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Chemistry and workshop

Dilute a solution

How much concentrated solution and how much water you need to lower a concentration (C1·V1 = C2·V2).

That of the concentrated solution, in any unit (% v/v, % w/v, g/L…), the same as the target.

In the same unit as the initial one. It must be lower.

L

Volume of diluted solution you want to obtain. 1 mL = 0.001 L.

Result

Concentrated solution to measure
— L
Water or diluent (approximate: fill up to the final volume)
— L
Dilution factor (times)
—

How it is calculated

The amount of solute does not change when water is added, so C1 × V1 = C2 × V2. Solving: V1 = C2 × V2 ÷ C1, and the water is V2 − V1.

Example: 70 % alcohol from 96 % alcohol, 1 L final. V1 = 70 × 1 ÷ 96 = 0.729 L of 96 % alcohol; water ≈ 1 − 0.729 = 0.271 L.

Example: 5 L of a 1 % solution from a 10 % one. V1 = 1 × 5 ÷ 10 = 0.5 L; water = 4.5 L. The dilution factor is 10 ÷ 1 = 10 times.

Recommended method: measure V1 in a graduated cylinder or marked container and add water up to the final-volume mark, instead of adding the two volumes separately.

Keep in mind

  • Both concentrations must be in the same unit. Do not mix % v/v (volume) with % w/w (weight): alcohol is sold in % v/v and the calculation is valid in that unit.
  • Ethanol and water contract when mixed: 0.729 L of 96 % alcohol plus 0.271 L of water give slightly less than 1 L, and the strength ends up slightly above 70 %. Filling up to the final volume corrects this; if the strength matters, measure it with an alcoholmeter at 20 °C.
  • With concentrated acids, always add the acid to the water, little by little and stirring, never water to acid: the heat of dilution can boil the water and spatter acid. Goggles, gloves and a heat-resistant container.
  • Do not mix bleach (hypochlorite) with acids (hydrochloric acid, vinegar) or with ammonia: they release chlorine or chloramines, toxic gases.
  • To dilute more than 100 times it is more accurate to do it in two steps (for example, 1:10 and then 1:10 again) than to measure a very small volume.

See also

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