Final answer:
The correct reaction of hydrazine with the bromate ion to produce nitrogen gas and the bromide ion is represented by option a) 3N₂H₄ + 10BrO₃⁻ → 6N₂ + 5Br⁻ + 12H₂O, which is properly balanced.
Step-by-step explanation:
The reaction of hydrazine with the bromate ion to produce nitrogen gas and the bromide ion is a redox reaction. To find the correct balanced equation, we should examine each option given.
- Option a) 3N₂H₄ + 10BrO₃⁻ → 6N₂ + 5Br⁻ + 12H₂O: Nitrogen goes from N(+1) to N(0), and bromine goes from Br(+5) to Br(-1).
- Option b) 2N₂H₄ + 5BrO₃⁻ → 3N₂ + 5Br⁻ + 4H₂O: This equation is not balanced correctly.
- Option c) 4N₂H₄ + 5BrO₃⁻ → 8N₂ + 5Br⁻ + 6H₂O: This equation is also improperly balanced.
- Option d) 5N₂H₄ + 5BrO₃⁻ → 10N₂ + 5Br⁻ + 8H₂O: This equation does not correctly represent the stoichiometry of the reactants and products.
After reviewing each option, it can be seen that option a) correctly represents the balanced equation for the reaction between hydrazine and bromate ions, where the coefficients of reactants and products satisfy the law of conservation of mass and charge balance.