refers to the molar concentration of water in for example a binary mixture such as acetone-water. Taking logarithms, a plot of log kobs vs. log [water] would have a slope of n (Equation (2)). To illustrate the lack of reliability of Equation (2), two examples using kinetic data from the recent literature (but not the published interpretation of the data) are: (a) solvolyses of benzoyl fluoride (3, Z = H) in acetone-water, which would have a kinetic order of 3.3 (kinetic data from Reference [10]); (b) solvolyses of p-nitrobenzoyl tosylate (4, Z = NO2), which would have a kinetic order of 0.3 (kinetic data from Reference [11]).
log kobs = n × log [water] + log kn An alternative, more credible explanation is that solvolyses of both 3, Z = H and 4, Z = OTs are third order. Solvolyses of 3, Z = H in water and D2O give a kinetic solvent isotope effect (KSIE) of 2.0 [9], and the KSIE for 4, Z = OTs in methanol and MeOD varies from 1.84 at −10 °C to 1.59 at 25 °C [11]. These values are consistent with some cleavage of O-H or O-D bonds in the rate determining step, as shown in Figure 1b. Various reactions of acid derivatives including esters are thought to react by such general base-catalysed processes [12].
There are many publications in which the KSIE for MeOH and MeOD were obtained (see below), and a wide range of KSIE data have been published by Koo et al. [13,14]; two of these were included in the recent DFT calculations [7]: values of KSIE in water are: for 2, Z = OMe (calc. 1.64, expt. 1.37); for 2, Z = NO2 (calc. 1.97, expt. 1.76). Both SN1 [15] and SN2 [16] reactions typically have KSIEs <1.3 (see also Table 5 of Reference [8]), so hydrolyses of 2, Z = OMe are close to those expected for SN2 reactions, but those for 2, Z = NO2 are significantly higher.
It should not be inferred that the linearity of the plots ( Figure 3) is by itself evidence for third order reactions, because a plot (not shown) of log [water] 2 vs. Y is close to linear, but curves downwards for 80% and 90% acetone-water; this curvature can lead to a "kink" in Equation (3) plots, Consequently, the main difference between Equation (3) and a GW plot of log kobs vs. Y is that the slopes of Equation (3) are lower, but it some cases (see below) mechanistic changes are indicated much more clearly using Equation (3); note however that for bimolecular reactions in 80% and 90% acetone-water, there may be a change in slope which is not due to a mechanistic change.
As with other mechanistic indicators, it is always desirable to provide independent evidence, and KSIE data will be quoted extensively during the following discussion. Multi-parameter equations provide a more comprehensive account of solvent effects, and these are discussed in Section 2.4.
Also, there are various examples of chloroformates (5,6) where the slope based on Equation (3) is close to zero, implying that a plot of log kobs vs. log [H2O] (Equation (2)) would give a value of n (the kinetic order with respect to water) of close to 2 (e.g., see Section 2.2.1).
An important advantage of Equation (3) over Equation (2) is that trends in slopes can be interpreted with the benefit of long experience of applications of the original GW equation [18]. The selection of Y rather than one of the other YX parameters [19] for solvent ionizing power ensures that none of the Y values are based on extrapolated data, and that slopes for all substrates are comparable (for further discussion on this choice, see Reference [20]). For many aqueous binary mixtures (including acetone-water), to a good approximation Y = YCl × 0.75 (see Table 8 of Reference [19]). The factors influencing the slopes of correlations based on Equation (3) were investigated for a wide range of substrates.

Chloroformates
In general, chloroformates (5,6) are much more likely than the corresponding carboxylic acid chlorides (2) to react via higher order (associative) reactions. Recent G3 calculations of gas phase heterolytic bond dissociation energies (HBDE) for the C-Cl bonds show for example that PhCOCl (1, Z = H) has an HBDE of 150.1 kcal/mol whereas the corresponding chloroformate (6, Z = H) has a much higher HBDE of 166.5 kcal/mol [21]. Consequently, the electrophilic "pull" is less for chloroformates, and a greater nucleophilic "push" might be expected [22].
Data for solvolyses of many other chloroformates [28] in a limited range of acetone-water solvent compositions, usually within the range 90%-60% show the same trends as those discussed above. Exceptions to these trends indicate the possibility of mechanistic changes, as discussed in Section 2.3.

