Acidity statistical effects

Statistical Effects. In a symmetrical diprotic acid, the first dissociation constant is twice as large as expected since there are two equivalent ionizable... 

This is a classical example of a statistical effect reflecting changes in the symmetry numbers of the various species involved in ionization equilibria. Furthermore, the acidity constant K, corresponding to ... 

Statistical effects. In a symmetrical diprotic acid, the first dissociation constant is twice as large as expected since there are two equivalent ionizable hydrogens, while the second constant is only half as large as expected because the conjugate base can accept a proton at two equivalent sites. So K IKi should be 4, and approximately this value is found... 

Scatter in free energy correlations may also be caused by a statistical effect when more than one reaction centre can be involved.The reactivity of a base or nucleophile possessing q identical basic or nucleophilic sites compared with a dissociation equilibrium where the conjugate acid possesses p identical acidic sites requires the following statistical correction to the simple Bronsted type relationship (Equations 23 and 24). 

Whenever an organic acid contains two or more chemically identical (i.e., stereochemically equivalent) functional groups, statistical factors that originate in the entropy of formation of the acid and/or its conjugate base contribute to the variation of thermodynamic dissociation constants with the degree of dissociation of the acid. Such statistical effects are implicitly included in equations that are often used to describe acid-base equilibria in synthetic and natural polymers. Because those equations have frequently been applied to proton binding by humic substances, a brief discussion of statistical ef-... 

In an analysis of the influence of charged substituents on the pK values of carboxylic acids, Bjerrum (1923) suggested that, for symmetrical proton transfer reactions such as Equation (4), pK differences can be accounted for in terms of purely electrostatic field effects (and statistical effects, whenever they are warranted). If the proton and charged substituent are treated as point charges separated by a distance r in a solvent continuum whose dielectric constant D is that of the bulk solvent, the work required to transfer the proton from r to infinity in the electrostatic field of the charged substituent can be calculated from classical electrostatic theory. The pK difference between the unsubstituted and substituted acids (ApK) is then given by... 

As a simple illustration of the importance of dipolar effects on acid strength, the pKa values of selected benzenecarboxylic acids are presented in Figure 3. Using benzoic acid as a reference, it is clear that the first ionization constants of all the other acids are greater, even though all the acids are uncharged. A small part of the increased acidity is due to statistical effects, but most of the effect is attributable to dipolar stabilization of the monoanion in the polyprotic acids. The dipolar effect is so pronounced in these molecules that the Ka values of several of the anions are greater than that of benzoic acid. 

The intrinsic binding site models represent a very simplified approach toward modeling a continuous distribution of proton binding ligands. As previously indicated, those models are severely limited by their assumption that only statistical effects and electrostatic effects of charged groups have any effect on the acidities of functional groups. 

The literature on proton binding by humic substances indicates that statistical effects, delocalization effects, and, probably most importantly, the effects of dipolar groups on the acidity of a functional group have generally been ignored. An attempt has been made in this chapter to provide the reader with a rather detailed discussion of the nature of substituent effects on the dissociation constants of organic acids. Statistical, electrostatic, and delocalization effects have been treated separately. 

There is a purely statistical effect which can be considered in the following way. For the first process, dissociation can occur in two ways (i.e. there are two protons, either of which may dissociate), but recombination in only one whereas in the second process, dissociation can occur in only one way, but recombination in two (i.e. the proton has two sites to which it may return and hence twice the probability of recombining). Thus, on purely statistical grounds one would expect Kl = 4K2. Bjerrum observed that for the dicar-boxylic acids, HOOC(CH2) COOH, the ratio Ki/K2 was always greater than four, but decreased rapidly as n increased (see Table 5-5). He suggested the following explanation. When the two points of attachment of protons are... 

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