Conductivity at high frequencies and potentials

A number of experimental tests have been made of equations (6.39) and (6.40), which are known as Debye-Hiickel-Onsager equations. Equation (6.40), for example, which applies to a uni-imivalent electrolyte, can be written in the form 

Various explanations have been given for deviations from the Debye-Hiickel-Onsager equations. A common type of behavior is for the negative slopes of the A versus /c plots to be greater than predicted by the equation that is, the experimental conductivities are lower than predicted by the theory. This has been explained in terms of ion pairing, a concept which was developed by the Danish physical chemist Niels Bjerrum (1879-1958) in 1926. Although most salts, such as sodium chloride, are present in the solid state and in solution as ions and not as covalent species, there is a tendency for them to come together from time to time to form ion pairs. 

This is quite different from covalent bond formation, in which the ion pairs have only a temporary existence, since there is a constant interchange between the various ions in the solution. At any instant of time a certain number of ions are paired together in this way, and these ions therefore do not contribute to the transport of electric current. Solvents of low dielectric constant give rise to higher electrostatic attractions between the ions than do high-dielectric-constant solvents such as water, and thus favor the formation of ion pairs. 

An important consequence of the existence of the ionic atmosphere is that the conductivity should depend upon the frequency if an alternating potential is applied to the solution. Suppose that the alternating potential is of sufficiently high frequency that the time of oscillation is small compared with the time it takes for the ionic atmosphere to relax. There will not be time for the atmosphere to relax behind the 

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