Final answer:
To balance a redox reaction involving UO2²+ and NO₃⁻ in an acidic environment, the half-reactions are first written and then balanced for mass and charge, where electrons are added to compensate for changes in oxidation states. These half-reactions are then combined to give a balanced equation.
Step-by-step explanation:
To balance the redox equation where uranyl ion (UO2²+) reacts with nitrate ion (NO₃⁻) in an acidic solution, we need to first write the half-reactions for the oxidation and reduction processes that describe the change in oxidation states of the reactants going to the products.
For the given unbalanced redox reaction:
UO2²+ + NO₃⁻ → U + N2
We start by balancing each half-reaction separately:
- For the uranium from UO2²+ to U:
UO2²+ → U + 2e⁻ (reduction) - For nitrogen from NO₃⁻ to N2:
NO₃⁻ + 4H+ + 3e⁻ → N2 + 2H2O (reduction)
Balance the electrons by multiplying the uranium half-reaction by 3 and the nitrogen half-reaction by 2. Combine the reactions, which gives the balanced redox equation in an acidic solution:
3UO2²+ + 2NO₃⁻ + 8H+ → 3U + N2 + 4H2O
Note that balancing redox reactions requires ensuring mass and charge are balanced in both halves and that the total number of electrons lost in the oxidation half-reaction equals the number of electrons gained in the reduction half-reaction. The balanced redox equation reflects the mass and charge balance.