Step 1: Understanding the Oxidizing Nature of KMnO\(_4\)
- In an acidic medium, KMnO\(_4\) is a strong oxidizing agent.
- In a neutral medium, its oxidizing power decreases but still oxidizes some species.
Step 2: Oxidation Reactions in Neutral Medium
- KMnO\(_4\) oxidizes I\(^-\) to IO\(_3^-\) in neutral medium:
\[
2MnO_4^- + I^- + H_2O \rightarrow IO_3^- + MnO_2 + OH^-
\]
- Other reactions:
- Oxidation of oxalate ion occurs in acidic medium.
- Precipitation of sulfur from \( H_2S \) occurs in acidic medium.
- Fe\(^{2+}\) to Fe\(^{3+}\) oxidation occurs in acidic medium.
Thus, the correct answer is \(Oxidation of iodide to iodate\).