Fluoroformates (7)
One of the first extensive study of solvent effects on these solvolyses was for n-octyl fluoroformate (7, R = n-octyl); data in 95%, 90%, 80% and 60% v/v acetone-water [29] give a positive slope based on Equation (3) of 0.22 ± 0.02. Positive slopes are observed for many other fluoroformates, as well as for benzoyl fluoride (3, Z = H)-see Figure 3. Details are not given here because of the limited range of acetone-water solvent compositions (usually between 90% and 60% v/v [28]). Instead, typical studies involve a much wider range of pure solvents and binary solvent mixtures (Section 2.4), and mechanistic assignments are supported by studies of KSIEs in MeOH [28].
Usually solvolyses of fluoroformates in MeOH give KSIEs >2, consistent with general base catalysis and the mechanism shown in Figure 1b. However, t-butyl fluoroformate (7, R = Bu t ) gives a KSIE in MeOH of 1.26 [30], characteristic of the cationic reaction channel (Figure 1a). Also based on Equation (3), the slope for 7, R = Bu t is 0.33 ± 0.02 in 90%, 80%, 70% and 60% acetone-water. Consequently, even if a wider range of data was available, changes in mechanism may not lead to convincing changes in slopes for solvolyses of fluoroformates in acetone-water mixtures. In contrast, carboxylic acid and sulfonyl chlorides do show clear changes in slopes (see Section 3).
When a wide range of solvents of varying ionizing power and nucleophilicity are investigated, it is possible to separate the two mechanisms; the extended Grunwald-Winstein equation (Section 2.4) can then be used to correlate the kinetic data and to obtain m values for each mechanism are obtained. It was found that the slopes (m values) for the cationic channel were lower than for the associative channel; both channels were observed for 1-adamantyl fluoroformates [31], and the ionization channel for t-butyl fluoroformate gave an m value of 0.41 [30], slightly lower than typical values for the associative channel (see Table 4 of Reference [28]). This is the opposite trend to that observed for chloroformates [32] and other acid chlorides (see below).

Carboxylic Acid Halides
Solvolyses of many carboxylic acid chlorides in a single binary solvent mixture (such as acetone-water) would give linear plots of log kobs or log k3 vs. Y. Examples discussed in this section will be restricted to those for which KSIE data indicates the possibility of an SN3 mechanism.
Solvolyses of 1, Z = NO2 from 90% acetone to water [33] and of 8 from 80% acetone to water [36] fit all of the suggested criteria for a third order associative mechanism (i.e., KSIE in MeOH and water >1.5, and a linear plot Equation (3), characteristic of the third order reaction channel (Figure 1b). Also, logarithms of observed rate constants for solvolyses of 1, Z = NO2 and methyl chloroformate (MeOCOCl) correlate linearly with those for chloroacetyl chloride (see Figure 1 of Reference [34]), showing strong similarities between solvolyses of chloroformates and other acid chlorides.
Based on the observations [9,10] for benzoyl fluoride (Figure 3), and the reduced "pull" of fluoride as a leaving group, it would be expected that solvolyses of typical acid fluorides would react via the third order mechanism. Supporting evidence includes: (i) the solvent effect, k (water)/k (50% acetone-water), of 14 for spontaneous hydrolyses of acetyl fluoride can be compared with that of 22.6 [10] for benzoyl fluoride-hydrolyses are also acid and base-catalysed [37]; (ii) observed rates of solvolyses of p-dimethylaminobenzoyl fluoride (3, Z = NMe2) are almost independent of solvent composition from 80% to 60% ethanol, before a mechanistic change occurs to a cationic pathway [9].

Sulfonyl Chlorides
Sulfonyl chorides have relatively high heterolytic bond dissociation energies [21], implying that formation of sulfonyl cations is unfavourable. Even when there is an adjacent nitrogen lone pair, as in Me2NSO2Cl, solvolyses do not show common-ion effects [38]. Comparison with reactions of various sulfonyl chlorides in acetone-water by plotting log kobs vs. Y gave a relatively high value of m = 0.69 for Me2NSO2Cl, leading to the conclusion that the transition state was more ionic (looser) than for other sulfonyl chlorides, but the mechanism was not SN1 as suggested by others [39]; the KSIE in water and D2O of 1.3 ( Table 2, References [38][39][40][41][42][43][44][45]) is compatible with either SN1 or SN2 mechanisms. In the terminology of Figure 1, the mechanism of solvolysis of Me2NSO2Cl, is SN2, and within the SN2-SN1 spectrum throughout the wide range of Y values, but is not SN1 even in water. Recent more extensive studies of solvent effects also led to the proposal of an SN2 mechanism [46]. Doubts about the interpretation of KSIE data in terms of general base catalysis were based [40,47] on the anomalously high value (2.54) for the KSIE of i-PrSO2Cl in MeOH (Table 2). Also the low value of 1.62 for MeSO2Cl does not fit the general trend. These outliers obscure the general trend of higher values for KSIE and very low and/or negative Equation (3) slopes for typical sulfonyl chlorides ( Table 2). Apart from the first and perhaps second entries in Table 2, the slopes and particularly the KSIE values of the remaining substrates are consistent with mechanistic changes within the SN2-SN3 spectrum (Figure 1b) throughout the range of acetone-water mixtures. As the concentration of acetone increases, ΔS ≠ becomes progressively more negative for solvolyses of 2, Z = NO2, Br, H and Me [48,49], indicating more highly ordered transition states.
Most of the slopes shown in Table 2 are so low that the correlation with Y is poor. Typical plots have a very shallow U-shape. Arenesulfonyl chlorides (2,10) permit the systematic introduction of more electron donating groups, and U-shaped curvature of the Equation (3) plots becomes progressively more pronounced. These results are discussed in Section 2.3.3.

