Here's how to determine the number of electrons involved in the reduction of nitrate ion (NO₃⁻) to hydrazine (N₂H₄):

1. Write the Half-Reaction:

The balanced half-reaction for the reduction of nitrate ion to hydrazine in acidic solution is:

NO₃⁻(aq) + 8H⁺(aq) + 8e⁻ → N₂H₄(aq) + 3H₂O(l)

2. Identify the Electron Transfer:

Notice that the nitrate ion (NO₃⁻) gains 8 electrons to become hydrazine (N₂H₄).

3. The Answer:

Therefore, 8 electrons are involved in the reduction of nitrate ion to hydrazine.