How do I calculate the mass of crystals formed on cooling?

First find the water and solute in the saturated solution: for a solution of mass m saturated at T₁, the water is m × 100 / (100 + S₁). On cooling the water stays the same but only water × S₂ / 100 of solute can remain dissolved, so the crystals are water × (S₁ − S₂) / 100. For example, 210 g of KNO₃ solution saturated at 60 °C contains 100 g water and 110 g solute; cooled to 20 °C (S = 31.6 g) it deposits 78.4 g. If a hydrate such as CuSO₄·5H₂O crystallises, the crystals remove water as well and an equation has to be solved — the tool does this automatically.

What does the intersection of two solubility curves mean?

Where two curves cross, the two substances have the same solubility at that temperature, so their saturated solutions also have the same mass fraction. KNO₃ and NaCl cross at about 23–24 °C, where both dissolve about 36 g per 100 g water. Below that temperature NaCl is more soluble, above it KNO₃ is. The intersection says nothing about the masses of the two solutions being equal.

When should I use cooling crystallisation rather than evaporation?

Substances whose solubility rises steeply with temperature, such as KNO₃, are crystallised by cooling a hot saturated solution. Substances whose solubility hardly changes, such as NaCl, give little on cooling and are crystallised by evaporating the solvent. So KNO₃ containing a little NaCl is purified by cooling (NaCl stays in the mother liquor), while NaCl containing a little KNO₃ is purified by evaporation and hot filtration. Ca(OH)₂ is less soluble when hot, so heating makes it come out of solution.

How do I find the mass percent of a saturated solution?

At a given temperature the saturated mass fraction is w = S / (100 + S) × 100%, where S is the solubility in g per 100 g water. At 20 °C NaCl has S = 36.0 g, so saturated brine is 36 / 136 ≈ 26.5%; for KNO₃ it is 31.6 / 131.6 ≈ 24.0%. This is the highest mass fraction possible at that temperature and does not depend on how much solution you have.

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📈Solubility Curves - Interactive Solubility Graph & Crystallisation Calculator

Solubility is the greatest mass of solute that dissolves in 100 g of water at a given temperature, and plotting it against temperature gives a solubility curve, a staple of school chemistry. This tool contains 0–100 °C data for 14 substances — KNO₃, NaCl, KCl, NH₄Cl, NaNO₃, KClO₃, CuSO₄, Na₂SO₄, KI, K₂Cr₂O₇, NH₄NO₃, sucrose, Li₂CO₃ and Ca(OH)₂ — taken from standard textbook tables and the CRC Handbook, joined by a shape-preserving monotone cubic (PCHIP) interpolation that never invents bumps between data points. Overlay any curves, move the mouse or tap to read every solubility and saturated mass fraction at a temperature, and see where curves cross: KNO₃ and NaCl, for instance, have equal solubility (about 36 g) near 23.5 °C. The calculators cover the classic questions. At 20 °C the solubility of KNO₃ is 31.6 g, so its saturated solution is 31.6 / 131.6 = 24.0% by mass; 210 g of KNO₃ solution saturated at 60 °C holds 100 g water and 110 g solute, and cooling it to 20 °C deposits 110 − 31.6 = 78.4 g of crystals; 40 g NaCl added to 100 g water at 20 °C dissolves only 36 g, giving 136 g of saturated solution. CuSO₄ and Na₂SO₄ crystallise as hydrates (CuSO₄·5H₂O and Na₂SO₄·10H₂O), and the tool accounts for the water the crystals carry away. A mixture module compares cooling and evaporative crystallisation for yield and purity, showing why KNO₃ with a little NaCl is purified by cooling while NaCl with a little KNO₃ is purified by evaporation. Curves for dissolved O₂ and CO₂, which fall with temperature, and a full data table are included.

Free · No sign-up · Runs in your browserLast updated: 2026-10-29

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How to use Solubility Curves

1Select the substances to compare, then move over or tap the graph to read solubilities and see the intersection points
2Choose a calculator — saturated solution, cooling crystallisation, evaporation, saturated or not, or separating mixtures — and enter temperatures and masses, or click a typical exam question
3Read the result and the working, and use the curves to understand crystallisation, saturation and purification

FAQ

How do I calculate the mass of crystals formed on cooling?: First find the water and solute in the saturated solution: for a solution of mass m saturated at T₁, the water is m × 100 / (100 + S₁). On cooling the water stays the same but only water × S₂ / 100 of solute can remain dissolved, so the crystals are water × (S₁ − S₂) / 100. For example, 210 g of KNO₃ solution saturated at 60 °C contains 100 g water and 110 g solute; cooled to 20 °C (S = 31.6 g) it deposits 78.4 g. If a hydrate such as CuSO₄·5H₂O crystallises, the crystals remove water as well and an equation has to be solved — the tool does this automatically.
What does the intersection of two solubility curves mean?: Where two curves cross, the two substances have the same solubility at that temperature, so their saturated solutions also have the same mass fraction. KNO₃ and NaCl cross at about 23–24 °C, where both dissolve about 36 g per 100 g water. Below that temperature NaCl is more soluble, above it KNO₃ is. The intersection says nothing about the masses of the two solutions being equal.
When should I use cooling crystallisation rather than evaporation?: Substances whose solubility rises steeply with temperature, such as KNO₃, are crystallised by cooling a hot saturated solution. Substances whose solubility hardly changes, such as NaCl, give little on cooling and are crystallised by evaporating the solvent. So KNO₃ containing a little NaCl is purified by cooling (NaCl stays in the mother liquor), while NaCl containing a little KNO₃ is purified by evaporation and hot filtration. Ca(OH)₂ is less soluble when hot, so heating makes it come out of solution.
How do I find the mass percent of a saturated solution?: At a given temperature the saturated mass fraction is w = S / (100 + S) × 100%, where S is the solubility in g per 100 g water. At 20 °C NaCl has S = 36.0 g, so saturated brine is 36 / 136 ≈ 26.5%; for KNO₃ it is 31.6 / 131.6 ≈ 24.0%. This is the highest mass fraction possible at that temperature and does not depend on how much solution you have.

Features

Solubility curves for 14 solids, including Ca(OH)₂ and Li₂CO₃ (less soluble when hot) and Na₂SO₄ with its maximum at 32.4 °C
Monotone PCHIP interpolation with mouse or touch read-out, including saturated mass fraction
Automatic intersection points where two substances have equal solubility
Saturated solution mass fraction and the maximum solute a given mass of water can dissolve
Crystal yield on cooling or evaporation, with CuSO₄·5H₂O and Na₂SO₄·10H₂O hydrates handled correctly
Saturated, unsaturated or excess solid, with how much solute, evaporation or temperature change would saturate or dissolve it
Mixture separation comparing cooling and evaporative crystallisation for yield and purity, with a recommendation
Gas solubility curves for O₂ and CO₂ and a 0–100 °C solubility table

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