Interionic attraction theory

The energy dissipation of a system containing free charges subjected to electric fields Is well known but this Indicates a non-equilibrium situation and as a result a thermodyanmlc description of the FDE Is Impossible. Within the framework of interionic attraction theory Onsager was able to derive the effect of an electric field on the Ionic dissociation from the transport properties of the Ions In the combined coulomb and external fields (2). It is not improper to mention here the notorious mathematical difficulty of Onsager s paper on the second Wien effect. 

According to the interionic attraction theory of Debye and Hiickel... 

The term a0 is frequently called the ion-size parameter or apparent ionic diameter, B is an empirically fitted coefficient. In reality, however, B has important theoretical significance in interionic attraction theory, and it is a higher-order function of the ion-size parameter. 

This dilemma led us to investigate the feasibility of a nonlinear extrapolation for the evaluation of E°. For the sake of brevity, we will not reproduce here the detailed mathematical derivations of Gronwall, LaMer, and Sandved s extended terms of the Debye-Hlickel theory. One can find these derivations in their original paper (4) or in Hamed and Owens classic monograph. For a description of the basic assumptions and the physical model of the interionic attraction theory one should consult Hamed and Owens monograph as well as the work of Gurney (8,9). 

S(f) = limiting theoretical slope of rational activity coefficient in interionic attraction theory a function of y, D, and T as expressed by Equation 5 T = temperature in Kelvin X, Y = function of DH extended theory equation z = valence of an ion... 

P. Debye and E. Htickel, The Interionic Attraction Theory of Deviations from Ideal Behavior in Solution, Z. Phys. 24 120 (1923). 

The object of this book is to provide an introduction to electrochemistry in its present state of development. An attempt has been made to explain the fundamentals of the subject as it stands today, devoting little or no space to the consideration of theories and arguments that have been discarded or greatly modified. In this way it is hoped that the reader will acquire the modern point of view in electrochemistry without being burdened by much that is obsolete. In the opinion of the writer, there have been four developments in the past two decades that have had an important influence on electrochemistry. They are the activity concept, the interionic attraction theory, the proton-transfer theory of acids and bases, and the consideration of electrode reactions as rate processes. These ideas have been incorporated into the structure of the book, with consequent simplification and clarification in the treatment of many aspects of electrochemistry. 

Debye, P. and Huckel, E., The interionic attraction theory of deviations from ideal behavior in solution, Z. Phys., 24, 185, 1923. 

Another policy in writing the book has been the attempt to base the deduction of all equations on first principles. What actually constitutes such principles is, to an extent, a matter of individual preference. Any attempt at definition would immediately lead one into the field of the professional philosopher. Such an intrusion the author is, above everything, anxious to avoid. Fie feels, however, that the attempt to build from the ground up has been accomplished in most of the subjects considered. Exceptions are, however, the extension of the Debye-Huckel theory, and the application of the interionic attraction theory to electrolytic conductance. In the latter case the fundamentals lie in the field of statistical mechanics, which cannot be adequately treated short of a book the size of this one, and which, in any case, would not be written by the author. 

Transference numbers will also be found useful in obtaining precise values of the activities of ion constituents. It was another of Arrhenius tacit assumptions that ion concentrations may be used without error in the law of mass action. To investigate the limits of validity of that assumption, and to lay a foundation for the modern interionic attraction theory of solutions, it is necessary to consider the thermodynamics of solutions, and of the galvanic cell, subjects which are discussed in Chapters 5 and 6. 

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. 

The Interionic Attraction Theory of Conductance of Aqueous Solutions of Electrolytes... 

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. 

This equation shows that even for solutions dilute enough for the Onsager equation to hold, the transference numbers should in general change with the concentration, if the interionic attraction theory is valid. 

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. 

Dielectric Constants of Some Solvents and Solutions. The dielectric constant of the solvent, as will be recalled from the discussion in Chapters 7 and 18, is important in the interpretation of the thermodynamic and conductance data on solutions of electrolytes, according to the interionic attraction theory. Up to the present time the data which are useful for tests of that theory have mostly been obtained on aqueous and alcoholic solutions, and on solutions in mixtures of dioxane and water. It is to be hoped that in the near future studies will be made on solutions in other solvents the dielectric constants and other relevant properties of which are now, in many cases at least, accurately... 

The conductance begins to decrease more rapidly than would correspond to the coefficient computed on the basis of the interionic attraction theory. 

If it is not of this type the degree of self-consistency of the interionic attraction theory is relatively Since, moreover, virtually... 

The form of the electrophoretic function A depends upon the particular version of the interionic attraction theory chosen. According to the limiting D-H-0 theory... 

Subsequent theories of non-ideality have been mainly concerned with explaining the concentration and temperature dependences of Y and 0 (3,16). For a comparison with various other theories for the non-ideal part of free energy of solutions, see (14). The interionic attraction theory (3,5,16-18) formulated on the assumption of complete dissociation of strong electrolytes, predicted the InV vs /m linear dependence and explained the Jc dependence of A found empirically by Kohlrausch (3,14) for dilute solutions. Since the square-root laws were found to hold for dilute solutions of many electrolytes in different solvents, the interionic attraction theory gained a wide acceptance. However, as the square root laws were found to be unsatisfactory for concentrations higher than about 0.01m, the equations were extended or modified by the successive additions of more terms, parameters and theories to fit the data for higher concentrations. See e.g., (3,16) for more details. 

This equation is often referred to as Ostwald s dilution law. It depends on the assumptions (a) that ionic conductivities have constant values, and are not dependent on the concentration and (b) that the ions in dilute solution behave as ideal solutes. Both of these assumptions proved to be mistaken, and were finally corrected in the interionic attraction theory of Debye and Huckel and the conductance equation of Onsager (see conductance of aqueous solutions, conductance equations). 

The interionic attraction theory provides a complete explanation for the concentration dependence of conductances in very dilute solutions. Debye and Hiickel s original treatment was improved by Onsager in 1926 and his equation has been convincingly tested over a wide range of conditions. 

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