Dilution Equation M₁V₁ = M₂V₂: How to Dilute
Use M₁V₁ = M₂V₂ to find how much stock solution to use, then add water to the final volume, with two worked chemistry examples.
The equation
- M₁V₁ = M₂V₂
1 = concentrated stock, 2 = diluted solution.
How to use it
- Know three of the four values
- Solve for the missing one
- Use the same volume units on both sides
Moles of solute stay the same when you add water.
Example 1
How many mL of 6.0 M HCl make 250 mL of 1.5 M HCl?
- V₁ = M₂V₂ / M₁
- = (1.5)(250) / 6.0
V₁ = 62.5 mL
Example 2
You dilute 50 mL of 2.0 M NaCl to 200 mL. What is the new molarity?
- M₂ = M₁V₁ / V₂
- = (2.0)(50) / 200
M₂ = 0.50 M
Common mistake
Add 250 mL of water to the stock
V₂ is the final total volume, not the water you add.
Water added = V₂ − V₁ (here 250 − 62.5 = 187.5 mL).
Add acid to water, not water to acid.
Want more Chemistry practice?
The free Chemistry study guide has quizzes, flashcards and practice exams. 100% free, no sign-up needed.
Open the Chemistry guide