Activities of Minor Components in Concentrated Solutions

One of the most difficult problems in working with natural aqueous solutions is assigning activities to trace or minor components that occur in concentrated salt solutions. An example might be calculating the activity coefficient of ppm ( lO m) concentrations of metal ions in hydrothermal solutions containing 1 to 5 molal concentrations of salts such as NaCl, KCl, and CaCl2. 

The approach most frequently used by geochemists over the past several decades for calculating activities of minor components in concentrated salt solutions was suggested by Helgeson (1969). This was an outgrowth of earlier work by other eminent chemists such as Scatchard and Hamed, summarized by Pitzer and Brewer (1961, pp. 326,578 and Appendix 4). The idea is to define a deviation function B ( B-dot ) as the difference between observed and predicted activity coefficients for an electrolyte such as NaCl. This was redefined by Helgeson as 

The second term in the numerator is the D-H equation (17.28) and the first term is the experimentally observed activity coefficient for NaCl at the concentration mNaci of interest. The ionic strength includes a correction for ion association (formation of NaCr) and is called true ionic strength by Helgeson. Various methods of calculating la are described by Brimhall and Crerar (1987, p. 280). 

B has been derived by fitting (17.34) to activity coefficient data for NaCl and is tabulated as a function of T by Helgeson (1969). Helgeson et al. (1981) provided revised values called for NaCl and several other salts, and for NaCl as a function of P as well as T as part of a more comprehensive study. The activity coefficient of a minor or trace species (say several ppm FeCr) in a concentrated NaCl solution is then given by rearranging (17.34)  

So (17.35) gives an estimate of the stoichiometric activity coefficient of a trace component, 7 , which includes the three major non-ideality corrections in a concentrated NaCl solution. In (17.35), Ig is the association-corrected ionic strength including all components of the solution, the parameters Zj and a refer to the trace component (not NaCl), and B is the value for the dominant salt in the solution, NaCl. Because (17.35) 

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