oxalates of calcium and magnesium for instance, both compounds have fairly low solubility products
(2.3 × 10 –^9 mol^2 dm–^6 for calcium oxalate and 8.6 × 10 –^5 mol^2 dm–^6 for magnesium oxalate). However,
in the case of the calcium salt, precipitation is complete within a few minutes whilst the magnesium salt
takes several hours. This difference in rates may even be used as a basis for the quantitative removal of
calcium from solution without interference from magnesium. In order to expedite precipitate formation
it is necessary first to look more closely at the processes by which precipitates are produced.
When a reagent is added to an analyte solution forming a sparingly soluble compound, the solubility
product for that compound is immediately exceeded and the solution is said to be supersaturated. The
relative supersaturation Rs is given by
where Q is the actual concentration of the solute and S is the equilibrium concentration. The rate at
which Q reduces to S determines the rate of precipitation. Precipitate formation takes place first by the
aggregation of small groups of ions or molecules, a process known as nucleation. It may occur either by
the chance aggregation of molecules or ions in a homogeneous nucleation process, or by heterogeneous
nucleation when aggregation is initiated by particulate impurities within the solution. Whilst the former
process depends exponentially on the relative supersaturation of the solution, the latter is largely
independent of it. After nucleation the precipitation continues by particle growth, with further ions or
molecules adding to the aggregates. The rate of particle growth will also be dependent upon the relative
supersaturation and on the surface area of the particles, but will not vary so dramatically as the rate of
homogeneous nucleation. The relation between these rates and the relative supersaturation is
summarized schematically in Figure 5.9.
In a particular system, the nature of the precipitated particles will be determined by the relative rates of
nucleation and particle growth. Where nucleation predominates, small particles are produced and a
colloid may
Figure 5.9
Nucleation and particle growth rates
related to relative supersaturation.