Dilution Explained
Dilution reduces concentration by adding solvent or increasing final volume. Learn the C1V1 = C2V2 formula, how to calculate added solvent volume, and common mistakes.
Definition
Dilution is the process of reducing the concentration of a solute by adding more solvent or by increasing the total final volume. The key relationship is C₁ × V₁ = C₂ × V₂, where C₁ and V₁ are the initial concentration and volume, and C₂ and V₂ are the final concentration and volume. The concentration basis (e.g. g/L, %, ppm) must be consistent on both sides of the equation.
Why it matters
Dilution is one of the most common operations in process plants, laboratories, and water treatment. Getting the dilution wrong means the downstream process receives the wrong dosage — too concentrated risks damage or waste, too dilute risks ineffective treatment. The C₁V₁ = C₂V₂ formula gives a quick, reliable way to calculate either the required final volume or the resulting concentration.
Formula
Units involved
- •C₁, C₂ — concentration in any consistent unit (g/L, mg/L, %, ppm)
- •V₁ — initial volume in litres, m³, gallons, etc.
- •V₂ — final volume in the same unit as V₁
Concept diagram
Worked example
You have 1 L of a solution at 100 g/L. You need to dilute it to 25 g/L. What final volume is required, and how much solvent must you add?
- 01C₁ = 100 g/L, V₁ = 1 L, C₂ = 25 g/L
- 02V₂ = C₁ × V₁ / C₂ = 100 × 1 / 25 = 4 L
- 03Added solvent = V₂ − V₁ = 4 − 1 = 3 L
Final volume = 4 L; add 3 L of solvent
Common mistakes
- •Using different concentration bases on each side — if C₁ is in g/L, C₂ must also be in g/L, not in % or ppm.
- •Forgetting that V₂ is the total final volume, not the amount of solvent added. The solvent to add is V₂ − V₁.
- •Assuming volumes are perfectly additive — for water-based dilutions this is a good approximation, but for some solvent mixtures the total volume can differ from the sum of component volumes.
- •Applying the formula to reactions — C₁V₁ = C₂V₂ assumes the solute amount is conserved. If a chemical reaction consumes or produces solute, this formula does not apply.
- •Ignoring that density may change with concentration — at high concentrations, density changes can make volume-based dilution arithmetic less accurate.
When to use the calculator
Use the Dilution calculator when you need to find the required final volume, the resulting concentration after dilution, or the volume of solvent to add. It handles the arithmetic and lets you focus on getting the inputs right.