Non-ideality in electrolyte solutions

Non-ideality in electrolyte solutions is primarily due to electrostatic interactions between the ions and is taken care of by the activity coefficient, for any species, i, defined by  

The Debye-Hiickel theory, developed in Chapter 10, gives theoretical expressions for calculating the activity coefficient of any species in solution. 

Non-ideality in electrolyte solutions manifests itself in experimental studies in the following ways  

In this chapter ways of modifying the theoretical expressions for the equihbrium constant for a reaction in solution to take account of non-ideality will be explained, while emf and conductance studies will be described in Chapters 9 and 11 respectively. 

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Non-ideality also corresponds to all ion-solvent interactions which are over and above those considered to be present in the ideal solution, i.e. any modified ion-solvent interactions resulting from the increase in solute concentration. These interactions become more important at high concentration, and the contribution of ion—solvent interactions to non-ideality in electrolyte solutions becomes more important at high concentrations. An ion can interact with the solvent and can modify the solvent around it, or two ions could modify the solvent in between them. This would correspond to an ion-solvent interaction different from the ideal case and would lead to non-ideality which would increase as the solute concentration increases. It would also lead to modified solvent-solvent interactions. 

For the ideal solution the activity coefficient will be unity. Comparing this with the results obtained shows how necessary it is to take account of non-ideality in electrolyte solutions. 

The potential due to the ionic atmosphere at the surface of the ion, i.e. at a distance a/2 from the centre of the central reference ion. Non-ideality in electrolyte solutions is a result of electrostatic interactions obeying Coulomb s Law. The potential energy of such interactions is given in terms of ... 

X 10 mol dm for a 2 2 electrolyte. This latter value corresponds to a concentration of 2.5 X lO" mol dm . What should also be noted is that it will only be possible to ignore non-ideality in electrolyte solutions when y 1, and the calculations show that this will not happen until ionic strengths < 1 x 10 mol dm are reached. 

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 above results illustrate the importance of non-ideality for electrolyte solutions and also of the use of the Gibbs-Duhem relationship in obtaining electrolyte... 

The theory of electrolyte solutions developed in this chapter relies heavily on the classical laws of electrostatics within the context of modern statistical mechanical methods. On the basis of Debye-Hiickel theory one understands how ion-ion interactions lead to the non-ideality of electrolyte solutions. Moreover, one is able to account quantitatively for the non-ideality when the solution is sufficiently dilute. This is precisely because ion-ion interactions are long range, and the ions can be treated as classical point charges when they are far apart. As the concentration of ions increases, their finite size becomes important and they are then described as point charges within hard spheres. It is only when ions come into contact that the problems with this picture become apparent. At this point one needs to add quantum-mechanical details to the description of the solution so that phenomena such as ion pairing can be understood in detail. 

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-Htickel theory deals with departures from ideality in electrolyte solutions. The main experimental evidence for this non-ideality is that ... 

Clearly if Ya is unity then the solution is ideal. Otherwise the solution is nonideal and the extent to which ya deviates from unity is a measure of the solution s non-ideality. In any solution we usually know [A] but not either a a or Ya- However we shall see in this chapter that for the special case of dilute electrolytic solutions it is possible to calculate ya- This calculation involves the Debye-Hdckel theory to which we turn in Section 2.4. It provides a method by which activities may be quantified through a knowledge of the concentration combined with the Debye-Huckel calculation of ya- First, however, we consider some relevant results pertaining to ideal solutions and, second in Section 2.3, a general interpretation of Ya-... 

The Debye-Huckel theory gives a way of dealing with non-ideality in solutions of electrolytes. The ideal free energy can be calculated, and the difference between the... 

Discussion of non-equilibrium processes involving ions in terms of the micropotential is especially helpful because it focuses attention on the fact that major source of non-ideality in these systems is electrical in character. The arbitrary nature of the separation of the electrochemical potential into chemical and electrical contributions has often been pointed out in the literature. In fact, chemical interactions are fundamentally electrical in nature. However, the formal separation discussed here is conceptually important. Its usefulness becomes clear when one tackles problems related to the movement of ions in electrolyte solutions under the influence of concentration and electrostatic potential gradients. These problems are discussed in the following section. 

In chapter 3, it was shown that the Debye-Hiickel theory for ion-ion interactions is able to account for solution non-ideality in very dilute systems. The same model forms the basis for understanding the concentration dependence of the conductance observed for strong electrolytes. Thus, Onsager [9] showed in 1927 that the limiting conductance law for 1-1 electrolytes has the form... 

There are a large number of modihed interactions which can be considered as contributing to the non-ideality of the electrolyte solution. All of them result in increasing non-ideality as the solute concentration increases. They will be discussed in Chapters 10 and 12. 

