Fuoss and Kraus

Conductivity curves (A versus c ) of salts in solvents of low-permittivity commonly show a weakly temperature-dependent minimum around 0.02 molL-1 followed by a strongly temperature-dependent maximum at about 1 mol L 1. According to Fuoss and Kraus [101,102] the increase of conductivity behind the minimum is due to the formation of new charge carriers from the ion pairs. They assume that coulombic forces suffice to form bilateral cationic [C+A-C+] and anionic [A C+A ] triple ions in solvents of low-permittivity ( <15) if the ions have approximately equal radii. 

Under the aforementioned circumstances, the two-step reaction 4.53 and the associated eqns. 4.54-4.62 are equally valid on the understanding that HS represents Hcres, etc. further, it must be realized that during titration various amounts of HX and B are simultaneously present. Therefore, from previous measurement of the conductivities (k) of dilution series of the separate acids, bases and salts in m-cresol, the overall constants KHX, KB and KBH+X were calculated by the Fuoss and Kraus method66,67 (with the use of e = 12.5 and viscosity = 0.208 P for m-cresol). For C6H6S03H and HC1 it was necessary to calculate the equivalent conductivity at zero concentration from the equation... 

Fuoss and Kraus [13] and Shedlovsky [14] improved Eq. (7.6) by taking the effect of ion-ion interactions on molar conductivities into account. Here, Fuoss and Kraus used the Debye-Huckel-Onsager limiting law [Eq. (7.1)] and Shedlovsky used the following semi-empirical equation ... 

Table XV.5 shows the rather dramatic change in Xeq for the dissociation of tetrisoamyl ammonium nitrate, (i-Am4N)+N03 ", with dielectric constant in mixtures of H2O and dioxane. Although it is possible to get much better agreement with the conductance data by using slightly different values of the case shown is used to emphasize the essential correctness of the method. Note also that no account has been taken of the preferential solvation of ions by one of the two solvents. The Fuoss and Kraus treatment also gives a simple model for the calculation of ion triplet and quadruplet concentrations.

A test of equation (79), based on the theory of ion association, is provided by the measurements of Fuoss and Kraus of the conductance of tetraisoamylammonium nitrate in a series of dioxane-water mixtures of dielectric constant ranging from 2.2 to 78.6 (cf. Fig. 21) at 25 . From the results in dilute solution the dissociation constants were calculated by the method described on page 158. 

Fiq. 54. Association constant and dielectric constant (Fuoss and Kraus)... 

The work of Fuoss and Kraus and their collaborators and of others has shown that equation (106) is obeyed in a satisfactory manner by a number of electrolytes, both salts and acids, in solvents of low dielectric constant. The results of plotting the values of F(x)/A against Kcf F x) for solutions of tetramethyl- and tetrabutyl-ammonium picrates in ethylene chloride are shown in Fig. 57 the intercepts are 0.013549 and 0.17421, and the slopes of the straight lines are 5.638 and 1.3337, re-... 

Apply the method of Fuoss and Kraus, described on page 167, to evaluate Ao and K for hydrochloric acid in a dioxane-water mixture, containing 70 per cent of the former, at 25 , utilizing the conductance data obtained by Owen and Waters [ J, Am, Chem, Soc. 60, 2371 (1938)] ... 

By means of the value of K obtained in the preceding problem, calculate the mean ionic diameter, a, of hydrochloric acid in the given solvent. For this purpose, use equation (79) and the tabulation of Q h) given by Fuoss and Kraus, J, Am, Chem, Soc, 55, 1019 (1933). 

Accurate methods for evaluating Ka based on this equation, involving the use of conductance measurements, have been already described in Chap. V these require a lengthy experimental procedure, but if carried out carefully the results are of high precision. For solvents of high dielectric constant the calculation based on the Onsager equation may be employed (p. 165), but for low dielectric constant media the method of Fuoss and Kraus (p. 167) should be used. 

By measuring the conductance of several picrates in di-wopropyl ketone at different concentrations, it was shown by the method of Fuoss and Kraus 6 that up to concentration of 01 M there is no detectable triple ion formation. Thus concentrations high enough to satisfy condition (ii) are attainable without the formation of multiple ions. The results of semi-quantitative preliminary experiments indicated that tetraethylammonium and picrate ions had nearly the same mobility in di-wopropyl ketone. This was confirmed by measuring the transport number of the picrate ion by the moving-boimdary method. The conditions for the successful use of the moving-boundary method have been fully examined by Longsworth and Maclnnes.7 A simplified apparatus was used and is shown in fig. 3 camphor-sulphonate was found to be a suitable indicator ion. 

The concept of coordination in the second sphere was introduced by Werner. All authors agree that such outer-sphere association exists in solution, hut they disagree about the kind and the extent of this association. Some advocate a second-sphere coordination which is closely analogous to the inner-sphere coordination. The data which support this hypothesis are not very convincing and can be criticized in various ways. The present author finds that the electrostatic theories of N. Bjerrum, Fuoss, and Kraus, according to which the formation of the ion-associates is a result of coulombic attraction, both qualitatively and quantitatively, give the most trustworthy picture of the outer-sphere association. However, this does not exclude the fact that some preferred mutual orientation exists in the ion pairs. 

The interpretation of the branch, where the WP increases, more sophisticated. A minimum of WP implies a redissociation of the pairs and/or the formation of charged ion clusters. Fuoss and Kraus [41] assumed the formation of charged ion triplets. Recent theory attributes the increase of the conductivity to redissociation, resulting from the interactions of the free ions with the ion pairs and the increase of the dielectric permittivity due to the formation of ion pairs that causes a decrease of the association constant [38],... 

This is in good agreement with the value K = 1.69 x 10 mole H obtained from conductance measurements by Fuoss and Kraus (J. Amer. Chem. Soc. 1933, 55, 486). 

Molar conductivity variations of ionic salts or aggregates in a low-polarity solvent as a function of salt concentration show a unique pattern, for which a number of explanations have been offered. Fuoss and Kraus [21 were the first to show that the graphical correlation of molar conductivity versus... 

Gileadi et al. [22], in their study of the conductivity characteristics of certain salts, namely AlBr3-LiBr and AlBr3-KBr, in toluene, have observed a behavior similar to that found by Fuoss and Kraus. The model proposed by them is based on a hopping mechanism of ionic species from one cluster to another. 

The conductance-concentration curves of electrolytes in solvents of dielectric constant below about 15 contain minima which appear at lower and lower concentrations as the dielectric constant falls. In a classic paper,Fuoss and Kraus proposed as an explanation the formation of... 

Fuoss and Kraus (1933) derived Equation (4.17) taking into account the effect of ion interactions... 

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