Concentration and dilution
Concentration tells you how many moles are in one litre of solution. When you dilute, the amount of substance stays the same and only the volume grows.
Formulas and rules
- c = n / V (mol/L); volume always in litres
- Making a solution: n = m / M, then divide by the final volume
- Dilution: c₁V₁ = c₂V₂
- Water to add = V₂ − V₁
Your turn
Three problems on this topic. Type numbers like 12.5 or 1,250 and elasticities with their sign.
Task
From sodium hydroxide solution with c = 1 mol/L you need 250 mL of solution with c = 0.168 mol/L. How many mL of the stock solution do you need?
Volume of stock solution in mL (2 decimal places)
Water to add in mL
Numbers like 12.5 or 0.025, with as many decimals as asked. Masses and amounts count within 1%, pH values within ±0.02.
Worked example
3.9 g of potassium permanganate (KMnO₄) are dissolved in water and made up to 500 mL. Work out the concentration. Atomic masses (g/mol): O 16.00 · K 39.10 · Mn 54.94.
Worked solution
- 1.M(KMnO₄) = 4 × 16.00 + 39.10 + 54.94 = 158.04 g/mol
- 2.n = m / M = 3.9 / 158.04 = 0.02468 mol
- 3.c = n / V = 0.02468 mol / 0.5 L = 0.0494 mol/L
Typical mistake: Using the volume in mL instead of L: 250 mL is 0.25 L. Otherwise the concentration comes out 1,000 times too small.
From sodium hydroxide solution with c = 2.5 mol/L you need 1000 mL of solution with c = 0.6 mol/L. How many mL of the stock solution do you need?
Worked solution
- 1.The amount of substance stays the same when diluting: c₁ · V₁ = c₂ · V₂
- 2.V₁ = c₂ × V₂ / c₁ = 0.6 × 1000 / 2.5 = 240 mL
- 3.Top up: 1000 − 240 = 760 mL of water
Typical mistake: Swapping c₁ and c₂: you need less of the concentrated solution, so V₁ must be smaller than V₂.
Common questions
Dissolve in 500 mL or make up to 500 mL?
Making up to 500 mL means the final volume is exactly 500 mL, which is what c = n / V needs.