Activity Coefficients at High Ionic Strengths

In many of the published applications of thermodynamics in hydrometallurgy, activity coefficients have been either omitted or crudely estimated. No doubt, this has been due in part to the difficulties in estimating ionic activity coefficients at high ionic strengths. However, with the recent surge of developments, some of the more current studies have addressed the activity coefficient problem more realistically. Representative published applications are presented in Table HI. 

One advantage of PALS is that, as far as 13 is concerned, the medium appears transparent to Ps even at high concentrations of some solutes (e.g. CIO, CL, alkali cations). A promising application would be then to measure stability constants in concentrated solutions, to assess the validity of equations for the activity coefficients at high ionic strengths [111]. 

With the arrival of the Pitzer method for calculating activity coefficients at high ionic strengths (si m), research by Harvie and Weare (1980) led to computations of equilibrium mineral solubilities for brines. They could calculate... 

None of these extensions has been really satisfactory and they are not very useful at high ionic strength. The Davies equation (19) differs from the others in providing an additional term which alters the response of the activity coefficient to changes in ionic strength, particularly at higher values. The authors have had some success with this type of equation by replacing the. 2 factor in the second term with a variable. The variable can be determined by experiment at a particular set of conditions. 

During a redox reaction, a potentiometric titration can be employed to determine a concentration of analyte rather than an activity, since we are only using the emf as a reaction variable in the accurate determination of an end point volume. For this reason, an absolute value of reference electrode need not be known, as we are only concerned with changes in emf. It is, however, advisable to titrate at high ionic strength levels in order to minimize fluctuations in the mean ionic activity coefficients. 

At low ionic strength, y I for neutral compounds. At high ionic strength, most neutral molecules can be salted out of aqueous solution. That is, when a high concentration (typically > 1 M) of a salt such as NaCl is added to an aqueous solution, neutral molecules usually become less soluble. Does the activity coefficient, -yclher, increase or decrease at high ionic strength ... 

The second term in the DAVIES and extended DEBYE-HUCKEL equations forces the activity coefficient to increase at high ionic strength. This is owed to the fact, that ion interactions are not only based on Coulomb forces any more, ion sizes change with the ionic strength, and ions with the same charge interact. 

The activity coefficient of a species is a measure of the effectiveness with which that species influences an equilibrium in which it is a participant. In very dilute solutions, in which the ionic strength is minimal, this effectiveness becomes constant, and the activity coefficient is unity. Under such circum.stances, the activity and the molar concentration are identical (as are thermodynamic and concentration equilibrium constants). As the ionic strength increases, however, an ion loses some of its effectiveness, and its activity coefficient decreases. We may summarize this behavior in terms of Equations 10-2 and 10-3. At moderate ionic strengths, yx< 1 tis the solution approaches infinite dilution, however, 7x —> 1 and thus ax —> [X] and X p —> K p. At high ionic strengths (/r > 0.1 M),... 

At high ionic strengths, the activity coefficients for some species increase and may even become greater than 1. The behavior of such solutions is difficult to interpret we shall confine our discussion to regions of low to moderate ionic strengths (i.e., where /r <0.1). The variation of typical activity coefficients as a function of ionic strength is shown in Figure a2-l. 

Provided the ionic strength is not too high, this equation is obeyed as well as (but no better than) the Debye-Huckel equation for activity coefficients. One can expect deviations at higher ionic strength, and they are in general more serious the higher... 

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