Activity of electrolyte solutes

On the basis of this definition, one can determine, for instance, the activity of electrolytic solutions in terms of the real hydrogen ion activity. Rybkin et al. found that the Ax effect may be stabilized by adding surface-active substances in small quantities to the solution. Ac-... 

All methods used in the study of nonelectrolytes also can be applied in principle to the determination of activities of electrolyte solutes. However, in practice, several methods are difficult to adapt to electrolytes because it is impractical to obtain data for solutions sufficiently dilute to allow the necessary extrapolation to infinite dilution. For example, some data are available for the vapor pressures of the hydrogen halides in their aqueous solutions, but these measurements by themselves do not permit us to determine the activity of the solute because significant data cannot be obtained at concentrations below 4 moM. 

Freezing point methods are often applied to the measurement of activities of electrolytes in dilute aqueous solution because the freezing point lowering, 6= T — T, can be determined with high accuracy, and the solute does not dissolve in the solid to any appreciable extent. Equations can be derivedgg relating a to 9 instead of T and T. The detailed expressions can be found in the literature.16... 

Most of the methods we have described so far give the activity of the solvent. Often the activity of the solute is of equal or greater importance. This is especially true of electrolyte solutions where the activity of the ionic solute is of primary interest, and in Chapter 9, we will describe methods that employ electrochemical cells to obtain ionic activities directly. We will conclude this chapter with a discussion of methods based on the Gibbs-Duhem equation that allow one to calculate activities of one component if the activities of the other are known as a function of composition. 

Analogonsiy, soinbiiity measurements yieid the mean activity of electrolyte (s = w, o), and the corresponding standard Gibbs energy AG i of solution (in the molar scale). 

The beginning of the twentieth century also marked a continuation of studies of the structure and properties of electrolyte solution and of the electrode-electrolyte interface. In 1907, Gilbert Newton Lewis (1875-1946) introduced the notion of thermodynamic activity, which proved to be extremally valuable for the description of properties of solutions of strong electrolytes. In 1923, Peter Debye (1884-1966 Nobel prize, 1936) and Erich Hiickel (1896-1981) developed their theory of strong electrolyte solutions, which for the first time allowed calculation of a hitherto purely empiric parameter—the mean activity coefficients of ions in solutions. 

Thus, the deviation in the behaviour of electrolyte solutions from the ideal depends on the composition of the solution, and the activity of the components is a function of their mole fractions. For practical reasons, the form of this function has been defined in the simplest way possible ... 

In view of the electrostatic nature of forces that primarily lead to deviation of the behaviour of electrolyte solutions from the ideal, the activity coefficient of electrolytes must depend on the electric charge of all the ions present. G. N. Lewis, M. Randall and J. N. Br0nsted found experimentally that this dependence for dilute solutions is described quite adequately by the relationship... 

The contribution of short-range forces to the activity coefficient can be described much better and in greater detail by the methods of the statistical thermodynamics of liquids, which has already created several models of electrolyte solutions. However, the procedures employed in the statistical... 

Conway, B. E., Ionic interactions and activity behaviour, CTE, 5, Chap. 2 (1982). Friedman, H. L., Ionic Solution Theory, Wiley-Interscience, New York, 1962. Harned, H. S., and B. B. Owen, The Physical Chemistry of Electrolytic Solutions, Reinhold, New York, 1950. 

Among other applications of electrolyte solution theory to defect problems should be mentioned the application of the Debye-Hiickel activity coefficients by Harvey32 to impurity ionization problems in elemental semiconductors. Recent reviews by Anderson7 and by Lawson45 emphasizing the importance of Debye-Hiickel effects in oxide semiconductors and in doped silver halides, respectively, and the book by Kroger41 contain accounts of other applications to defect problems. However, additional quantum-mechanical problems arise in the treatment of semiconductor systems and we shall not mention them further, although the studies described below are relevant to them in certain aspects. 

The concentrations of electrolyte solutions are generally expressed in chemical units known as milliequivalents (mEq). The milliequivalent weight represents the amount, in milligrams, of a solute equal to 1/1000 of its gram equivalent weight. A milliequivalent is a unit of measurement of the amount of chemical activity of an electrolyte. A milliequivalent unit is related to the total number of ionic charges in solution and it takes the valence of the ions into consideration. Table 5.1 provides valence, atomic and milliequivalent weights, and formulae of selected ions. 

Roughly half of the data on the activities of electrolytes in aqueous solutions and most of the data for nonelectrolytes, have been obtained by isopiestic technique. It has two main disadvantages. A great deal of skill and time is needed to obtain reliable data in this way. It is impractical to measure vapor pressures of solutions much below one molal by the isopiestic technique because of the length of time required to reach equilibrium. This is generally sufficient to permit the calculation of activity coefficients of nonelectrolytes, but the calculation for electrolytes requires data at lower concentrations, which must be obtained by other means. 

