Which of the following reaction is an example of autoreduction?

\(Cu_2O + \frac{1}{2}Cu_2S \longrightarrow 3Cu + \frac{1}{2}SO_2\)

The correct answer is option 4. \(Cu_2O + \frac{1}{2}Cu_2S \longrightarrow 3Cu + \frac{1}{2}SO_2\).

Autoreduction, also known as self-reduction, is a type of reduction reaction where a substance is reduced by itself without the use of an external reducing agent. Let's analyze the given reactions:

1. \(Fe_3O_4 + 4CO \longrightarrow 3Fe + 4CO_2\)
This reaction involves the reduction of iron(II, III) oxide (\(Fe_3O_4\)) to iron (\(Fe\)) using carbon monoxide (\(CO\)) as a reducing agent. It is not an example of autoreduction.

2. \(Cu_2O + C \longrightarrow 2Cu + CO\)
This is the reduction of copper(I) oxide (\(Cu_2O\)) to copper (\(Cu\)) by carbon (\(C\)). It is an example of autoreduction because carbon is acting as a self-reducing agent.

3. \(Cu^{2+}(aq) + Fe(s) \longrightarrow Cu + Fe^{3+}(aq)\)
This is a redox reaction, but it involves the transfer of electrons from iron (\(Fe\)) to copper ions (\(Cu^{2+}\)). It is not an example of autoreduction.

4. \(Cu_2O + \frac{1}{2}Cu_2S \longrightarrow 3Cu + \frac{1}{2}SO_2\)
This reaction involves the reduction of copper(I) oxide (\(Cu_2O\)) and copper(I) sulfide (\(\frac{1}{2}Cu_2S\)) to copper (\(Cu\)) with the formation of sulfur dioxide (\(SO_2\)). It is an example of autoreduction because copper is acting as a self-reducing agent.

Therefore, the correct answer is: (4) \(Cu_2O + \frac{1}{2}Cu_2S \longrightarrow 3Cu + \frac{1}{2}SO_2\)