Fuoss method

Reynolds and Kraus (17) obtained conductance for 14 salts in acetone at 25°C, and used the Fuoss method to calculate their equivalent conductances at infinite dilution. Among the salts were tetra-n-butylammonium fluorotri-phenylborate, tetra-n-butylammonium picrate, lithium picrate, and tetra-n-butylammonium bromide. They then derived ionic equivalent conductances at infinite dilution by the method of Fowler (18) using tetra-n-butylammonium fluorotriphenylborate as the reference electrolyte and obtained a value of 188.7 12 1 cm2 eq-1 for Aq for lithium bromide. 

In 1953 Olson and Konecny (19) studied the conductance of lithium bromide in acetone-water mixtures at 25°C and 35°C. They calculated KD and Ao in the acetone-rich solvents by the Fuoss method and Ao in the water-rich solvents by extrapolation of the phoreogram. They found that as the water content increases Kd increases, Ao decreases but then undergoes an increase, and a increases from slightly less than the sum of the crystal ionic radii to the sum of the radii of the fully hydrated ions. Extrapolation of their data for A0 to zero water content is not reliable because of the large concave upward negative slope however, it would appear to lead to a value of about 220 U l cm2 eq-1. Similar extrapolations of values for Kd and a yield 2.0 X 10 4 and 2.2 A, respectively. 

Two years later Nash and Monk (20) also measured conductances at 25°C using aqueous acetone (12.5 wt % water) as the solvent. For KD they obtained values of 1 X 10 3 and 6 X 10 3 for lithium bromide and hydrogen bromide, respectively, by the Davies (21) method and 101.1 Q 1 cm2 eq-1 and 117.1Q-1 cm2 eq-1 for A0 for lithium bromide and hydrogen bromide, respectively, by the Fuoss method. 

Further, the thermogravimetric analysis of metal diols of HBP and respective metal-containing polymers was done to study the thermal stability of the polyesters. The TG data show that all the polyesters are very stable up to 250°C. The energies of activation of degradation of these polyesters have been calculated using the Fuoss method [106]. 

Assays. Nitrogen assays to determine 1-amidoethylene unit content were done by Kjeldahl method. Limiting viscosity numbers were determined from 4 or more viscosity measurements made on a Cannon-Fenske capillary viscometer at 30°C. Data was extrapolated to 0 g/dL polymer concentration using the Huggins equation(44) for nonionic polymers and the Fuoss equation(45) for polyelectrolytes. Equipment. Viscosities were measured using Cannon-Fenske capillary viscometers and a Brookfield LV Microvis, cone and plate viscometer with a CP-40, 0.8° cone. Capillary viscometers received 10 mL of a sample for testing while the cone and plate viscometer received 0.50 mL. 

Another defect problem to which the ion-pair theory of electrolyte solutions has been applied is that of interactions to acceptor and donor impurities in solid solution in germanium and silicon. Reiss73>74 pointed out certain difficulties in the Fuoss formulation. His kinetic approach to the problem gave results numerically very similar to that of the Fuoss theory. A novel aspect of this method was that the negative ions were treated as randomly distributed but immobile while the positive ions could move freely. 

Fuoss and Accascina 36) present graphical methods for treating conductance data according to either equation. Kay 8 43> describes a computer program for least squares analysis in which standard deviations for the parameters are calculated as well. A similar program is described in Ref. H>. 

A also depends on the depth of immersion of the electrodes up to a certain value and the electrodes should always be at such a depth that A is independent of it. In most modern instruments either the electrodes are constructed to have >4 = 1 cm or there is a facility for compensating for values of A other than 1 cm. For accurate work the cell constant is usually measured for each set of electrodes by a standard method (Lind, Zwolenik and Fuoss, 1959). 

Considering these different limiting forms of the recombination term an Important tentative conclusion emerges the concentration dependence of the reciprocal relaxation time is a direct measure of the main ionic recombination process and yields therefore information on the ionic species present in solution. A linear dependence on total ion-pair concentration would therefore indicate unilateral triple ion formation or, if both kinds of triple ions are present as indicated by conductance, a sufficient difference in their stability. At this point it should be noted that the usual method of Fuoss and Draus... 

A computer program for the solution of the FOS equation, which is a modification of the method of Fuoss, Onsager, and Skinner (5), was written in Fortran IV and executed on an IBM System 360/50 (Operating System—H Level) computer. The program uses the method of Wentworth (35) for least-squares... 

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. 

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)] ... 

