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 of the given compounds has the shortest carbon-carbon bond length, we need to analyze the types of carbon-carbon bonds present in each compound. The bond length is influenced by the type of hybridization and bond order, which are related to the number of bonds between the carbon atoms.

### Step-by-Step Solution:

1. **Identify the Types of Carbon-Carbon Bonds**:
- Carbon can form single (C-C), double (C=C), or triple (C≡C) bonds.
- Each type of bond has a different bond length due to the number of shared electron pairs.

2. **Understand Hybridization**:
- A carbon-carbon single bond (C-C) involves **sp³ hybridization**.
- A carbon-carbon double bond (C=C) involves **sp² hybridization**.
- A carbon-carbon triple bond (C≡C) involves **sp hybridization**.

3. **Determine Bond Order**:
- The bond order is defined as the number of shared electron pairs between two atoms.
- For a single bond (C-C), the bond order is **1**.
- For a double bond (C=C), the bond order is **2**.
- For a triple bond (C≡C), the bond order is **3**.

4. **Relate Bond Order to Bond Length**:
- Generally, as the bond order increases, the bond length decreases.
- Thus, the order of bond lengths from longest to shortest is:
- C-C (single bond) > C=C (double bond) > C≡C (triple bond).

5. **Analyze the Given Compounds**:
- If we consider compounds like ethane (C₂H₆, with C-C single bonds), ethylene (C₂H₄, with C=C double bonds), and acetylene (C₂H₂, with C≡C triple bonds), we can apply our understanding of bond lengths.
- Ethane has the longest bond length due to single bonds.
- Ethylene has a shorter bond length due to double bonds.
- Acetylene has the shortest bond length because of the triple bonds.

6. **Conclusion**:
- Among the compounds mentioned, **acetylene (C₂H₂)** has the shortest carbon-carbon bond length due to its triple bond.

### Final Answer:
**Acetylene (C₂H₂) has the shortest carbon-carbon bond length.**