Crystallizer Yield Calculator
Estimates the mass of crystals obtained from a cooling crystallization process given initial concentration, temperature drop, and solubility data. Ideal for process chemists optimising batch crystallizer design.
About this calculator
In cooling crystallization, yield is the mass of solute that precipitates when a saturated solution is cooled from an initial temperature T₁ to a final temperature T₂. The solubility decreases with temperature, forcing excess solute to crystallize. The yield formula used here is: Yield = solution_mass × [C_i − C_i × (1 − k × (T₁ − T₂) / 100)] / 100, where C_i is the initial concentration (g/100 g water), k is the solubility temperature coefficient (g/100 g·°C), and solution_mass is in kg. This simplifies to Yield = solution_mass × C_i × k × ΔT / 10000. The solubility coefficient k captures how many grams of solute dissolve per 100 g of water per degree Celsius — a steeper curve means higher yield per degree of cooling. Losses due to mother liquor adhering to crystals are not included in this estimate.
How to use
Example: 200 kg of solution contains C_i = 40 g/100 g water of potassium nitrate. It is cooled from T₁ = 60 °C to T₂ = 20 °C (ΔT = 40 °C). The solubility coefficient k = 0.5 g/100 g·°C. Step 1: Yield = 200 × [40 − 40 × (1 − 0.5 × 40 / 100)] / 100. Step 2: Inner term: 1 − 0.5 × 40 / 100 = 1 − 0.2 = 0.8. Step 3: 40 − 40 × 0.8 = 40 − 32 = 8. Step 4: Yield = 200 × 8 / 100 = 16 kg of crystals. This means 16 kg of solute crystallises out of 200 kg of the original solution.
Frequently asked questions
How does the solubility temperature coefficient affect crystallizer yield?
The solubility temperature coefficient k (g/100 g·°C) describes how sharply solubility changes with temperature. A high k means a large amount of solute drops out of solution for each degree of cooling, giving a high yield per unit energy spent on refrigeration. Substances like potassium nitrate have a high k (~0.5), making them excellent candidates for cooling crystallization. Substances with low k, like sodium chloride, yield very little product by cooling alone and require evaporative crystallization instead.
What is the difference between crystallizer yield and overall process recovery?
Crystallizer yield, as calculated here, represents the theoretical mass of crystals formed from the change in solubility. Overall process recovery is lower because it accounts for crystals lost in the mother liquor, wet cake washing losses, and mechanical losses during filtration and drying. A typical industrial batch crystallizer achieves 85–95% recovery relative to the theoretical yield. Wash efficiency and centrifuge performance are the dominant factors controlling the gap between theoretical yield and actual recovery.
Why is cooling crystallization preferred over evaporative crystallization for some compounds?
Cooling crystallization is preferred when the target compound has a steep solubility–temperature curve (high k), making it possible to recover large amounts of product simply by reducing temperature without evaporating solvent. It is also preferred for heat-sensitive products that degrade at elevated temperatures, and for processes where energy costs are a concern, since cooling is often cheaper than steam-driven evaporation. Evaporative crystallization is the better choice for compounds with relatively flat solubility curves or when removing solvent is a processing objective in itself.