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 Fuoss estimate of is based on a more reasonable model than that of Bjerrum and therefore is preferred. However, there are also problems with the Fuoss treatment in so far as it considers the solvent to be a dielectric continuum. Dielectric saturation effects are expected to be important, especially near the ions involved in ion pair formation. The second problem relates to the choice of the effective size for the ions. In the calculation made here the value of a for MgS04 was chosen to be much bigger than the crystallographic radius of Mg. This presumably is because the cation is strongly hydrated in aqueous solution. One is then faced with the question whether the ion pair involves contact of the two ions or whether it is better considered to be a species in which the two ions are separated by at least one water molecule. These questions can only be properly resolved using other experimental methods. 

In summary, the models discussed in this chapter focus on the physical aspects of electrolyte solutions but they ignore the chemical aspects. This is especially apparent in the treatment of ion solvation where an empirical correction to the MSA model was applied to treat the differences in behavior seen for cations and anions in water. The same problem arises in using classical electrostatics to describe ion pairing. In spite of the fact that the Bjerrum and Fuoss models give a good qualitative description of an ion association, this phenomenon can only be understood in detail by using quantum-mechanical methods. Needless to say, such calculations in condensed media are much more difficult to carry out. 

Table VII. Limiting Conductances and Dissociation Constants of the Halogen Acids in Ethyl Alcohol at 25° as Calculated by the Method of Fuoss and Kraus...

Assuming the equality of angles ft and <5, Fuoss and Kirkwood 82 using a method proposed by Eyring14 found the following value for the mean square dipole ... 

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. 

Further difficulties are encountered in the determination of Ac s. The 1/A s are large for scarcely dissociated pairs hence, the Fuoss lines are steep. Consequently, the intercepts of such lines, plotted in the appropriate scale, are too small to be measured. Therefore, some alternative methods are needed for their evaluation (see,... 

TWO DISTINCT FORMS OF ION pairs IN solution were suggested by Sadek and Fuoss (I) and Winstein et al. (2) in 1954. These forms are now customarily referred to as either (a) loose or solvent-separated ion pairs or (b) tight or contact ion pairs. During the past few decades, these species have been studied in great detail with optical and magnetic resonance techniques and conductivity methods. Numerous experiments carried out by Szwarc (3) showed that ion pairs are well-defined chemical species with their own physical properties. For instance, the rate of anionic polymerization reactions can change by a factor of 103 from free (unassociated) solvated ionic species to completely associated ones (3). 

Let us review other iq>proadies to the solutkm ai the kinetic problem ". The successful attempt was made by Fuoss. Akhou] there is no final kfa tic equation in his work, the suggested method of solution is the same as McQuarrie s and thereby leads one to expect the same result. 

Tuan and Fuoss have evaluated coefficients in acetonitrile for several tetraalkylammonium salts. They observe that the Bjj coefficients are additive as in other solvents, and that for the larger ions the experimental value of Br, used in conjunction with the Einstein model, gives radii consistent with other methods of measurement. As in most other non-aqueous solvents all the B j coefficients are positive. 

The conductance method is satisfactory only if the solvent can be rigorously purified. Through failure to appreciate this, the first values of pKa of picric acid in acetonitrile proved to be much too small, 5.6 and 8.9 as compared with 11.0 from electromotive force measurements on buffered solutions. D Aprano and Fuoss found that acetonitrile having a satisfactory specific conductance of about 10 cm still contained a trace of ammonia. This was converted to ammonium pic-rate when acid was added to the solvent giving a spurious contribution to the conductance of picric acid solutions. This discovery moved them to make the flat assertion that dissociation constants of weak acids cannot be determined in aprotic solvents conductimetrically . This may be an overly pessimistic view, conductance values of pKa for acids in di-methylsulphoxide and dimethylformamide agree well with those from spectrophotometric and electromotive force measurements. Approximate values of pKa and pKf can be obtained from conductometric titrations of a weak acid with a weak base. ... 

Later, Falkenhagen and co-workers and Onsager and Fuoss established a method of calculating parameter A starting from the Debye-Huckel theory. However, the above equation is only valid for concentrations up to about 0.01 mol/L. According to the above equation the relative viscosity should always increase with concentration. However, experiments show non-monotonic behavior for several electrolytes such as most of the potassium halides, and several mbidium and cesium halides [12]. 

Recently W. T. Busse and R. M. Fuoss have contributed very important applications of the dipole method by the investigation of polyvinylchloride and similar substances at different temperatures, frequencies and with different amounts of plasticizers. Cincinnati meeting of the ACS, April 1940. 

Extended laws are available for the variation with concentration of the transport coefficients of strong and associated electrolyte solutions at moderate to high concentrations. Like the CM calculations, this work is based on the Fuoss-Onsager transport theory. The use of MSA pair distribution functions leads to analytical expressions. Ion association can be introduced with the help of the chemical method. A simplified version of the equations, by taking average ionic diameters, reduces the complexity of the original formulas without really reducing the accuracy of the description and is therefore recommendable for practical use for up to 1-M solutions. 

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