Formula & Calculator
Dilution Equation
Calculates how to dilute a concentrated stock solution to a desired lower concentration by conserving total moles of solute.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| C1 | Initial (stock) concentration | mol/L |
| V1 | Initial (stock) volume | L |
| C2 | Final (diluted) concentration | mol/L |
| V2 | Final (diluted) volume | L |
What it means
The dilution equation is derived from the conservation of moles of solute. When a stock solution of concentration C₁ and volume V₁ is diluted to a final volume V₂ with solvent, the final concentration C₂ is given by C₁ V₁ = C₂ V₂. This equation is fundamental in analytical chemistry for preparing working standards from concentrated reagents. It is also used in biological assays, pharmaceutical compounding, and environmental sample preparation. The equation assumes that the solute amount remains constant during dilution. In practice, volumetric flasks are used to achieve accurate final volumes. The dilution equation is also applied in serial dilutions, where each step uses the same ratio. Understanding this equation is crucial for accurate quantitative analysis and for minimising errors in experimental procedures.
Worked example
Dilution Equation – Two Examples
Real‑World| Parameter | Value |
|---|---|
| C₁ | 12 M |
| V₁ | 0.1 L |
| C₂ | 1 M |
| Parameter | Value |
|---|---|
| C₁ | 6 M |
| V₁ | 0.5 L |
| C₂ | 0.5 M |
Common mistakes
- Conservation of moles: The equation assumes moles of solute are conserved during dilution – no reaction or loss.
- Units: C₁V₁ = C₂V₂ works if both concentrations are in the same units and both volumes in the same units.
- Volume additivity: Assumes volumes are additive (ideal solution); for real solutions, slight deviations may occur.
- Stock solution: Use the concentrated solution as the source; ensure you mix thoroughly.
- Final volume: V₂ is the total volume after dilution, not the amount of solvent added.
Applications
The dilution equation, C₁V₁ = C₂V₂, expresses that the number of moles of solute is conserved when diluting a solution. It is used to prepare working solutions from concentrated stock solutions, a common task in laboratories, quality control, and industrial processes. Engineers and chemists apply this equation to achieve target concentrations for reactions, analytical standards, and process streams. The equation is also used in environmental chemistry to calculate dilution of effluent streams in water bodies. By using the dilution equation, professionals can accurately prepare solutions of any desired concentration, minimising waste and ensuring reproducibility. It is a fundamental skill in any chemistry‑related field.
- Preparation of dilute solutions from concentrated stock
- Calibration of analytical instruments
- Dilution of process streams in chemical plants
- Environmental dilution calculations for discharge permits
- Laboratory solution preparation and standardisation