How rock candy grows
To make rock candy, you dissolve a huge amount of sugar in boiling water, hang a string in the jar, and wait. Over the next week, big sugar crystals grow on the string. Why does sugar that dissolved perfectly well in hot water come back out as the solution cools? The answer is in how solubility changes with temperature.
Solubility of a solid
The solubility溶解度 of a solid is the mass of it that dissolves in 100 g of solvent to make a saturated solution at a given temperature. If no solvent is named, it means water.
Example: at 20 °C, the solubility of sodium chloride is 36.0 g. That means at 20 °C, 100 g of water can dissolve at most 36.0 g of sodium chloride, giving 136.0 g of saturated solution.
Based on solubility at 20 °C, substances are often grouped like this:
| Solubility at 20 °C | Description | Examples |
|---|---|---|
| More than 10 g | Very soluble | Potassium nitrate, sodium chloride |
| 1–10 g | Soluble | Potassium chlorate |
| 0.01–1 g | Slightly soluble | Calcium hydroxide |
| Less than 0.01 g | Insoluble | Calcium carbonate |
Solubility curves
Plot temperature on the horizontal axis and solubility on the vertical axis, and the solubility of a substance at different temperatures traces out its solubility curve溶解度曲线. Before reading one, here’s what each position on the graph means:
🔧 Math tool card · Reading GraphsSkip it if you already know this
A point on the curve: the solubility at that temperature; the solution is exactly saturated.
A point below the curve: less solute is dissolved than the solubility allows, so the solution is unsaturated.
A point above the curve: more solute was added than can dissolve, so the solution is saturated with extra solid left over. (If, unusually, all of it stays dissolved, the solution is supersaturated, which is how rock candy forms.)
Where two curves cross: the two substances have equal solubility at that temperature.
How steep the curve is: the steeper the curve, the more the solubility depends on temperature.
On a solubility curve graph, a point lies below a substance's curve. What kind of solution does it represent?
Below the curve, less is dissolved than the solubility at that temperature, so more could still dissolve: the solution is unsaturated.
Drag the top slider to read the solubilities at different temperatures. In the “Crystallization by cooling” panel, pick a substance and a final temperature to see how many crystals form:
- Potassium nitrate KNO₃
- Ammonium chloride NH₄Cl
- Potassium chloride KCl
- Sodium chloride NaCl
Calcium hydroxide (vertical scale magnified)
Calcium hydroxide Ca(OH)₂
Crystallization by cooling
The curves show three patterns:
- For most solids, solubility increases with temperature; for potassium nitrate the increase is dramatic.
- For a few solids, solubility barely changes with temperature; sodium chloride’s curve is almost flat.
- For a very few solids, solubility decreases as temperature rises, as with calcium hydroxide.
Getting crystals to form
- If a substance’s solubility depends strongly on temperature (like potassium nitrate), cool a hot saturated solution.
- If it depends only weakly on temperature (like sodium chloride), evaporate the solvent.
So potassium nitrate contaminated with a little sodium chloride can be purified by cooling: most of the potassium nitrate crystallizes while the small amount of sodium chloride stays dissolved.
Solubility of gases
Gases become less soluble as temperature rises and more soluble as pressure increases:
- Open a can of soda and the pressure drops, so dissolved carbon dioxide escapes as bubbles.
- A warm soda goes flat faster than a cold one, because carbon dioxide is less soluble at higher temperatures.
- In hot summer weather, fish in a pond may gasp at the surface, because warm water holds less dissolved oxygen.
Example 1: Using solubility
At 60 °C, the solubility of potassium nitrate is 110 g. At 60 °C, 60 g of potassium nitrate is added to 50 g of water and stirred well. Is the solution saturated? What is its mass?
- Scale to 50 g of water. 100 g of water can dissolve 110 g, so 50 g of water can dissolve 110 g × 50/100 = 55 g.
- Compare. 60 g is more than 55 g, so only 55 g dissolves and 5 g is left over. The solution is saturated.
- Find the mass. Mass of solution = 50 g + 55 g = 105 g.
Example 2: How much crystallizes on cooling?
210 g of saturated potassium nitrate solution at 60 °C is cooled to 20 °C. How many grams of potassium nitrate crystals form? (Solubility: 110 g at 60 °C, 31.6 g at 20 °C.)
- Find the water. At 60 °C, 100 g of water dissolves 110 g, and 100 g + 110 g = 210 g, exactly this solution: 100 g of water and 110 g of potassium nitrate.
- After cooling. At 20 °C, 100 g of water can hold only 31.6 g of potassium nitrate.
- Crystals. 110 g − 31.6 g = 78.4 g. The water doesn’t change, so the extra potassium nitrate comes out as crystals.
- Getting potassium nitrate crystals from its solution
Potassium nitrate's solubility drops sharply on cooling, so lots of crystals form.
- Making sea salt in sunny salt ponds
Sodium chloride's solubility barely changes with temperature, so the water has to evaporate.
- Purifying potassium nitrate that contains a little sodium chloride
On cooling, potassium nitrate crystallizes while the little sodium chloride stays dissolved.
- Purifying sodium chloride that contains a little potassium nitrate
Evaporating gives sodium chloride crystals, and the small amount of potassium nitrate stays in the remaining solution.
- Getting ammonium chloride crystals from its solution
Ammonium chloride's solubility changes quite a lot with temperature, so cooling works.
- Growing rock candy from a sugar syrup made with boiling water
Sugar is far more soluble in hot water than in cold water, so crystals grow as the syrup cools.
- Getting salt back from a pot of salt water on the stove
Boiling off the water leaves the salt behind.
Common mistakes
Mistake 1: “Solubility of 36 g at 20 °C means 100 g of solution contains 36 g of salt.” Solubility is per 100 g of solvent, not 100 g of solution. It’s 136 g of saturated solution that contains 36 g of salt.
Mistake 2: Comparing solubilities without a temperature. Solubility changes with temperature. At 20 °C sodium chloride is more soluble than potassium nitrate, but at 60 °C it’s far less soluble. Always say which temperature.
Mistake 3: “Everything dissolves better when it’s hotter.” That’s only true for most solids. Calcium hydroxide and all gases become less soluble as the temperature rises.
Quick check
The solubility of potassium nitrate at 20 °C is 31.6 g. Which statement is correct?
Solubility is the mass that saturates 100 g of solvent at a given temperature. A confuses solvent with solution, and D leaves out the temperature.
On a hot, muggy summer day, fish in a pond swim up to gulp air at the surface. What's the main reason?
Gases become less soluble as temperature rises, so there's less dissolved oxygen in the water.
Summary
- Solubility has four parts: a given temperature, 100 g of solvent, a saturated solution, and a mass in grams.
- On a solubility curve, a point on the line is exactly saturated, below it unsaturated, and above it saturated with extra solid. Where two curves cross, the solubilities are equal.
- Most solids get more soluble as temperature rises (potassium nitrate dramatically); sodium chloride barely changes; calcium hydroxide gets less soluble.
- Crystallize by cooling when solubility depends strongly on temperature, and by evaporation when it doesn’t.
- Gases become less soluble at higher temperatures and more soluble at higher pressures.
On to AP (for later)
AP topic 3.10 uses intermolecular forces to explain why some substances dissolve well and others don’t. Topic 7.11 puts numbers on “insoluble” with the solubility product, . And deciding whether a point lies above or below a curve is exactly the kind of data reading AP calls Science Practice 3, Representing Data and Phenomena.