Suppose you were preparing 1.0 L of a bleaching solution in a volumetric flask, and it calls for 0.21 mol of NaOCl. If all you had available was a jug of bleach that contained 0.82 M NaOCl, what volume of bleach would you need to add to the volumetric flask before you added enough water to reach the 1.0 L line?

V₁ = 0.26 L

Explanation:

The final solution requires 0.21 moles in V₂ = 1.0 L, which means a concentration of C₂ = 0.21 mol / 1.0 L = 0.21 M. The concentration of the initial solution is C₁ = 0.82 M. We can find the volume V₁ required using the dilution rule.

C₁ * V₁ = C₂ * V₂

0.82 M * V₁ = 0.21 M * 1.0 L

V₁ = 0.26 L

0.256 L

Explanation:

We should use the following formula:

concentration (1) * volume (1) = concentration (2) * volume (2)

concentration (1) = 0.82 M NaOCl

volume (1) = ?

concentration (2) = 0.21 M NaOCl

volume (2) = 1 L

volume (1) = [concentration (2) * volume (2) ] / concentration (1)

volume (1) = [0.21 / 1] / 0.82 = 0.256 L