Crystallization Yield Calculator
Estimate theoretical crystallization yield when cooling a saturated solution from a hot to a cold temperature, based on solubility difference. Used in pharmaceutical, food, and specialty chemical processes to predict crystal recovery.
About this calculator
Cooling crystallization exploits the decrease in solubility as temperature falls. The theoretical yield is the fraction of dissolved solute that exceeds the cold-temperature solubility. The formula is: Yield (%) = ((C₀ − S_cold) / C₀) × 100, where C₀ is the initial concentration (g/L) and S_cold is solubility at the final cold temperature (g/L). If C₀ exceeds the hot solubility S_hot, the solution is already supersaturated before cooling and a practical efficiency factor of 0.85 is applied (accounting for incomplete crystal growth, occlusions, and mother liquor losses). If C₀ ≤ S_hot, the full theoretical yield applies. The result represents the percentage of the dissolved solute recovered as crystals, guiding batch recipe development and evaporator-crystallizer design.
How to use
Example: C₀ = 300 g/L, S_hot = 350 g/L, S_cold = 100 g/L. Since C₀ (300) ≤ S_hot (350), no pre-cooling supersaturation penalty applies, factor = 1. Yield = ((300 − 100) / 300) × 100 × 1 = (200/300) × 100 = 66.7%. If instead C₀ = 400 g/L (exceeding S_hot = 350), the factor becomes 0.85: Yield = ((400 − 100) / 400) × 100 × 0.85 = 75% × 0.85 = 63.75%. Enter C₀, S_hot, and S_cold into the calculator to instantly see the expected crystal recovery percentage for your process.
Frequently asked questions
How does solubility difference between hot and cold temperatures determine crystallization yield?
The driving force for crystallization yield is entirely the gap between solubility at the initial (hot) temperature and solubility at the final (cold) temperature. A large solubility difference — common in salts like potassium nitrate — means most of the dissolved material crystallizes out and high yields are achievable by simple cooling. A small solubility difference — as with common table salt (NaCl) — means little material crystallizes on cooling, so evaporative crystallization is used instead. Consulting published solubility tables for your specific solute-solvent system over the intended temperature range is the essential first step in crystallizer design.
Why is actual crystallization yield lower than the theoretical maximum?
Several practical factors reduce actual yield below the theoretical value. Mother liquor — the saturated liquid remaining after crystal separation — inevitably wets and coats the crystals, carrying away dissolved solute even after filtration and washing. Incomplete crystallization due to insufficient cooling time, poor nucleation, or agglomeration traps solute in solution. Crystal occlusions (pockets of mother liquor trapped inside large crystals) also reduce purity and apparent yield. The 0.85 efficiency factor in this calculator is a conservative rule of thumb; actual recovery efficiency should be validated experimentally for each system.
When should evaporative crystallization be used instead of cooling crystallization?
Evaporative crystallization is preferred when the target compound has a flat solubility curve — meaning its solubility changes little with temperature — so cooling alone cannot drive sufficient crystallization. Sodium chloride is the classic example: its solubility changes by less than 5 g/L between 0°C and 100°C, making cooling crystallization impractical. Evaporating water raises the concentration above the saturation limit at the operating temperature, forcing crystals to form. Some processes combine both methods (vacuum cooling evaporation) to maximize yield. Energy cost of evaporation is significantly higher than simple cooling, so cooling crystallization is always the preferred choice when solubility is strongly temperature-dependent.