Rate constant exchange mechanism

There are only few main group metal ion hydrates open to detailed mechanistic study of water exchange by NMR Be , Mg , Al" , Ga" and to a less extent, In" . They provide the opportunity to study the influence of size and charge on exchange rate constant and mechanism without the complicating effects of the variation of the electronic occupancy of the d-orbitals. All of the alkali ions as well as Ca , Sr, and Ba are very labile as a consequence of their relatively low surface charge density. However, indications on water exchange on Sr " can be obtained from... 

Aside from merely calculational difficulties, the existence of a low-temperature rate-constant limit poses a conceptual problem. In fact, one may question the actual meaning of the rate constant at r = 0, when the TST conditions listed above are not fulfilled. If the potential has a double-well shape, then quantum mechanics predicts coherent oscillations of probability between the wells, rather than the exponential decay towards equilibrium. These oscillations are associated with tunneling splitting measured spectroscopically, not with a chemical conversion. Therefore, a simple one-dimensional system has no rate constant at T = 0, unless it is a metastable potential without a bound final state. In practice, however, there are exchange chemical reactions, characterized by symmetric, or nearly symmetric double-well potentials, in which the rate constant is measured. To account for this, one has to admit the existence of some external mechanism whose role is to destroy the phase coherence. It is here that the need to introduce a heat bath arises. 

The rate of hydrolysis of sarin on Dowex-50 cation exchange resin is insensitive to the stirring rate. However, with a more active catalyst (Amberlite-IRA 400), the rate constant at 20°C was 5.3, 7.5, and 8.5 h at 60,800 and 1000 revolutions/min , respectively, suggesting that film diffusion was the rate-limiting. step. Thus, the mechanism of the rate-limiting step depends on the nature of the catalyst [34]. 

McDowell and Stirling194 studied electronic effects upon the reactivity of aryl vinyl sulfones towards amines. Rate constants for t-butylamine addition in ethanol at 25 °C were well correlated by the Hammett equation, with p = 1.59. Comparison of this with p values for H-D exchange mentioned above191 suggested considerable carbanionic character in the transition state, perhaps in a concerted mechanism. Rates of addition of amines to alkenyl, allenyl and alkynyl p-tolyl sulfones have also been measured195. 

This all seemed very reasonable at the time, but subsequent work was not consistent with it. A small but measurable amount of 180 exchange was reported for some amides in reasonably concentrated HC1 media,277,278 and for at least one amide the amount of exchange decreased with increasing acidity,277 which is the opposite of what would be expected with the Scheme 14 one-water-molecule mechanism taking over from the equation (74) three-water-molecule mechanism as the acidity increased. Also, the solvent deuterium isotope effect was found to be close to unity for at least one amide,278 a result that has since been confirmed,279 which is not what would be expected on the basis of either a three- or a one-water-molecule process.280 Because of this it was decided to reexamine the lactam hydrolysis data subsequent to the publication of the excess acidity analysis of the H NMR results for these,268 a new study appeared with rate constant data for four of these molecules in aqueous H2S04 media obtained by UV spectroscopy at several temperatures,281 and this was included too.282... 

Where solvent exchange controls the formation kinetics, substitution of a ligand for a solvent molecule in a solvated metal ion has commonly been considered to reflect the two-step process illustrated by [7.1]. A mechanism of this type has been termed a dissociative interchange or 7d process. Initially, complexation involves rapid formation of an outer-sphere complex (of ion-ion or ion-dipole nature) which is characterized by the equilibrium constant Kos. In some cases, the value of Kos may be determined experimentally alternatively, it may be estimated from first principles (Margerum, Cayley, Weatherburn Pagenkopf, 1978). The second step is then the conversion of the outer-sphere complex to an inner-sphere one, the formation of which is controlled by the natural rate of solvent exchange on the metal. Solvent exchange may be defined in terms of its characteristic first-order rate constant, kex, whose value varies widely from one metal to the next. 

For such a mechanism, the overall second-order formation rate constant is given by the product of the first-order constant ktx and the equilibrium constant Kos. The characteristic solvent exchange rates are thus often useful for estimating the rates of formation of complexes of simple monodentate ligands but, as mentioned already, in some cases the situation for macrocyclic and other polydentate ligands is not so straightforward. 

Measuring the pressure dependence of the exchange rate constant leads to activation volumes, AV and this technique has become a major tool for the mechanistic identification of solvent exchange mechanisms (8,16,17). In the last 25 years high-pressure, high-resolution NMR probes were developed which allow the application of all NMR techniques described to pressures up to several hundreds of mega Pascals (18). 

An NMR investigation of water exchange at [Pt(H20)2(oxalate)2] is relevant to the mechanism of formation of one-dimensional mixed valence oxalatoplatinum polymers. In fact the rate constant for this presumably dissociative (AS = + 42 JK mol-1) reaction is considerably too low for water loss to be, as recently proposed, the first step in formation of these polymers. The mechanism of trans to cis isomerization for this oxalate complex, and for its (2 -methyl)malonate analogues, is intramolecular (Bailar or Ray-Dutt twist), since there is no concurrent incorporation of labeled solvent (177). 

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