Electrolytes Nernst-Einstein relation

The conductivity of a strong 1 1 electrolyte in an aqueous solution at infinite dilution is well known [6]. The Nernst-Einstein relation shows that the limiting molar conductivity,, of an electrolyte is related to the diffusion coefficient, D°, of the ions by Equation 1.1 ... 

The same evaluation can be done for charged particles and will give the relation between electrical and diffusional transport known as Nernst Einstein relation. The expression of the charge flow will also give Ohm s law for ionic transport in an electrolyte. 

This is the Nernst-Einstein equation, which relates the conductivity to the diffusion coefficients of the ions. The form of the expression in Eq. (31.63) raises the question of how the diffusion coefficients of the ions combine to yield a diffusion coefficient for the electrolyte. It is to this question that we now turn our attention. 

Walden s rule — This empirical rule states that the product of the equivalent conductivity and the viscosity of the solvent for a particular electrolyte at a given temperature is a constant. Its rational explanation is based on the Stokes-Einstein equation that connects the diffusion coefficient and the viscosity of the medium, and the Nernst-Einstein equation that relates the diffusion coefficient to the equivalent conductivity. Hence, the product of the equivalent conductivity and viscosity is inversely proportional to the radius of the moving entity in conductance. As a first approximation, Waldens rule applies to organic solvents if the radius of solvated ions in various media is not significantly different. 

The ionic conductivity of a polymer electrolyte is closely related to the concentration of metal ions, which is usually expressed by the Nernst-Einstein equation ... 

Nernst(74), and later Einstein (75), found a relation between the diffusion constant in electrolytic solutions and the conductivity. The relation is... 

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