Weak electrolyte theory

Thermodynamics of charge carriers weak electrolyte theory... 

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 ... 

Incomplete Dissociation into Free Ions. As is well known, there are many substances which behave as a strong electrolyte when dissolved in one solvent, but as a weak electrolyte when dissolved in another solvent. In any solvent the Debye-IIiickel-Onsager theory predicts how the ions of a solute should behave in an applied electric field, if the solute is completely dissociated into free ions. When we wish to survey the electrical conductivity of those solutes which (in certain solvents) behave as weak electrolytes, we have to ask, in each case, the question posed in Sec. 20 in this solution is it true that, at any moment, every ion responds to the applied electric field in the way predicted by the Debye-Hiickel theory, or does a certain fraction of the solute fail to respond to the field in this way In cases where it is true that, at any moment, a certain fraction of the solute fails to contribute to the conductivity, we have to ask the further question is this failure due to the presence of short-range forces of attraction, or can it be due merely to the presence of strong electrostatic forces ... 

According to modem views, the basic points of the theory of electrolytic dissociation are correct and were of exceptional importance for the development of solution theory. However, there are a number of defects. The quantitative relations of the theory are applicable only to dilute solutions of weak electrolytes (up to 10 to 10 M). Deviations are observed at higher concentrations the values of a calculated with Eqs. (7.5) and (7.6) do not coincide the dissociation constant calculated with Eq. (7.9) varies with concentration and so on. For strong electrolytes the quantitative relations of the theory are altogether inapplicable, even in extremely dilute solutions. 

Hence, the theory of electrolyte solutions subsequently developed in two directions (1) studies of weak electrolyte solutions in which a dissociation equilibrium exists and where because of the low degree of dissociation the concentration of ions and the electrostatic interaction between the ions are minor and (2) studies of strong electrolyte solutions, in which electrostatic interaction between the ions is observed. 

The first theory of solutions of weak electrolytes was formulated in 1887 by S. Arrhenius (see Section 1.1.4). If the molar conductivity is introduced into the equations following from Arrhenius concepts of weak electrolytes, Eq. (2.4.17) is obtained, known as the Ostwald dilution law this equation... 

At the end of the last century S. Arrhenius formulated the first quantitative theory describing the behaviour of weak electrolytes. The... 

Interionic forces are relatively less important for weak electrolytes because the concentrations of ions are relatively rather low as a result of incomplete dissociation. Thus, in agreement with the classical (Arrhenius) theory of weak electrolytes, the concentration dependence of the molar conductivity can be attributed approximately to the dependence of the degree of dissociation a on the concentration. If the degree of dissociation... 

At the microscopic level, the Arrhenius theory defines acids as substances which, when dissolved in water, yield the hydronium ion (H30+) or H+(aq). Bases are defined as substances which, when dissolved in water, yield the hydroxide ion (OH). Acids and bases may be strong (as in strong electrolytes), dissociating completely in water, or weak (as in weak electrolytes), partially dissociating in water. (We will see the more useful Brpnsted-Lowry definitions of acids and bases in Chapter 15.) Strong acids include ... 

Electrolytic chemistry and solution theory continued to be a principal source of speculation about chemical bonding. As John Servos has noted, it was Noyes s attempt to visualize the difference between strong and weak electrolytes, to explain anomalies in the dilution law, that led him to make a distinction between "electrical molecules" and "chemical molecules" in the early 1900s. 

Recently, the Pitzer equation has been applied to model weak electrolyte systems by Beutier and Renon ( ) and Edwards, et al. (10). Beutier and Renon used a simplified Pitzer equation for the ion-ion interaction contribution, applied Debye-McAulay s electrostatic theory (Harned and Owen, (14)) for the ion-molecule interaction contribution, and adoptee) Margules type terms for molecule-molecule interactions between the same molecular solutes. Edwards, et al. applied the Pitzer equation directly, without defining any new terms, for all interactions (ion-ion, ion-molecule, and molecule-molecule) while neglecting all ternary parameters. Bromley s (1) ideas on additivity of interaction parameters of individual ions and correlation between individual ion and partial molar entropy of ions at infinite dilution were adopted in both studies. In addition, they both neglected contributions from interactions among ions of the same sign. 

