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ION–ION INTERACTIONS 273





















                      Fig. 3.27. The experimental log versus   curve is
                      a straight line only at extremely low concentrations.
             What then are the inadequacies of the Debye–Hückel limiting law? One does not
          have to look far. If one examines the experimental log  versus  curve, not  just in
          the extreme dilution regions, but at higher concentrations, it turns out that the simple
          Debye–Hückel limiting law falters. The plot of log versus   is a curve (Fig. 3.27
          and Table 3.8) and not a straight line as promised by Eq. (3.90). Further, the curves
          depend not only on valence type (e.g., 1:1 or 2:2) but also (Fig. 3.28) on the particular
          electrolyte (e.g., NaCl or KC1).
             It appears that the Debye–Hückel law is the law for the tangent to the log   versus
             curve at very low concentrations, say, up to 0.01 N for 1:1 electrolytes in aqueous
          solutions. At higher concentrations, the model must be improved. What refinements
          can be made?

          3.5.2.  Ions Are of Finite Size, They Are Not Point Charges

             One of the general procedures for refining a model that has been successful in an
          extreme situation is to liberate the theory from its approximations. So one has to recall
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