Chemistry and laboratory
Dilution calculator (C1V1 = C2V2) and serial dilutions
Solve C1V1 = C2V2 for any value in molar, mass, percent or fold units, or plan a serial dilution series with transfer and diluent volumes.
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Result
- Stock volume V₁
- 25.0 mL
- Diluent to add (V₂ − V₁)
- 75.0 mL
- Dilution factor
- 1 : 4.00
Working
- C₁V₁ = C₂V₂
- V₁ = C₂ × V₂ ÷ C₁ = 0.5000 M × 100 mL ÷ 2.000 M = 25.0 mL
- Diluent = V₂ − V₁ = 100 mL − 25.0 mL = 75.0 mL
- Assumes volumes add (true for dilute aqueous solutions; mixing concentrated solutions such as ethanol and water can shrink the total).
- Rounded to 3 significant figures.
Method and limits
For one dilution, choose the unknown and enter the other three values; units can differ between fields as long as both concentrations are the same kind (both molar, both mass per volume, both % or both fold). For a series, enter the starting concentration, the factor per step and the tube volume.
C₁V₁ = C₂V₂ diluent = V₂ − V₁ dilution factor = C₁ ÷ C₂
The amount of solute is the same before and after adding solvent, so concentration times volume is conserved. In a serial dilution each tube is diluted by the same factor F from the previous one, so tube k holds C₀ ÷ Fᵏ.
Transfer = V ÷ F and diluent = V − V ÷ F (volume after mixing), or transfer = V ÷ (F − 1) and diluent = V (volume kept after passing on)
Limits
Volumes are assumed to add, which holds for dilute aqueous solutions; mixing concentrated solutions (ethanol and water, strong acids) can change the total volume and release heat. Always add concentrated acid to water. Answers keep the significant figures of the least precise number you enter (at least 3, at most 6); counts and coefficients are exact and do not limit precision.
Worked example
Diluting 2.00 M stock to 100 mL of 0.500 M: V₁ = 0.500 M × 100 mL ÷ 2.00 M = 25.0 mL of stock plus 75.0 mL of diluent (a 1 : 4 dilution). A 1:10 series of six 1 mL tubes from 100 µM: move 100 µL into 900 µL each time, giving 10, 1, 0.1 … 0.0001 µM.
References
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