Calculating Concentrations

Concentration tells us how much solute (the substance that dissolves) is in a certain volume of solution. Think of squash and water: more squash in the same cup means a higher concentration.

Units and volume conversions

• g/dm³: grams of solute per cubic decimetre of solution (per litre).
• mol/dm³ (molarity): moles of solute per cubic decimetre.
• Volume conversions: 1 dm³ = 1000 cm³ and 1 dm³ = 1 litre. So to change cm³ to dm³, divide by 1000.
• Note: 1 cm³ = 1 mL.

Key formulas

Use these with volume in dm³:

$$c_{\text{mol/dm}^3} = \frac{n}{V} \quad\text{and}\quad c_{\text{g/dm}^3} = \frac{m}{V}$$

Linking mass and moles with molar mass $M_r$:

$$n = \frac{m}{M_r} \quad\Rightarrow\quad c_{\text{mol/dm}^3} = \frac{c_{\text{g/dm}^3}}{M_r}$$

A mole is a counting unit for particles. It uses the Avogadro constant (number of particles in 1 mole), but you do not need the number to calculate concentration.

Worked examples

Common mistakes to avoid

• Forgetting to convert cm³ to dm³ (this makes answers 1000 times too big or small).
• Using the wrong $M_r$ (check the formula of the compound).
• Mixing up solute and solution (mass of solute only in g/dm³).