The formula
C₁ · V₁ = C₂ · V₂
| Symbol | Quantity | Unit |
|---|---|---|
| C₁ | Initial concentration | M |
| V₁ | Initial volume | ml |
| C₂ | Final concentration | M |
| V₂ | Final volume | ml |
What it means
Diluting adds solvent without adding solute, so the number of moles stays fixed. Concentration times volume gives that fixed amount, which is why the products on both sides must be equal.
How to work it out by hand
- Multiply the starting concentration by the starting volume
- Divide by the concentration you want
- The result is the final total volume, not the volume to add
What is worth knowing
The commonest slip is treating the answer as the volume of solvent to add: it is the final total. To get from 100 mL of 2 M to 0.5 M you need 400 mL in total, so you add 300 mL. The units only need to be consistent, not SI — millilitres on both sides work fine. And for concentrated acids the order matters for safety: always add acid to water, never the reverse, because the dilution releases heat and can spit if it goes the wrong way.