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268 CHAPTER 3

2. J. C. Rasaiah, “Theories of Electrolyte Solutions,” in The Liquid State and Its Electrical
Properties, E. E. Kunhardt, L. G. Christophorou, and L. H. Luessen, eds., NATO ASI Series
B 193: 135 (1987).

Papers
1. C. F. Baes, Jr., E. J. Reardon, and B. A. Bloyer, J. Phys. Chem. 97:12343 (1993).
2. H. P. Diogo, M. E. Minas da Piedade, and J. J. Moura Ramos, J. Chem. Ed. 70: A227
(1993).
3. H. Schönert, J. Phys. Chem. 98: 643 (1994).
4. H. Schönert, J. Phys. Chem. 98: 654 (1994).
5. B. Honig and A. Micholls, Science 268: 1144 (1995).
6. B. B. Laird and A. D. J. Haymet, J. Chem. Phys. 100: 3775 (1996).

3.5. THE TRIUMPHS AND LIMITATIONS OF THE DEBYE–HÜCKEL
THEORY OF ACTIVITY COEFFICIENTS

3.5.1. How Well Does the Debye–Hückel Theoretical Expression for
Activity Coefficients Predict Experimental Values?

The approximate theoretical equation

indicates that the logarithm of the activity coefficient must decrease linearly with the
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square root of the ionic strength or, in the case of 1:1-valent electrolytes, with
Further, the slope of the log versus straight line can be unambiguously
evaluated from fundamental physical constants and from Finally, the slope does
not depend on the particular electrolyte (i.e., whether it is NaCl or KBr, etc.) but only
on its valence type, i.e., on the charges borne by the ions of the electrolyte, whether it
is a 1:1-valent or 2:2-valent electrolyte, etc. These are clear-cut predictions.
Even before any detailed comparison with experiment, one can use an elementary
spot check: At infinite dilution, where the interionic forces are negligible, does the
theory yield the activity coefficient that one would expect from experiment, i.e., unity?
At infinitedilution, c or which means that log or The properties
of an extremely dilute solution of ions should be the same as those of a solution
containing nonelectrolyte particles. Thus, the Debye–Hückel theory emerges success–
fully from the infinite dilution test.
Furthermore, if one takes the experimental values of the activity coefficient (Table
3.6) at extremely low electrolyte concentration and plots log versus curves, it

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That is, For a 1:1 electrolyte, As