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Process Utilities

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.

TypeEngineering guide — concept explainer

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

Dilution equation
C₁ × V₁ = C₂ × V₂
Solve for final volume
V₂ = C₁ × V₁ / C₂
Added solvent volume
Added solvent = V₂ − V₁

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

C₁V₁Before+ solventC₂V₂AfterC₁V₁ = C₂V₂added solvent= V₂ − V₁

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?

  1. 01C₁ = 100 g/L, V₁ = 1 L, C₂ = 25 g/L
  2. 02V₂ = C₁ × V₁ / C₂ = 100 × 1 / 25 = 4 L
  3. 03Added solvent = V₂ − V₁ = 4 − 1 = 3 L
Result

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.

FAQ

Can I use any concentration unit with C₁V₁ = C₂V₂?
Yes, as long as both C₁ and C₂ use the same unit. You can use g/L, mg/L, %, ppm, or mol/L — the formula works for any consistent basis because the units cancel in the ratio.
Does dilution change the amount of solute?
No. Dilution only changes the concentration by increasing the total volume. The total mass (or moles) of solute remains the same. That is exactly what C₁V₁ = C₂V₂ expresses: the solute amount before equals the solute amount after.
Why does the formula not work for concentrated acid dilution?
The formula still gives a reasonable first approximation, but concentrated acids have density significantly different from water. Volume addition is not perfectly linear, and the heat of mixing can be substantial. For safety-critical acid dilution, consult specific dilution tables or procedures.
What is the difference between dilution and dissolution?
Dilution starts with a solution and adds more solvent to reduce concentration. Dissolution starts with a solid (or pure liquid) solute and adds it to a solvent to create a solution. The C₁V₁ = C₂V₂ formula applies to dilution, not dissolution.