Mean distance of closest approach of ions: Lithium salts in aqueous solutions

Abstract

Numerical values for the mean distance of closest approach of ions, "a", for lithium salts in aqueous solutions are presented and discussed. These values were obtained from both experimental activity and diffusion coefficients, and estimated by using different theoretical approaches.

On the analogy between the restricted primitive model and capacitor circuits. Part II: A generalized Gibbs-Duhem consistent extension of the Pitzer-Debye-Hückel term with corrections for low and variable relative permittivity

“…where 𝜇 𝑖 𝑒𝑙 stands for the electrostatic contribution to the chemical potential of species 𝑖, 𝐶 𝑖 𝑋 stands for an effective capacitance given by electrolyte theory 𝑋, 𝑧 𝑖 𝑒 is the charge of particle 𝑖 and 𝜀 𝑟 stands for the relative permittivity of some arbitrary dielectric medium. It has been shown in the literature, 48,59 that the qualitative behavior of the logarithmic activity coefficient ln(𝛾 𝑖 𝑒𝑙 ) from different theories performs similarly when linearly scaling of the distance of closest approach (hard-core collision diameter) 𝑎 = 𝑟 + + 𝑟 − , where 𝑟 + and 𝑟_ are ion specific as discussed by Ribeiro et al 60 This similarity of performance was thoroughly evaluated for the first time by Maribo-Mogensen et al 59 In their work, Debye-Hückel theory yielded very similar qualitative results when compared to the unrestricted MSA if the hard-core collision diameter was scaled by 5/6 of the value applied in MSA. The same effect was observed for the chemical potential in our previous work when the hard-core collision diameter in the PDH term is equal to 3/2 of the hard-core collision diameter applied in MDE-DH theory.…”

Diffusion coefficients of nickel chloride in aqueous solutions of lactose at T=298.15K and T=310.15K

“…There is no direct method for measuring the ion size parameter a, ''mean distance of closest approach" from the Debye-Huckel theory, but it may be estimated by using finite-ion-size equations (e.g., [45]), as an adjustable parameter, and also from different theoretical approaches (e.g., [45]). In our case, the estimation of this parameter has been done by using the mean value, presented by Kielland [46], of the effective radii of the hydrated ionic species of this electrolyte (that is, the value a = 4.5 Á 10 À10 m, respectively) (table 1).…”

Diffusion of cadmium chloride in aqueous solutions at physiological temperature 310.15K

“…There is no direct method for measuring the ion size parameter a, the ''mean distance of closest approach'' from the Debye-Huckel theory, but it may be estimated from the data of Marcus (table XIII in [17]), considering two approximations [18][19][20][21][22][23]. The first one considers the a-value as the sum of the ionic radii (R ion ) reported by Marcus [17] (i.e., a = 2.7Á10 À10 m).…”