Final answer:
The balanced half-reaction for the reduction of gaseous nitrogen (N2) to aqueous hydrazine (N2H4) in an acidic solution is N2(g) + 4 H+(aq) + 4 e- → N2H4(aq). This reaction demonstrates the balance of both the number of atoms and the overall charge in a redox process.
Step-by-step explanation:
To balance the half-reaction for the reduction of gaseous nitrogen (N₂) to aqueous hydrazine (N₂H₄) in an acidic aqueous solution, we need to ensure that the number of nitrogen atoms and the overall charge is balanced on both sides of the reaction. The initial, unbalanced half-reaction is:
N₂(g) + H₂(g) → N₂H₄(aq)
First, we balance the nitrogen atoms by noting that there are still two nitrogen atoms present on both sides of the equation, so no change is needed here.
Then, to balance hydrogen atoms, we add 4 H⁺ ions to the right side:
N₂(g) + H⁺(aq) → N₂H₄(aq)
To balance the charge, we need to add electrons to the side with a positive charge. Since we have added four protons (4 H⁺ ions) on the right side, we must balance the charge by adding 4 electrons to the left side:
N₂(g) + 4 H⁺(aq) + 4 e⁻ → N₂H₄(aq)
All atoms and the charge are now balanced, making this the correct reduced half-reaction for the reduction of nitrogen to hydrazine in acidic solution.