Final answer:
The balanced half-reaction for the reduction of nitrate to nitrogen dioxide in basic solution is: NO₃⁻(aq) + 2H₂O(l) + 2e⁻ → NO₂(g) + 4OH⁻(aq).
Step-by-step explanation:
The balanced half-reaction for the reduction of nitrate ion (NO₃⁻) to nitrogen dioxide (NO₂) in basic aqueous solution is shown below.
NO₃⁻(aq) + 2H₂O(l) + 2e⁻ → NO₂(g) + 4OH⁻(aq)
In this reduction process, water (H₂O) is added to balance the oxygen atoms, hydroxide ions (OH⁻) are added to balance the hydrogen atoms and charge in the basic solution, and electrons (e⁻) are added to balance the overall charge. The balanced half-reaction includes the physical state symbols for the aqueous solutions, gas, and liquid involved in the reaction.