Problem 58 - Chemistry: The Central Science

Question

Write complete balanced half-reactions for (a) reduction of nitrate ion to \(\mathrm{NO}\) in acidic solution, (b) oxidation of \(\mathrm{HNO}_{2}\) to \(\mathrm{NO}_{2}\) in acidic solution.

Step-by-Step Solution

Answer

The short answers for the complete balanced half-reactions are: (a) Reduction of nitrate ion to NO in acidic solution: \(NO_3^- + 4H^+ + 3e^- → NO + 2H_2O\) (b) Oxidation of HNO₂ to NO₂ in acidic solution: \(HNO_2 → NO_2 + H^+ + e^-\)

Step 1: (a) Reduction of nitrate ion to NO in acidic solution

1. Write the unbalanced half-reaction: NO₃⁻ → NO 2. Balance the atoms other than oxygen and hydrogen: In this case, the nitrogen atoms are already balanced. 3. Balance the oxygen atoms by adding water molecules: Since there are 3 oxygen atoms in the reactant and only 1 in the product, we need to add 2 water molecules to the product side: NO₃⁻ → NO + 2H₂O 4. Balance hydrogen atoms by adding H⁺ ions: Since we have 4 hydrogen atoms on the product side, we need to add 4 H⁺ ions to the reactant side: NO₃⁻ + 4H⁺ → NO + 2H₂O 5. Balance the charges by adding electrons: The overall charge on the reactant side is 1⁻ + 4⁺ = 3⁺, while the overall charge on the product side is 0. Therefore, we need to add 3 electrons to the reactant side to balance the charges: NO₃⁻ + 4H⁺ + 3e⁻ → NO + 2H₂O Finally, the balanced half-reaction for the reduction of nitrate ion to NO in acidic solution is: \(NO_3^- + 4H^+ + 3e^- → NO + 2H_2O\).

Step 2: (b) Oxidation of HNO₂ to NO₂ in acidic solution

1. Write the unbalanced half-reaction: HNO₂ → NO₂ 2. Balance the atoms other than oxygen and hydrogen: In this case, the nitrogen atoms are already balanced. 3. Balance the oxygen atoms by adding water molecules: There are 2 oxygen atoms on both the reactant and the product, so no water molecules need to be added. 4. Balance hydrogen atoms by adding H⁺ ions: Since we have 1 hydrogen atom in the reactant and none in the product, we need to add 1 H⁺ ion to the product side: HNO₂ → NO₂ + H⁺ 5. Balance the charges by adding electrons: The overall charge on the reactant side is 0, while the overall charge on the product side is 1⁺. Therefore, we need to add 1 electron to the product side to balance the charges: HNO₂ → NO₂ + H⁺ + e⁻ Finally, the balanced half-reaction for the oxidation of HNO₂ to NO₂ in acidic solution is: \(HNO_2 → NO_2 + H^+ + e^-\).