Calculating Concentration
Section: 3. Stoichiometry | Syllabus: Cambridge IGCSE Chemistry (0620)
Concentration of Solutions
Concentration is the amount of solute dissolved in a given volume of solution. It can be measured in two ways:
| Type | Units | Formula |
|---|---|---|
| Mass concentration | g/dm³ | concentration = mass (g) ÷ volume (dm³) |
| Molar concentration | mol/dm³ | concentration = moles (mol) ÷ volume (dm³) |
1 dm³ = 1000 cm³ - always convert a volume given in cm³ to dm³ (divide by 1000) before using either formula.
A volumetric flask is filled exactly to its graduation mark to give a precisely known volume of solution
The Concentration Triangle
- Moles = Concentration × Volume
- Concentration = Moles ÷ Volume
- Volume = Moles ÷ Concentration
Worked Example: Concentration from Moles and Volume
- Question: 2 mol of HCl is dissolved to make 4 dm³ of solution. Calculate the concentration. [1]
- Answer: concentration = moles ÷ volume = 2 ÷ 4 = 0.5 mol/dm³ [1]
Worked Example: Moles from Concentration and Volume
- Question: calculate the number of moles of HCl in 50 cm³ of 2 mol/dm³ hydrochloric acid. [2]
- Answer: convert volume: 50 ÷ 1000 = 0.05 dm³ [1]; moles = concentration × volume = 2 × 0.05 = 0.1 mol [1]
Converting Between Mass and Molar Concentration
If given a mass concentration (g/dm³), first convert the mass to moles using Mr (moles = mass ÷ Mr), then divide by volume to get mol/dm³.
Worked Example: Finding Mass from Concentration and Volume
- Question: what mass of sodium hydroxide, NaOH, is dissolved in 500 cm³ of a 0.5 mol/dm³ solution? (Mr of NaOH = 40) [3]
- Answer: volume = 500 ÷ 1000 = 0.5 dm³ [1]; moles = concentration × volume = 0.5 × 0.5 = 0.25 mol [1]; mass = moles × Mr = 0.25 × 40 = 10 g [1]
Dilution
When a solution is diluted with water, the number of moles of solute stays the same - only the volume increases, so the concentration decreases.
C₁V₁ = C₂V₂
Worked Example: Dilution
- Question: 100 cm³ of 2 mol/dm³ HCl is diluted with water to a total volume of 500 cm³. Calculate the new concentration. [2]
- Answer: C₁V₁ = C₂V₂: 2 × 100 = C₂ × 500 [1]; C₂ = 200 ÷ 500 = 0.4 mol/dm³ [1]
Common Mistakes
- ❌ Using a volume in cm³ directly in the concentration formula
- ✓ concentration formulae require volume in dm³ - always divide a cm³ value by 1000 first
- ❌ Mixing up mass concentration (g/dm³) and molar concentration (mol/dm³)
- ✓ check the units given in the question carefully - they tell you which formula to use, and whether Mr is needed as an extra step
Interactive revision notes, videos and practice questions load below.