A solution of 0.20 M NaOH is used to prepare 0.10 M NaOH. How much of the 0.20 M solution is needed to prepare 455 mL of the diluted NaOH?

Dilution is the process of reducing the concentration of solute in solution, which is accomplished by simply adding more solvent to the solution at the same amount of solute.

In a dilution the amount of solute does not change, but as more solvent is added, the concentration of the solute decreases, as the volume (and weight) of the solution increases.

A dilution is mathematically expressed as:

Ci×Vi = Cf×Vf

where

Ci: initial concentration
Vi: initial volume
Cf: final concentration
Vf: final volume

Initial volume

In this case, you know:

Ci= 0.20 M
Vi= ?
Cf= 0.10 M
Vf= 455 mL

Replacing in the definition of dilution:

0.20 M× Vi= 0.10 M× 455 mL

Solving:

(0.10 M× 455 mL)÷ 0.20 M= Vi

227.5 mL= Vi

In summary, 227.5 mL of the 0.20 M solution is needed to prepare 455 mL of the diluted NaOH.

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