Kinetics equivalence

These examples illustrate the relationship between kinetic results and the determination of reaction mechanism. Kinetic results can exclude from consideration all mechanisms that require a rate law different from the observed one. It is often true, however, that related mechanisms give rise to identical predicted rate expressions. In this case, the mechanisms are kinetically equivalent, and a choice between them is not possible on the basis of kinetic data. A further limitation on the information that kinetic studies provide should also be recognized. Although the data can give the composition of the activated complex for the rate-determining step and preceding steps, it provides no information about the structure of the intermediate. Sometimes the structure can be inferred from related chemical experience, but it is never established by kinetic data alone. 

The rate terms A [HA] and A [H ][A ] are said to be kinetically equivalent or kinetically indistinguishable. There is no purely kinetic basis upon which to make a choice between them in Chapter 5 we will see why this is so, but a simple interpretation is that the two terms describe equivalent chemical compositions of atoms and charges. 

In these circumstances a decision must be made which of two (or more) kinet-ically equivalent rate terms should be included in the rate equation and the kinetic scheme (It will seldom be justified to include both terms, certainly not on kinetic grounds.) A useful procedure is to evaluate the rate constant using both of the kinetically equivalent forms. Now if one of these constants (for a second-order reaction) is greater than about 10 ° M s-, the corresponding rate term can be rejected. This criterion is based on the theoretical estimate of a diffusion-controlled reaction rate (this is described in Chapter 4). It is not physically reasonable that a chemical rate constant can be larger than the diffusion rate limit. 

In Section 3-3 we discussed the problem of kinetically equivalent rate terms. Suppose one of the rate constants evaluated for such a rate equation were larger than the diffusion-limited value this is a reasonable basis upon which to reject the formulation of the rate equation leading to this result. Jencks has given examples of this argument. 

As with intermolecular catalysis, the form of the rate equation may not decisively indicate the meehanism of the catalysis because of kinetic equivalences. Consider a substrate containing the acyl function -COX and an ionizable catalytic function -YH. 

Three kinetically equivalent rate terms involving intramolecular participation are shown in Table 6-3 with representations of appropriate transition states (mechanisms). Differentiation among these possibilities can be difficult. 

Table 6-3. Kinetically Equivalent Intramolecular Catalysis Mechanisms...

Kinetic schemes other than that embodied in Eq. (6-77) can give rise to a bellshaped curve. As in Eq. (6-77), however most of these involve two ionizations. Thus Scheme V, where HS is a monoprotic acid and B is a base (or the kinetic equivalent of S + BH ) yields a bell-shaped curve. 

Sketch the kinetic scheme that is kinetically equivalent to Scheme VII. 

Finally we should note that the demonstration of a Br nsted relationship does not constitute proof that general acid or general base catalysis is occurring. Because of the problem of kinetic equivalence of rate terms, we may not be able unequivocally to distinguish between these possibilities ... 

The mechanisms available to intramolecular reactions are the same as those of intermolecular reactions. The same problems of kinetic equivalence of rate terms may arise, and Table 6-3 shows some kinetically equivalent mechanisms for intramolecular reactions of the acyl function. The efficiency of intramolecular reactivity may be difficult to assess. One technique, described above as a method for the detection of an intramolecular reaction, is to make a comparison with an analog incapable of the intramolecular process. Thus p-nitrophenyl 5-nitrosalicylate, 17, hydrolyzes about 2500 times faster than p-nitrophenyl 2-methoxy-5-nitrobenzoate, 18. 

An important cautionary note must be inserted here. It may seem that the study of the salt effect on the reaction rate might provide a means for distinguishing between two kinetically equivalent rate terms such as k[HA][B] and k [A ][BH ], for, according to the preceding development, the slope of log k vs. V7 should be 0, whereas that of log k vs. V7 should be — 1. This is completely illusory. These two rate terms are kinetically equivalent, which means that no kinetic experiment can distinguish between them. To show this, we write the rate equation in the two equivalent forms, making use of Eq. (8-26) ... 

The dissociation constants are thermodynamic constants, independent of ionic strength. Equation (8-33), which was derived from (8-30), is, therefore, identical in its form, and its salt effect, with Eq. (8-31). Therefore, salt effects cannot be used to distinguish between Eqs. (8-30) and (8-31). Another way to express this is that if kinetically equivalent forms can be written, it is not possible to determine, on the... 