Anhydrides
Data [11] for solvolyses of p-nitrobenzoyl tosylate (4, Z = NO2) show a linear plot (Figure 3 [53]. These results are consistent with changes within the SN2-SN1 spectrum. A rationalization is that the electrophilic "pull"of sulfonates is much larger than for chlorides (e.g., kOMs/kCl ~ 10 3 for methanesulfonyl derivatives [52]), so the extra "push" of a third order process is not required.
For solvolyses p-bromophenylsulfonic acid anhydride in acetone-water mixtures, an Equation (2) slope of 1.75 was reported [54]. However, these data do not provide sufficient support for a third order mechanism, because of the unreliability of Equation (2)-see Section 2.1. Slopes of plots vs. Y depend on the size of the leaving group, probably due to the extent of charge delocalisation in the developing anion; for SN1 solvolyses of 1-adamantyl substrates an order of slopes Cl > Br > I > OTs was established [55]; tosylates have relatively low slopes, and given the trend, it would be expected that fluorides would have the highest slopes (e.g., Figure 3).

Carboxylic Acid Chlorides
From the results given in Section 2.2.3 (supported by the more extensive data for chloroformates in Section 2.2.1), the normal expectation is that third order solvolyses in acetone-water will fit Equation (3) with zero or negative slopes (mechanism shown in Figure 1b). In contrast, when the cationic mechanism (Figure 1a) operates, there is a much higher and positive slope (e.g., see Figure 1 of Reference [66]). Consequently, it is possible to detect a change in mechanism from third order to cationic by plotting log kobs vs. Y; e.g., for solvolyses of benzoyl chloride (1, Z = H) in a wide range of acetone-water mixtures [67]. In addition, a much clearer change in slopes is obtained by plotting log k3 vs. Y (Equation (3)) instead of log kobs; the two plots are compared in Figure 6. Figure 6. Comparison of plots of logarithms of first order rate constants (log kobs) and third order rate constants (log k3, Equation (3)) vs. Grunwald-Winstein Y values [4,17] for solvolyses of benzoyl chloride (1, Z = H) in acetone-water mixtures at 25 °C; kinetic data from Reference [68].
Close to the point where the two lines intersect (Figure 6, around Y = 1, ~60% acetone-water), the two mechanisms are assumed to be concurrent, and so values of log kobs and log k3 are corrected by subtracting log 2 = 0.3 from both Y = 1 values (these points are then fitted to both relevant correlation lines).
Solvolyses of p-chlorobenzoyl chloride (1, Z = Cl) and phenylacetyl chloride in acetone water also show sharp changes in slope when log k3 is plotted vs. Y for acetone-water mixtures (see Figure 4 of Reference [69] and Figure 3 of Reference [34]). In contrast, the same plots for p-nitrobenzoyl chloride (1, Z = NO2) and chloroacetyl chloride are linear throughout the range of acetone-water mixtures (see Section 2.2.3). Solvolyses of trimethylacetyl chloride give a similar plot to Figure 6 when log kobs is plotted vs. Y (see Figure 2 of Reference [70]). For solvolyses of p-dimethylaminobenzoyl fluoride (3, Z = NMe2) in ethanol-water mixtures, a sharp change in slope is readily apparent even in plots [9] of first order rate constants (log kobs).
The above results are significant because they show that a change in hydrolysis mechanism can occur when the % water in a binary mixture such as acetone-water is altered.

