We’re being asked to determine the percentage composition by mass of NaClO in the bleach product.

Recall the **mass percent formula**:

$\overline{){\mathbf{\%}}{\mathbf{}}{\mathbf{mass}}{\mathbf{=}}\frac{\mathbf{mass}\mathbf{}\mathbf{component}}{\mathbf{total}\mathbf{}\mathbf{mass}}{\mathbf{\times}}{\mathbf{100}}}$

$\mathbf{mole}\mathbf{}{\mathbf{I}}_{\mathbf{2}}\mathbf{=}\mathbf{moles}\mathbf{}\mathbf{NaClO}\mathbf{=}\mathbf{45}\mathbf{}\overline{)\mathbf{mL}\mathbf{}{\mathbf{Na}}_{\mathbf{2}}{\mathbf{S}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{3}}}\mathbf{\left(}\frac{{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\mathbf{}\overline{)\mathbf{L}}}{\mathbf{1}\mathbf{}\overline{)\mathbf{mL}}}\mathbf{\right)}\mathbf{(}\mathbf{0}\mathbf{.}\mathbf{390}\frac{\overline{)\mathbf{mol}\mathbf{}{\mathbf{Na}}_{\mathbf{2}}{\mathbf{S}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{3}}}}{\overline{)\mathbf{L}\mathbf{}{\mathbf{Na}}_{\mathbf{2}}{\mathbf{S}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{3}}}}\mathbf{)}\mathbf{\left(}\frac{\mathbf{1}\mathbf{}\mathbf{mol}\mathbf{}\mathbf{NaClO}}{\mathbf{2}\overline{)\mathbf{}\mathbf{mol}\mathbf{}{\mathbf{Na}}_{\mathbf{2}}{\mathbf{S}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{3}}}}\mathbf{\right)}\mathbf{=}$**0.008775 mol **

A sample of a new cleaning product, "Joe's Famous Cleaner," with a mass of 64.0 g, was diluted with an acetic acid solution containing excess I^{-}.^{ }A small amount of starch indicator solution was then added turning the solution a deep bluish-purple. The solution was then titrated with 0.390 M sodium thiosulfate, Na_{2}S_{2}O_{3}, containing the ion S_{2}O_{3}^{2-.} A volume of 45.0 mL of sodium thiosulfate, the titrant, was needed to turn the solution colorless.

What is the percentage composition by mass of NaClO in the bleach product?

Express your answer to three significant figures and include the appropriate units.