Mean activity

The following data (for 25°C) were obtained at the pzc for the Hg-aqueous NaF interface. Estimate and plot it as a function of the mole fraction of salt in solution. In the table,/ is mean activity coefficient such that a = f m , where m is mean molality. 

The Debye-Htickel limiting law predicts a square-root dependence on the ionic strength/= MTLcz of the logarithm of the mean activity coefficient (log y ), tire heat of dilution (E /VI) and the excess volume it is considered to be an exact expression for the behaviour of an electrolyte at infinite dilution. Some experimental results for the activity coefficients and heats of dilution are shown in figure A2.3.11 for aqueous solutions of NaCl and ZnSO at 25°C the results are typical of the observations for 1-1 (e.g.NaCl) and 2-2 (e.g. ZnSO ) aqueous electrolyte solutions at this temperature. 

Figure A2.4.6. Mean activity coefFicient for NaCl solution at 25 °C as a function of the concentration full curve from ((A2A61 ) dashed curve from ((A2A63 ) dot-dashed curve from (A2.4.64). The crosses denote experimental data. From [2],...

The activity of an ion is related to its molality through the mean activity coefficient 7+ therefore... 

Ise, N. The Mean Activity Coefficient of Polyelectrolytes in Aqueous Solutions and Its Related Properties. Vol. 7, pp. 536—593. 

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. 

The studies of U in river waters has enabled to assess the mean activity ratio of the dissolved U flux carried by rivers to ocean. The value of 1.17, based on 50% of the global exported U flux (Table 1), is in the lower range of older estimates based on smaller data sets (e.g., Mangini et al. 1979 Borole et al. 1982). Such an estimate is too low compared to the ratios of seawater. The point has been already raised by... 

In contrast with the individual ion activity coefficients fit the mean activity coefficient ft can be measured, calculation of which can be achieved through eqn. 2.46 as follows ... 

R. Hoppe, Effective coordination numbers and mean Active ionic radii. Z Kristallogr. 150 (1979) 23. 

Fig. 1.1 The activity coefficient y of a nonelectrolyte and mean activity coefficients y of electrolytes as functions of molality...

For a solution of a single electrolyte, the relationship between the mean activity coefficient and the osmotic coefficient is given by the equation... 

In view of the definition of the mean activity coefficient and of the electroneutrality condition, v+z+ = -v z, the limiting law also has the form... 

Fig. 1.8 Dependence of the mean activity coefficient y tC of NaCl on the square root of molar concentration c at 25°C. Circles are experimental points. Curve 1 was calculated according to the Debye-Hiickel limiting law (1.3.25), curve 2 according to the approximation aB = 1 (Eq. 1.3.32) curve 3 according to the Debye-Hiickel equation (1.3.31), a = 325nm curve 4 according to the Bates-Guggenheim approximation (1.3.33) curve 5 according to the Bates-Guggenheim approximation + linear term 0.1 C curve 6 according to Eq. (1.3.38) for a = 0.4nm, C = 0.055dm5-mor ...

In the above two equations, the former value is valid for basic SI units and the latter value for / in moles per cubic decimetre and a in nanometres. The parameter a represents one of the difficulties connected with the Debye-Hiickel approach as its direct determination is not possible and is, in most cases, found as an adjustable parameter for the best fit of experimental data in the Eq. (1.3.29). For common ions the values of effective ion radii vary from 0.3 to 0.5. Analogous to the limiting law, the mean activity coefficient can be expressed by the equation... 

If the validity of Eq. (1.3.31) is assumed for the mean activity coefficient of a given electrolyte even in a mixture of electrolytes, and quantity a is calculated for the same measured electrolyte in various mixtures, then different values are, in fact, obtained which differ for a single total solution molality depending on the relative representation and individual properties of the ionic components. 

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