A Theory of Ion Association as a Complement of the Debye-Hückel Theory

Abstract

The classical Debye-Hückel theory of strong electrolyte solutions was re-examined in order to explain ion association. Regarding a symmetrical electrolyte in very dilute solutions, a more precise expression was derived for excess chemical potential due to electrostatic ion-ion interactions. This expression has, in addition to the Debye-Hückel term, a supplementary term resulting from a more proper account of the energy of the interactions of ions existing near each other. If the concept of ion association is taken as a complement of the Debye-Hückel theory, the contribution to the chemical potential of the electrolyte from ion association should correspond to the supplementary term. The following equation was thus obtained for the ion-association constant: K=(8πNa^3/1000) \overset∞\undersetn=1∑b^2n+2/[(2n+2)! (2n-1)] This equation is in agreement with that derived by Ebeling on the basis of the cluster theory and has an asymptotic representation (at b→∞) in common with Bjerrum’s. For practical b values, the present equation has the merit that it gives moderate K values, decreasing monotonously with an increase in the a value, and eliminates the disadvantages of Fuoss’s result, giving a minimum K value at b=3, and of Bjerrum’s, giving K=0 at ≤2.

Capillary zone electrophoretic studies of ion association between inorganic anions and tetraalkylammonium ions in aqueous–dioxane media

“…Other theories on ion association were later proposed by Denison and Ramsey [31], Fuoss [32], Ebeling [33] and, more recently Yokoyama and Yamatera [34]. However, it is the Bjerrum's theory that has been widely used despite its shortcomings such as counting as associated ions which are not in actual contact.…”

The effect of temperature on association constants and conductivities of ferrous chloride and ferric chloride in DMF-water mixtures

“…Obtained positive and high ΔH o values can be attributed to the presence of endothermic interactions between of the ions for FeCl2 and FeCl3. The negative ΔH o values could not be predicted from the ion association theories [32,33]. ΔH o values for both FeCl2 and FeCl3 in all DMF-water mixtures increased with an increase in the temperature.…”

Phase transitions of a neutral polyampholyte

“…This leads to an energy of the mixture [33,34] [18,19,21,28]. Then, the value of the association constant is found to be [35] …”

“…If the quality of the solvent is decreased, the second virial coefficient W~ becomes zero, and the leading order terms in Eq. (35) are…”

“…In the limit of very long chains, the main contributions in Eq. (35) are the second and the third virial coefficients, namely The network is, therefore, in a dense globular state for which…”