Final answer:
To balance the given half-reactions, analyze each option and determine which one has an equal number of atoms and charge on both sides of the reaction.
Step-by-step explanation:
To balance the given half-reactions, we need to balance the number of atoms and the charge. Let's analyze each option:
a. MnO₄- + 2H₂O = MnO₂ + 4OH-
b. MnO₄- + H₂O = MnO₂ + 2OH-
c. MnO₄- + 3H₂O = MnO₂ + 2OH-
d. 2MnO₄- + 4H₂O = 2MnO₂ + 8OH-
From the given options, option d is the correct balanced half-reaction for atoms and charge. Both sides of the reaction have the same number of atoms and the same charge. Therefore, the correct answer is d.