Which one of the following has the shortest carbon-carbon bond length ?

Options

A. Benzene
B. Ethene
C. Ethyne
D. Ethane

Explanation

To determine which compound has the shortest carbon-carbon bond length among the given options, we need to analyze the bond order of each compound. The bond order is directly related to the bond length: the higher the bond order, the shorter the bond length.

### Step-by-Step Solution:

1. **Identify the Compounds**: The question provides four options, which we assume to be:
- A) Benzene (C6H6)
- B) Ethene (C2H4)
- C) Ethyne (C2H2)
- D) Ethane (C2H6)

2. **Determine the Structure and Bond Order**:
- **Benzene (C6H6)**: Benzene has a cyclic structure with alternating single and double bonds. The bond order is calculated as:
\[ \text{Bond Order} = \frac{\text{Number of bonding electrons}}{\text{Number of bond groups}} = 1.5 \]
- **Ethene (C2H4)**: Ethene has a double bond between the two carbon atoms. The bond order is:
\[ \text{Bond Order} = 2 \]
- **Ethyne (C2H2)**: Ethyne has a triple bond between the two carbon atoms. The bond order is:
\[ \text{Bond Order} = 3 \]
- **Ethane (C2H6)**: Ethane has a single bond between the two carbon atoms. The bond order is:
\[ \text{Bond Order} = 1 \]

3. **Compare Bond Orders**: Now we compare the bond orders:
- Benzene: 1.5
- Ethene: 2
- Ethyne: 3
- Ethane: 1

4. **Determine the Shortest Bond Length**: Since the bond length decreases with increasing bond order, we find that:
- Ethyne has the highest bond order (3), which means it has the shortest carbon-carbon bond length.

5. **Conclusion**: Therefore, the compound with the shortest carbon-carbon bond length is **C) Ethyne**.