The Fuoss-Onsager equation

Various treatments of these effects have been developed over a period of years. The conductance equations of Fuoss and Onsager l, based on a model of a sphere moving through a continuum, are widely used to interpret conductance data. Similar treatments n 3, as well as more rigorous statistical mechanical approaches 38>, will not be discussed here. For a comparison of these treatments see Ref. 11-38) and 39>. The Fuoss-Onsager equations are derived in Ref.36), and subsequently modified slightly by Fuoss, Onsager and Skinner in Ref. °). The forms in which these equations are commonly expressed are... 

Sometimes, the conductivity of the solution may decrease due to the formation of electroneutral ion pairs. Under these conditions, the Fuoss-Onsager equation can be used to calculate the molar conductivity (A) of associated electrolytes [57] ... 

When the Aobsvd approach the limiting slope from above this is due to the approximations made in the derivation of the conductance equation. Empirical corrections (see Section 12.8) have been made which postulate higher order terms to be necessary, viz. terms in c, clogc and < with the coefficients of these terms being determined experimentally. But an explanation of this behaviour had to wait until the Fuoss-Onsager equation of 1957 had been formulated (see Section 12.10). 

The formulation of these modifications to the external field are complex and lengthy and lie in the field of highly advanced mathematics, but eventually they are resolved into the Fuoss-Onsager equation for unassociated symmetrical electrolytes ... 

Also take note the base for the logarithmic term in Equation (12.52) is not specified. This is because the Fuoss-Onsager equation (Equation 12.52) can be quoted in terms of logio or loge. This will affect the expression for Ei, E2, J, J2, and their values (see Appendix 2, Table 12.3). 

The Fuoss-Onsager equation is also often used in the more approximate form ... 

For a given solvent at a fixed temperature and making the approximations for , and rj given above, the equation reduces to one in terms of the concentration. A and a and so is an equation in two unknowns. However, it is not possible to solve the equation as a simultaneous equation in the two unknowns using values of A at two concentrations. This is because of the complexity of the functional form of the Fuoss-Onsager equation. 

Implications of the Fuoss-Onsager equation for unassociated symmetrical electrolytes... 

Within the range of concentrations for which the Fuoss-Onsager equation is expected to be valid, this equation accounts well for the effects of non-ideality in solutions of symmetrical electrolytes in which there is no ion association. It can thus be taken as a base-line for non-associated electrolytes and any deviations from this predicted behaviour can be taken as evidence of ion association (see Section 12.12). 

In the period between 1957 and 1978 various modifications and extensions were made to the Fuoss-Onsager equations for unassociated and associated electrolytes, but there were no major changes in the model. All that these studies had done was to produce modified conductance equations. 

These formulae for E and lEi are given for the case of the Fuoss-Onsager equation written in terms of logarithms to base e. They should be multiplied by 2.303 if base 10 is used. 

Evans, Zawoyski and Kay analysed data for R4N salts in acetone (AC) " with the Fuoss-Onsager equation. They found Ka decreases with cation size, and for the anions, association decreases in the order Bu4NBr(i = 264) > I-(143) NOg > CIO4 (80) > Pic-(17). This agrees with data for methylethylketone. The fact that association of Bu4NC104 in AC, benzonitrile, and methylethyl-ketone corresponds to = 4.85 A for the three solvents, indicates formation of contact ion pairs. Tetraalkylammonium halides in dimethyl-formamide (DMF) have small association constants when the data are evaluated with Shedlovsky s eqn. 5.4.10. When the data for Me4NPic in is assessed with Fuoss and Hsia s eqn. 5.2.31, a is 6.0 A. 

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