Debye-Hilckel theory

Let us now consider a pair of ions in aqueous solution from such a crystal. In the Debye-Hilckel theory it is assumed that in pure solvent, the mutual potential energy is — e2/ r, where e is the macroscopic dielectric constant of the solvent,2 until the ions come into contact with each... 

The best functions to use in the extrapolation can be determined from the dependence of 7+ and on the ionic strength. Theoretically, httle is known about the dependence of on concentration (6), but from the Debye-Hilckel theory, we should expect log 7 + to depend on with the dependence approaching linearity with increasing dilution. 

A second example is provided by a semiempirical correlation for multi-component activity coefficients in aqueous electrolyte solutions shown in Fig. 2. This correlation, developed by Fritz Meissner at MIT [3], presents a method for scale-up activity-coefficient data for single-salt solutions, which are plentiful, are used to predict activity coefficients for multisalt solutions for which experimental data are rare. The scale-up is guided by an extended Debye-Hilckel theory, but essentially it is based on enlightened empiricism. Meissner s method provides useful estimates of thermodynamic properties needed for process design of multieffect evaporators to produce salts from multicomponent brines. It will be many years before sophisticated statistical mechanical techniques can perform a similar scale-up calculation. Until then, correlations such as Meissner s will be required in a conventional industry that produces vast amounts of inexpensive commodity chemicals. 

According to the Debye-Hilckel theory (Chapter XVII), A should bo 0.375 for all uni-univalent strong electrolytes in aqueous solution at 0 C x should be exactly 0.5 for all strong electrolytes. 

One way of coping with observed deviations from the behaviour predicted by the Debye-Hilckel expression is not to do any further theoretical calculations, but to work at empirical extensions to the Debye-Hiickel expression to take it to higher concentrations. These methods assume that the Debye-Hiickel theory is valid at low concentrations. 

The work of the Danish chemists was based on Lewis and Randall s introduction of the concept of the ionic strength and on the Debye-Hlickel theory. Two years before Debye and Hilckel had formulated their theory Lewis and Randall (39) had introduced the idea of the ionic strength of a solution, which they defined as... 

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