Free volume-entropy interpretation of the electrical conductance of aqueous electrolyte solutions in the concentration range 2-20 N

The electrical conductance of concentrated aqueous solutions of Ca(NO₃)₂ and Mg(NO₃)₂ has been studied at temperatures up to 180° and concentrations up to 9 M in order to test transport equations which recognize the liquid-glass transition phenomenon as a natural consequence of the dependence of particle packing density on temperature and cohesive energy. The data strongly suggest that on sufficient cooling or on sufficient concentration (e.g., by isothermal evaporation of the solvent) at low enough temperatures, any supersaturated electrolyte solution would pass through a glass transition. The equivalent conductance of 7-8 M solutions has been followed as a function of temperature over three orders of magnitude and shown to conform to the equation Λ = AT^-1/2 e exp[-k/(T-T₀)] where T₀ is the theoretical glass transition temperature. The following new equation, derived from the above on the basis of a simple relation between T₀ and the electrostatic charge concentration, i.e., equivalent concentration, N, is proposed to give a first approximation account of the isothermal composition dependence of conductance in the high concentration range Λ_(T) = A exp[-k′/(N₀-N)] where N₀, conceptually akin to T₀, is the charge concentration at which T₀ equals the isothermal temperature T. Although the derivation oversimplifies the solution behavior, the form of this equation correctly describes the composition dependence of A for Ca(NO₃)₂ solutions over the concentration range 2-15 N despite changes in A amounting to three orders of magnitude. Equations of the same form will also be valid for solution fluidities. The results are also consistent with the existence of distinct hydrated cation species at the higher concentrations.