Methylbromide, $\mathrm{CH}_{3} \mathrm{Br}$, is used in agriculture to fumigate soil to rid it of pests such as nematodes. It is injected directly into the soil, but over time it has a tendency to escape before it can undergo natural degradation to innocuous products. Soil chemists have found that ammonium thiosulfate, $\left(\mathrm{NH}_{4}\right)_{2} \mathrm{~S}_{2} \mathrm{O}_{3}$, a nitrogen and sulfur fertilizer, drastically reduces methylbromide emissions by causing it to degrade. In a chemical analysis to determine the purity of a batch of commercial ammonium thiosulfate, a chemist first prepared a standard solution of iodine following the procedure in Problem 5.91. First, $0.462 \mathrm{~g}$ $\mathrm{KIO}_{3}$ was dissolved in water to make $125 \mathrm{~mL}$ of solution. The solution was made acidic and treated with excess potassium iodide, which caused the following reaction to take place:
$$
\mathrm{IO}_{3}^{-}+8 \mathrm{I}^{-}+6 \mathrm{H}^{+} \longrightarrow 3 \mathrm{I}_{3}^{-}+3 \mathrm{H}_{2} \mathrm{O}
$$
The solution containing the $\mathrm{I}_{3}^{-}$ ion was then diluted to exactly $250.0 \mathrm{~mL}$ in a volumetric flask. Next, the chemist dissolved $0.2180 \mathrm{~g}$ of the fertilizer in water, added starch indicator, and titrated it with the standard $\mathrm{I}_{3}^{-}$ solution. The reaction was
$$
2 \mathrm{~S}_{2} \mathrm{O}_{3}^{2-}+\mathrm{I}_{3}^{-} \longrightarrow \mathrm{S}_{4} \mathrm{O}_{6}^{2-}+3 \mathrm{I}^{-}
$$
The titration required $27.99 \mathrm{~mL}$ of the $\mathrm{I}_{3}^{-}$ solution.
(a) What was the molarity of the $\mathrm{I}_{3}^{-}$ solution used in the titration?
(b) How many grams of $\left(\mathrm{NH}_{4}\right)_{2} \mathrm{~S}_{2} \mathrm{O}_{3}$ were in the fertilizer sample?
(c) What was the percentage by mass of $\left(\mathrm{NH}_{4}\right)_{2} \mathrm{~S}_{2} \mathrm{O}_{3}$ in the fertilizer?