Fuoss-Onsager conductance equation for symmetrical electrolytes

14 Limitations of the treatment given by the 1957 Fuoss-Onsager conductance equation for symmetrical electrolytes 

In many respects it is perverse and verging on the impertinent to criticise this equation when the following points are considered  

However, despite the sophistication of the mathematics, it is necessary to realise that this is only a very primitive treatment at the microscopic level. 

The properties of the ions and the solvent which are ignored are similar to those ignored in the Debye-Hiickel treatment. These are very important properties at the microscopic level, but it would be a thankless task to try to incorporate them into the treatment used in the 1957 equation. Furthermore, Stokes Law is used in the equations describing the movement of the ions. This law applies to the motion of a macroscopic sphere through a structureless continuous medium. But the ions are microscopic species and the solvent is not structureless and use of Stokes Law is approximate in the extreme. Likewise, the equations describing the motion also involve the viscosity which is a macroscopic property of the solvent and does not include any of the important microscopic details of the solvent structure. The macroscopic relative permittivity also appears in the equation. This is certainly not valid in the vicinity of an ion because the intense electrical field due to an ion will cause dielectric saturation of the solvent immediately around the ion. In addition, alteration of the solvent stmcture by the ion is an important feature of electrolyte solutions (see Section 13.16). However, solvation is ignored. As in the Debye-Hiickel treatment the physical meaning of the distance of closest approach, i.e. a is also open to debate. 

It is quite obvious that further modification to this conductance theory to take account of the shortcomings of the Debye-Hiickel model as outiined would be even less fintitful than similar attempts on the Debye-Hiickel theory itself. 

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