To answer the question about how \(KMnO_4\) oxidizes \(I^{{-}}\) in different solutions, we need to consider the chemical reactions involved.
When \(KMnO_4\) is used as an oxidizing agent in an acidic medium, it reduces to \(Mn^{2+}\) ions and oxidizes iodide ions \((I^{-})\) to iodine \((I_2)\). The reaction can be expressed as:
\(2KMnO_4 + 10I^{-} + 16H^{+} \rightarrow 2Mn^{2+} + 5I_2 + 8H_2O + 2K^+\)
Thus, in acidic solution, iodide is oxidized to \(I_2\) (iodine).
In neutral or faintly alkaline conditions, \(KMnO_4\) oxidizes \(I^{-}\) to iodate, \(IO_3^{-}\):
\(2KMnO_4 + I^{-} + H_2O \rightarrow 2MnO_2 + IO_3^{-} + 2K^+ + 2OH^{-}\)
Here, \(I^{-}\) is oxidized to \(IO_3^{-}\) in neutral or faintly alkaline medium.
Thus, \(KMnO_4\) oxidizes \(I^{-}\) to different products in different solutions:
Based on the explanation above, the correct answer is \(I_2\) & \(IO_3^{-}\), which corresponds to the option "I2 & IO3-".