The C-H bond distance is the longest in:

Options

A. `C_(2)H_(2)`
B. `C_(2)H_(4)`
C. `C_(2)H_(6)`
D. `C_(2)H_(2)Br_(2)`

Explanation

To determine which C-H bond distance is the longest among the given options, we need to understand the relationship between bond multiplicity and bond length. Here’s a step-by-step solution:

### Step-by-Step Solution:

1. **Understand Bond Multiplicity**: Bond multiplicity refers to the number of bonds between two atoms. A single bond has a multiplicity of 1, a double bond has a multiplicity of 2, and a triple bond has a multiplicity of 3. Generally, as the bond multiplicity increases, the bond length decreases.

2. **Identify the Structures**: We have four compounds to analyze:
- **A: C2H2 (Ethylene)**: Contains a triple bond between the two carbon atoms (C≡C) and single bonds to hydrogen.
- **B: C2H4 (Ethane)**: Contains a double bond between the two carbon atoms (C=C) and single bonds to hydrogen.
- **C: C2H6 (Ethane)**: Contains single bonds between the carbon atoms (C-C) and single bonds to hydrogen.
- **D: C2H4Br2 (Dibromoethene)**: Contains a double bond between the two carbon atoms (C=C) and single bonds to hydrogen and bromine.

3. **Analyze Bond Multiplicity**:
- In **C2H2**, the C-H bond is involved with a carbon that has a triple bond (multiplicity = 3).
- In **C2H4**, the C-H bond is involved with a carbon that has a double bond (multiplicity = 2).
- In **C2H6**, the C-H bond is involved with a carbon that has a single bond (multiplicity = 1).
- In **C2H4Br2**, the C-H bond is involved with a carbon that has a double bond (multiplicity = 2).

4. **Determine the Longest Bond**: Since bond length increases as bond multiplicity decreases, we can conclude:
- C2H2 has the shortest C-H bond due to the triple bond.
- C2H4 and C2H4Br2 have shorter C-H bonds due to the double bond.
- **C2H6 has the longest C-H bond because it has single bonds (multiplicity = 1)**.

5. **Final Answer**: Therefore, the C-H bond distance is the longest in **C2H6 (Ethane)**.