Theory of partial dissociation

The dissolved state of the electrolytes in water has long been of great interest. More than a century ago, Mendelejew [12] suggested that sulphuric acid forms hydrates, and Arrhenius [13] put forward the theory of partial dissociation of electrolytes, both in the same Jorrmal. These pioneering ideas have eventually proved to be correct [14] for electrolyte solutions from zero to saturation. 

A Reappraisal of Arrhenius Theory of Partial Dissociation of Electrolytes... 

A century ago, van t Hoff s (1 ) pioneering work on the gas-solution analogy was followed by Arrhenius (2 ) theory of partial dissociation of electrolytes in solutions. Later, electrolytes came to be classified as weak or strong with the supposition that the former are partially dissociated whereas the latter are completely dissociated in the given solvent However, with... 

On the whole, one finds that the existing interpretations of the non-ideal behavior of solutions are fairly complicated and that there is no simple, meaningful and unified explanation of the properties of dilute and concentrated solutions. Therefore, the present author decided to interpret directly, without presupposed models, the actual experimental data as such rather than their deviations from ideality (or complete dissociation) represented by formal coefficients like 9 and V. Attention is paid here mainly to aqueous solutions of strong electrolytes, since these are considered anomalous (15). Extensive work on univalent and multivalent electrolytes has shown (8,9a-i) that when allowance is made for the solvation of solutes, Arrhenius theory of partial dissociation of electrolytes explains the properties of dilute as well as concentrated solutions. This finding is in conformity with the increasing evidence for ion association of recent years mentioned above. 

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 ... 

Presented in 1887, Svant Arrhenius (l) theory of electrolytic dissociation, that partial dissociation of the solute into negatively and positively charged ions takes place, and his proposed method of calculating the degree of dissociation helped open the way for organized theoretical and experimental investigations of electrolyte solutions. This theory held that these ions in solution are in a state of chaotic motion similar to that in an ideal gas and that the interaction of ions in a solution does not affect their distribution and motion. 

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 ... 

However the question of whether the salt should be considered as a molecular or ionic constituent is raised. The laws of solution theory suggest the latter. Hence, unless the salt is either fully associated or fully dissociated over the entire liquid composition range, the varying degree of salt dissociation over this range is important. In other words, since both species of ion and salt molecules contribute to the total effect caused by a partially dissociated salt, the total number of salt particles (ions and molecules) present should be considered. This would suggest that an even more correct expression of liquid composition for use in calculating liquid phase activity coefficients would be... 

For fixed total energy E, Equation (2.59) defines one possible set of Nopen degenerate solutions I/(.R, r E, n),n = 0,1,2,..., nmax of the full Schrodinger equation. As proven in formal scattering theory they are orthogonal and complete, i.e., they fulfil relations similar to (2.54) and (2.55). Therefore, the (R,r E,n) form an orthogonal basis in the continuum part of the Hilbert space of the nuclear Hamiltonian H(R, r) and any continuum wavefunction can be expanded in terms of them. Since each wavefunction (R, r E, n) describes dissociation into a specific product channel, we call them partial dissociation wavefunctions. 

In the experimental determination of activity coefficients of strong electrolytes, by the methods described below, the molalities, etc., of the ions are taken as the stoichiometric values, that is, the total possible molality, etc., disregarding incomplete dissociation, For example, in the last problem, the molalities of the sodium and sulfate ions in the 0.5 molal solution of sodium sulfate were taken as exactly 1.0 and 0.5, respectively, without allowing for the possibility that the salt may be only partially dissociated at the specified concentration. The activity coefficients obtained in this manner are called stoichiometric activity coefficients they allow for all variations from the postulated ideal behavior, including that due to incomplete dissociation. If the treatment is based on the actiuil ionic molalities, etc., in the given solution, as in the Debye-Httckel theory (Chapter XVII), there is obtained the true (or actual) activity coefficient. TTie ratio... 

In terms of the Arrhenius theory, sodium chloride in solution partially dissociates according to the equation ... 

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. 

HX-f H20=F H30 -fX-The ion HaO is the oxonium ion (or hy-droxonium ion or hydronium ion). This definition of acids comes from the Arrhenius theory. Such acids tend to be corrosive substances with a sharp taste, which turn litmus red and give colour changes with other indicators. They are referred to as protonic acids and are classified into strong acids, which are almost completely dissociated in water (e.g. sulphuric acid and hydrochloric acid), and weak acids, which are only partially dissociated (e.g. ethanoic acid and hydrogen sulphide). The strength of an acid depends on the extent to which it dissociates, and is measured by its dissociation constant. See also base. 

In order to account for the above behavior we have replaced the conventional rate equations by a Smoluchowski equation, describing diffusion in the potential of mutual interaction. In this picture one introduces explicitly the R 0 /H distance distribution, thus obtaining a partial (instead of an ordinary) differential equation for the time evolution of proton dissociation. The fact that the observed reaction is reversible in the excited-state, has promoted the development of the theory of reversible diffusion influenced reactions [14], as an (almost obvious) extension of the theory of (irreversible) diffusion influenced reactions [15, 16]. 

A more quantitative prediction of activity coefficients can be done for the simplest cases [18]. However, for most electrolytes, beyond salt concentrations of 0.1 M, predictions are a tedious task and often still impossible, although numerous attempts have been made over the past decades [19-21]. This is true all the more when more than one salt is involved, as it is usually the case for practical applications. Ternary salt systems or even multicomponent systems with several salts, other solutes, and solvents are still out of the scope of present theory, at least, when true predictions without adjusted parameters are required. Only data fittings are possible with plausible models and with a certain number of adjustable parameters that do not always have a real physical sense [1, 5, 22-27]. It is also very difficult to calculate the activity coefficients of an electrolyte in the presence of other electrolytes and solutes. Even the definition is difficult, because electrolyte usually dissociate, so that extrathermodynamical ion activity coefficients must be defined. The problem is even more complex when salts are only partially dissociated or when complex equilibriums of gases, solutes, and salts are involved, for example, in the case of CO2 with acids and bases [28, 29]. 

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