Chain transfer is kinetically equivalent to copolymerization. The Q-e and Patterns of Reactivity schemes used to predict reactivity ratios in copolymerization (Section 7.3.4) can also be used to predict reactivities (chain transfer constants) in chain transfer and the same limitations apply. Tabulations of the appropriate parameters can be found in the Polymer Handbook 3 ... 

The mechanism of decarboxylation of acids containing an amino substituent is further complicated by the possibility of protonation of the substituent and the fact that the species NH2ArCOOH is kinetically equivalent to the zwitterion NHj ArCOO. Both of these species, as well as the anion NH2 ArCOO" and even NH3 ArCOOH must be considered. Willi and Stocker644 investigated by the spectroscopic method the kinetics of the acid-catalysed decarboxylation of 4-aminosalicyclic acid in dilute hydrochloric acid, (ionic strength 0.1, addition of potassium chloride) and also in acetate buffers at 20 °C. The ionisation constants K0 = [HA][H+][H2A+] 1 (for protonation of nitrogen) and Kx = [A"][H+] [HA]-1, were determined at /i = 0.1 and 20 °C. The kinetics followed equation (262)... 

How does one know when the complete roster of reaction schemes that are consistent with the rate law has been obtained One method is based on an analogy between electrical circuits and reaction mechanisms.13 One constructs an electrical circuit analogous to the reaction scheme. Resistors correspond to transition states, junctions to intermediates, and terminals to reactants and products. The precepts are these (1) any other electrical circuit with the same conductance corresponds to a different but kinetically equivalent reaction scheme, and (2) these circuits correspond to all of the fundamentally different schemes. 

FIGURE 18 Rates of degradation of PCL in water at 40°C and in rabbit, demonstrating the kinetic equivalency of the two processes. (From Ref. 53.)... 

Single Reactions—For all reactions of orders above zero, tire CSTR gives a lower production rate than the batch, semi-batch, or kinetically equivalent plug-flow reactor. 

Contrary to the above expectations, the bromination of anisole (Tee and Bennett, 1984) and of phenols (Tee and Bennett, 1988a) in the presence of a-CD is not strongly retarded, so that some form of catalysis must occur. In some cases, actual rate increases are observed in spite of the several complexations that reduce the free reactant concentrations. Analysis of the effects of substituents on the kinetics leads to the conclusion that the catalysis by a-CD most probably results from reaction of CD-bound bromine with free substrate (12a) and that the a-CD-Br2 complex is 3-31 times more reactive than free Br2 towards phenols and phenoxide ions (cf. Tee et al., 1989). For the kinetically equivalent reaction of the substrate CD complex with free bromine (12b), the rate constants (A 2 ) for phenols do not correlate sensibly with the nature and position of the substituents, and for three of the phenoxide ions they have unrealistically high values, greater than 10u m 1 s . 

In initial studies with /3-CD it was noted that values of ka vary in inverse proportion to the inhibition constant, Kt, suggesting that PI is bound in the CD cavity in the transition state (Tee and Hoeven, 1989). Therefore, the Pi-mediated reaction is more reasonably viewed as being between the ester and the PI-CD complex. The third-order processes in (21) and (24) are kinetically equivalent (k2 = k.JKs = kJKy), and so kb values are easily found from k.t. Such values of kb show some variation with structure but they are quite similar for different Pis and not very different from k2 for the reaction of the CD with pNPA For example, for pNPA reacting with 15 different alcohol /3-CD complexes values of kb span the range 10-95 m 1 s l (Table A5.14), close to k2 = 83m-1s-1 for the reaction of pNPA with /3-CD alone. Similar behaviour was observed for other Pis (Table A5.14) and for aCD (Table A5.13), for which k2 = 26 m-1 s 1. 

In principle, reactions which are subject to electrophilic catalysis by protons can be catalysed by metal ions also (e.g. Tee and Iyengar, 1988 Suh, 1992). However, metal ions may function in other ways, such as to deliver a hydroxide ion nucleophile to the reaction centre (e.g. Dugas, 1989 Chin, 1991), and it is often difficult to decide between kinetically equivalent mechanisms without resorting to extensive (and intensive) model studies. Use of the Kurz approach may help to resolve such ambiguities, as shown below. 

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