Chloroformates
Solvolyses of isopropyl chloroformate (5, R = i Pr) show a KSIE in water at 25 °C of only 1.25 [71], in contrast to values of 1.8-2.2 for methyl, ethyl and aryl derivatives [72]; also, values of log k3 in water for 5, R = i Pr deviate substantially from the downward trend set by 90%-70% acetone-water compositions (Figure 7). These results are in marked contrast to solvolyses of ethyl chloroformate (5, R = Et), which shows a close to constant value of log k3 from 95% v/v acetone-water to 100% water ( Table 1). It can be concluded that both 5, R = Et and 5, R = i Pr are hydrolysed by the third order mechanism (Figure 1b) in 90% and 80% acetone-water mixtures, but the mechanism changes to cationic for hydrolysis of 5, R = i Pr in water. The minimum at Y~0 corresponds to 70% acetone, and log 2 = 0.3 was subtracted from this data point before fitting it to both correlation lines (Figure 7). The above conclusion is in good agreement with published work [72], using an independent approach. From the extended GW equation (Section 2.4) for only seven solvents clearly favouring the cationic mechanism (water, formic acid, and various CF3CH2OH-water and (CF3)2CHOH-water mixtures), it was calculated [72] that the mechanistic changeover for 5, R = i Pr occurred between 70 and 80% acetone-water. The prediction in Figure 7 that the mechanistic change occurs in 70% acetone-water is based on deviations from an independent correlation for the third order mechanism.
The plot (red in Figure 7) of log k3 vs. Y for solvolyses of isobutyl chloroformate (5, R = CH2CH(CH3)2) show very similar values to those for 5, R = i Pr in 90%-60% acetone-water (first 4 data points); note that the temperatures are not identical (40 and 45 °C). Compared with the line drawn for 5, R = i Pr, additional data in 50%-10% acetone for 5, R = CH2CH(CH3)2 show a smaller change in slope; also the KSIE in water of 1.54 [73] is larger. The KSIE in methanol of 2.03 [73] and the low slope of the plot for 90%-60% acetone (Y values from −2 to 1) are consistent with third order reactions, and a change to a bimolecular mechanism was suggested for reaction in water [73]. Comparing slopes and KSIE values in water, it appears that the change in mechanism begins slightly later and is more gradual for 5, R = CH2CH(CH3)2 than for 5, R = i Pr.
Both 9-fluorenylmethyl chloroformate (14, Figure 8) and 5, R = CH2CH(CH3)2 have a β,β-dialkyl group and solvolyses of 14 in acetone-water [74] also give shallow U-shaped plot (not shown); values of log k3 at 45 °C vary from −5.75 (90% acetone) to −6.11 (50% acetone) and then up to −5.70 (20% acetone); the KSIE in methanol is 2.2, but there are no KSIE data for water [74]. An almost identical pattern of results is observed (Figure 9) for solvolyses of phenyl chlorothionoformate (15); log k3 values are close to constant from Y = −1 to +2 (80%-40% acetone); then there is an increase in slope ( Figure 9); the KSIE value are 2.02 for methanol, but only 1.45 for water [75], so a gradual change to a bimolecular mechanism may be underway. Equation (3) plots for isopropenyl chloroformate (5, R = CH3C=CH2) at 10 °C show close to constant values of log k3 from 90% acetone to water (Figure 9, middle), whereas the upper plot at 35 °C is U-shaped. Solvent effects and KSIE values in water and methanol of >2.0 at 10 °C are very similar to those for 1, Z = NO2 [76], so there is strong evidence for the third order mechanism in acetone-water. At 35 °C [77], there may be an increase in slope from 50% to 20% acetone-water (Y > 1.4, Figure 9) and a bimolecular cationic mechanism (Figure 1a) having a higher activation energy may start to be competitive. Evidence for a change to the cationic reaction mechanism was later obtained by comparing solvolyses in fluorinated alcohols with those for phenyl chloroformate [78].

