Library / Foundations: Chemistry / FCH-15
Foundations: Chemistry
Dilution
Concentration after adding solvent to a stock solution.
- Ref
- FCH-15
- Rev
- v1
- Field
- Foundations: Chemistry
- Result
- c₂ [mol/dm³]
The amount of solute stays the same, so c₁V₁ = c₂V₂. V₂ is the final volume (not the volume of water added). Both volumes must use the same unit.
Adding water does not change how much solute you have; it just spreads it through more volume.
Calculator
- Dilution factor10
- Water to add225 cm³
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- Tenfold dilution: take 25 cm³ and make up to 250 cm³.
- Serial dilutions repeat the same factor and multiply, so three tenfold steps give a 1000-fold dilution.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (mol/dm³) | Local step | Change in result |
|---|---|---|---|---|---|---|
| V₂ Final volume | 1 to 5,000 cm³ | 0.01 | 50 | 49.99 | +10% | −9.09 % |
| V₁ Volume of stock | 0.1 to 1,000 cm³ | 8e-4 | 8 | 7.999 | +10% | +10 % |
| c₁ Initial concentration | 0.001 to 20 mol/dm³ | 1e-4 | 2 | 2 | +10% | +10 % |
Sweep of Final volume
| Final volume (cm³) | Final concentration (mol/dm³) |
|---|---|
| 1 | 50 |
| 2.9 | 17.24 |
| 8.409 | 5.946 |
| 24.38 | 2.05 |
| 70.71 | 0.7071 |
| 205 | 0.2438 |
| 594.6 | 0.08409 |
| 1,724 | 0.029 |
| 5,000 | 0.01 |
Sweep one variable
Variables and how each one contributes
Final concentration
What the equation gives you. Everything else feeds it.
Initial concentration
Stock concentration. Directly proportional.
Volume of stock
Volume of stock solution taken. Directly proportional.
Final volume
Total volume after dilution. Inversely proportional.
Worked example with the values above
- Moles of solute: 2 × 25 = 50 mmol (unchanged).
- Final volume: 250 cm³.
- c₂ = 50 / 250 = 0.2 mol/dm³.
Assumptions and limits
- Solute does not react or evaporate.
- Volumes are additive.
Common mistakes
- Using the volume of water added for V₂.
- Mixing cm³ and dm³ on the two sides.
Statistics and uncertainty
Pipette errors (±0.06 cm³ on 25 cm³, 0.24%) carry through each step of a serial dilution.
Where it is used
- Preparing working solutions.
- Calibration standards.
Maths you need
- Concentration: mol/dm³
- Ratios: dilution factor