Debye-Huckel theory deviations from

The theory proposed by Debye and Huckel dominated the study of aqueous electrolytes from around 1920 to near the end of the 1950 s. The Debye-Huckel theory was based on a model of electrolyte solutions in which the ions were treated as point charges (later as charged spheres), and the solvent was considered to be a homogeneous dielectric. Deviations from ideal behaviors were assumed to be due only to the long range electrostatic forces between ions. Refinements to include ion-ion pairing and ion... 

Marshall s extensive review (16) concentrates mainly on conductance and solubility studies of simple (non-transition metal) electrolytes and the application of extended Debye-Huckel equations in describing the ionic strength dependence of equilibrium constants. The conductance studies covered conditions to 4 kbar and 800 C while the solubility studies were mostly at SVP up to 350 C. In the latter studies above 300°C deviations from Debye-Huckel behaviour were found. This is not surprising since the Debye-Huckel theory treats the solvent as incompressible and, as seen in Fig. 3, water rapidly becomes more compressible above 300 C. Until a theory which accounts for electrostriction in a compressible fluid becomes available, extrapolation to infinite dilution at temperatures much above 300 C must be considered untrustworthy. Since water becomes infinitely compressible at the critical point, the standard entropy of an ion becomes infinitely negative, so that the concept of a standard ionic free energy becomes meaningless. 

The first accurate calculation of the activity coefficient based on energetic effects of inter-ionic interactions in solvents was carried out by -> Debye and -> Huckel in 1923 by assuming that all the deviations from ideality at low concentrations of electrolyte were due to interionic interactions (- Debye-Huckel theory) with this it is possible to show that... 

In addition to the short-range interactions between species in all solutions, long-range electrostatic interactions are found in electrolyte solutions. The deviation from ideal solution behavior caused by these electrostatic forces is usually calculated by some variation of the Debye-Huckel theory or the mean spherical approximation (MSA). These theories do not include terms for the short-range attractive and repulsive forces in the mixtures and are therefore usually combined with activity coefficient models or equations of state in order to describe the properties of electrolyte solutions. 

Debye-Huckel theory. A theory advanced in 1923 for quantitatively predicting the deviations from ideality of dilute electrolytic solutions. It involves the assumption that every ion in a solution is surrounded by an ion atmosphere of opposite charge. Results deduced from this theory have been verified for dilute solutions of strong electrolytes, and it provides a means of extrapolating the thermodynamic properties of electrolytic solutions to infinite dilution. 

Electrostatic interactions give a large deviation from ideality in equilibrium properties of solutions containing low molecular weight electrolytes. This deviation was most successfully disposed of by the Debye-Huckel theory [2]. According to this theory, the ionic species are not distributed in solution in a random manner, but form an ionic atmosphere structure, and the thermodynamic properties such as the activity coefficient of solvent (or the osmotic coefficient), the mean activity coefficient of solute, and the heat of dilution, decrease linearly with the square root of the concentration, in conformity with experimental observations. 

A number of other attempts have been made to account for the properties of concentrated aqueous solutions of ionic compounds by procedures that represent further improvements on the simple Debye-Huckel approach. However, they lie outside the scope of the present chapter. The important point to emphasize is that the concentrated aqueous solutions that are generally employed in the preparation of AB cements tend to exhibit significant ion-ion interactions such interactions lead to significant deviations from ideality which may be accounted for by substantial extension of the ideas of simple dilute solution theory. 

Debye, P. and Huckel, E., The interionic attraction theory of deviations from ideal behavior in solution, Z. Phys., 24, 185, 1923. 

In highly charged macromolecules Eq. (5.8.16) does not apply. It is then necessary to generalize these arguments to include hydration and deviations from spherical shape. However there are even more formidable complications to consider first. In aqueous solution, the macroion is surrounded by an ion atmosphere composed mainly of ions of opposite charge. This means that the local field —the field felt by the macroion— will be considerably different than the applied field. Corrections for this effect can be made if one uses the Debye-Huckel-Henry theory to calculate the properties of the ion atmosphere (see Chapters 9 and 13). An estimate (Tanford, 1961) gives... 

Clearly if Ya is unity then the solution is ideal. Otherwise the solution is nonideal and the extent to which ya deviates from unity is a measure of the solution s non-ideality. In any solution we usually know [A] but not either a a or Ya- However we shall see in this chapter that for the special case of dilute electrolytic solutions it is possible to calculate ya- This calculation involves the Debye-Hdckel theory to which we turn in Section 2.4. It provides a method by which activities may be quantified through a knowledge of the concentration combined with the Debye-Huckel calculation of ya- First, however, we consider some relevant results pertaining to ideal solutions and, second in Section 2.3, a general interpretation of Ya-... 

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