Which of the following has minimum C-H bond length

Options

A. `C_2H_4`
B. `C_2H_2`
C. `C_2H_6`
D. `C_6H_6`

Answer

To determine which of the given compounds has the minimum C-H bond length, we will analyze the hybridization of carbon in each compound and its corresponding s-character. The greater the s-character, the shorter the C-H bond length.

### Step-by-Step Solution:

1. **Identify the Compounds:**
The compounds given are:
- C2H4 (Ethylene)
- C2H2 (Acetylene)
- C2H6 (Ethane)
- C6H6 (Benzene)

2. **Determine the Structure and Hybridization:**
- **C2H4 (Ethylene):**
- Structure: H2C=CH2 (double bond between the two carbon atoms)
- Hybridization: The carbon atoms are sp² hybridized (3 regions of electron density).
- s-character: 33% (1 s orbital out of 3 orbitals).

- **C2H2 (Acetylene):**
- Structure: HC≡CH (triple bond between the two carbon atoms)
- Hybridization: The carbon atoms are sp hybridized (2 regions of electron density).
- s-character: 50% (1 s orbital out of 2 orbitals).

- **C2H6 (Ethane):**
- Structure: H3C-CH3 (single bonds between carbon atoms)
- Hybridization: The carbon atoms are sp³ hybridized (4 regions of electron density).
- s-character: 25% (1 s orbital out of 4 orbitals).

- **C6H6 (Benzene):**
- Structure: A cyclic structure with alternating double bonds (C6H6)
- Hybridization: The carbon atoms are sp² hybridized (3 regions of electron density).
- s-character: 33% (similar to C2H4, but slightly more due to resonance).

3. **Compare the s-character:**
- C2H4: 33% s-character
- C2H2: 50% s-character
- C2H6: 25% s-character
- C6H6: ~33% s-character (slightly more due to resonance)

4. **Conclusion:**
The compound with the highest s-character is C2H2 (Acetylene) with 50% s-character. According to the relationship between s-character and bond length, a higher s-character results in a shorter bond length. Therefore, C2H2 has the minimum C-H bond length.

### Final Answer:
**C2H2 (Acetylene) has the minimum C-H bond length.**