Concepts and Theory of Non-ideality

Electrolyte solutions are non-ideal, with non-ideality increasing with increase in concentration. When experimental results on aspects of electrolyte solution behaviour are analysed, this non-ideality has to be taken into consideration. The standard way of doing so is to extrapolate the data to zero ionic strength. However, it is also necessary to obtain a theoretical description of non-ideality, and to deduce theoretical expressions which describe non-ideality for electrolyte solutions. Non-ideality is taken to be a manifestation of the electrostatic interactions which occur as a result of the charges on the ions of an electrolyte, and these interactions depend on the concentration of the electrolyte solution. Theoretically this non-ideaUty is taken care of by an activity coefficient for each ion of the electrolyte. 

The Debye-Hiickel theory discusses equilibrium properties of electrolyte solutions and allows the calculation of an activity coefficient for an individual ion, or equivalently, the mean activity coefficient of the electrolyte. Fundamental concepts of the Debye-Hiickel theory also form the basis of modern theories describing the non-equilibrium properties of electrolyte solutions such as diffusion and conductance. The Debye-Huckel theory is thus central to all theoretical approaches to electrolyte solutions. 

Sections 10.16 to 10.22 give a brief description of modem developments in electrolyte theory. This is a much more difficult section conceptually and can be omitted until after the Debye-Hiickel and Bjermm theories have been assimilated. 

An Intmduction to Aqueous Electrolyte Solutions. By Margaret Robson Wright 2007 John Wiley Sons Ltd ISBN 978-0-470-84293-5 (cloth) ISBN 978-0-470-84294-2 (paper) 

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For a given concentration, the relaxation time is directly related to ( + + )/ + , to A/2+2- and to A for the given electrolyte. The relaxation time is thus afundamental quantity in any theory of conductance. In turn, the relaxation time is a property of the ionic atmosphere which is regarded as the crucial concept in the Debye-Hiickel theory of non-ideality. These statements could be summarised as ... 

Chapters 10 and 12 can be thought of as in two parts, the first part of which is the basic theory of non-ideality and the basic theory of conductance. The development of these theories is explained in a step-by-step manner, with the essential concepts coming first followed by a statement of what the physical problem is which has to be overcome by the mathematical treatment, which then follows. These are difficult sections conceptually and mathematically, but the author has found that it is possible, by going sufficiently slowly and with sufficient explanation, to convey this to the ordinary student, i.e. a student who is not mathematically orientated. The resultant final equations of these theories are those on which the manipulation and interpretation of experimental data such as are discussed in Chapters 1-9 and 11 are based. 

Rigorous convective diffusion theory [19] doubtlessly brings a valuable contribution to the exact mathematical analytical description of FFF. On the other hand, it must be realized that under real experimental conditions a number of non-ideal conditions exist, such as imperfect smoothness of the surface of the FFF channel walls, and others which can cause fundamental deviations from the theory, of the data observed. The above, and a number of other possible conditions have not been considered by any of these theories. It is the simpleness and the easy distinction of the physical conception of the derived relationships that are, in spite of some simplifying asymptotic assumptions, an advantage of the non-equilibrium theory. 

As a result of these electrostatic effects aqueous solutions of electrolytes behave in a way that is non-ideal. This non-ideality has been accounted for successfully in dilute solutions by application of the Debye-Huckel theory, which introduces the concept of ionic activity. The Debye-Huckel Umiting law states that the mean ionic activity coefficient y+ can be related to the charges on the ions, and z, by the equation... 

There are many varieties of density functional theories depending on the choice of ideal systems and approximations for the excess free energy functional. In the study of non-uniform polymers, density functional theories have been more popular than integral equations for a variety of reasons. A survey of various theories can be found in the proceedings of a symposium on chemical applications of density functional methods [102]. This section reviews the basic concepts and tools in these theoretical methods including techniques for numerical implementation. 

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 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. 

In order to ensure the contimiity and clarity of the presentation some frequently-used concepts of chromatography ivith a mobile gas phase are briefly considered the mechanism of separation the retention parameters and the theories of gas chromatography. The employment of this technique as an important method of studying solutions through the most representor-live statistical models is also discussed it has hec7i of use in testing the non-ideal behaviour of some systems. 

A concept of distribution function 7 of active sites was introduced in the deduction of Temkin theory, from which well-known expressions for adsorption isotherms, such as Freundlich s and Prumkin-Temkin s isotherms and others, and for rate laws of adsorption such as Elovich s one were obtained. Analjdical forms of isotherms depend on the forms of adsorptive energy distribution function, because the physical meaning of these distribution function is based on the inherent non-uniform of catalyst surfaces and the interaction between adsorbed species. Therefore, this formulation accounts for two physical effects caused by non-ideality of adsorptive phase. 

The original Flory-Huggins Theory assumed random distribution of contiguous segments of polymer chains. Modem polymer solution theories have diverged significantly from this original concept and contain many correction terms for non-ideal behaviour. 

The slip flow near the boundary surface can be analyzed based on the type of fluids, i.e., gas and Newtonian and non-Newtonian liquids. The sUp flow in gases has been derived based on Maxwell s kinetic theory. In gases, the concept of mean free path is well defined. Slip flow is observed when characteristic flow length scale is of the order of the mean free path of the gas molecules. An estimate of the mean free path of ideal gas is /m 1/(Vlna p) where p is the gas density (here taken as the number of molecules per unit volume) and a is the molecular diameter. The mean free path / , depends strongly on pressure and temperature due to density variation. Knudsen number is defined as the ratio of the mean free path to the characteristic length scale... 

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