Zucker-Hammett hypothesis

As originally proposed, the Zucker-Hammett hypothesis states that for A1 reactions log kobs is linear in —Ho, whereas for A2 reactions log kobs is linear in log ch+. This latter statement is now known not to be generally correct. Moreover, the slopes of plots against —Ho often differ from unity. Bunnett and Olsen... 

The Aq dependence of the oxidation in strongly acidic media was taken by Rodek as implying that no water molecule is involved in the transition state and that consequently the ester mechanism as portrayed above cannot hold. However, the Zucker-Hammett hypothesis upon which this argument is based, i.e. that a reaction forming a transition state containing a water molecule will follow a [H30 ] dependence, but that otherwise an dependence will be followed, may not be valid, and in any case the ester can be depicted as breaking down as fol-lows - ... 

The acidity dependences of V(V) oxidations are significant. That of pinacol , which undergoes 100% C-C cleavage, is a+bh ). The first (acid-independent) term is rare in V(V) oxidations and implies that V02 is the active oxidant the second term implies, on the basis of the Zucker-Hammett hypothesis, that the transition state has the structure (J5), the mechanism being... 

If the substrate is predominantly unprotonated in the acidity range covered, the protonation correction term (second on the left in equation (35)) will be zero, and if the activity coefficient term on the right cancels to zero, log values will be linear in —Ho with unit slope (the Zucker-Hammett hypothesis).146 In practice, linearity is usually observed,23 e.g. for the trioxane depolymerization in equation (31),144 although the slopes are seldom exactly unity. For more strongly basic substrates that are predominantly protonated in the acidity range covered, equation (36) is easily derived this is acidity independent and should have zero slope against — H0 if the substrate is fully protonated and the last term cancels.145... 

Since the hydrolysis of methyl mesitoate conforms with the Zucker-Hammett hypothesis, it is not unexpected that the parameters calculated from the same data should meet Bunnett s more recent mechanistic criteria The value of Bunnett s w for the reaction in sulphuric acid is calculated as —1.1. and in perchloric acid as — 2.55W, both values falling in the region (w belween—2.5 and 0) characteristic of reactions not involving a molecule of solvent in the transition state. Bunnett s is also negative, as expected, values of —0.25 and —0.425 being found for the same two sets of data at 90°C4 . 

Although the Zucker-Hammett hypothesis works rather well in most cases, and usually gives the correct answer in ester hydrolysis reactions, for example, it does lead on occasion to incorrect conclusions, and since it is now quite clear that one of its main underlying assumptions, that the protcnation behaviour of all neutral substrates is quantitatively similar, is incorrect, it has been superseded by more accurate treatments. Unfortunately, none of these is as simple to operate as the Zucker-Hammett hypothesis, nor has any yet attained widespread use. But these improved treatments have resulted in a distinct advance in our understanding of ester hydrolysis in strong acid, and one recent approach will be discussed here in some detail. 

In retrospect it is clear that the Zucker-Hammett hypothesis was regarded too uncritically too soon, and sometimes treated almost as a law which reactions were expected to obey. Criteria of mechanism are almost invariably... 

A criterion of mechanism based on the Hammett acidity function, H0 (Section 3.2, p. 130),has long been used to decide the type of question raised by the choice between Mechanisms I and II in Scheme 8. Since in strongly acidic media the concentration of the protonated substrate should be proportional to h0, the reaction rate for a unimolecular decomposition of this protonated substrate (Mechanism I) should also be proportional to h0, whereas if a water molecule is required (Mechanism II), the rate should follow H30+ concentration instead. This test, known as the Zucker-Hammett hypothesis,76 when applied to acetal and ketal hydrolysis, appears to confirm the A-l mechanism, since a linear relationship is found between rate constant and h0 at high acidity.77 Inconsistencies have nevertheless been found in application of the Zucker-Hammett hypothesis, for example failure of the plots of log k vs. — H0 to have the theoretical slope of unity in a number of cases, and failure to predict consistent mechanisms for forward and reverse reactions the method is therefore now considered to be of doubtful validity.78 Bunnett has devised a more successful treatment (Equation 8.45), in which the parameter to measures the extent of... 

According to the Zucker—Hammett hypothesis [84], experimental data of log k (k = apparent first-order rate coefficient) are linearly dependent on H0 for A1 reactions, viz. 

