Fuoss-Kraus equation

Once again, in this paper, the electrochemical aspects of the ions and their equilibria are prominent. The Fuoss-Kraus equation is applied to the pairing of the carbenium ions with the anions. It is shown that since an increase in the solvent polarity reduces the propagation rate-constant, the increase in rate in changing from a less polar to a more polar solvent must be due to the increase in polarity augmenting the ratio of the concentrations of unpaired to paired cations, (here called Up and in later papers yip) on the assumption that as in anionic polymerisations, the unpaired ions propagate faster than the paired ions. 

If T is very low the contribution of tiie charged triple ions to the conductivity becomes important. In tiiat case the Fuoss-Kraus equation becomes ... 

The precision of the experimental data is a key issue in choosing a conductivity equation to fit the concentration dependence of the molar conductivity and, in the case of associated electrolytes, the association constant. Old meas-mements of conductivity, particularly those by Franck and co-workers in Germany and by Marshall and co-workers in ORNL (USA), having imcertainties aroimd 1% were fitted using the Shedlovsky or the Fuoss-Kraus equations, which allows the simultaneous determination of A° and K,. 

It is recognized that FHFP equation accounts for the concentration dependence of electrolyte solutions up to moderate concentrations and yields more reliable association constants than the Shedlovsky or Fuoss-Kraus equations. However, it was observed that the FHFP Equation (4.18), or the more simple Shedlovsky Equation (4.16), give similar fitting results, for some supercritical electrolyte solutions at low density (p < 0.3 g cm" ). The contribution of the electrophoretic effect to the concentration dependence of the molar conductivity is expected to be lower in supercritical water than in ambient water because of the much smaller viscosity and dielectric constant. Moreover, the higher-order terms in Equation (4.18) nearly cancel each other at moderate concentration in supercritical water (Ibuki et al., 2000). This could be the reason why differences among several conductivity equations vanish at supercritical conditions. 

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 ... 

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. 

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-... 

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. 

Accascina F, Kay RL, Kraus CA (1959) The Fuoss-Onsager conductance equation at high concentration. Proc Natl Acad Sci 45 804—807... 

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

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