Dilution Formula
The dilution formula M₁V₁ = M₂V₂ calculates the new concentration when a solution is diluted.
Essential for lab work and solution preparation.
The Formula
When you dilute a solution, the number of moles of solute stays the same. The product of concentration and volume before dilution equals the product after dilution.
Variables
| Symbol | Meaning |
|---|---|
| M₁ | Initial molarity (concentration before dilution) |
| V₁ | Initial volume (volume before dilution) |
| M₂ | Final molarity (concentration after dilution) |
| V₂ | Final volume (volume after dilution) |
Example 1
You have 100 mL of 6 M HCl and want to dilute it to 2 M. What final volume do you need?
Identify the values: M₁ = 6 M, V₁ = 100 mL, M₂ = 2 M
Rearrange: V₂ = M₁V₁ / M₂ = (6 × 100) / 2
V₂ = 300 mL (add 200 mL of water to the original 100 mL)
Example 2
You dilute 25 mL of a 12 M stock solution to a final volume of 500 mL. What is the new concentration?
Identify the values: M₁ = 12 M, V₁ = 25 mL, V₂ = 500 mL
Rearrange: M₂ = M₁V₁ / V₂ = (12 × 25) / 500
M₂ = 0.6 M
When to Use It
Use the dilution formula when adding solvent to an existing solution.
- Preparing dilute solutions from concentrated stock solutions
- Calculating how much water to add to achieve a target concentration
- Laboratory solution preparation
- The volumes must be in the same units (both mL or both L)