In which compound the C – H bond distance is longest ?

Options

A. `C_2H_2`
B. `C_2H_4`
C. `C_2H_4Br_2`
D. `C_6H_5OH`

Answer

To determine which compound has the longest C-H bond distance, we will analyze the hybridization of carbon in each compound and how it affects the bond length.

### Step 1: Identify the compounds and their structures
1. **C2H2 (Ethine)**: This compound has a triple bond between the two carbon atoms (C≡C), resulting in sp hybridization for the carbon atoms.
2. **C2H4 (Ethylene)**: This compound has a double bond between the two carbon atoms (C=C), resulting in sp² hybridization for the carbon atoms.
3. **C2H4Br2 (Dibromoethane)**: This compound also has a double bond (C=C) but is substituted with bromine atoms. The carbon atoms are still sp² hybridized.
4. **C6H5OH (Phenol)**: In this compound, the carbon atoms are part of a benzene ring, which involves sp² hybridization.

### Step 2: Analyze the hybridization and s-character
- **sp Hybridization (C2H2)**: The carbon atoms have 50% s-character and 50% p-character. The C-H bond is shorter due to the high s-character.
- **sp² Hybridization (C2H4, C2H4Br2, C6H5OH)**: The carbon atoms have 33% s-character and 67% p-character. The C-H bond is longer than in sp hybridization but shorter than in sp³ hybridization.
- **sp³ Hybridization (not present in the given compounds)**: If we consider a compound like CH4 (methane), it has 25% s-character and 75% p-character, resulting in the longest C-H bond length.

### Step 3: Determine the compound with the longest C-H bond
Among the compounds analyzed:
- C2H2 has the shortest C-H bond due to sp hybridization.
- C2H4 and C2H4Br2 have longer C-H bonds due to sp² hybridization.
- C6H5OH also has sp² hybridization, similar to C2H4.

However, C2H4Br2 (dibromoethane) has sp² hybridized carbons but the presence of bromine can slightly influence the bond length due to steric effects.

### Conclusion
The compound with the longest C-H bond distance is **C2H4Br2 (Dibromoethane)** due to its sp³ hybridization character being the least among the given compounds.