The three topics of ion pairing, complex formation and solubilities are typical aspects of equilibrium in electrolyte solutions, and are handled in precisely the same manner as acid-base equilibria. As in the calculations on acid-base equilibria, only the ideal case is considered. Discussion of corrections for non-ideality are deferred until Sections 8.22 to 8.28. In this chapter pay special attention to ... 

The conclusion from the early work was that the equation was as successfid as the Debye-Hiickel theory relating to mean ionic activity coefficients was in coping with the effects of non-ideality in solutions of electrolytes. 

Within the range of concentrations for which the Fuoss-Onsager equation is expected to be valid, this equation accounts well for the effects of non-ideality in solutions of symmetrical electrolytes in which there is no ion association. It can thus be taken as a base-line for non-associated electrolytes and any deviations from this predicted behaviour can be taken as evidence of ion association (see Section 12.12). 

We could write all non-ideal properties of solutions in terms of activity coefficients. For electrolyte (salt) solutions we usually do use activity coefficients, but for solid and gaseous solutions Earth scientists have traditionally used other approaches based on excess properties. This is not to say the other approaches are fundamentally different or better. They are simply different ways of representing the same physical properties. However, we have just seen that using excess functions instead of activity coefficients can simplify notation, and this is always an advantage. The next section discusses the method most commonly used to express the activity coefficients and excess functions of solid solutions. 

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. 

Calculations of departures from ideality in ionic solutions using the MSA have been published in the past by a number of authors. Effective ionic radii have been determined for the calculation of osmotic coefficients for concentrated salts [13], in solutions up to 1 mol/L [14] and for the computation of activity coefficients in ionic mixtures [15]. In these studies, for a given salt, a unique hard sphere diameter was determined for the whole concentration range. Also, thermodynamic data were fitted with the use of one linearly density-dependent parameter (a hard core size o C)., or dielectric parameter e C)), up to 2 mol/L, by least-squares refinement [16]-[18], or quite recently with a non-linearly varying cation size [19] in very concentrated electrolytes. 

Lastly, the uniformity of ionic strength provided to a solution by the presence of ample supporting electrolyte limits effects due to the non-ideality of the solution. According to the Debye-Htickel theory, the presence of electrostatic interactions between ions causes solution non-ideality because these forces are on average stabihsing. Therefore, activity, the quantity appearing in the Nernst equation, differs from concentration by a factor known as the activity coefficient, y, in a maimer which for a dilute (<0.01 M) solution is given by a simplified formula ... 

In this study, the ePC-SAFT EOS as well as the MSA-NRTL model were applied to describe thermodynamic properties of numerous aqueous electrolyte solutions. Whereas only activity coefficients are obtained by the G model, volumetric properties can be calculated with an EOS. Ion-specific parameters were used independent of the electrolyte which the ions are part of. The model parameters possess a physical meaning and show reasonable trends within the ion series. Two ion parameters are needed in ePC-SAFT, whereas six parameters are necessary for applying MSA-NRTL. Next to the standard alkali halide electrolyte systems, both models even capture the non-ideal behaviour of solutions containing acetate or hydroxide anions where a reversed MIAC series is experimentally observed. Until now, thermodynamic properties of more than 120 aqueous systems could be successfully modelled with ePC-SAFT. The MSA-NRTL parameter set has also been applied to a couple of systems (so far 19 solutions). Implementing an ion-pairing reaction in ePC-SAFT,... 

The situation for electrolyte solutions is more complex theory confimis the limiting expressions (originally from Debye-Htickel theory), but, because of the long-range interactions, the resulting equations are non-analytic rather than simple power series.) It is evident that electrolyte solutions are ideally dilute only at extremely low concentrations. Further details about these activity coefficients will be found in other articles. 

The standard state of an electrolyte is the hypothetical ideally dilute solution (Henry s law) at a molarity of 1 mol kg (Actually, as will be seen, electrolyte data are conventionally reported as for the fonnation of mdividual ions.) Standard states for non-electrolytes in dilute solution are rarely invoked. 

The calomel electrode Hg/HgjClj, KCl approximates to an ideal non-polarisable electrode, whilst the Hg/aqueous electrolyte solution electrode approximates to an ideal polarisable electrode. The electrical behaviour of a metal/solution interface may be regarded as a capacitor and resistor in parallel (Fig. 20.23), and on the basis of this analogy it is possible to distinguish between a completely polarisable and completely non-polarisable... 

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... 

For strong electrolytes, the activity of molecules cannot be considered, as no molecules are present, and thus the concept of the dissociation constant loses its meaning. However, the experimentally determined values of the dissociation constant are finite and the values of the degree of dissociation differ from unity. This is not the result of incomplete dissociation, but is rather connected with non-ideal behaviour (Section 1.3) and with ion association occurring in these solutions (see Section 1.2.4). 

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