Conductivity of concentrated salt solutions

TL;DR

This paper presents a simple mean-field model that accurately predicts the conductivity of concentrated univalent salt solutions, resolving a long-standing challenge in electrolyte theory.

Contribution

It introduces a minimalistic analytical model based on electrostatic and colloid electrophoresis principles to describe concentrated salt solution conductivity.

Findings

Model fits experimental data well up to a few mol/l concentration.

Predicts conductivity ratio depends only on ion radii and concentration.

High dilution requires relaxation correction for accuracy.

Abstract

The conductivity of concentrated salt solutions has posed a real puzzle for theories of electrolytes. Despite a quantitative understanding of dilute solutions, an analytical theory for concentrated ones remains a challenge for almost a century, although a number of parameters and effects incorporated into theories increases with time. Here we show that the conductivity of univalent salt solutions can be perfectly interpreted using a simplest model that relies on a modified mean-field description of electrostatic interactions and on a classical approach to calculating colloid electrophoresis. We derive a compact equation, which predicts that the ratio of conductivity to that at an infinite dilution is the same for all salt and depends only on a product of the harmonic mean of ion hydrodynamic radii and the square root of concentration. Our equation fits very well the data for inorganic salts (up to a few mol/l), although at a very high dilution the relaxation correction seems necessary.