Heat evolved in the reaction
`H_(2)+Cl_(2) rarr 2HCl` is 182 kJ Bond energies H- H = 430 kJ/mole, `Cl-Cl = 242kJ//"mole"`. The H-Cl bond energy is

Options

A. 763 kJ/mole
B. 427 kJ/mole
C. 336 kJ/mole
D. 154 kJ/mole

Explanation

To find the bond energy of H-Cl in the reaction \( H_2 + Cl_2 \rightarrow 2HCl \), we can use the concept of bond energies and the heat evolved in the reaction.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Heat evolved in the reaction (\( \Delta H \)): -182 kJ (negative because heat is released)
- Bond energy of \( H-H \): 430 kJ/mole
- Bond energy of \( Cl-Cl \): 242 kJ/mole
- Let the bond energy of \( H-Cl \) be \( x \) kJ/mole.

2. **Write the Reaction:**
The reaction can be broken down into bonds broken and bonds formed:
\[ H_2 + Cl_2 \rightarrow 2HCl \]

3. **Calculate the Total Energy of Bonds Broken:**
- Bonds broken: 1 \( H-H \) bond and 1 \( Cl-Cl \) bond.
- Total energy required to break these bonds:
\[ \text{Energy of bonds broken} = \text{Bond energy of } H-H + \text{Bond energy of } Cl-Cl = 430 \, \text{kJ} + 242 \, \text{kJ} = 672 \, \text{kJ} \]

4. **Calculate the Total Energy of Bonds Formed:**
- Bonds formed: 2 \( H-Cl \) bonds.
- Total energy released when forming these bonds:
\[ \text{Energy of bonds formed} = 2 \times x \, \text{kJ} \]

5. **Apply Hess's Law:**
According to Hess's law, the heat evolved in the reaction can be expressed as:
\[ \Delta H = \text{Energy of bonds broken} - \text{Energy of bonds formed} \]
Substituting the values:
\[ -182 \, \text{kJ} = 672 \, \text{kJ} - 2x \]

6. **Rearranging the Equation:**
Rearranging the equation to solve for \( x \):
\[ 2x = 672 \, \text{kJ} + 182 \, \text{kJ} \]
\[ 2x = 854 \, \text{kJ} \]
\[ x = \frac{854}{2} \, \text{kJ} = 427 \, \text{kJ/mole} \]

7. **Conclusion:**
The bond energy of \( H-Cl \) is \( 427 \, \text{kJ/mole} \).