The Activity Coefficient of a Single Ionic Species Cannot Be Measured

The Activity Coefficient of a Single Ionic Species Cannot Be Measured 

Before the activity coefficients calculated on the basis of the Debye-Hiickel model can be compared with experiment, there arises a problem similar to one faced in the discussion of ion-solvent interactions (Chapter 2). Thae, it was realized the heat of hydration of an individual ionic species could not he measured because such a measurement would involve the transfer of ions of only one species into a solvent instead of ions of two species with equal and opposite charges. Even if such a transfer were physically possible, it would result in a charged solution and therefore an extra, undesired interaction between the ions and the electrified solution. The only way out was to transfer a neutral electrolyte (an equal number of positive and negative ions) into the solvent, but this meant that one could only measure the heat of interactions of a salt with the solvent and this experimental quantity could not be separated into the individual ionic heats of hydration. 

When ionic lattices, i.e., salts, are dissolved instead of individual ionic species, one eliminates the problem of ending up with charged solutions but another problem emerges. If one increases the concentration of sodium ions by adding the salt sodium chloride, one has perforce to produce a simultaneous increase in the concentration of chloride ions. This means, however, that there are two contributions to the change in 

Since neither the positive nor the negative ions can be added separately, the individual contributions of the ionic species to the free energy of the system are difficult to determine. Normally, one can only measure the activity coefficient of the net electrolyte, i.e., of at least two ionic species together. It is necessary therefore to establish a conceptual link between the activity coefficient of an electrolyte in solution (that quantity directly accessible to experiment) and that of only one of its ionic species [not accessible to experiment, but calculable theoretically from Eq. (3.60)]. 

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