Guides
Dilution Calculation: the C₁V₁ = C₂V₂ Formula with Examples
Diluting just adds solvent; the amount of solute does not change, so before and after dilution C₁V₁ = C₂V₂ (initial concentration × volume = final concentration × volume).
Formula & principle
The amount of solute n = c·V is conserved, so C₁V₁ = C₂V₂. Know any three of the four quantities and you can solve for the fourth.
Steps
- List knowns Identify the three known quantities among C₁, V₁, C₂, V₂.
- Substitute Put them into C₁V₁ = C₂V₂.
- Solve Solve for the unknown, e.g. V₁ = C₂V₂ / C₁.
- Keep units consistent Use consistent units for concentration and volume on both sides.
Worked example
How much 6 mol/L concentrated HCl is needed to make 300 mL of 1 mol/L dilute HCl?
V₁ = C₂V₂ / C₁ = (1 mol/L × 300 mL) / 6 mol/L = 50 mL
Measure 50 mL of the concentrated acid and add water up to 300 mL.
Safety
- When diluting strong acids, add acid to water slowly with stirring — never pour water into concentrated acid.
- Diluting concentrated sulfuric acid is very exothermic; stir and cool as needed.
Leave one field blank in the dilution calculator to solve automatically.