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The tendency of modern theory is to assume that strong electrolytes are practically completely ionised at dilutions greater than 0.1N and that the change of conductivity with concentration is due, not to changes in the number of ions with constant speeds, as in Arrhenius's theory, but to changes of speed with constant number. In the theory of Debye and Hückel (1923) the electrical forces between the charged ions are assumed to cause each ion to surround itself with an "atmosphere" of ions of opposite charge. When the ion moves it tends to leave this atmosphere behind, and to build up a new one, but owing to the slowness of motion (p. 249) this takes time and there will be an excess of ions of opposite sign behind the moving ion, tending to drag it back. This effect is greater the larger the concentration, hence the ions will move faster in more dilute solutions and the equivalent conductivity, Λ, will increase on dilution, until at infinite dilution, when the ionic forces are negligible, it reaches a constant value, Λ∞. A second effect retarding the motion of the ions is due to the friction opposed by the solvent to the motion of the positive and negative ions composing the ion atmosphere about any central ion. This atmosphere must be dragged by the moving ion through the solvent, thus giving rise to retarding forces which also disappear, like the first effect, at infinite dilution when the frictional force on the central ion alone remains.
The theory shows that the equivalent conductivity Λ∞, which would be shown if the ions exerted no action on one another, is reduced to the value  , where c = concentration and a is a constant, and
 | Fig: Equivalent conductivities Equivalent conductivities of uni-univalent salts (M˙X') in water at 18°C. |
shows that Λ when plotted against the square-root of the concentration gives, at small concentrations, very nearly a straight line. This was discovered empirically by Kohlrausch many years ago. The theory shows that the slope of the Λ and √c curves should be greater with ions of higher valency (e.g., Cu˙˙, SO4'' ) and this also had been found by Kohlrausch.
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