To determine which of the given half-reactions is an oxidation half-reaction, we need to understand what happens in oxidation and reduction reactions:
1. Oxidation involves the loss of electrons, which causes an increase in the oxidation state (the charge of the ion or atom becomes more positive).
2. Reduction involves the gain of electrons, which causes a decrease in the oxidation state (the charge of the ion or atom becomes more negative).
Let's analyze each option step by step:
### Option 1: [tex]\(V^{3+}+e^{-} \rightarrow V^{2+}\)[/tex]
- This reaction shows [tex]\(V^{3+}\)[/tex] gaining an electron ([tex]\(e^{-}\)[/tex]).
- Gaining an electron reduces the charge from [tex]\(3+\)[/tex] to [tex]\(2+\)[/tex].
- Since the charge is decreasing, this is a reduction reaction.
### Option 2: [tex]\(Fe \rightarrow Fe^{3+}+3 e^{-}\)[/tex]
- This reaction shows [tex]\(Fe\)[/tex] losing three electrons, as indicated by the [tex]\(3e^{-}\)[/tex] on the products side.
- Losing electrons increases the oxidation state of [tex]\(Fe\)[/tex] from [tex]\(0\)[/tex] (neutral iron atom) to [tex]\(3+\)[/tex] (iron ion).
- Since the charge is increasing, this is an oxidation reaction.
### Option 3: [tex]\(C^{4+}+2 e^{-} \rightarrow C^{2+}\)[/tex]
- This reaction shows [tex]\(C^{4+}\)[/tex] gaining two electrons ([tex]\(2 e^{-}\)[/tex]).
- Gaining electrons reduces the charge from [tex]\(4+\)[/tex] to [tex]\(2+\)[/tex].
- Since the charge is decreasing, this is a reduction reaction.
Given these analyses, the only reaction that represents an oxidation half-reaction is:
### [tex]\(Fe \rightarrow Fe^{3+}+3 e^{-}\)[/tex]
Thus, the correct answer is option 2.
