Dilution
Leave exactly one field blank — it will be solved
Uses the conservation of moles, M₁V₁ = M₂V₂. Methodology & sources →
Need more practice? The General Chemistry Workbook covers dilution and solution stoichiometry with worked examples and a full answer key.As an Amazon Associate we earn from qualifying purchases.
View on Amazon →How Dilution Works
When you dilute a solution you add more solvent but the amount of solute (in moles) stays the same. Because moles = concentration × volume, the product M × V is conserved:
Subscript 1 is the concentrated stock; subscript 2 is the diluted solution. Rearrange to solve for whichever value you are missing. To find how much solvent to add, subtract the stock volume from the final volume. Make a solution from scratch instead with the Molarity Calculator.
Worked Example — Diluting a Stock Solution
Question: What volume of 6.00 M HCl stock is needed to prepare 500.0 mL of 0.150 M HCl?
Step 1 — identify the two states: stock (concentrated) is state 1, the diluted solution is state 2. M₁ = 6.00 M, M₂ = 0.150 M, V₂ = 500.0 mL.
Step 2 — rearrange M₁V₁ = M₂V₂: V₁ = (M₂V₂) ÷ M₁ = (0.150 × 500.0) ÷ 6.00
Step 3 — calculate: V₁ = 12.5 mL
Procedure: measure 12.5 mL of the 6.00 M stock, then add water until the total volume reaches 500.0 mL — do not simply add 500.0 mL of water to the 12.5 mL.
Answer: 12.5 mL of stock solution.
Common Mistakes
- "Dilute to" vs. "dilute by." "Dilute to 500 mL" means the final volume is 500 mL. "Dilute by adding 500 mL of water" gives a different, larger final volume. M₁V₁ = M₂V₂ uses the final total volume.
- Mixing up subscripts. Subscript 1 is always the concentrated stock you start from; subscript 2 is the dilute solution you want. Swapping them inverts the answer.
- Units must match for each pair. M₁ and M₂ must use the same concentration unit, and V₁ and V₂ must use the same volume unit — but concentration units don't need to match volume units.
Frequently Asked Questions
M₁V₁ = M₂V₂. The concentration × volume of the stock equals the concentration × volume of the diluted solution, because the moles of solute do not change.
Find the final volume V₂, then subtract the stock volume V₁. The calculator shows this as "solvent to add".
It means the final, total volume of the solution after adding solvent is 500 mL — not that you add 500 mL of solvent. You add solvent until the combined volume reaches the mark on a volumetric flask.
Yes. The relationship holds for any concentration unit as long as the same unit is used on both sides for concentration, and the same volume unit is used on both sides for volume — for example, C1V1 = C2V2 works for percent (w/v) concentrations the same way it does for molarity.