Bjerrum contact distance

For most of the salts the slope of the phoreogram is steeper (i.e., more negative or catabatic) than would be calculated by the Onsager limiting law. Most researchers have rejected the possibility of ionic association as a cause of this deviation - principally because the Bjerrum contact distance in NMA, for the temperature range of 30 to 60 °C, is less than 0.2 nm and thus less than the sum of the crystallographic radii of most possible cation-anion contact pairs. 

NO3 in acetonitrile has been obtained by Janz and Muller. Associated structures of ions have been studied in nonaqueous solvents over a wide range of dielectric constants. LiCNS in solvents of low dielectric constant, such as ethers and thioethers, gives rise to several different types of ion aggregates. Many different types of contact ion pairs or agglomerates have been identified, and the role the solvent has in this association—whether the solvent separates the ions or not—has been determined. The Bjerrum critical distance, that is, the distance at which the ion is able to interact with other ions to form ion-pair stmctures (see Section 4.8.8), is of great use in these types of studies. Table 4.25 shows some values for 1 1, 2 2, and 3 3 electrolytes in different solvents. 

Perhaps the greatest uncertainty in the evaluation is caused by the selection of the appropriate ionic radii, / . In accordance with the introduction of Bjerrum s association constant [Bj 26], Justice [Ju 71b, Ju 75a, Ju 75b] assumes the equation Ry = R = q From chemical considerations, Barthel [Ba 78a] considers it more correct to describe the radius Ry as the sum of the contact distance, a, of the ions and the size, s, of the solvent molecule Xy=a4-s. 

For dissociation reactions in which the reverse, recombination step is slow, dissociation is virtually complete once the pair has separated to the contact distance. Under these conditions the magnitude of the interaction in the dissociated pair, in particular the screening of this interaction by ions, would not affect the dissociation rate. In terms of the Hammond postulate [22] and its extensions [23] an exothermic dissociation process would have its transition state close to the bound state, so that the equilibrium and recombination rate coefficients would change in parallel. In such a case one expects no salt effect on the dissociation reaction, in agreement with the classical picture of Bronsted and Bjerrum for kinetic salt effects [7]. 

The value of the Bjerrum distance depends on the ionic charges, the nature of the solvent and the temperature but not on electrolyte concentration. For aqueous solutions of 1-1 electrolytes at 25°C, it is equal to 357 pm. Bjerrum proposed that all ions contained in a sphere with this radius are paired. This is a reasonable proposal for aqueous systems, since ions of typical size would be close to contact at such small separations. However, if the solvent has a lower dielectric permittivity, the distance over which ions are considered to be paired increases and the assumption that they are in contact is more diiScult to accept. For example, when the solvent s relative permittivity is 10, the Bjerrum distance r-Q increases to 2800 pm. 

Examination of electrostatic principles allows some conclusions to be drawn regarding the effect of ion pairing on the selectivity of salt partitioning or, equivalently, on the driving force for cation exchange. As outlined in a standard text [234], treatments of Fuoss [235] or of Bjerrum [236] may be applied to estimate the ion-pair association constant /Ca.,soc- The Fuoss treatment assumes contact ion pairs and is conceptually simpler to use and apply. As the simplification will not affect the conclusions to be drawn here, it will be employed with the additional proviso that the effect of water in the solvent will be neglected for the moment. According to Fuoss, the ion-pair association constant at 298 K may be expressed in terms of the solvent dielectric constant 6 and the internuclear distance i m-x (in nm) between the cation and anion ... 

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