C: 0.012 mol.
Start with 0.0020 moles of iodate ions [tex]{\text{IO}_{3}}^{-}[/tex].
How many moles of iodine [tex]\text{I}_2[/tex] will be produced?
[tex]{\text{IO}_{3}}^{-}[/tex] converts to [tex]\text{I}_2[/tex] in the first reaction. The coefficient in front of [tex]\text{I}_2[/tex] is three times the coefficient in front of [tex]{\text{IO}_{3}}^{-}[/tex]. In other words, each mole of [tex]{\text{IO}_{3}}^{-}[/tex] will produce three moles of [tex]\text{I}_2[/tex]. 0.0020 moles of [tex]{\text{IO}_{3}}^{-}[/tex] will convert to 0.0060 moles of [tex]\text{I}_2[/tex].
How many moles of thiosulfate ions [tex]{\text{S}_2\text{O}_3}^{2-}[/tex] are required?
[tex]\text{I}_2[/tex] reacts with [tex]{\text{S}_2\text{O}_3}^{2-}[/tex] in the second reaction. The coefficient in front of [tex]\text{I}_2[/tex] is twice the coefficient in front of [tex]{\text{S}_2\text{O}_3}^{2-}[/tex]. How many moles of [tex]{\text{S}_2\text{O}_3}^{2-}[/tex] does each mole of [tex]\text{I}_2[/tex] consume? Two. 0.0060 moles of [tex]\text{I}_2[/tex] will be produced. As a result, [tex]2 \times 0.0060 = 0.0120[/tex] moles of [tex]{\text{S}_2\text{O}_3}^{2-}[/tex] will be needed.