Fuoss experimental results

A comparison of experimental results with those calculated from the Fuoss (2) theory is presented in Table I. The theory 1s only valid approximately so that the order of magnitude agreement is fairly good, except in the cases of MgC03° and CaC03 . Stoichiometric association constants K are then obtained from the activity coefficients, expressions for K, and from equations for the conservation of mass. The latter express the total concentration of a given ion as the sum of the concentrations of the free ion and of the ion-pairs. Values of K and of the activity coefficients of free ions in ionic media depend only upon the effective ionic strength as is shown later. 

In order to obtain better agreement with experimental results, the concept of a distribution of correlation times was introduced in nuclear magnetic relaxation. Different distribution functions, G(i c), such as Gaussian, and functions proposed by Yager, Kirkwood and Fuoss, Cole and Cole, and Davidson and Cole (asymmetric distribution) are introduced into the Eq. (13), giving a general expression for... 

The Conductance of Salts in Solvents of Low Dielectric Constant. In order to approach a discussion of phenomena that are encountered in solvents of low dielectric constants, Le., less than 25, it will be of service to consider as examples the experimental results of Kraus and Fuoss 20 who have determined the conductance of a single salt (tetraiso-amylammonium nitrate) in mixtures of widely varying composition of dioxane and water. The dielectric constants of these mixtures covered the range of values from the dielectric constant of 2.2 for pure dioxane to 78.6 for water. The experimental results are plotted in Fig. 5, in... 

The extension of the theory to higher concentrations has been undertaken particularly by Falkenhagen and his co-workers, by Pitts, and by Onsager and Fuoss. The theory is very difficult, and the final equations inevitably involve assumptions and mathematical approximations that have been the subject of discussion they are too complicated to reproduce here, and require computer time for their solution. All three can satisfy the best experimental results for uniunivalent salts up to 0.1 g-equiv. dm" for unsymmetrical valence types the mathematical problems are intractable, and above 0.1 g-equiv. dm for any salt the model on which they are based becomes unreliable. 

In the preceeding section mention was made of ion association (ion-pairing) which, for the purposes of this paper, will refer to coulombic entities with or without cosphere overlap. Experimental support for ion-pairing has come from sound attenuation (2). Raman spectroscopy (2) and potentiometry (2, 2). Credibility has resulted from the model of Fuoss (2) applied by Kester and Pytkowicz (2). 

In fact, given the distance dependencies of A0 and V, electron transfer is expected to be dominated by reactants in close contact. In that limit the experimentally observed rate constant is related to ktt and the association constant between reactants, KA, as in equation (32). KA can be estimated for spherical reactants, using the Eigen-Fuoss result in equation (33). The electrostatic term, wR, was defined in equations (19) and (20). 

This process is partially overlapped with the next process, the j3 relaxation. To analyze the loss permittivity in the subglass zone in a more detailed way, the fitting of the loss factor permittivity by means of usual equations is a good way to get confidence about this process [69], Following procedures described above Fig. 2.42 represent the lost factor data and deconvolution in two Fuoss Kirwood [69] as function of temperature at 10.3 Hz for P4THPMA. In Fig. 2.43 show the y and relaxations that result from the application of the multiple nonlinear regression analysis to the loss factor against temperature. The sum of the two calculated relaxations is very close to that in the experimental curve. 

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. 

However, this must be seen in the context of the considerable impetus and stimulus which the Fuoss-Onsager treatment of conductance has given to the experimentalist who has striven to find more and more precise methods with which to test the various theories outlined. This has resulted in very considerable improvements being made to conductance apparatus. It has also placed a very detailed emphasis on obtaining precision and accuracy of the measurements themselves. This has been of considerable import when making measurements at very low concentrations where the experimental difficulties are greatest, but where it is important to test the theory in regions where it is expected to be valid. Such expectations have been vindicated by precision low concentration work where confidence can be placed in the accuracy of the conductance equation. This is reminiscent of the impetus to experimentalists after the Debye-Hiickel equation had been put forward. 

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. 

Data from these models for different types of electrolytes in dilute aqueous solutions have been presented in the literature [25, 26], From those data we conclude that for symmetrical uni-univalent, both theories (Onsager and Pikal) give similar results, and they are consistent with experimental ones. In fact, if Pikal s theory is valid, AM must be the major term all other terms are much smaller and they partially cancel each other. Concerning symmetrical but polyvalent electrolytes [25, 26], we can well see that PikaTs theory is a better approximation than the Onsager-Fuoss . The ion association, taken into account in this model [27], can justify this behavior. 

Later, some publications postulated the reduced viscosity to decrease again at very high dilution [144-147], thus questioning the validity of the Fuoss-Strauss extrapolation procedure. However, due to the enormous experimental difficulties (influence of dust particles, atmospheric carbon dioxide altering the ionic strength, adsorption problems) these results were mostly considered as unreliable. In recent years measurements with highly sensitive and sophisticated viscometers [148-158] provided overwhelming evidence for the presence of a maximum and proved the Fuoss-Strauss extrapolation to be one of the big errors in polyelectrolyte history. 

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