Introduction to Crystallization of Fine Chemicals and Pharmaceuticals - Molecules: Nucleation, Aggregation and Crystallization - page 147

Solubility and Supersaturation

The solubility of a substance in solution is the concentration that is
reached in the solution after a long period of contact with the substance in
the solid form. The solubility does not depend on how well you stir the
solution, nor on the amount of solid material present: these things only
affect the time it takes to reach the final equilibrium concentration. The
solubility does, on the other hand, depend on temperature and composi-
tion of the solution. In the literature, solubility data are usually published
for pure solvents and substances. In industry, however, that kind of purity
is rarely achieved, and it is therefore advisable to verify data in the litera-
ture with experiments on the actual solutions. The solubility of small crys-
tals, m, depends on the particle size. The smaller the crystal, the

higher the solubility. This results in large crystals in solution growing at
the expense of small ones. The phenomenon is called “Ostwald ripening”
and complicates the production of small crystals of uniform size, which is
sometimes of importance in the pharmaceutical industry.
The supersaturation denotes the concentration, c

< 10 µ

[ kg/kg inert ] , of a

substance in excess of its solubility, c * [ kg/kg inert ] . The supersaturation

can be expressed as a concentration difference ∆ c [ kg/kg inert ] , as the

supersaturation ratio s , or as relative supersaturation σ :

c
c

D c

D ccc =- = *, s

* ,

s = . (1)

c *

The base for concentration is chosen as the mass of non-crystallizing com-
pounds (often mainly the solvent) and is called inert. All expressions for
supersaturation above are approximations only, the true driving force being
the difference in chemical potential. Normally, the solubility increases with
increasing temperature, as is illustrated in Fig. 1. For all states below the
solubility curve the solution is undersaturated, and crystallization is not pos-
sible. All states above the curve signify a supersaturated solution, for which
crystallization is possible (but not necessarily probable). Suppose a solution
is initially at the temperature and concentration of point A in the figure.
Making the solution supersaturated corresponds to moving to a point above