Solution Dilution (M₁·V₁ = M₂·V₂) – Tutorial

What Is Solution Dilution?

Dilution is the process of lowering the concentration of a stock solution by adding solvent (usually water). The amount of solute stays the same — it is simply spread over a larger volume.

This is especially critical in the laboratory: many experiments require dilute solutions (0.1 M, 0.01 M) while only a concentrated stock (e.g. 1 M acid) is available.

The Core Idea: Solute Amount Is Conserved

During dilution, the solute neither disappears nor is created — only the total volume increases. This is the law of conservation of matter applied to solutions.

Finding V₁ from the Formula

• M₁: stock concentration
• V₁: volume to take from stock
• M₂: target concentration
• V₂: final volume to prepare

Step-by-Step Example

Prepare 0.1 M, 250 mL from a 1.0 M stock:

1. V₁ = (0.1 × 250) / 1.0 = take 25 mL of stock
2. V_water = 250 − 25 = add 225 mL of water
3. Dilution factor = 1.0 / 0.1 = 10×

5 Golden Rules to Avoid Mistakes

• Unit consistency: V₁ and V₂ must use the same unit (mL–mL or L–L).
• Same concentration unit: C₁ and C₂ must be of the same type.
• C₂ ≤ C₁: otherwise it is concentration, not dilution.
• Sanity check: V₁ should generally be smaller than V₂.
• Acid safety: Add acid to water — never water to acid.

Summary: Dilution = "same solute, larger volume". The safest approach: think in moles first, then apply M₁·V₁ = M₂·V₂.