Activity Coefficient of Electrolyte and an Ion

The activity coefficient of an ion cannot be experimentally measured (as any other thermodynamic property of a single ion) but can be theoretically calculated for a dilute solution when 7 is less than about 0.05 mol kg . However, the activity coefficient of an electrolyte, y , can be experimentally measured, and such values are given in [Chapter 10, Tables 10.16 and 10.17]. is called the mean activity coefficient and is related to the activity coefficient of the cation, y+, and anion, y, as follows  

Therefore, the mean activity coefficient is simply the geometric average of the individual activity coefficients of the cation and anion. 

It is interesting to note the different limitations between theoretically and experimentally determining activity coefficients for dilute and concentrated solutions. Theoretical calculations are possible, and quite accurate, at low concentrations where any experimental measurements are usually difficult to perform. However, at high concentrations, it is possible to experimentally measure the mean activity coefficients, whereas accurate theoretical calculations from first principles are not currently possible. 

Let us find out where the relationship (1.17) is coming from taking into account that in a completely dissociated electrolyte b+ = v+ b, and b = v. bi, where fc is the concentration of a strong (completely dissociated to ions) electrolyte  

comparing Equations 1.4 and 1.18 and taking into account that p and p, are the same values as well as p = p , the activity of a strong electrolyte, and the activity coefficient y, b can be defined as follows  

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