Experimental Determination of Solution Activities

In order to determine the activity of a component in solution, one must measure its vapor pressure. In the case of volatile liquids such as those discussed in most of this chapter, vapor pressure measurement is not a problem so that very accurate determination of activity is possible over the whole composition range for which a solution is formed. However, many solutes, for example, most solids, have negligible vapor pressures. Under these circumstances, one makes use of the Gibbs-Duhem relationship between the activities of the two-components in solution. Since the vapor pressure of the solvent can be measured, its activity can be determined, and then used to estimate the activity of the solute. 

On the basis of equation (1.4.28), for any infinitesimal change in a two-component system, one may write 

From the first and second laws of thermodynamics for this system (equation (1.3.21)), one has 

This is the form of the Gibbs-Duhem equation needed to relate the activity of component B in solution to that of component A. Choosing the Raoult law activity for the solvent A, and the Henry law activity for the solute B, equation (1.13.4) may be rewritten as 

In the limit of very dilute solutions, both activity coefficients approach unity so that the activity of A can be replaced by xa, and the activity of B by its molality (assuming that one has chosen molality as the concentration unit). However, as becomes very small the ratio xj jx becomes very large. Thus, in practice, one may not choose the infinitely dilute solution as a reference point but instead a very dilute solution for which Henry s law is valid. Then, integrating equation (1.13.5) between this very dilute concentration designated mj, to any other concentration rrij, one obtains 

---