To identify which of the given reactions is a half-reaction, we need to understand what constitutes a half-reaction. A half-reaction is a part of the redox (reduction-oxidation) process and can be either an oxidation half-reaction or a reduction half-reaction.
In a half-reaction:
- An oxidation half-reaction involves the loss of electrons.
- A reduction half-reaction involves the gain of electrons.
Let's analyze each option:
- \(Zn + Cu^{2+} \rightarrow Zn^{2+} + Cu\): This is a full redox reaction composed of both oxidation and reduction. Zinc oxidizes while copper reduces, so this is not a half-reaction.
- \(H^{+} + OH^{-} \rightarrow H_2O\): This is a neutralization reaction between an acid and a base, forming water. It is not a redox reaction, hence not a half-reaction.
- \(Ag^{+} + e^{-} \rightarrow Ag\): This equation represents the gain of one electron by silver ion to form silver metal. It is a reduction half-reaction.
- \(Ag^{+} + Cl^{-} \rightarrow AgCl\): This is a precipitation reaction where silver ions react with chloride ions to form silver chloride. It is not a half-reaction as it does not involve transfer of electrons in a redox sense.
Therefore, the correct half-reaction from the given options is \(Ag^{+} + e^{-} \rightarrow Ag\).