Debye-Hiickel-Onsager equation

These equations are known as the Debye-Hiickel-Onsager equations. 

Up to concentration of 2 X 10-3 gram-equivalents per litre there is a satisfactory agreement between the results calculated from the Debye-Hiickel-Onsager equation and the actual values of conductance of uni-univalent electrolytes. The validity of this equation has been verified even for uni-bivalent electrolytes, while for bi-bivalent electrolytes there are greater deviations to be observed. 

Onsager equation — (a) - Debye-Hiickel-Onsager equation, see also - Debye-Hiickel-Onsager theory. 

This is the well-known Debye-Hiickel-Onsager equation for a symmetrical electrolyte. By defining the following constants... 

Figure 4.101 shows the variation of the equivalent conductivity versus concentration for a number of alkali sulfocyanates in a methanol solvent. The agreement with the theoretical predictions demonstrates the applicability of the Debye-Hiickel-Onsager equation up to at least 2 x 10" mol dm . ... 

When one switches from water to some nonaqueous solvent, the magnitudes of several quantities in the Debye-Hiickel-Onsager equation alter, sometimes drastically, even if one considers the same true electrolyte in aU these solvents. These quantities are the viscosity and the dielectric constant of the medium, and the distance of closest approach of the solvated ions (i.e., the sum of the radii of the solvated ions). As a result, the mobilities of the ions at infinite dilution, the slope of the A versus... 

W course, the validity of the calculation depends upon whether the theoretical expression for the equivalent conductivity (e.g., the Debye-Hiickel-Onsager equation) is valid in the given concentration range. 

The concentration c that appears in the Debye-Hiickel-Onsager equation pertains only to the free ions. This concentration becomes equal to the analytical concentration (which is designated here as only if every ion from the ionic lattice from which the electrolyte was produced is stabilized in solution as an independent mobile charge carrier i.e., c if there is ion-pair formation. Whether ion-pair formation occurs depends on the relative values of a, the distance of closest approach of oppositely charged ions, and the Bjerrum parameter g = (z z Co/2 T) 1/e. When the condition for ion-pair formation is satisfied and when a > the ions remain free. 

Data for 1-2 and 1-3 electrolytes which are unassociated at concentrations < 1 X 10 moldm also appear to fit the Debye-Hiickel-Onsager equation up to concentrations < 1 X 10 moldm but at higher concentrations some of these electrolytes approach the limiting slope from above, but others approach it from below. 

The apparent close fit to the Debye-Hiickel-Onsager equations at low concentrations has to be reassessed in the light of the cross-over predicted by the later Fuoss-Onsager 1957 equation (see Section 12.10.2). 

If A° is known independently, a can be obtained for each experimental stoichiometric concentration by a series of successive approximations using the Debye-Hiickel-Onsager equation and the known value of A° ... 

In the early 1950s several workers suggested modifications to the 1927 Debye-Hiickel-Onsager equation and to the 1932 Fuoss-Onsager equation. All of these modifications allowed for ko. 

Pay particular note the direct effect of considering both relaxation, AXreiaxation, and electrophoresis, AXeiectrophoresis, Contributes a term in i.e. they give the S /c term in the Debye-Hiickel-Onsager equation. When the effects of the cross terms are considered they have no term in and thus do not contribute to the Sy/c term. But all five corrections contribute to the other terms in the final Fuoss-Onsager equation. 

If the treatment is restricted to very low concentrations these higher terms drop out and the equation reduces to the simple Debye-Hiickel-Onsager equation ... 

A number of experimental tests have been made of equations (6.39) and (6.40), which are known as Debye-Hiickel-Onsager equations. Equation (6.40), for example, which applies to a uni-imivalent electrolyte, can be written in the form... 

Various explanations have been given for deviations from the Debye-Hiickel-Onsager equations. A common type of behavior is for the negative slopes of the A versus /c plots to be greater than predicted by the equation that is, the experimental conductivities are lower than predicted by the theory. This has been explained in terms of ion pairing, a concept which was developed by the Danish physical chemist Niels Bjerrum (1879-1958) in 1926. Although most salts, such as sodium chloride, are present in the solid state and in solution as ions and not as covalent species, there is a tendency for them to come together from time to time to form ion pairs. 

For very dilute solutions, the equivalent conductivity for any electrolyte of concentration c can be approximately calculated using the Debye-Hiickel-Onsager equation, which can be written for a symmetrical (equal charge on cation and anion) electrolyte as... 

Both Kohlrausch s law and the Debye-Hiickel-Onsager equations break down as the concentration of the electrolyte increases above a certain value. As already mentioned, the reason for this breakdown is that as eoncentration inereases the average separation between cation and anion decreases, so that there is more interionic interaction. 

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