Industrial crystallization is a separation and purification process in which solute molecules are transferred from a supersaturated solution into an ordered solid crystal lattice structure. It is widely used in the chemical, pharmaceutical, and food industries to produce high-purity solids such as sugar, salt, fertilizers, and active pharmaceutical ingredients. The process is controlled by manipulating temperature, solvent composition, or evaporation rate to achieve a desired crystal size distribution and purity.
σ = (c − c*) / c*
LaTeX: \sigma = \frac{c - c^*}{c^*}
| Symbol | Meaning | Unit |
|---|---|---|
| σ | Supersaturation ratio (dimensionless) | — |
| c | Actual solute concentration | kg/m³ |
| c* | Equilibrium (saturation) solute concentration | kg/m³ |
Problem
A crystallizer operates with a solution of potassium nitrate. The actual concentration is 320 kg/m³ and the saturation concentration at the operating temperature is 250 kg/m³. Calculate the supersaturation ratio.
Solution
Step 1: Identify values — c = 320 kg/m³, c* = 250 kg/m³. Step 2: Apply the supersaturation formula: σ = (c − c*) / c* = (320 − 250) / 250 = 70 / 250 = 0.28.
Answer
σ = 0.28 (28% supersaturation), indicating moderate driving force for crystal nucleation and growth.
| Method | Driving Force | Typical Product | Temperature Change |
|---|---|---|---|
| Cooling crystallization | Reduced solubility at low T | KNO₃, sugar | Decrease |
| Evaporative crystallization | Solvent removal | NaCl, urea | Moderate increase |
| Anti-solvent crystallization | Reduced solubility in mixed solvent | APIs, dyes | Minimal |
| Reactive crystallization | Chemical reaction produces sparingly soluble salt | CaCO₃, BaSO₄ | Varies |
| Melt crystallization | Solidification from melt | Naphthalene, paraxylene | Decrease below melting point |
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