Debye-Huckel-Onsager theory concentration

Debye-Huckel-Onsager theory — (- Onsager equation) Plotting the equivalent conductivity Aeq of solutions of strong electrolytes as a function of the square root of concentration (c1/2) gives straight lines according to the - Kohlrausch law... 

It is a function expressing the effect of charge of the ions in a solution. It was introduced by -> Lewis and Randall [iii]. The factor 0.5 was applied for the sake of simplicity since for 1 1 electrolytes I = c (electrolyte). It is an important quantity in all electrostatic theories and calculations (e.g., - Debye-Huckel theory, - Debye-Htickel limiting law, - Debye-Huckel-Onsager theory) used for the estimation of -> activity coefficients, -> dissociation constants, -> solubility products, -> conductivity of -> electrolytes etc., when independently from the nature of ions only their charge is considered which depends on the total amount (concentration) of the ions and their charge number (zj). 

One caimot, however, expect the Debye-Huckel-Onsager theory of the nonequilibrium conduction properties of ionic soiutions to fare better at high concentration than the corresponding Debye-Hiickel theory of the equilibrium properties (e.g.. 

One point that had long puzzled physical chemists is why the concentration dependence of acids obeys the Debye-Huckel-Onsager theory. Pitts et have now calculated from Conway s theory that... 

Conductivity equations based on Debye-Huckel-Onsager theory, such as Equation 17.9, cannot predict the conductance maxima. They are valuable tools to study dilute solutions in a concentration range below the maximum where the solvent may be described as a homogeneous medium with permittivity and viscosity of the pure solvent compound. For extension of the transport equations in the theory of transport properties, especially the continuity equation approach, the reader is referred to Ref [183] and the references given there. 

The Debye-Huckel-Onsager equation has been tested against a large body of accurate experimental data. A comparison of theory and experiment is shown in Fig. 4.93 and Table 4.21 for aqueous solutions of true eiectroiytes, i.e., substances that consisted of ions in their crystal lattices before they were dissolved in water. At very low concentrations (< 0.(X)3 N), the agreement between theory and experiment is very good. There is no doubt that the theoretical equation is a satisfactory expression for the limiting tangent to the experimentaiiy obtained/ versus curves. 

The correction factor,/, relates the actual mobility of a fully charged particle at the ionic strength under the experimental conditions to the absolute mobility. It takes ionic interactions into account and is derived for not-too-concentrated solutions by the theory of Debye-Huckel-Onsager using the model of an ionic cloud around a given central ion. It depends, in a complex way on the mean ionic activity coefficient. The resulting equation contains the solvent viscosity and dielectric constant in the denominator. In all cases, the factor is < 1. The actual mobility is always smaller than the absolute mobility. 

There have been many studies of the effect of added electrolytes on ET rates [171, 234, 235], The main effect of ionic atmosphere is electrostatic screening, which is usually accounted for in terms of Debye-Huckel theory (mean-field, low-concentration approximation). At sufficiently low ionic strength, the corresponding component of the activation energy is simply proportional to the ratio of the Onsager radius (also referred to as the... 

Later, Falkenhagen and co-workers and Onsager and Fuoss established a method of calculating parameter A starting from the Debye-Huckel theory. However, the above equation is only valid for concentrations up to about 0.01 mol/L. According to the above equation the relative viscosity should always increase with concentration. However, experiments show non-monotonic behavior for several electrolytes such as most of the potassium halides, and several mbidium and cesium halides [12]. 

This equation is often referred to as Ostwald s dilution law. It depends on the assumptions (a) that ionic conductivities have constant values, and are not dependent on the concentration and (b) that the ions in dilute solution behave as ideal solutes. Both of these assumptions proved to be mistaken, and were finally corrected in the interionic attraction theory of Debye and Huckel and the conductance equation of Onsager (see conductance of aqueous solutions, conductance equations). 

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