Geochemistry. William M. White

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solvent–solute and solute–solute interactions in electrolytes give rise to excess free energies and nonideal behavior. By developing a model to account for these two kinds of interactions, we can develop an equation that will predict the activity of ions in electrolyte solution.

      In an electrolyte solution, each ion will exert an electrostatic force on every other ion. These forces will decrease with the increase in square of distance between ions. The forces between ions will be reduced by the presence of water molecules, due to its dielectric nature. As total solute concentration increases, the mean distance between ions will decrease. Thus, we can expect that activity will depend on the total ionic concentration in the solution. The extent of electrostatic interaction will also obviously depend on the charge of the ions involved: the force between Ca2+ and Mg2+ ions will be greater at the same distance than between Na+ and K+ ions.

Schematic illustration of an ion surrounded by a cloud of oppositely charged ions, as assumed in Debye-Hückel theory.

       All electrolytes are completely dissociated into ions.

       The ions are spherically symmetrical charges (hard spheres).

       The solvent is structureless; the sole property is its permittivity.

       The thermal energy of ions exceeds the electrostatic interaction energy.

      I is ionic strength, in units of molality or molarity, calculated as:

      For very dilute solutions, the denominator of eqn. 3.74 approaches 1 (because I approaches 0), hence eqn. 3.74 becomes:

      (3.76)equation

T°C A B (108 cm)
0 0.4911 0.3244
25 0.5092 0.3283
50 0.5336 0.3325
75 0.5639 0.3371
100 0.5998 0.3422
125 0.6416 0.3476
150 0.6898 0.3533
175 0.7454 0.3592
200 0.8099 0.3655
225 0.8860 0.3721
250 0.9785 0.3792
275 1.0960 0.3871
300 1.2555 0.3965

      From Helgeson and Kirkham (1974).

Ion å (10–8 cm)
Rb+, Cs+, images, Ag+ 2.5
K+, Cl, Br, I, images 3
OH, F, HS, images, images, images 3.5
Na+,

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