Ferrous sulfate \(\left(\mathrm{FeSO}_{4}\right)\) is often used as a coagulant in water purification. The iron(II) salt is dissolved in the water to be purified, then oxidized to the iron(III) state by dissolved oxygen, at which time gelatinous \(\mathrm{Fe}(\mathrm{OH})_{3}\) forms, assuming the \(\mathrm{pH}\) is above approximately \(6 .\) Write balanced chemical equations for the oxidation of \(\mathrm{Fe}^{2+}\) to \(\mathrm{Fe}^{3+}\) by dissolved oxygen and for the formation of \(\mathrm{Fe}(\mathrm{OH})_{3}(s)\) by reaction of \(\mathrm{Fe}^{3+}(a q)\) with \(\mathrm{HCO}_{3}^{-}(a q)\).

First, we have to write a balanced equation for the oxidation of iron(II), which is represented as Fe²⁺, to iron(III), represented as Fe³⁺, by dissolved oxygen (O₂). In this process, the iron ions will lose one electron (e⁻) due to oxidation. To balance the equation, we must ensure that there are the same number of atoms of each element on both sides of the equation. Here is the balanced equation for the oxidation of Fe²⁺ to Fe³⁺ by dissolved oxygen: \(4 \ Fe^{2+} (aq) + O_{2} (aq) + 4 \ H^{+} (aq) \rightarrow 4 \ Fe^{3+} (aq) + 2 \ H_{2}O (l)\)

Now we need to write a balanced chemical equation for the formation of gelatinous Fe(OH)₃(s) from the reaction of Fe³⁺ with bicarbonate ions (HCO₃⁻). This dissolved iron(III) will react with the bicarbonate ions to form the precipitate Fe(OH)₃(s) and the gaseous carbon dioxide (CO₂). Here is the balanced equation for the formation of Fe(OH)₃(s) by the reaction of Fe³⁺ with HCO₃⁻: \(Fe^{3+} (aq) + 3 \ HCO_{3}^{-} (aq) \rightarrow Fe(OH)_{3} (s) + 3 \ CO_{2} \ (g) + 3 \ H^{+} (aq)\) In summary, the balanced equations for the water purification process using ferrous sulfate are: 1. The oxidation of iron(II) ions to iron(III) ions by dissolved oxygen: \(4 \ Fe^{2+} (aq) + O_{2} (aq) + 4 \ H^{+} (aq) \rightarrow 4 \ Fe^{3+} (aq) + 2 \ H_{2}O (l)\) 2. The formation of gelatinous iron(III) hydroxide precipitate by the reaction of iron(III) ions with bicarbonate ions: \(Fe^{3+} (aq) + 3 \ HCO_{3}^{-} (aq) \rightarrow Fe(OH)_{3} (s) + 3 \ CO_{2} \ (g) + 3 \ H^{+} (aq)\)