Activities, Activity Coefficients and Standard States

It is generally more convenient in aqueous solution thermodynamics to describe the chemical potential of a species i, in terms of its activity, a. The basic relationship between activity and chemical potential was developed by G.N. Lewis who first established a relationship for the chemical potential for a pure ideal gas, and then generalized his results to all systems to define the chemical potential of species i in terms of its activity aj as 

Here is a reference chemical potential or the standard chemical potential at an arbitrarily chosen standard state. The activity is a measure of the difference between the component s chemical potential at the state of interest and at its standard state. Thus as the chemical potential of component i approaches the chemical potential of component i at its arbitarUy chosen standard state, the component s activity approaches unity. 

For aqueous solutions in which the composition of the solution is expressed in terms of molality, the arbitrarily chosen standard state is the hypothetical ideal solution of unit molality at the system temperature and pressure. It is chosen so that as the molality approaches zero, the ratio of aj/mj tends to unity. This ratio aj/mi is called the molal activity coefficient, yj. 

The standard state chosen must be such that these equations hold at all pressures and temperatures. In these equations there appears to be an inconsistency of units, since the activity coefficient, Y, is dimensionless, whereas molality has the units moles/kilogram. To avoid this inconsistency the activity coefficient should be defined as 

We have defined the activity and activity coefficient of a species i. Unfortunately, in solutions of electrolytes we find that we cannot make a solution containing only cations or only anions and need to introduce a mean or average activity coefficient. For example, when one mole of NaCl is dissolved in a 

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