Solubility

How the model works

Solubility is the most solute that dissolves in a given amount of solvent at a given temperature. It is usually quoted as grams of solute per 100 g of water. Below that amount the solution is unsaturated and everything dissolves. At it the solution is saturated. Any extra stays as undissolved solid, in dynamic equilibrium with the dissolved ions.

dissolved = min(added, S(T) × water / 100)
excess solid = added − dissolved

For most solids, solubility rises with temperature, but by very different amounts. Potassium nitrate rises steeply, sodium chloride barely changes, and cerium(III) sulfate even falls. The curves here are interpolated from tabulated data. Cooling a saturated solution makes it hold less, so the difference crystallises out. This is how many salts are purified by recrystallisation.

Equilibrium values only: real dissolving takes time, and solutions can stay supersaturated briefly. Data from standard solubility tables, rounded; linear interpolation between tabulated points.

Guided experiments

1. Saturate at 20 °C. Add potassium nitrate to 100 g of water at 20 °C. Prediction: about 32 g dissolves; beyond that the extra settles as solid. 50 g KNO₃ at 20 °C
2. Heat to dissolve. Same mixture heated to 60 °C. Prediction: solubility rises to about 110 g per 100 g, so all 50 g dissolves. Heat to 60 °C
3. Recrystallise. Saturate at 80 °C, then cool to 20 °C. Prediction: about 169 − 32 = 137 g of KNO₃ crystallises. Table salt in the same experiment gives only about 2 g. Cool a hot saturated solution

Challenge

You need to recover as much solid as possible by cooling a solution from 80 °C to 0 °C. Which salt here works best, and which one would be useless?

References

• OpenStax, Chemistry 2e, §11.3 “Solubility”.
• CRC Handbook of Chemistry and Physics, “Aqueous solubility of inorganic compounds at various temperatures”.