Improvements to the Debye-Huckel Limiting Law

By using this equation for the ionic atmosphere potential in the derivation, the molal activity coefficient equation (4.32) becomes  

Calculations done with this equation can be satisfactory up to an ionic strength of. 1 molal. It also works best for l-I electrolytes, decreasing in applicability for 1-2, 2-2 etc. electrolytes. The distance a is also assumed to be the same for all ions in the system, although this may not be the case. Problems also arise as this parameter is not a measurable quantity, but by choosing values close to the hydrated radius, often in the range rf 3.5 to 6.2 X (suggested by Robinson and Stokes (4)), reasonable results may be obtained. 

The numerator of equation (4.34) deals with the long range interaction effects and the denominator makes a correction for short range effects. Nonetheless, the short range effects are not adequately compensated for due to the fact that possible ion-solvent molecule and possible ion-ion interactions are ignored. HUckel attempted to improve equation (4.34) by adding a term meant to account for the reduction of the dielectric constant D by increased concentration  

The general usage of this equation has usually had an empirically chosen C. 

A comparison of the calculated activity coefficients using the limiting law (4.32). the extended Debye-HUckel (4.34) and the HUckel equation (4.36) for sodium chloride at 26 Celsius can be found in figures 4.1 and 4.2. Also plotted are experimental values of the molal activity coefficient as published by Robinson and Stokes (5). The value used for a is 4.0 and. as suggested by Robinson and Stokes, C =. 055 l.roole . 

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