Fuoss-Hsia equation

Ion-pair association constants K A determined with the set of conductivity equations (7)—(15) agree with those obtained from Eq. (18) and (19) [100]. Salomon and Uchiyama have shown that it is also possible to extend the directly Fuoss-Hsia equation to include triple-ion formation [104],... 

The results provided by Eq. (1.153) can be improved by using the Fuoss-Hsia equation modified by Femandez-Prini (for 1 1 electrolytes [58-60]) ... 

In Eq. (61) every coefficient, S, E, Ji, and J2, contains the contributions of the electrophoretic and relaxation effects, A and A . The coefficients of the series-developed Fuoss-Hsia equation, including the so-called Chen effect (see Section III.D), are given in Table I. Onsager s limiting law in terms of Eq. (61) would be given by the series development... 

Table 3. Coefficients S, E J, and J, for IcCM evaluations based on the non developed Fuoss-Hsia conductivity equation [96],...

Table 5.2.2 illustrates the performance of the Pitts and the Fuoss and Hsia equations for some dissociated electrolytes in organic solvents at 25 C. The values of the fitting parameters for salts in DMF and in... 

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. 

The strategies for including these higher order contributions in the conductance equation have been analyzed in detail in the literature (Fem dez-Prini, 1973). At the end of the 1970s there were several alternative equations to the original treatment by Fuoss and Onsager (1957) to account for the effect of concentration on electrolyte conductances the Pitts (1953) equation (P), the Fuoss-Hsia (Fuoss and Hsia, 1967) equation (FH) later modified by Femandez-Prini (1969) (FHFP) and valid only for dilute, binary, symmetrical electrolytes, and the Lee and Wheaton (1978) equation (LW) valid for unsymmetrical electrolytes. 

Conductometry paved the way for the development of the ion-pair concept [3]. The oldest experimental evidence of ion-pairing was obtained from colligative properties and electrical conductivity measurements. It is generally accepted that electroneutral ion-pairs do not contribute to solution conductivity. Conductometry is now a reliable and well established technique even in low millimolar concentration ranges, but the full description of conductance in the presence of ion-pairing is anon-trivial task. To date the most accepted equation was developed by Fuoss and Hsia [92] and expanded by Fernandez-Prini and Justice [93] ... 

The original F-O equation has been further modified by Fuoss and Hsia, who recalculated the relaxation field, retaining terms which had previously been neglected. 

The expressions for the A terms are given in Table 5.2.1 according to the Pitts (P) and Fuoss and Hsia (F-H) treatments. Another theoretical treatment of conductances has been given by Kremp and by Kremp, Kraeft and Ebeling. Their result has been approximated by Kraeft to an equation of the form 5.2.31 with = 0 the expression for /i has been included in Table 5.2.1. 

It is noteworthy that the majority of the conductance data have been analysed with the equations of Fuoss and Onsager and of Fuoss and Accascina. However, since it has been recently shown that both equations are incomplete and in some cases fail to fit experimental data, we quote here only the improved Fuoss and Hsia result. 

J2 = 0 is in some cases capable of representing the experimental data for ku < 0.2, but obviously the value of the a parameter must be different. Comparing the Pitts and the Fuoss and Hsia expanded conductance equations, it is clear that for a given electrol)rte Pitt s equation predicts a larger molar conductance, i.e., smaller interionic effects. 

Comparison of Pitts (P) and Fuoss and Hsia (F-H) Expanded Conductance Equations... 

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