Effect of Aggregation Upon Solubility

The solubility profiles obtained for a compound which aggregates have the different regions as described previously, but the mathematical functions describing the change in solubility with pH are much more complex. The additional equilibrium for a monoprotic weak base when the charged species is aggregating is  

The solubility of the weak base is then given by the equation  

This scheme assumes that aggregation is only occurring with the charged species. When this equilibrium is taken into consideration, the equations which describe the solubility in the two regions become  

The contribution of the aggregation to the solubility is given by the last terms in Equations (4.24) and (4.25). Similarly an equation can be derived which gives the pH of maximum solubility, pH,.  

The data were fit to a model which had an aggregate species with the formula (BH + )2(X ). Additional studies were conducted using different techniques which confirmed an aggregate of this composition is present in the solution. In this figure the dotted line is the calculated curve for which the solution had an additional 0.05 M NaCl added. The significant decrease in the solubility when a salt is present having a common ion with the strong acid or base used to adjust the pH is not restricted to 

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