Although potential measurements are used primarily to determine activities of electrolytes, such measurements can also be used to obtain information on activities of nonelectrolytes. In particular, the activities of components of alloys, which are solid solutions, can be calculated from the potentials of cells such as the following for lead amalgam ... 

A great deal of information on activities of electrolytes also has been obtained by the isopiestic method, in which a comparison is made of the concentrations of two solutions with equal solvent vapor pressure. The principles of this method were discussed in Section 17.5. 

A useful concept that is used when the activities of electrolytes are calculated is that of the ionic strength of the solution. This is defined (on the molar scale) as ... 

Chapter 2 discussed the various forms of interaction between solute and the solvent molecules (see section 2.3), which leads to a certain solubility of the solute in the solvent phase. It was also described how the ratio of the solubility of the solute between two immiscible solvents could be used to estimate distribution ratios (or constants) for the solute in the particular system (see section 2.4). It was also pointed out that in the case of aqueous solute electrolytes, specific consideration had to be applied to the activity of the solute in the aqueous phase, a consideration that also was extended to solutes in organic solvents. 

A new theory of electrolyte solutions is described. This theory is based on a Debye-Hiickel model and modified to allow for the mutual polarization of ions. From a general solution of the linearized Poisson-Boltzmann equation, an expression is derived for the activity coefficient of a central polarized ion in an ionic atmosphere of non-spherical symmetry that reduces to the Debye-Hiickel limiting laws at infinite dilution. A method for the simultaneous charging of an ion and its ionic cloud is developed to allow for ionic polarization. Comparison of the calculated activity coefficients with experimental values shows that the characteristic shapes of the log y vs. concentration curves are well represented by the theory up to moderately high concentrations. Some consequences in relation to the structure of electrolyte solutions are discussed. 

The extreme nonidealities characteristic of electrolyte solutions warn of the dangers inherent in approximations commonly employed in general chemistry. Except in the crossover region of intermediate m where y + 1, blithe replacement of activity by molarity is seldom justified for strong electrolytes. Elementary treatments of acid dissociation, solubility products, and the like may therefore be subject to considerable error unless the realistic variations of chemical potential with concentration are properly considered. 

Figure 8-5 Activity coefficient of H in solutions containing 0.010 0 M HCIO and varying amounts of NaCI04. [Data derived from L Pezza, M. Molina, M. de Moraes, C. B. Melios, and J. O. Tognoili, Talanta 1996,43, 1689] The authoritative source on electrolyte solutions is H. S. Harned and B. B. Owen, The Physical Chemistry of Electrolyte Solutions (New York Reinhold, 1958).

Solutions are usually classified as nonelectrolyte or electrolyte depending upon whether one or more of the components dissociates in the mixture. The two types of solutions are often treated differently. In electrolyte solutions properties like the activity coefficients and the osmotic coefficients are emphasized, with the dilute solution standard state chosen for the solute.c With nonelectrolyte solutions we often choose a Raoult s law standard state for both components, and we are more interested in the changes in the thermodynamic properties with mixing, AmjxZ. In this chapter, we will restrict our discussion to nonelectrolyte mixtures and use the change AmjxZ to help us understand the nature of the interactions that are occurring in the mixture. In the next chapter, we will describe the properties of electrolyte solutions. 

In the previous chapter, we described the thermodynamic properties of nonelectrolyte solutions. In this chapter, we focus on electrolytes as solutes. Electrolytes behave quite differently in solution than do nonelectrolytes. In Chapter 11, we described the strong electrolyte standard state and summarized relationships between the activity of the solute ai, the mean activity coefficient 7 , and the molality m in Table 11.3. 

We will see in Chapter 10, when we deal with the dissociation of electrolytes into ions, that, in general, the chemical potential of a dissociating solute is the chemical potential of its component parts, whereas the activity of the solute is the product of the component parts. 

Biniak, S., Swiatkowski, A., and Pakula, M. Electrochemical studies of phenomena at active carbon-electrolyte solution interfaces, in Radovic, L. R. (ed.), Chemistry and Physics of Carbon, Vol 27, 2001, New York Marcel Dekker, pp. 125-225. 

See, for example, Chap. 9 in K. Denbigh, The Principles of Chemical Equilibrium, Cambridge University Press, Cambridge, 1981. ThelUPAC recommendation for the symbol to represent rational activity coefficients is yx, which is not used in this book in order to make the distinction between solid solutions and aqueous solutions more evident. In strict chemical thermodynamics, however, all activity coefficients are based on the mole fraction scale, with the definition for aqueous species (Eq. 1.12) actually being a variant that reflects better the ionic nature of electrolyte solutions and the dominant contribution of liquid water to these mixtures. (See, for example, Chap. 2 inR. A. RobinsonandR. H. Stokes,Electrolyte Solutions, Butterworths, London, 1970.)... 

The shapes of these curves are markedly similar to those of Figure 1, although the maxima do not correspond exactly. This is not surprising since the herbicide itself must have some effect on the surface activity of the solution (if nothing more than an electrolyte effect), and the surface-active compounds used here were not identical in chemical type to those used by Jansen. 

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