Concentration of solutions
A solution's concentration is how much solute is dissolved per unit volume. GCSE uses two forms: g/dm³ (for foundation) and mol/dm³ (for higher).
Volume conversions
- 1 dm³ = 1000 cm³ = 1 litre
- 250 cm³ = 0.25 dm³
- 1 m³ = 1000 dm³
You will almost always need to convert cm³ to dm³ before calculating: divide by 1000.
Concentration in g/dm³
concentration (g/dm³) = mass of solute (g) ÷ volume of solution (dm³)
Worked example: 5 g of NaCl is dissolved in water to make 250 cm³ of solution. Calculate concentration in g/dm³.
- Volume = 250/1000 = 0.25 dm³
- Concentration = 5 ÷ 0.25 = 20 g/dm³
Concentration in mol/dm³ (HT)
Also called molar concentration or molarity. Symbol: c. Often written mol dm⁻³ or M.
c (mol/dm³) = moles ÷ volume (dm³)
Or rearranged:
- moles = c × V (in dm³)
- V = moles ÷ c
To convert g/dm³ ↔ mol/dm³, divide or multiply by M_r:
mol/dm³ = (g/dm³) ÷ M_r
✦Worked example— Worked examples (HT)
Example 1
What is the concentration in mol/dm³ of a solution containing 4.0 g of NaOH in 250 cm³? (M_r NaOH = 40)
- moles NaOH = 4.0/40 = 0.1 mol
- volume = 0.250 dm³
- concentration = 0.1/0.250 = 0.4 mol/dm³
Example 2
What mass of HCl is in 50 cm³ of 0.2 mol/dm³ solution? (M_r HCl = 36.5)
- volume = 0.05 dm³
- moles = 0.2 × 0.05 = 0.01 mol
- mass = 0.01 × 36.5 = 0.365 g
Example 3 — Converting between concentration units
A solution is 9.8 g/dm³ H₂SO₄. Express in mol/dm³. (M_r H₂SO₄ = 98)
- mol/dm³ = 9.8/98 = 0.1 mol/dm³
Diluting solutions
When you dilute a solution by adding more solvent:
- moles of solute stay the same.
- volume increases → concentration decreases.
Worked example: 25 cm³ of 2.0 mol/dm³ HCl is diluted to 100 cm³. Calculate the new concentration.
- moles = 2.0 × 0.025 = 0.05 mol
- new c = 0.05 ÷ 0.100 = 0.5 mol/dm³ (a 1-in-4 dilution).
Titrations link
Titrations (covered in C4.7) are practical applications of concentrations. The relationship:
c₁V₁ = c₂V₂ (when the mole ratio is 1 : 1)
For other mole ratios, multiply by the ratio.
⚠Common mistakes
- Using cm³ directly in c = n/V — V must be in dm³.
- Forgetting to convert mass to moles before dividing by volume (when calculating mol/dm³).
- Using wrong M_r for compound (count brackets, water of crystallisation).
- Confusing dilution and addition. Adding 25 cm³ of water to 25 cm³ of solution doubles total volume, so concentration halves.
Links
Required for C4.7 (titrations) and connects to C6.2 (effect of concentration on rate).
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