To determine the overall change in the oxidation number of manganese in the reaction between potassium permanganate (\(KMnO_4\)) and oxalic acid in acidic medium, we need to analyze the redox reaction that occurs.
In this redox reaction, potassium permanganate (\(KMnO_4\)) acts as an oxidizing agent. The manganese in \(KMnO_4\) has an oxidation state of +7. During the reaction, the manganese is reduced, and its oxidation state changes.
The reaction in acidic medium can be represented as follows:
2 KMnO_4 + 5 H_2C_2O_4 + 6 H^+ \rightarrow 2 Mn^{2+} + 10 CO_2 + 8 H_2O + 2 K^+
In this reaction, the manganese (\(Mn\)) in \(KMnO_4\) is reduced from an oxidation state of +7 to an oxidation state of +2 in \(Mn^{2+}\).
The change in oxidation state for manganese is calculated as follows:
Thus, the overall change in the oxidation number of manganese in the reaction is 5.
The correct answer is, therefore, 5.
This process illustrates a typical redox reaction in acidic medium where \(KMnO_4\) is a common laboratory reagent, often used due to its strong oxidizing properties.