CalculateY
Quick Answer
Diluting 50 mL of a 2.0 M solution to 0.5 M requires a final volume of 200.00 mL (add 150.00 mL of solvent).
Common Examples
| Input | Result |
|---|---|
| C1 = 2.0 M, V1 = 50 mL, C2 = 0.5 M | V2 = 200.00 mL (add 150.00 mL solvent) |
| C1 = 6.0 M, V1 = 25 mL, C2 = 1.5 M | V2 = 100.00 mL (add 75.00 mL solvent) |
| C1 = 12.0 M, V1 = 10 mL, V2 = 500 mL | C2 = 0.24 M |
| C2 = 0.1 M, V2 = 250 mL, C1 = 1.0 M | V1 = 25.00 mL |
| V1 = 100 mL, C2 = 0.25 M, V2 = 400 mL | C1 = 1.00 M |
How It Works
This calculator uses the dilution equation:
C₁V₁ = C₂V₂
Where:
- C₁ = initial (stock) concentration
- V₁ = initial volume (amount of stock solution to use)
- C₂ = final (diluted) concentration
- V₂ = final total volume after dilution
The equation expresses conservation of solute: the amount of solute (concentration times volume) remains the same before and after dilution. Only the solvent volume changes.
Rearranged Forms
- V₂ = (C₁ x V₁) / C₂ (find final volume)
- C₂ = (C₁ x V₁) / V₂ (find final concentration)
- V₁ = (C₂ x V₂) / C₁ (find initial volume needed)
- C₁ = (C₂ x V₂) / V₁ (find initial concentration)
Solvent to Add
The amount of solvent (typically water) to add equals V₂ - V₁. This is the difference between the final and initial volumes.
Important Notes
This equation assumes that volumes are additive and that the solute does not significantly affect the total volume. It applies to most dilute aqueous solutions. For very concentrated solutions or solutions involving significant volume changes upon mixing, more precise methods may be needed.
The concentration units must be consistent (both in M, both in % w/v, etc.), and the volume units must also match (both in mL, both in L, etc.).
Worked Example
A laboratory needs to prepare 500 mL of 0.1 M HCl from a stock solution of 12.0 M HCl. How much stock solution is needed?
V₁ = (C₂ x V₂) / C₁ = (0.1 x 500) / 12.0 = 50 / 12 = 4.17 mL
So 4.17 mL of 12.0 M HCl is diluted to a total volume of 500 mL by adding 495.83 mL of water.