Sulfonyl Chlorides
Although most sulfonyl chlorides react by the third order mechanism within the SN3-SN2 spectrum (Section 2.2.4), there is evidence for a mechanistic changeover to the SN2-SN1 spectrum for electron-rich substrates; however, formation of sulfonyl cations is relatively unfavourable [21], and there is no evidence for an SN1 mechanism. Evidence for the changeover will be based on KSIE data ( Table 4, References [79][80][81]) and non-linear Equation (3) plots (Figures 10 and 11), but there is also support from independent evidence on alcohol/water selectivities [79,81,82].
In all four examples (Table 4), the KSIE decreases from >1.5 in methanol (SN3-SN2 spectrum) to reach a value of 1.3-1.4 more characteristic of the SN2-SN1 spectrum. Also, the substituent effect for 4-substituted 2,6-dimethyl substrates (10) changes from kOMe < kMe on the left side of Figure 11 (SN3-SN2 spectrum) to kOMe > kMe on the right side (consistent with relatively more bond breaking for the SN2-SN1 spectrum).  Figure 11 a Data from Reference [13]  For solvolyses of 2, Z = OMe, the changes in slopes based on Equation (3) are large, and the minimum value of log k3 calculated from experimental data was lowered by log 2 = 0.3, before fitting the two correlation lines (Figure 10).
For solvolyses of 10, Z = Me (Figure 11), and 16 ( Figure 10), there are two minimum values of log k3 between Y = 0 and Y = 1; each of these was lowered by 0.15 before fitting the two correlation lines; for solvolyses of 10, Z = OMe, there is no clear minimum, so lines are drawn through the unadjusted values of log k3 (coded in blue, Figure 11).

Multi-Parameter Equations
Most of the above discussion has been concerned with solvolyses in water, acetone-water and methanol. Correlations of kinetic data for a wider range of solvents require multi-parameter correlations. In theory these are more comprehensive, but they are also more complex, and caution is recommended [83].
Retaining the assumption of third order rate laws and water as one of the solvents, the possibility of cosolvent acting as general base and/or as nucleophile leads to additional third order rate constants. Assuming that the cosolvent (e.g., acetone, acetonitrile, dioxan) acts as general base (or in some other way), but not as nucleophile, two third order rate constants (kww and kwc) contribute to kobs, and Equation (5) is obtained [35,44].

kobs/[water] 2 = kww + kwc [cosolvent]/[water] (5)
If the cosolvent is an alcohol, it could act as nucleophile and/or general base, and four third order rate constants are then possible. In such cases there are two products, and product ratios provide useful additional information [35,44].
A more general approach, applicable to a very wide range of solvents and solvent mixtures, is to extend the Grunwald-Winstein equation to include a term for solvent nucleophilicity. In this Equation (6), logarithms of observed first order rate constants in any solvent (log k), relative to solvolyses in 80% ethanol-water (ko), are correlated with Y and a term (N) for solvent nucleophilicity [5]; m is the response to changes in Y and l is the response to changes in N and c is a residual term.
Equation (6) was first applied to the SN2-SN1 spectrum of solvolyses of primary and secondary alkyl tosylates [5]. Solvolyses closer to the SN1 extreme have relatively high values of m and low values of l; as the substrates become more susceptible to nucleophilic attack (e.g., 2-propyl, ethyl, methyl tosylates), values of m decrease and values of l increase in accordance with Equation (7). In terms of mechanism, a higher m implies more electrophilic "pull", and a higher l implies greater nucleophilic "push"; a further implication of Equation (7) is that if there is more "pull" then less push is required (and vice versa).
For many of the studies of substrates discussed above, it has become standard practice to interpret l/m ratios. For an SN1 reaction, l = 0, so l/m = 0. As l increases and m decreases, l/m ratios >2 can be obtained [40]. Consequently, l values and/or l/m ratios help to position substrates within a spectrum of mechanisms (e.g., for sulfonyl chlorides [40]). Values of m depend on how the N scale is defined [84], and published values are usually based on the NT scale [85,86].
Deviations from a single correlation can be interpreted as evidence for a second reaction channel, and a correlation based on Equation (6) can often be obtained for each reaction channel (e.g., for solvolyses of a variety of ROCOCl, RSCOCl, ROCSCl, and RSCSCl substrates [87]). The two channels can be compared or characterized using l and m values or the l/m ratios.

Mechanistic Insights from Theoretical Calculations
Mechanistic conclusions from kinetic studies of hydrolyses of benzenesufonyl chlorides (2) have recently been supported by theoretical calculations [7]. The calculations for water clusters in acetone indicate that reactions do not involve the formation of an intermediate and the SN3 reaction is favoured by electron withdrawing substituents and by clusters having a small number of water molecules (i.e., low Y).
The spectrum of mechanisms from nucleophilic attack by water (SN2), often assisted by general base catalysis by a second water molecule (SN3) can be illustrated (Figure 12) by the changes in bond lengths calculated [7] for a series of substrates (2, Z = OMe, Me, H, Cl and NO2).  Figure 12. Calculated [7] changes in bond lengths (Angstroms) in transition states for hydrolyses of benzenesulfonyl chlorides (2) in a cluster of 17 water molecules in acetone.
The results, including numbering of atoms, are taken from Table 3 of Reference [7], and focus only on the substrate, the water molecule acting as nucleophile via O (16) and the water molecule acting as general base through O (22). Except for the approximately constant O(16)-H(17) distance, bond lengths extend significantly as the substituent changes from Z = NO2 to OMe; as expected for the proposed SN3 mechanism, the O(22)-H(17) distance in the second water molecule is considerably shorter than the value of 1.8 expected for a hydrogen bonded water molecule, and is shortest for Z = NO2.

