Crystallization Yield Calculator
Estimate how many grams of crystals you can recover when cooling or evaporating a solution. Essential for pharmaceutical, food, and chemical engineers designing batch crystallization steps.
Last updated: September 2026
Formula below · 2 sources (aiche.org, Wikipedia) · Updated Sep 2026
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About this calculator
Crystallization yield depends on how much solute exceeds the solubility limit at the final temperature. The formula is: Yield = ((C₀ − S_f) / (100 + C₀)) × m_solution × (η / 100), where C₀ is the initial concentration (g/100 g water), S_f is the solubility at the final temperature (g/100 g water), m_solution is the total initial solution mass (g), and η is the crystallization efficiency (%). The first fraction converts the concentration difference (per 100 g of water) into grams of crystal per gram of starting solution, because every 100 + C₀ g of solution contains 100 g of water. It assumes no water evaporates and the crystals are anhydrous (no water of hydration). Multiplying by solution mass gives the theoretical crystal mass available, and the efficiency factor accounts for real-world losses such as incomplete nucleation, mother liquor retention, and handling. A higher temperature drop or lower final solubility produces a greater yield.
How to use
Suppose you have 1,000 g of a potassium nitrate solution at an initial concentration of 80 g/100 g water, cooled to 20 °C where solubility is 31.6 g/100 g water, with 90% crystallization efficiency. Step 1 — the 1,000 g of solution contains 1,000 × 100/180 = 555.6 g of water. Step 2 — crystals per 100 g water: 80 − 31.6 = 48.4 g, so (48.4 / 180) × 1,000 = 268.9 g theoretical yield. Step 3 — apply efficiency: 268.9 × 0.90 = 242.0 g of crystals recovered.
Frequently asked questions
How does final temperature affect crystallization yield?
Lower final temperatures generally reduce solubility, which increases the concentration driving force (C₀ − S_f) and therefore raises yield. However, very low temperatures can slow crystal growth kinetics and make filtration more difficult. Engineers balance yield against cycle time and crystal quality when choosing the target temperature. Always verify solubility data at your specific final temperature for accurate predictions.
What is crystallization efficiency and what values are typical?
Crystallization efficiency (η) expresses what fraction of the theoretically available crystals are actually recovered, expressed as a percentage. Losses occur because some crystals remain suspended in the mother liquor, fine crystals pass through filters, or incomplete nucleation leaves solute in solution. Industrial batch crystallizers typically achieve 85–95% efficiency for well-optimized processes. Pilot-scale or poorly mixed systems may see values as low as 70%.
Why is the denominator in the yield formula (100 + C₀) instead of just 100?
The concentration C₀ is expressed as grams of solute per 100 g of water, not per 100 g of total solution. Each 100 g of water in the starting solution carries C₀ g of solute, so the solution mass is (100 + C₀) g per 100 g of water. Cooling releases (C₀ − S_f) g of crystal per 100 g of water, so per gram of starting solution the yield is (C₀ − S_f)/(100 + C₀). Using 100 + S_f instead would overstate the yield (by 22% for 40 → 15 g/100 g water).