Proton dissociation, diffusion-controlled

The rate of proton dissociation is controlled by three parameters the frequency of ion pair formation, the rate of stabilization of the proton by hydration, and the rate of escape out of the Coulomb cage. Measurements carried out in dilute salt solutions, that is, 10— lOOmM, will not be influenced by the two later steps. The activity of the water is invariable whereas the ionic atmosphere will screen the electrostatic attraction. Under such conditions, the rate of dissociation should be a direct function of the probability that the stretching covalent bond will reach the dissociation distance. As demonstrated in Figure 2, this expected correlation is observed over a wide range of pKs. Under these conditions, a reversible dissociation will comply with the relationship Kdiss = ki/k-i. As the recombination reaction for all acids is a diffusion-controlled reaction, we can approximate = k-t Kdlss — 1010 Kdiss(sec-1). 

If HA is a stronger acid than the ammonium function of 2, the rate constant for proton transfer to 2, kuA, will be for diffusion and the observed rate constant will be independent of the acidity of HA. On the other hand, if HA is a weaker acid than the ammonium function of 2, the proton transfer from general acids, HA, to the nitrogen of 1 in Scheme 11.8 will be given by k K /K, where K A is the acid dissociation constant of HA and kA is the diffusion-controlled rate constant. The observed rate will nowbe dependent upon the acidity of the catalyst HA as described by a Bronsted correlation with slope equal to —1. 

Actually a very crudal kinetic aspect has apparently always been overlooked so far. The original assumption of a proton mobility comparable to that in free solution which allows for dispersion frequencies in the MHz range must not be made in this special case. It is only applicable to the diffusion-controlled polarization of counterion atmospheres as discussed before. In contrast to those counterions the protons of the Kirkwood-Shumaker model are diemically bound at specific sites and must dissociate before they can jump to another site. Thus the lifetime of protons at a given site has to be taken into account with regard to the relaxation time of the overall fluctuation process. Its effect can be readily estimated on the basis of the rate constant of protolytic dissociation... 

The rate-limiting step in proton transfer between electronegative atoms is either /c, the diffusion-controlled encounter of the acid-base pair for thermodynamically favourable transfers or the diffusion-controlled dissociation of the acid-base pair, for thermodynamically unfavourable transfers (Figure 1). The rate-limiting step is rarely the proton transfer within the encounter complex. Eigen plots are predominantly observed in reactions in which proton transfer occurs to or from heteroatoms in reactive intermediates. 

As first espoused by Knowles and Albery, the limiting selective pressure on enzymatic function is the diffusion-controlled limit by which substrates bind and products dissociate [7]. In the case of triose phosphate isomerase [8], ketosteroid iso-merase [9], mandelate racemase [10], and proline racemase [11], the energies of various transition states on the reactions coordinates have been quantitated, with the result that the free energies of the transition states for the proton transfer reactions to and from carbon are competitive with those for substrate association/ product dissociation. However, as discussed in later sections, the energies of the... 

The laser-induced proton pulse is a young, high-resolution method recently introduced to biochemistry. It is a system capable of measuring the diffusion-controlled reaction of a proton with its environment, solvent, and solutes. The information derived from these measurements is divided according to the time scale of the event The primary reaction of proton dissociation, recorded in the nano- and subnanosecond time frames, and slower (microsecond) diffusion-controlled reaction of a proton with other solutes. 

In such a mechanism, what is the effect of increasing the nucleophilicity of the nucleophile and the basicity of the catalyst For a constant nucleophile changing the basicity of the catalyst would affect the rate as shown in the Eigen curve of Fig. 2a. When proton transfer from to B is thermodynamically favourable the rate of proton transfer is diffusion controlled and hence independent of the basicity of the catalyst B. When it is thermodynamically unfavourable the rate decreases proportionally to the decreased basicity of the catalyst, and is given by Kk K] /, where ATj and AT are the acid dissociation constants of T- and BH", respectively. 

There is other evidence that the exchange of water molecules between the site in A W B and bulk solvent is slow compared to both proton transfer within the complex and the separation of A from B. Regarding the former, the fact that so many proton-transfer reactions in which AG° is negative are diffusion-controlled proves that the proton-transfer step is fast compared to the dissociation of the complex. Regarding the latter, if the departure of a water molecule from A W B were fast compared to the dissociation of the complex, one would expect to find more examples of rapid direct bimolecular proton transfer without solvent participation. 

For acid dissociation in water, the two mechanisms are readily distinguished by means of HOD—D2O solvent isotope effects if the reverse reaction (rate constant or kL ) is diffusion controlled. For bimolecular proton transfer according to equation 18 the resulting lyonium ion is HOD2, while for proton transfer with water participation equation 19 it is DsO. ... 

---