Extension of Debye-Heckel theory to concentrated solution

Debye-Heckel used the concepts of electrostatics, fluid mechanics and statistical mechanics to derive a theory describing the properties of electrolyte solutions dominated by the interaction between ions. Obviously, Debye-Shocker's extreme law applies only to extremely dilute electrolyte solutions. When the concentration of the strong electrolyte solution of the 1:1 type exceeds 10 -3 mol∕L or the ionic strength of other types of electrolyte solutions is similar, the application of the polar limit law begins to be difficult, and thus, after their theory, there have been repeated corrections. To extend it into a more concentrated solution. Most of the corrections were made by adding corrections to the Debye-Heckel equation. The Debye-Huckel equation reflects the long-range effects between ions, and the corrections reflect their short-range effects. These activity coefficient extension equations use empirical terms to fit the activity measurements of the experimental observations. For example, Bjerreum considers ion association, or more precisely, ion pairing to form an ion pair, which is modified to assume that the ions are in a paired state and are not centered on the ion due to the ionic atmosphere. The contribution of electrical energy. The degree of ion pair formation increases very rapidly as the ion spacing r value decreases, and the associated equilibrium constant can be calculated. Finally, the extended Debye-Hake equation

Where B is another constant. If the solution contains more than one electrolyte, the equation cannot be thermodynamically used to calculate the activity coefficient. In addition, the closest distance between ions is not known. In order to eliminate this quasi-basic parameter, the following form of equation is used.

Where z + = z - ; β is an empirical constant that can be selected for a particular system by fitting the data. Davies takes β=0.2 to get the equation

It is quite consistent with the measured value of the average activity coefficient of the dilute solution. For example, the average deviation of the 0.1 mol ∕L solution is only about 2%. This is an empirical equation based on published data. As long as there is enough experimental data about the salt γ ± so that the tunable parameters α and β can be accurately calculated, such equations can be used to calculate richer solutions, for low A 1:1 type simple electrolyte solution of valence can be calculated to a concentration of about 1 mol ∕L. In general, however, no equation is satisfactory.

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