The scattering center is the metal ion, the Coulomb potential of which is screened in the manner of the Debye-Huckel theory of weak electrolytes. The screened potential has the form... 

The theory of Arrhenius has proved its value with some minor supplements in explaining the behaviour of weak electrolytes, it failed, however, completely when applied to strong electrolytes. Success in the case of weak electrolytes can be explained by the fact that because of the comparatively small number of ions and because of the considerable distances between them, there is no substantial difference between ions and undissociated molecules as far as their individual behaviour is concerned. We may, therefore, assume that all these particles regardless of their nature play an equal part in the determination of the thermodynamic properties of the solution. The degree of dissociation has in this case a concrete meaning and individual weak electrolytes can be differentiated by their characteristic dissociation constants. 

In the case of strong electrolytes with a = 1 the last, mentioned equation changes to the form of Onsager s equation, while for very weak electrolytes or substantially diluted solutions (o, si 0, /A 1) it changes to the classical formula of Arrhenius. If we consider the problem of electrolytes from the point of view of the equation (III-31) we can see that there is no sharp dividing line between strong and weak electrolytes. It can equally be seen that the Debye-Hiickel-Onsager theory does not replace the theory of Arrhenius but merely corrects and suitably supplements it. 

Although Debye and Hiickel worked out their theory to solve the problem of strong, completely dissociated electrolytes, the results may be applied to weak and transition electrolytes as well, if the actual ionic concentration is substituted in the equation for ionic strength. With strong electrolytes, which are completely dissociated, it is possible to substitute in the term directly the analytical concentration of the substance, but with weak electrolytes their dissociation degree a has to be considered. For example with uni-... 

The purpose of this chapter is to get a better insight of the first problem listed above, i.e., the polarization of interfaces (colloidal particles) during their interaction. Because of tutorial reasons, the electrolyte solution will be described using a rather simple, mean field approximation, that, however, allows to obtain an analytical solution of the problem. It is clear that this elaboration can easily be followed, and one can extend our model on more advanced situations. This model is identical with so-called weak-coupling theory for point ions treated in a course of the Debye-Hiickel approximation. Before going to make an elaboration for two interacting macrobodies immersed into an electrolyte solution, we would like to introduce a method, which is usually used to model this polarization, and to compute the electrical field next to a polarized medium. Then we will also discuss consequences of the polarization for the ion distribution at the particle-solution interface. 

DEGREE OF DISSOCIATION. STRONG AND WEAK ELECTROLYTES When discussing the theory of electrolytic dissociation, it was stated that it is a reversible process and its extent varies with concentration (and also with other physical properties, like temperature). The degree of dissociation (a) is equal to the fraction of the molecules which actually dissociate. 

The free ions of weak electrolytes, even in relatively concentrated solutions, are present in such small quantities that they still conform to the simple laws. It is possible that the free electric charges on the ions exert appreciable forces on one another in concentrated solutions. This would cause deviations from the simple laws analogous to the deviations from the simple gas laws which are accounted for by van der Waals theory. 

Figs. 3,80 and 3.81) for weak electrolyte is substantially higher than that for strong electrolyte. Dukhin et al. [411] discussed the errors that can be caused by interpretation of electroacoustic data obtained at high solid to liquid ratios by means of theories that are only valid for dilute systems. These theories give severely underestimated (1 at high solid to liquid ratios. 

Many studies of electrolyte conductivity have been carried out [7]. This work certainly helped to confirm modern ideas about electrolyte solutions. One aspect of the behavior of strong electrolytes which was initially not well understood is the fact that their molar conductance decreases with increase in concentration. Although this is now attributed to ion-ion interactions, early work by Arrhenius [8] ascribed the decrease in all electrolytes to partial dissociation. However, it is clear from the vast body of experimental data that one can distinguish two types of behavior for these systems, namely, that for strong electrolytes and that for weak electrolytes, as has been illustrated here. The theory of the concentration dependence of the molar conductance of strong electrolytes was developed earlier this century and is discussed in detail in the following section. 

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