The Theory of Electrolytic Conductance

The Degree of Dissociation.—An expression for the degree of dissociation which will be found useful at a later stage is based on a con- 

For a weak electrolyte the sum u% -f ul, for infinite dilution, does not differ greatly from in the actual solution, and so the degree of 

If equation (1) is divided into its constituent parts, for positive and negative ions, it is seen that 

Interionic Attraction The Ionic Atmosphere.—The possibility that the attractive forces between ions might have some influence on electrolytic conductance, especially with strong electrolytes, was considered by Noyes (1904), Sutherland (1906), Bjerrum (1909), and Milner (1912) 

The net charge of the atmosphere is, of course, equal in magnitude but opposite in sign to that of the central ion the charge density will obviously be greater in the immediate vicinity of the latter and will fall off with increasing distance. It is possible, nevertheless, to define an effective thickness of the ionic atmosphere, as will be explained shortly. 

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There are many sources of this paradoxical situation, in which a theoretical understanding lags far behind experiment in such a practically relevant area as electro-diffusion. There was a period of intense qualitative development in this area in the 1920s until the early 1950s when the modern classics of chemical physics developed the theory of electrolytic conductance and related phenomena [11]—[13]. These works were mainly concerned with the mean field approach to microscopic mechanisms determining such properties of electrolyte solutions as ion diffusivity, dielectric susceptibility, etc. in particular, they were concerned with the effects of an externally applied stationary and alternating electric field upon the above properties... 

ONSAGER, LARS (1903-1976). A Norwegian chemist who won the Nobel pnze for chemistry in 1968. He studied and wrote on the theory of electrolytic conduction and theory of dielectrics. He also worked with stiperfluids and crystal statistics and reciprocal relations in irreversible processes. After receiving his doctorate in Norway, he came to the U.S. and became a citizen. See also Dielectric Theory. 

It may be pointed out in conclusion that the conductance phenomena with very high frequency currents and at high potential gradients provide striking evidence for the theory of electrolytic conductance, based on the existence of an ionic atmosphere surrounding every ion, proposed by Debye and Huckel and described in this chapter. Not only does the theory account qualitatively for conductance results of all types, but it is also able to predict them quantitatively provided the solutions are not too concentrated. 

The Debye-Hiickel Theory.—The first successful attempt to account for the departure of electrolytes from ideal behavior was made by Milner (1912), but his treatment was very complicated the ideas were essentially the same as those which were developed in a more elegant manner by Debye and Hiickel. The fundamental ideas have already been given on page 81 in connection with the theory of electrolytic conductance, and the application of the Debye-Hiickel theory to the problem of activity coefficients will be considered here. ... 

Non-ideality has been shown to be due to ionic interactions between the ions and consideration of these led to the concept of the ionic atmosphere (see Sections 10.3 and 10.5). These interactions must be taken into account in any theory of conductance. Most of the theories of electrolyte conduction use the Debye-Hiickel model, but this model has to be modified to take into account extra features resulting from the movement of the ions in the solvent under the applied field. This has proved to be a very difficult task and most of the modern work has attempted many refinements all of which are mathematically very complex. Most of this work has focused on two effects which the existence of the ionic atmosphere imposes on the movement and velocity of the ions in an electrolyte solution. These are the relaxation and electrophoretic effects. 

The theory of electrolytic conductance was successfully extended during the fifties so that it could be used to predict the conductance of solutions having a concentration such that kcI < 0.2-0.5 (see Notation). In the last five years a revision of the theoretical treatments has enabled the establishment of a firmer basis for the methods employed to evaluate conductance data. 

In the theory of electrolyte conductance, reference is made to the density of charges eoNxCiZi (C m ) rather than to the density of particles. Then Eqs. (2) and (3) are transformed to... 

The theory of electrolyte conductivity is based on the two-particle continuity equation... 

Fuoss RM (1978) Review of the theory of electrolytic conductance. J Soln Chem 7 771-782. doi 10.1007/ BF00643581... 

Such a chemical approach which links ionic conductivity with thermodynamic characteristics of the dissociating species was initially proposed by Ravaine and Souquet (1977). Since it simply extends to glasses the theory of electrolytic dissociation proposed a century ago by Arrhenius for liquid ionic solutions, this approach is currently called the weak electrolyte theory. The weak electrolyte approach allows, for a glass in which the ionic conductivity is mainly dominated by an MY salt, a simple relationship between the cationic conductivity a+, the electrical mobility u+ of the charge carrier, the dissociation constant and the thermodynamic activity of the salt with a partial molar free energy AG y with respect to an arbitrary reference state ... 

