The balanced chemical equation for the reaction of hydrazine (N₂H₄) and hydrogen peroxide (H₂O₂) to produce nitrogen gas (N₂) and water (H₂O) is:

N₂H₄ + 2 H₂O₂ → N₂ + 4 H₂O

Therefore, the coefficients for the reaction are:

* 1 for N₂H₄ (hydrazine)

* 2 for H₂O₂ (hydrogen peroxide)

* 1 for N₂ (nitrogen gas)

* 4 for H₂O (water)