Which of the following reactions would give caproic acid ?

Options

A. `n-C_5 H_11 Br overset ((i) Mg//ether) underset((ii) CO_2) rarr`
B. `n-C_5 H_11 Li overset ((i) CO_2) underset((ii) H_3 O) rarr`
C. `n-C_(4)H_(9)Br underset({:((i)CO_(2)),((iii)H_(3)O^(o+)):})overset((i)Mg//"ether")(to)`
D. `n-C_5 H_11 MgBr + (CN)_2 overset((i) Delta) underset((ii) H_3 O^(oplus))rarr`

Explanation

To determine which reactions would yield caproic acid (hexanoic acid, C6H12O2), we will analyze each option provided in the question step by step.

### Step-by-Step Solution:

1. **Identify Caproic Acid**:
- Caproic acid is also known as hexanoic acid, with the molecular formula C6H12O2.

2. **Analyze Option 1**:
- The reaction involves C5H11Br with magnesium (Mg) in ether to form a Grignard reagent (C5H11MgBr).
- This Grignard reagent then reacts with carbon dioxide (CO2).
- The reaction can be represented as:
\[ C5H11MgBr + CO2 \rightarrow C5H11C(=O)O^-MgBr^+ \]
- Upon hydrolysis (adding H+), it forms hexanoic acid:
\[ C5H11C(=O)O^- + H^+ \rightarrow C5H11C(=O)OH \]
- **Conclusion**: This option produces caproic acid.

3. **Analyze Option 2**:
- This option also involves C5H11Li (another organolithium reagent) reacting with CO2.
- The reaction is similar:
\[ C5H11Li + CO2 \rightarrow C5H11C(=O)O^-Li^+ \]
- Hydrolysis leads to:
\[ C5H11C(=O)O^- + H^+ \rightarrow C5H11C(=O)OH \]
- **Conclusion**: This option also produces caproic acid.

4. **Analyze Option 3**:
- Here, C4H9Br is used with magnesium to form C4H9MgBr.
- The reaction with CO2 gives:
\[ C4H9MgBr + CO2 \rightarrow C4H9C(=O)O^-MgBr^+ \]
- Hydrolysis yields:
\[ C4H9C(=O)O^- + H^+ \rightarrow C4H9C(=O)OH \]
- This results in pentanoic acid (not caproic acid).
- **Conclusion**: This option does not produce caproic acid.

5. **Analyze Option 4**:
- The reaction involves C5H11MgBr and cyanide (CN).
- The reaction can be represented as:
\[ C5H11MgBr + CN \rightarrow C5H11C≡N + MgBr \]
- Hydrolysis of the nitrile (C5H11C≡N) leads to:
\[ C5H11C≡N + H3O^+ \rightarrow C5H11C(=O)OH \]
- This produces caproic acid.
- **Conclusion**: This option also produces caproic acid.

### Final Answer:
The reactions that would give caproic acid are **Option 1, Option 2, and Option 4**.