Chemical potentials and mean activity coefficients

The Debye-Huckel theory gives a calculation of the activity coefficients of individual ions. However, although the individual concentrations of the ions of an electrolyte solution can be measured, experiment cannot measme the individual activity coefficients. It does, however, furnish a sort of average value of the activity coefficient, called the mean activity coefficient, for the electrolyte as a whole. The term mean is not used in its common sense of an average quantity, but is used in a different sense which reflects the number of ions which result from each given formula. Such mean activity coefficients are related to the individual activity coefficients in a manner dictated by the stoichiometry of the electrolyte. 

Demonstrating the thermodynamic arguments leading up to such relations requires use of the chemical potential for the solid electrolyte and the aqueous ions. 

In Section 8.11 the chemical potential was defined as /a, = ( j/ i)7-,p,aUothern Consider the case of the dissolution of NaCl(s) in water  

For constant temperature and pressure, and using the arguments developed in Section 

The individual ion activity coefficients cannot be measured, but an analogous equation to Equation (8.70) can be written involving the mean activity coefficient y for the electrolyte as a whole. This is a quantity which can be measured (see emf measurements. Section 9.20.5, Worked Problems 9.28 and 9.29 and Sections 10.6.15, 10.7, 10.10 and 10.11). 

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This sum conesponds to the work done in transferring 2 moles of ions (one mole of K and one mole of Cl ) from infinity into the solution. In order to refer to the chemical potential of 1 mole of transferred ions, one is talking about a mean chemical potential and mean activity coefficients/+, and Eq. (A7) must be divided by two ... 

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