Let's analyze the given chemical reaction and identify the correct half reaction that represents reduction.
The overall reaction is:
[tex]\[Zn ( s )+2 H ^{+}(a q) \longrightarrow Zn ^{2+}(a q)+ H _2(g)\][/tex]
In this reaction, zinc (Zn) and hydrogen ions (H[tex]\(^+\)[/tex]) are participating. To better understand the redox process, we need to break it down into its half-reactions. Recall that oxidation involves the loss of electrons, while reduction involves the gain of electrons.
### Step-by-Step Analysis:
1. Oxidation Half-Reaction:
- Zinc (Zn) is transforming into [tex]\(Zn^{2+}\)[/tex] ion.
- This process involves the loss of electrons because zinc goes from a neutral state (0 oxidation state) to a +2 oxidation state.
- The oxidation half-reaction is:
[tex]\[Zn (s) \longrightarrow Zn ^{2+}(aq) + 2 e ^{-}\][/tex]
2. Reduction Half-Reaction:
- Hydrogen ions ([tex]\(H^{+}\)[/tex]) are transforming into hydrogen gas ([tex]\(H_2\)[/tex]).
- This process involves the gain of electrons because hydrogen ions go from a +1 oxidation state to a 0 oxidation state in [tex]\(H_2\)[/tex].
- The reduction half-reaction is:
[tex]\[2 H ^{+}(aq) + 2 e ^{-} \longrightarrow H _2(g)\][/tex]
Next, we compare the given options with the correct reduction half-reaction. Here are the options again:
1. [tex]\(Zn (s) \longrightarrow Zn ^{2+}(aq) + 2 e ^{-}\)[/tex]
2. [tex]\(2 H ^{+}(aq) + 2 e ^{-} \longrightarrow H _2(g)\)[/tex]
3. [tex]\(Zn (s) \longrightarrow Zn ^{2+}(aq) + e ^{-}\)[/tex]
4. [tex]\(2 H ^{+}(aq) + e ^{-} \longrightarrow H _2(g)\)[/tex]
### Matching the Correct Reduction Half-Reaction:
- The correct reduction half-reaction, as we identified, is [tex]\(2 H ^{+}(aq) + 2 e ^{-} \longrightarrow H _2(g)\)[/tex].
Therefore, the correct answer is:
[tex]\[2 H ^{+}(aq) + 2 e ^{-} \longrightarrow H _2(g)\][/tex]
### Conclusion:
The half reaction that correctly represents reduction for the given overall reaction is the second option:
[tex]\[
2 H ^{+}(aq) + 2 e ^{-} \longrightarrow H _2(g)
\][/tex]
Thus, the corresponding number is:
[tex]\[ \boxed{2} \][/tex]