Feb. 19,1859, Wijk, Sweden - Oct. 2,1927, Stockholm, Sweden). Arrhenius developed the theory of dissociation of electrolytes in solutions that was first formulated in his Ph.D. thesis in 1884 Recherches sur la conductibilit galvanique des dectrolytes (Investigations on the galvanic conductivity of electrolytes). The novelty of this theory was based on the assumption that some molecules can be split into ions in aqueous solutions. The - conductivity of the electrolyte solutions was explained by their ionic composition. In an extension of his ionic theory of electrolytes, Arrhenius proposed definitions for acids and bases as compounds that generate hydrogen ions and hydroxyl ions upon dissociation, respectively (- acid-base theories). For the theory of electrolytes Arrhenius was awarded the Nobel Prize for Chemistry in 1903 [i, ii]. He has popularized the theory of electrolyte dissociation with his textbook on electrochemistry [iv]. Arrhenius worked in the laboratories of -> Boltzmann, L.E., -> Kohlrausch, F.W.G.,- Ostwald, F.W. [v]. See also -> Arrhenius equation. 

The phenomenon of electrolysis also receives a simple explanation on the basis of the theory of electrolytic dissociation. The conductance of electrolyte solutions is due to the fact that ions (charged particles) are present in the solution, which, when switching on the current, will start to migrate towards the electrode with opposite charge, owing to electrostatic forces. In the case of hydrochloric acid we have hydrogen and chloride ions in the solution ... 

The results of moving boundary determinations of transference numbers in which the modern developments of the method have been employed are given in Table IV, and are mainly due to the investigations of Longsworth. The figures in this table will be referred to a number of times in following chapters. The transference numbers are of use in interpreting the results of determinations of the potentials of concentration cells as activity coefficients which, in turn, may be used to test the validity of the thermodynamic aspects of the interionic attraction theory of electrolytes. In addition the transference numbers, alone, and with conductance measurements, are of utility in connection with tests of the interionic attraction theory of electrolytic conductance. 

It must be emphasized that the transference number measurements are at concentrations at which the Onsager equation, on which expressions (28) and (28a) are based, is only approximately valid. In general the transference data lend strong support to the interionic attraction theory of electrolytic conductance. 

The Debye-Htickel model considered the solvent to be a structureless medium whose only property is to reduce the interactions between ions in a vacuum by a factor given by the macroscopic relative permittivity, e. No cognisance was taken of the possibility of ion-solvent interactions, and the size of the ion was assumed to be that of the bare ion. Gurney in the 1930s introduced the concept of the co-sphere and this has proved to be a useful concept in the theory of electrolyte solutions. Many recent theories of conductance are based on the Gurney co-sphere concept (see Section 12.17). 

The whole of Section 12.17 discusses the more recent thoughts on conductance theory. This is given in a qualitative manner, and should be useful in illustrating modern concepts in the microscopic description of electrolyte solutions. These sections, taken in conjunction with Sections 10.14 onwards in Chapter 10 on the theory of electrolyte solutions, and with Chapter 13 on solvation, should give the student a qualitative appreciation of more modern approaches to non-ideality in electrolyte solutions. 

The treatment of particles of different shapes is more complicated, and various theories have been presented. In their theory of electrolytic conductivity (see Section 6.5) Debye and Hiickel concluded in 1924 that for a spherical particle equation (11.130) should be replaced by... 

These solid electrolytes do conform to the conditions laid out in Wagner s theory and many important applications cein be foreseen which would require devices based on such solid electrolytes. Some of these applications aire of the open circuit variety such as solid electrolyte emf sensors for high temperature environments where contamination of the electrolyte may be a problem. But many other applications will be of the closed circuit variety and to a large extent this aspect has not been negotiated very rigorously in the traditional theory. Significant extensions of the traditional theory will have to be made before the performance characteristics of fuel cells and high temperature steam hydrolyzers can be successfully analyzed via the theory of mixed conduction in solids. 

Another type of approach to transport properties, also frequently used in the theory of electrolyte solutions, is based on statistical mechanics and starts with Liouville s theorem. Electrolyte conductance is chosen to exemplify the features of this theory. 

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