Interpreting Solubility Curves

A solubility curve is a graph that shows how many grams of a solute dissolve in 100 g of water at each temperature; a point on the curve represents a saturated solution, a point below it an unsaturated solution and a point above it a supersaturated one. In brief: the solubility of potassium nitrate rises from about 31.6 g/100 g at 20 °C to 110 g/100 g at 60 °C, whereas the solubility of sodium chloride hardly changes.

Solubility curves let chemists predict how much solid will dissolve or crystallize when a solution is heated or cooled. They are used in laboratories and in industries from salt production to pharmaceuticals. This article shows how to read a curve, gives a data table with typical values and works through three common types of question.

How do you read a solubility curve?

The horizontal axis shows the temperature in °C and the vertical axis shows the solubility in grams of solute per 100 g of water. To use a curve:

1. Find the temperature on the horizontal axis.
2. Move vertically up to the curve of the substance.
3. Read the solubility on the vertical axis.

For a point (T, S) on the graph, three cases are possible. A point exactly on the curve is a saturated solution. A point below the curve is unsaturated, because less than the maximum amount is dissolved. A point above the curve is supersaturated if it is a solution at all, since more than the maximum would be dissolved.

Solubility data for four salts

These are rounded literature values, and different sources give slightly different numbers. For exact work, use the table or graph that your course or laboratory prescribes.

What do different curve shapes mean?

• Steep upward curve (KNO₃): the solubility depends strongly on temperature, so cooling a hot saturated solution produces a lot of crystals. This is the ideal case for purification by recrystallization.
• Nearly flat curve (NaCl): temperature has little effect, so salt cannot be recovered efficiently by cooling. It is obtained by evaporating the water.
• Downward curve (gases such as O₂ and CO₂): the solubility falls as the temperature rises.
• Sharp bend: sudden changes of slope can show that the solid changes form, for example from a hydrate to the anhydrous salt, as with sodium sulfate near 32 °C.

How do you solve solubility curve problems?

Example 1: how much solute dissolves

How much KCl can dissolve in 250 g of water at 80 °C? The solubility is 51 g per 100 g, so the answer is 51 × 250 / 100 = 128 g.

Example 2: how much crystallizes on cooling

A solution that is saturated at 60 °C contains 100 g of water. It is cooled to 20 °C. How much KNO₃ crystallizes?

1. At 60 °C, 100 g of water holds 110 g of KNO₃.
2. At 20 °C, 100 g of water holds only 32 g.
3. Mass crystallized = 110 − 32 = 78 g.

Example 3: finding the saturation temperature

A solution contains 64 g of KNO₃ in 100 g of water. At what temperature does the solution become saturated? According to the table, the solubility is 64 g/100 g at 40 °C. Above 40 °C the solution is unsaturated, and below 40 °C it is supersaturated or crystals appear.

Example 4: comparing two salts

At 80 °C, which dissolves more in 100 g of water, NaNO₃ or KNO₃? NaNO₃ dissolves 148 g and KNO₃ 169 g, so KNO₃ dissolves more. At 40 °C the order is reversed (104 g against 64 g), so the curves cross between those temperatures, near 70 °C.

Why do gas curves slope downward?

Dissolving a gas in water is usually exothermic, so according to Le Châtelier’s principle, heating shifts the equilibrium towards the undissolved gas. For example, the solubility of oxygen at a partial pressure of 1 atm is about 0.0069 g per 100 g of water at 0 °C and falls to about 0.0040 g at 30 °C. This is the reason why warm lakes hold less oxygen for fish, and why warm soda goes flat faster.

How are solubility curves obtained?

The curves are determined experimentally. A solution is prepared at a fixed temperature, stirred with excess solid until equilibrium is reached, and the concentration of the saturated solution is measured by evaporating a known mass of it or by another analytical method. Repeating this at many temperatures gives the points of the curve. Systematic collections of solubility data were compiled in the 19th century by chemists such as Gay-Lussac, and are now maintained in large critically evaluated databases.

Where are solubility curves used?

• Industrial crystallization: choosing cooling or evaporation for the production of salts, sugar and fertilizers.
• Pharmaceuticals: controlling the form and size of drug crystals.
• Environmental science: estimating how much oxygen a river can hold at a given temperature.
• Laboratory purification: selecting a solvent and temperatures for recrystallization.

Which mistakes are common?

• Forgetting that the values are per 100 g of water: scale them for other amounts.
• Misreading the type of solution: below the curve is unsaturated, above it is supersaturated.
• Mixing up grams of solute with grams of solution: the denominator is the mass of water.
• Interpolating carelessly: read between points along the curve and not along a straight line when the curve bends.
• Assuming that every solid is more soluble when hot: a few salts, for example Li₂SO₄ and Ce₂(SO₄)₃, behave in the opposite way.