One test for vitamin $\mathrm{C}$ (ascorbic acid, $\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6}$ ) is based on the reaction of the vitamin with iodine:
$$
\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6}(a q)+\mathrm{I}_{2}(a q) \longrightarrow \mathrm{C}_{6} \mathrm{H}_{6} \mathrm{O}_{6}(a q)+2 \mathrm{HI}(a q)
$$
(a) A $25.0 \mathrm{~mL}$ sample of a fruit juice requires $13.0 \mathrm{~mL}$ of $0.0100 M \mathrm{I}_{2}$ solution for reaction. How many moles of ascorbic acid are in the sample?
(b) What is the molarity of ascorbic acid in the fruit juice?
(c) The Food and Drug Administration recommends that $60 \mathrm{mg}$ of ascorbic acid be consumed per day. How many milliliters of the fruit juice in part (a) must a person drink to obtain the recommended dosage?