Comments on Mechanistic Details
The mechanism of Song and Jencks [9] is illustrated in Figure 13 for benzoyl fluorides (3). The key features are the same as those shown in Figure 1b. General base catalysis by a base (B, e.g., water) assists nucleophilic attack by activating the attacking water nucleophile and by preventing the reverse reaction. The transition state could lead to a tetrahedral intermediate or there may be an "uncoupled concerted reaction" [9,88] in which the C-F bond is cleaved before the intermediate can be formed. In contrast, nucleophilic attack at the carbonyl group of chloro-and fluoroformates (5,7) is usually [29,77,87,89] described as shown in Figure 14. Two tetrahedral intermediates (18,19), not transition states are usually drawn. It is implied that there may be general base catalysis, but it not usually shown by these authors. However, general base catalysis is a key component of the proposed mechanism (Figures 1b and 13), so the fast deprotonation step is avoided, and the first tetrahedral intermediate (18) Figure 14.
Also, it does not seem likely that the alkoxide intermediate (19) could be formed under typical reaction conditions of ca. 10 −2 M substrate hydrolysed in unbuffered media, so the pH < 3; under these conditions, protonation of 19 would be expected, but the development of negative charge in the transition state is needed to explain the relatively high response to changes in Y for solvolyses of acid fluorides (Section 2.2.2 and Figure 3). As well as the proposed [29] developing charge on oxygen, there may be a partial charge on fluorine in a transition state similar to 17. F/Cl rate ratios of ca. 1 [29] provide evidence for the addition character of either a transition state or a tetrahedral intermediate [88].
Previously, it has been proposed that tetrahedral intermediates such as 19 may be by-passed during nucleophilic substitution reactions of acid chlorides [68] and chloroformates [90]. A single transition state has also been proposed for acyl group transfer between phenolate nucleophiles [91] and also for SN(Ar) reactions [92]. Therefore, although these reactions are often drawn to show stepwise mechanisms, there is substantial evidence for the concerted alternative.
The proposal that water as base assists water as nucleophile (Figure 1b) can be extended to hydroxide-catalysed hydrolyses of esters [93,94] and to SN(Ar) reaction [95]. For base-catalysed hydrolysis of methyl formate, the kinetic isotope effect on the oxygen nucleophile was explained [93] by water acting as nucleophile and hydroxide acting as general base. This mechanism was later supported by proton inventory measurements on the base-catalysed hydrolysis of ethyl acetate [94]. Alkoxide-catalysed hydrolysis of a chlorotriazine indirectly indicates that hydroxide-catalysed hydrolysis also occurs in SN(Ar) reactions [95].

Experimental Section
Kinetic data are from the references cited. Correlations were performed using Microsoft Excel.

Conclusions
Equation (3) provides a useful additional way to investigate mechanisms of hydrolyses, particularly for the SN2-SN3 spectrum (Tables 1-3) and for changes in reaction channel (e.g., Figures 6, 7 and 9-11); it is more reliable than Equation (2) because solvent effects are included, and less complex than multi-parameter correlations (Section 2.4). KSIE data in water and methanol provide very useful additional information.
For sulfonyl chlorides, hydrolyses usually involve a second water molecule acting as a general base (SN2-SN3 channel), but there is no reliable evidence for an addition-elimination process involving an intermediate. For the most electron-rich substrates, Equation (3) plots (Figures 10 and 11) support previous evidence for a gradual change in transition structure to the SN2-SN1 (cationic) reaction channel in the more polar mixtures; in less polar mixtures (lower Y), the SN2-SN3 channel becomes significant.
The same trends may apply to hydrolyses of other acid derivatives (e.g., haloformates and carboxylic acid halides), except that cationic reactions are more favourable for carboxylic acid halides. When the alternative "addition-elimination" process occurs (e.g., for fluoroformates), tetrahedral intermediates may be by-passed.