Step 1: Understand Redox Reactions
A redox reaction is a type of chemical reaction in which the oxidation states of atoms are changed. Oxidation involves the loss of electrons, and reduction involves the gain of electrons.
Step 2: Identify the Redox Reaction
- In option (1), \( \text{H}_2 + \text{Cl}_2 \rightarrow 2 \text{HCl} \), hydrogen (\( \text{H}_2 \)) is oxidized, and chlorine (\( \text{Cl}_2 \)) is reduced. This is a redox reaction.
- In option (2), \( \text{NaCl} + \text{AgNO}_3 \rightarrow \text{NaNO}_3 + \text{AgCl} \), there is no change in oxidation states; this is a double displacement reaction, not a redox reaction.
- In option (3), \( \text{C}_2 \text{H}_5 \text{OH} + \text{O}_2 \rightarrow 2 \text{H}_2 \text{O} \), there is no clear change in oxidation states.
- In option (4), \( \text{H}_2 + \text{O}_2 \rightarrow 2 \text{H}_2 \text{O} \), oxygen is reduced, but hydrogen is not oxidized.
Answer: The correct answer is option (1): \( \text{H}_2 + \text{Cl}_2 \rightarrow 2 \text{HCl} \).