The amount of sodium hypochlorite in a bleach solution can be determined by
using a given volume of bleach to oxidize excess iodide ion to iodine, because
the reaction goes to completion. The amount of iodine produced is then
determined by titration with sodium thiosulfate, \(\mathrm{Na}_{2}
\mathrm{~S}_{2} \mathrm{O}_{3},\) which is oxidized to sodium tetrathionate,
\(\mathrm{Na}_{2} \mathrm{~S}_{4} \mathrm{O}_{6} .\) Potassium iodide was added
in excess to \(5.00 \mathrm{~mL}\) of bleach (density \(=1.00 \mathrm{~g} /
\mathrm{mL}\) ). This solution, containing the iodine released in the reaction,
was titrated with \(0.100 \mathrm{M} \mathrm{Na}_{2} \mathrm{~S}_{2}
\mathrm{O}_{3}\). If \(34.6 \mathrm{~mL}\) of
sodium thiosulfate was required to reach the endpoint (detected by
disappearance of the blue color of the starch-iodine complex), what was the
mass percentage of \(\mathrm{NaClO}\) in the bleach?