Dilution Formula

The Formula

M_1V_1 = M_2V_2 (molarity × volume before = molarity × volume after)

When to use: Watering down a drink—same amount of flavor, more liquid, weaker taste.

Quick Example

Dilute 100 mL of 2M HCl with water to 200 mL total → resulting concentration is 1M.

Notation

M_1 and M_2 are the initial and final molarities (mol/L), V_1 and V_2 are the initial and final volumes. The product MV equals total moles of solute.

What This Formula Means

The process of decreasing the concentration of a solution by adding more solvent while keeping the total amount of solute constant.

Watering down a drink—same amount of flavor, more liquid, weaker taste.

Formal View

Dilution conserves the moles of solute: n_1 = n_2, therefore c_1V_1 = c_2V_2, where c is molar concentration and V is volume. This assumes ideal mixing with no volume change upon mixing (valid for dilute solutions).

Worked Examples

Example 1

easy
How much water must be added to 100\,\text{mL} of 6.0\,\text{M HCl} to make a 1.0\,\text{M} solution?

Solution

  1. 1
    Use M_1V_1 = M_2V_2: 6.0 \times 100 = 1.0 \times V_2.
  2. 2
    V_2 = 600\,\text{mL}.
  3. 3
    Water to add = 600 - 100 = 500\,\text{mL}.

Answer

500\,\text{mL of water}
Dilution does not change the number of moles of solute — it only increases the total volume. The dilution equation M_1V_1 = M_2V_2 reflects this conservation.

Example 2

medium
A stock solution of \text{H}_2\text{SO}_4 is 12.0\,\text{M}. What volume is needed to prepare 500\,\text{mL} of 0.60\,\text{M} solution?

Common Mistakes

  • Using the volume of solvent added instead of the total final volume — V_2 is the total volume of the final solution, not just the amount of solvent added
  • Forgetting to match units — both volumes must be in the same unit (both mL or both L) for the equation to work
  • Adding water to concentrated acid instead of acid to water — this is a safety hazard because the exothermic mixing can cause violent boiling and splashing

Why This Formula Matters

Dilution is how laboratory solutions of precise concentrations are prepared from concentrated stock solutions. Pharmacists dilute medications to safe dosages, water treatment plants dilute chemicals for purification, and biologists prepare serial dilutions for cell culture experiments.

Frequently Asked Questions

What is the Dilution formula?

The process of decreasing the concentration of a solution by adding more solvent while keeping the total amount of solute constant.

How do you use the Dilution formula?

Watering down a drink—same amount of flavor, more liquid, weaker taste.

What do the symbols mean in the Dilution formula?

M_1 and M_2 are the initial and final molarities (mol/L), V_1 and V_2 are the initial and final volumes. The product MV equals total moles of solute.

Why is the Dilution formula important in Chemistry?

Dilution is how laboratory solutions of precise concentrations are prepared from concentrated stock solutions. Pharmacists dilute medications to safe dosages, water treatment plants dilute chemicals for purification, and biologists prepare serial dilutions for cell culture experiments.

What do students get wrong about Dilution?

Always add acid to water when diluting, never water to acid — the heat released can cause dangerous splashing.

What should I learn before the Dilution formula?

Before studying the Dilution formula, you should understand: concentration.

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Related Concepts

ConcentrationTitration