Onsager equation deviations from

The method of calculating of complex mixtures using the above equation would theoretically be correct only if the mixture behaves like an ideal solution. Since, most solvent mixtures may exhibit a high degree of intermolecular association af such system would lead to a deviation from the experimental data. The simpliLed Onsager-Kirkwood equation provides only a good approximate dielectric constant for mixed solvent systems. 

Up to concentration of 2 X 10-3 gram-equivalents per litre there is a satisfactory agreement between the results calculated from the Debye-Hiickel-Onsager equation and the actual values of conductance of uni-univalent electrolytes. The validity of this equation has been verified even for uni-bivalent electrolytes, while for bi-bivalent electrolytes there are greater deviations to be observed. 

The fact that the type of deviation from Onsager s equation under discussion is not observed, at least up to relatively high concentrations, with many simple electrolytes, e.g., the alkali halides in both aqueous... 

The experimental data show that the deviations from the Onsager equation which may be attributed to incomplete dissociation occur more readily the smaller the ions, the higher their valence and the lower the dielectric constant of the medium. This generalization, as far as ionic size is concerned, appears at first sight not to hold for the salts of the alkali metals, for the deviations from the Onsager equation become more marked as the atomic weight of the metal increases owing to the effect... 

The evidence just given, which is typical of that obtained from all recent measurements, shows that the Onsager equation is valid for very dilute aqueous solutions of strong electrolytes. This fact is important as it lends additional and strong support to the correctness and utility of the interionic attraction theory. As has already been emphasized Onsager s equation is a limiting equation and deviations from it, even for completely dissociated electrolytes, are to be expected as the concentration is increased. 

Within the range of concentrations for which the Fuoss-Onsager equation is expected to be valid, this equation accounts well for the effects of non-ideality in solutions of symmetrical electrolytes in which there is no ion association. It can thus be taken as a base-line for non-associated electrolytes and any deviations from this predicted behaviour can be taken as evidence of ion association (see Section 12.12). 

These conclusions were based on the severe curvature of the plots of chemical shift against reaction field calculated from both the simple Onsager and the more complex Diehl and Freeman equations. Fontaine et al. have found similar curvature in plots of for acetone versus the Onsager reaction field of cyclohexane-acetone mixtures. Some interesting results recently obtained show that if e is substituted for the dielectric function (e —l)/(e- - ) of equation (5), the curvature of these plots is effectively removed, especially for protons near the dipole location in the large molecules studies by Laszlo and Musher. No explanation for the dependence of on e has been offered. Deviations from linearity in plots of versus in some haloethylenes are explained by the occurrence of excess dispersion forces in the solvents producing the deviations. 

Various explanations have been given for deviations from the Debye-Hiickel-Onsager equations. A common type of behavior is for the negative slopes of the A versus /c plots to be greater than predicted by the equation that is, the experimental conductivities are lower than predicted by the theory. This has been explained in terms of ion pairing, a concept which was developed by the Danish physical chemist Niels Bjerrum (1879-1958) in 1926. Although most salts, such as sodium chloride, are present in the solid state and in solution as ions and not as covalent species, there is a tendency for them to come together from time to time to form ion pairs. 

The dominant forces that determine deviations from ideal behaviour of transport processes in electrolytes are the relaxation and electrophoretic forces [16]. The first of these forces was discussed by Debye [6, 17]. When the equilibrium ionic distribution is perturbed by some external force in an ionic solution, electrostatic forces appear, which will tend to restore the equilibrium distribution of the ions. There is also a hydrodynamic effect. It was first discussed by Onsager [2, 3]. Different ions in a solution will respond differently to external forces, and will thus tend to have different drift velocities The hydrodynamic (friction) forces, mediated by the solvent, will tend to equalize these velocities. The electrophoretic ( hydrodynamic) correction can be evaluated by means ofNavier-Stokes equation [18, 19]. Calculating the relaxation effect requires the evaluation of the electrostatic drag of the ions by their surroundings. The time lag of this effect is known as the Debye relaxation time. 

We have seen that deviations from the Onsager equation in its limiting form occur for uni-univalent electrolytes at higher concentrations where observed molar conductivities are somewhat higher than predicted so that the slope of the A versus graph is somewhat lower than the theoretical Onsager slope. 

Deviations from the Onsager equation, shown by electrolytes with valency product 4 and 6, indicating ion-pairing. The dotted lines are the Onsager slopes. 

The fundamental question in transport theory is Can one describe processes in nonequilibrium systems with the help of (local) thermodynamic functions of state (thermodynamic variables) This question can only be checked experimentally. On an atomic level, statistical mechanics is the appropriate theory. Since the entropy, 5, is the characteristic function for the formulation of equilibria (in a closed system), the deviation, SS, from the equilibrium value, S0, is the function which we need to use for the description of non-equilibria. Since we are interested in processes (i.e., changes in a system over time), the entropy production rate a = SS is the relevant function in irreversible thermodynamics. Irreversible processes involve linear reactions (rates 55) as well as nonlinear ones. We will be mainly concerned with processes that occur near equilibrium and so we can linearize the kinetic equations. The early development of this theory was mainly due to the Norwegian Lars Onsager. Let us regard the entropy S(a,/3,. ..) as a function of the (extensive) state variables a,/ ,. .. .which are either constant (fi,.. .) or can be controlled and measured (a). In terms of the entropy production rate, we have (9a/0f=a)... 

Table 7.11 shows the thermal diffusion ratios obtained from Onsager s reciprocal rules for toluene (1), chlorobenzene (2), and bromobenzene (3) at 1 atm and 35°C. The heats of transport for the ternary mixtures are shown in Tables 7.12 and 7.13. For the ternary mixture of toluene (l)-chlorobenzene (2)-bromobenzene (3), the heats of transport are tabulated at 298 and 308 K. The temperature- and composition-dependent heats of transport values are fitted by the following equations by Platt et al. (1982) with a deviation below 5% ... 

However, although the results of the conductance measurements follow an equation of the form A = A0 — KyJc the value of the constant K does not in every case correspond to that predicted by Onsager s equation. A comparison of the observed values of AT, (the slopes of the lilies in plots similar to Fig. 1) and the computed values from equation (1) are given in Table I, Although the data for a number of the salts agree with the predictions of the theory almost within the experimental error, pronounced deviations are observed particularly for cesium salts and some of the nitrates. However, as mentioned in Chapter 18, nitrates... 

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