Thermodynamics of Crystallization and Crystal Morphology 51 Aspects of Macroscopic Thermodynamics

In the search for temperature dependence of the solubility, crystals were grown in the flat cell, allowing good optical microscopic observation. At various stages in the development of the individual crystals, corresponding to crystal sizes between 20 and 400 mm, the temperature was varied between 0 and 40°C. A significantly faster growth rate that would correspond to a higher supersaturation at a lower solubility was not noticed at either the low or the high limits of this temperature range. Furthermore, no rounding of the crystal edges was detected that would indicate crystal dissolution owing to higher solubility. These observations are interpreted as an indication of none or very weak temperature dependence of the solubility (56).

Temperature-independent solubility means that the equilibrium constant of crystallization is also independent of temperature. Hence (57),

dT J rT

in which R is the gas constant, or dAG

Equation 11 has a simple solution:

Using AG° = AH° - TAS°, we obtain that AH° = 0 and AS° = const. The lack of temperature dependencies of the solubility leads to the following conclusions: (1) the enthalpy of crystallization is zero (or extremely small), and (2) the entropy of crystallization is temperature independent (or a weak function of temperature).

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