Solubility of solids

When the sugar stops dissolving

Stir spoon after spoon of sugar into a cup of warm tea. The first spoons vanish. Later, grains lie at the bottom, even if you stir for a long time.

The tea can hold no more sugar at that temperature. The solution is saturated. How much it can hold is the solubility of sugar in water.

Saturated, unsaturated and supersaturated

• A solution is unsaturated if it holds less solute than the solubility allows. More solute can dissolve.
• A solution is saturated if it holds exactly as much as the solubility allows. Extra solid stays undissolved.
• A solution is supersaturated if it holds more than the solubility allows. It is not stable.

A saturated solution with solid at the bottom is not quiet. Particles leave the solid and enter the solution. Other particles leave the solution and join the solid. The two rates are equal, so the amounts stay the same. This is a dynamic equilibrium:

A supersaturated solution can be made by cooling a hot saturated solution slowly, without shaking it. Drop in one tiny crystal, or scratch the glass, and the extra solute crystallises at once. A hand warmer made with sodium acetate works this way. It gets warm as the crystals form.

How we write solubility

The usual unit is grams of solute in 100 g of solvent. For water, that is g per 100 g of water. The unit mol/L is also used, called the molar solubility.

Take care: g per 100 g of water is not a mass percent. At $20\ ^\circ\text{C}$ the solubility of sodium chloride is $35.9\ \text{g}$ per $100\ \text{g}$ of water. The saturated solution has a mass of $135.9\ \text{g}$, so its mass percent is $\dfrac{35.9}{135.9} \times 100 = 26.4\ \%$.

What decides how much dissolves

The nature of the solute and the solvent. The rule is that like dissolves like.

• A polar or ionic solid dissolves in a polar solvent such as water. Water molecules pull ions out of the crystal, and they surround the ions. Sugar dissolves because its OH groups form hydrogen bonds with water.
• A non-polar solid dissolves in a non-polar solvent. Iodine gives a pale brown solution in water but a deep violet one in hexane.

For an ionic solid, the energy that water gives back when it surrounds the ions must pay for breaking the crystal. For a very weakly soluble salt such as barium sulphate, it does not. You met its solubility product, $K_{sp}$, in Class 11 equilibrium. For a salt that gives one cation and one anion, the molar solubility is $s = \sqrt{K_{sp}}$.

A saturated solution of a weakly soluble salt is very dilute. So saturated does not mean strong.

Pressure. Solids and liquids are almost incompressible, so pressure has almost no effect on how much solid dissolves.

Temperature. Think of dissolving as a reaction that takes in or gives out heat.

• If dissolving takes in heat (it is endothermic), Le Chatelier's principle says that heating helps it. The solubility rises with temperature. Potassium nitrate and ammonium chloride behave like this.
• If dissolving gives out heat (it is exothermic), heating works against it. The solubility falls with temperature. Calcium hydroxide behaves like this.
• If the heat is small, the temperature has little effect. Sodium chloride is the usual example.

Reading a solubility curve

The blue curve shows how much potassium nitrate dissolves in $100\ \text{g}$ of water at each temperature. A point on the curve is a saturated solution. A point below it is unsaturated. A point above it is supersaturated and unstable.

The green curve is almost flat. Sodium chloride is nearly as soluble in cold water as in hot water.

Example. A solution holds $150\ \text{g}$ of potassium nitrate in $100\ \text{g}$ of water at $80\ ^\circ\text{C}$. Where is it on the graph, and what happens when it cools?

• At $80\ ^\circ\text{C}$ the solubility is $169\ \text{g}$ per $100\ \text{g}$ of water. The solution holds $150\ \text{g}$, which is less. It is unsaturated, with room for $19\ \text{g}$ more.
• As it cools, the curve falls. It reaches $150\ \text{g}$ at about $74\ ^\circ\text{C}$. Below that temperature the solution is saturated, and then crystals form.
• At $20\ ^\circ\text{C}$ the solubility is $31.6\ \text{g}$. Crystals $= 150 - 31.6 = 118.4\ \text{g}$.

Use the sliders to cool the solution. Watch the dot turn red when the curve drops below the dashed line, and the crystals grow as the temperature falls.

Try it yourself: crystals

Crystals from solutions

Cooling a hot saturated solution is a way to get pure crystals. This is called crystallisation. Impure salt is dissolved in the least hot water that can dissolve it. When the solution cools, the main salt crystallises, because less of it can stay dissolved. The small amount of impurity stays dissolved, because the solution is still far from saturated with it. The crystals are filtered off.

The mass of crystals is the difference in solubility, scaled to the mass of water in the solution:

Here $s$ is the solubility in grams per 100 g of water. This works when the hot solution was saturated.

Try it yourself: a saturated solution

Try it in Python

The program reads the measured solubility at a few temperatures, finds the value between them, and works out the crystals when a saturated solution is cooled to different temperatures.

Common mistakes

• Thinking saturated means concentrated. A saturated solution of a weakly soluble salt is very dilute.
• Thinking dissolving stops. In a saturated solution, dissolving and crystallising go on at equal rates.
• Reading g per 100 g of water as a mass percent. The solution is heavier than the water.
• Thinking every solid dissolves better in hot water. It depends on the sign of the heat of dissolving. Sodium chloride hardly changes.
• Forgetting to scale the crystals to the mass of water. The table gives the change for 100 g of water.

Remember these

• Saturated: holds the most that can dissolve. The dissolving and the crystallising go on at the same rate.
• Solubility is usually g of solute per 100 g of solvent, at a stated temperature.
• Like dissolves like. Pressure hardly matters for solids.
• Endothermic dissolving: solubility rises with temperature. Exothermic: it falls.
• Crystals from cooling $= (s_{hot} - s_{cold}) \times \dfrac{\text{mass of water}}{100}$.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. Sugar lies at the bottom of a saturated solution. Has dissolving stopped?

2. A salt dissolves with the release of heat. What happens to its solubility when the water is heated?

3. At $40\ ^\circ\text{C}$ a salt has a solubility of $36\ \text{g}$ per $100\ \text{g}$ of water. A solution holds $20\ \text{g}$ of this salt in $100\ \text{g}$ of water at $40\ ^\circ\text{C}$. Is it saturated?

4. Why does a change of pressure hardly change how much sugar dissolves in water?

5. A hot saturated solution is cooled, and nothing crystallises, even at a temperature where the solubility is lower. What is this solution called, and how can you make it crystallise?