Household bleach is an aqueous solution of sodium hypochlorite (NaClO), and its concentration is often measured as a percent by weight. For example, concentrated household bleach has a concentration of 8.25% (w/w), which means there are 8.25 g of NaCl per every 100 g total of solution (NaClO water). For a kinetics experiment, 10 mL of a 5% (w/w) bleach solution was diluted in a 100 mL volumetric flask. 6 mL of this diluted solution is added to 6 mL of dye in a reaction vessel. What is the concentration of bleach (in M) in the reaction vessel

The correct answer is 0.033 M

Explanation:

We have a solution of NaClO with a concentration of 5%w/w:

5% w/w = 5 g NaClO/100 g solution

The first dilution is 10 ml of solution in 100 ml. That is a 1/10 dilution (10ml/100 ml = 1/10). That means we are diluting 10 times the solution. We can calculate the resulting concentration after this first dilution as follows:

5%w/w x 10 ml/100 ml = 5% w/w/10 = 0.5%w/w

Then, we take 6 ml of 0.5% w/w solution and we add 6 ml of dye in a reaction vessel. The total volume of the solution in the reaction vessel is 6 ml + 6 ml = 12 ml, and we are diluting twice the solution because 6 ml/12 ml = 1/2. We can calculate the resulting concentration of the solution after this second dilution as follows:

0.5% w/w x 6 ml/12 ml = 0.5% w/w/2 = 0.25%w/w

Finally, we need to convert the concentration from %w/w to M (mol solution/1L solution). For this, we assume a density of the solution close to the density of water (1.00 g/ml) and we use the molecular weight of NaClO (74.44 g/mol):

0.25 g NaClO/100 g solution x 1 mol NaClO/74.44 g x 1.00 g solution/1 ml x 100 ml/0.1 L = 0.033 mol/L

= 0.033 M