The interatomic distance in `H_(2)` and `CI_(2)` molecules are 74 an d198 pm respectively. The bond length of HCI is

Options

A. 272pm
B. 136pm
C. 127pm
D. 248pm

Answer

To find the bond length of HCl given the interatomic distances of H2 and Cl2, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Interatomic Distance**: The interatomic distance in a diatomic molecule (like H2 or Cl2) is the distance between the centers of the two atoms. For a diatomic molecule, this distance can be expressed as \( d = 2r \), where \( r \) is the atomic radius.

2. **Calculate the Radius of H2**:
- The interatomic distance for H2 is given as 74 pm.
- Using the formula \( d = 2r \), we can find the radius of H2:
\[ r_{H2} = \frac{d_{H2}}{2} = \frac{74 \text{ pm}}{2} = 37 \text{ pm} \]

3. **Calculate the Radius of Cl2**:
- The interatomic distance for Cl2 is given as 198 pm.
- Similarly, we find the radius of Cl2:
\[ r_{Cl2} = \frac{d_{Cl2}}{2} = \frac{198 \text{ pm}}{2} = 99 \text{ pm} \]

4. **Calculate the Bond Length of HCl**:
- The bond length of HCl is the sum of the radii of H and Cl:
\[ \text{Bond length of HCl} = r_{H2} + r_{Cl2} = 37 \text{ pm} + 99 \text{ pm} = 136 \text{ pm} \]

5. **Final Answer**: The bond length of HCl is 136 pm.