Activity Coefficients in Solutions

Examples of this procedure for dilute solutions of copper, silicon and aluminium shows the widely different behaviour of these elements. The vapour pressures of the pure metals are 1.14 x 10, 8.63 x 10 and 1.51 x 10 amios at 1873 K, and the activity coefficients in solution in liquid iron are 8.0, 7 X 10 and 3 X 10 respectively. There are therefore two elements of relatively high and similar vapour pressures, Cu and Al, and two elements of approximately equal activity coefficients but widely differing vapour pressures. Si and Al. The right-hand side of the depletion equation has the values 1.89, 1.88 X 10- , and 1.44 X 10 respectively, and we may conclude that there will be depletion of copper only, widr insignificant evaporation of silicon and aluminium. The data for the boundaty layer were taken as 5 x lO cm s for the diffusion coefficient, and 10 cm for the boundary layer thickness in liquid iron. 

Therefore, the activity coefficients in solutions are determined primarily by the energy of electrostatic interaction w j between the ions. It is only in concentrated solutions when solvation conditions may change, that changes in (but not the existence of) solvation energy must be included, and that nonelectrostatic interactions between ions must be accounted for. 

The case of activity coefficients in solutions is easily but tediously implemented since well-constrained expressions exist, like those produced by the Debye-Hiickel theory for dilute solutions or the Pitzer expressions for concentrated solutions (brines). The interested reader may refer to Michard (1989) for a recent and still reasonably simple account. However simple to handle, activity coefficients introduce analytically cumbersome expressions incompatible with the size of a textbook. Real gas theory demands even more complicated developments. 

Voltammetry and polarography are performed under diffusion control, which is ensured by keeping the solution still, and using an excess of inert electrolyte. The latter also has the effect of equalizing all activity coefficients in solution, so values of concentration, rather than activity, may be derived during measurements. 

Having defined various activities and activity coefficients in solutions made up from strong electrolytes we now turn to the determination of 7. For this purpose we briefly discuss some aspects of the Debve—Huckel Theory. 

In order to cast results of other studies in terms of our model, some transformation of data has been necessary. In some cases we have had to estimate activity coefficients in solutions, and this has been done via the Davies equation ( ),... 

The molecular-interaction parameter can give rise to either positive or negative contributions to the term In y,. If the solvent tends to be self-associated, then the addition of a nonpolar solute disrupts solvent structure. Figure 2-5 indicates that n-decane in water has an activity coefficient of about 100,000. This high activity coefficient in solution is typical of the weak interaction of solute and solvent. On the other hand, where the molecular interaction between solute and solvent is strong, the activity coefficient would be expected to be low, and solute-solvent interactions and association constants may be measurable. ... 

The main interest of equations (25.9) and (25.10), or more particularly (25.7) and (25.8), is to enable us to calculate the orders of magnitude of the activity coefficients in solutions from a knowledge of the properties of the pure substances. The following table, due to Benesi and Hildebrand, illustrates clearly the usefulness of these formulae. It refers to saturated solutions of iodine in various solvents at 25 °C. Knowing the composition of the saturated solutions, equations (22.4) or (22.5) enable us to calculate the activity coefficients of iodine in these solutions. If we then apply equation (25.9) to different solvents for which is known, we can calculate in each case the parameter 8 for iodine, and compare it with that measured directly, AbIv%). Despite the fact that the activity coefficients vary over the range 1400 to 3 3, the values of... 

The importance of using activity rather than concentration in definition of the equilibrium constants of chemical reactions was already emphasized in Section I, Nevertheless, in many original publications, the stability constants of surface species are defined in terms of concentrations. These stability constants are reported in Tables in Chapter 4 without any comment of correction, although the approach neglecting the activity coefficients in solution is not recommended. 

The activity coefficient expresses the nonideal-solution behavior of fugacity. The formal development of models for the activity coefficient in solution thermodynamics follows. 

In this section we discuss certain characteristics of electrolyte solutions and present equations for the prediction or correlation of electrolyte activity coefficients in solution. Since the derivations of these equations are complicated and beyond the scope of this book, they are not given. 

The determination of the activity coefficients of species that exist dominantly as neutral molecules, such as Si02(ag), H2S(ag) and C02(ag), is much simpler. In these cases it is usually possible to establish a two-phase equilibrium between the substance in its pure state (solid or gaseous) and the substance in its aqueous or dissolved state. This leads to a simple and rigorous determination of the activity coefficient in solutions of varying composition. 

C. Formation of Chlorine Hydrate. Because of the presence of traces of water in compressed chlorine, the chlorine hydrate discussed in Section 9.1.3.5 again becomes a problem. As chlorine condenses, some of the water accompanies it. Depending on the temperature, a certain amount of water is soluble in the chlorine. So long as this solubility is not exceeded, the condensate remains homogeneous and solid hydrate does not form. Below we develop an estimate of the solubility of water in liquid chlorine and show that, because of its very low solubility in chlorine and therefore its very high activity coefficient in solution, it behaves as a volatile component. The practical effect of this is that water tends to concentrate in the gas phase in most first-stage liquefiers. 

Although there is ample evidence of its existence, the NaSO ion is generally ignored when calculating activity coefficients in solutions containing sodium and sulfate ions. Sodium sulfate is treated as a completely dissociating electrolyte. As early as 1930. Righellato and Davies (S34) stated that, even in dilute solutions, most uni-bivalent salts are incompletely dissociated. Based on conductance measurements at 18 C, they presented dissociation constants for a number of intermediate ions. For the salt MzX the dissociations were defined ... 

Volatilizational loss of chemicals from water to air is an important fate process for chemicals with low aqueous solubility and low polarity. Many chemicals, despite their low vapor pressure, can volatilize rapidly owing to their high activity coefficients in solution. Volatilizational loss from surfaces is a significant transport process. Volatilization of organic chemicals from the soil surface is complicated by other variables. There is no simple laboratory... 

Before leaving the subject of activity coefficients in solution, it will be instructive to discuss the mean activity coefficient,/+, for an electrolyte. For an electrolyte, Bj, which ionizes as... 

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