The coefficient a in eqn. (27) is between 0.8 and 1.4 in most cases. For A2 reactions, a linear relationship between log k and H0 is not expected, but k is supposed to be directly proportional to the stoichiometric concentration of the strong acid [84]. The Zucker—Hammett hypothesis has been applied most successfully to the field of ester hydrolysis. It is not generally valid, however [13]. 

Since the Zucker—Hammett hypothesis does not lead to the correct answer in several examples, Bunnett [89] suggested another criterion for a distinction among the different mechanisms for acid catalyzed reactions. He observed that straight lines are obtained if either log k + H0 or log k — log CH x (Ch x = stoichiometric concentration of the strong acid, HX) is... 

Zucker-Hammett hypothesis This hypothesis states that, if in an acid-catalyzed reaction, lg k] (first-order rate constant of the reaction) is linear in H0 (Hammett acidity function), water is not involved in the transition state of the rate-controlling STEP. However, if lg k, is linear in lg[H+], then water is involved. This has been shown to be incorrect by Hammett. 

TimelP investigated the effect of the acid used. Rate constants were determined for hydrochloric, perchloric, sulfuric, and phosphoric acids at concentrations ranging from 0.5 M to 9 M. Log k was found to vary linearly with Ho, as required by the Zucker-Hammett hypothesis, but a slope of unity is only approximately given by the first three acids and not at all for phosphoric acid and, instead of coinciding, the plots are displaced with respect to each other. These observations led TimeU to conclude that data obtained with one of these four acids cannot accordingly be recalculated to be valid for another acid by referring to the same value for Ho, as has often been done in the past. ... 

Because the Zucker-Hammett hypothesis is invalid and Bunnett s criterion is unreliable, Withey and Whalley studied the effect of pressure on the rate of acid hydrolysis of methyl a-n-glucopyranoside. The value they obtained for the volume of activation clearly shows that the reaction must be unimolecular. 

Recently an extension of the Zucker-Hammett hypothesis has been... 

The hydrolysis of anhydrides is in many ways similar to the hydrolysis of esters. The volume of activation for the acid-catalyzed hydrolysis of acetic anhydride in 44-1% w/w acetone-water at 0°C is —17T l-3 cm mole (Koskikallio et al., 1959). The volume of activation for the hydrolysis of methyl acetate in the same solvent is — 13-6 cm mole- (Withey et al., unpublished), and so it seems likely that the mechanism for acetic anhydride is bimolecular. This was originally taken as a failure of the Zucker-Hammett hypothesis (Koskikallio et al., 1959) because the rate in water is approximately proportional to (Gold and Hilton, 1955). However, it appears (Bunton and Perry, 1960), largely on the grounds of the changing entropy of activation with changing solvent, that the mechanism may change between pure water and aqueous dioxane. 

The interest of organic chemists in the interpretation of acid catalyzed reactions dates back to the very early measurements of reaction rates(l). The most widely known and applied theory is the one proposed more than 40 years ago by Zucker and Hammett(2) and later reviewed by Paul and Long(3). According to this theory we could reveal whether the reaction mechanism is of the A-1 or A-2 type by checking whether the increase in logarithm of the experimental reaction rate depends on the first power of H or log c +, respectively. Probably because of its deceptive simplicity, this criterium has found very wide applications. Although Hammett himself has pointed out(4) on the shortcomings of this criterium there are few researchers who still apply the Zucker-Hammett hypothesis. Let s quickly discuss the reasons why this criterium is not valid. The rate expression for the A-1 mechanism, depicted in equation 1 and 2, is reported in equation 3... 

It follows that the Zucker-Hammett hypothesis, requiring that log k + Ho = constant, holds only if... 

A very similar discussion for the A-2 reactions shows that the Zucker-Hammett hypothesis (i.e. log k - log c + = constant) holds only in the very unlikely case where log(fjj+ fg... 

The experimental failure of the Zucker-Hammett hypothesis led other authors to propose alternative equations even before its theoretical weakness was completely clAar. Bunnett proposed(7) that the amount of variation in the experimental rate constant which cannot be accounted.for by the acidity function Ho should depend on variations in the activity of water and defined, according to equation 7, a parameter... 

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