In basic medium, H$$_2$$O$$_2$$ exhibits which of the following reactions?
(A) Mn$$^{2+} \rightarrow$$ Mn$$^{4+}$$
(B) I$$_2 \rightarrow$$ I$$^-$$
(C) PbS $$\rightarrow$$ PbSO$$_4$$
Choose the most appropriate answer from the options below :

In basic medium, $$\text{H}_2\text{O}_2$$ can act as both an oxidising agent (getting reduced to $$\text{OH}^-$$) and a reducing agent (getting oxidised to $$\text{O}_2$$). The relevant half-reactions in basic medium are:

As an oxidising agent: $$\text{H}_2\text{O}_2 + 2e^- \rightarrow 2\text{OH}^-$$

As a reducing agent: $$\text{H}_2\text{O}_2 \rightarrow \text{O}_2 + 2\text{H}^+ + 2e^-$$ (in basic medium, $$\text{H}^+$$ ions combine with $$\text{OH}^-$$, so this becomes $$\text{H}_2\text{O}_2 + 2\text{OH}^- \rightarrow \text{O}_2 + 2\text{H}_2\text{O} + 2e^-$$).

(A) $$\text{Mn}^{2+} \rightarrow \text{Mn}^{4+}$$: Manganese is oxidised from +2 to +4. Here $$\text{H}_2\text{O}_2$$ acts as the oxidising agent. In basic medium, $$\text{Mn}^{2+}$$ reacts with $$\text{H}_2\text{O}_2$$ and $$\text{OH}^-$$ to form $$\text{MnO}_2$$ (which contains $$\text{Mn}^{4+}$$). The half-reaction for Mn is: $$\text{Mn}^{2+} \rightarrow \text{MnO}_2 + 2e^-$$. The $$\text{H}_2\text{O}_2$$ provides the oxidising power by accepting these electrons. This reaction is feasible in basic medium.

(B) $$\text{I}_2 \rightarrow \text{I}^-$$: Iodine is reduced from 0 to $$-1$$. For this reduction, something must supply electrons to $$\text{I}_2$$. Here $$\text{H}_2\text{O}_2$$ acts as the reducing agent, getting oxidised to $$\text{O}_2$$. The half-reactions are: $$\text{I}_2 + 2e^- \rightarrow 2\text{I}^-$$ and $$\text{H}_2\text{O}_2 + 2\text{OH}^- \rightarrow \text{O}_2 + 2\text{H}_2\text{O} + 2e^-$$. In basic medium, the reducing power of $$\text{H}_2\text{O}_2$$ is enhanced by $$\text{OH}^-$$, making this reaction feasible.

(C) $$\text{PbS} \rightarrow \text{PbSO}_4$$: Here sulfur must be oxidised from $$-2$$ in $$\text{PbS}$$ to $$+6$$ in $$\text{PbSO}_4$$. This is an 8-electron change per sulfur atom, requiring an extremely strong oxidising agent. The standard electrode potential of $$\text{H}_2\text{O}_2$$ as an oxidiser is not sufficient to drive such a large change, even in basic medium. Concentrated $$\text{HNO}_3$$ or similar powerful oxidisers are needed for this transformation. Therefore, this reaction is not feasible with $$\text{H}_2\text{O}_2$$ in basic medium.

Since reactions (A) and (B) are feasible but (C) is not, the correct answer is Option D: (A), (B) only.