Crystallization Yield Calculator
Estimate the mass of crystals recovered when a solution is cooled or partly evaporated, from its starting concentration, final solubility, batch mass, water evaporated and recovery efficiency.
Last updated: October 2026
Crystals recovered
151.79 g
Formula below · 1 source (people.utm.my) · Updated Oct 2026
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About this calculator
Crystallization yield comes from a mass balance: whatever solute the remaining water can no longer hold at the final temperature comes out as crystals. Textbook treatments (for example the cooling-crystallizer examples in Geankoplis) use solubility expressed as grams of solute per 100 g of water, as this calculator does.
The mass balance
For a starting solution of mass m with concentration C₀ (g per 100 g water): • Water in the batch W = m × 100 ÷ (100 + C₀) • Solute in the batch = m − W • Water left after evaporating E% = W × (1 − E ÷ 100) • Solute still dissolved at the end = S_f × water left ÷ 100, where S_f is the solubility at the final temperature • Theoretical crystals = solute − solute still dissolved • Crystals recovered = theoretical crystals × recovery efficiency ÷ 100
With no evaporation this reduces to m × (C₀ − S_f) ÷ (100 + C₀). The defaults, 1,000 g at 40 g/100 g water cooled to a solubility of 15 g/100 g water, give 178.57 g of theoretical crystals and 151.79 g at 85% recovery.
Assumptions
The crystals are anhydrous (they carry no water of crystallization) and the mother liquor ends exactly saturated. For hydrated salts, such as sodium carbonate decahydrate, part of the water leaves with the crystals and the balance must include it, which raises the yield. Real processes may also leave the liquor slightly supersaturated, lose fines through the filter or retain liquor on the cake; the recovery efficiency lumps those losses together. Read solubilities for your compound and temperature from a handbook or your own data.
How to use
Enter the starting concentration and the solubility at the end temperature, both in grams of solute per 100 g of water, the mass of solution you start with, any water evaporated during the step, and the share of the theoretical crystals you expect to recover. The defaults give 151.79 g of crystals from 1,000 g of solution. Set the efficiency to 100% to see the theoretical maximum (178.57 g). Evaporating 20% of the water raises the theoretical yield to 200 g.
Frequently asked questions
How do I calculate crystallization yield?
Work out the water and solute in the starting solution, then subtract the solute that the remaining water can still dissolve at the final temperature. What is left is the theoretical crystal mass; multiply by your recovery efficiency for the practical yield.
Why is solubility given per 100 g of water?
Because the water, unlike the total solution mass, does not change when crystals form (for anhydrous crystals). Solubility tables in handbooks usually use this basis, which keeps the mass balance simple.
How does evaporation increase the yield?
Removing water lowers the amount of solute that can stay dissolved. In the default example, evaporating 20% of the water raises the theoretical yield from 178.57 g to 200 g.
What if my crystals contain water of hydration?
Then each kilogram of crystals also removes water from the liquor, and this simple balance underestimates the yield. Write the balance with the hydrate's molar masses, as in the sodium carbonate decahydrate textbook example.
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