Which of the following correctly balances the half-reaction for the reduction of nitrate ion in acidic solution, including hydrogen atoms and charges?NO_3^- → NO_2

• A. NO_3^- + 2 e^- → NO_2 + 2 H^+
• B. NO_3^- + H_2O → NO_2 + 2 H^+ + e^-
• C. NO_3^- + H^+ → NO_2 + H_2O + e^-
• D. NO_3^- + 2 H^+ + e^- → NO_2 + H_2O

Answer: (D)

Verified step by step guidance

1. Identify the species involved in the half-reaction: nitrate ion (NO_3^-) is being reduced to nitrite (NO_2). Since the reaction occurs in acidic solution, H^+ ions and H_2O molecules may be used to balance hydrogen and oxygen atoms.
2. Balance all atoms except hydrogen and oxygen first. Here, nitrogen is already balanced with one atom on each side.
3. Balance oxygen atoms by adding H_2O molecules. NO_3^- has 3 oxygen atoms, and NO_2 has 2 oxygen atoms, so add one H_2O molecule to the product side to balance oxygen.
4. Balance hydrogen atoms by adding H^+ ions. Since one H_2O molecule was added on the product side, add 2 H^+ ions to the reactant side to balance the hydrogens.
5. Balance the charge by adding electrons (e^-). Calculate the total charge on each side and add electrons to the side that is more positive to make the charges equal. This will give the balanced half-reaction.