Given the bond energies of `H - H` and `Cl - Cl` are `430 kJ mol^(-1)` and `240 kJ mol^(-1)`, respectively, and `Delta_(f) H^(@)` for `HCl` is `- 90 kJ mol^(-1)`. Bond enthalpy of `HCl` is

Options

A. `245 kJ mol^(-1)`
B. `290 kJ mol^(-1)`
C. `380 kJ mol^(-1)`
D. `425 kJ mol^(-1)`

Explanation

To find the bond enthalpy of HCl, we can use the given bond energies and the heat of formation of HCl. Here are the steps to solve the problem:

### Step 1: Write the reaction for the formation of HCl
The formation of HCl from its elements can be represented as:
\[ \frac{1}{2} \text{H}_2(g) + \frac{1}{2} \text{Cl}_2(g) \rightarrow \text{HCl}(g) \]

### Step 2: Identify the heat of formation
The heat of formation (\(\Delta_f H^\circ\)) for HCl is given as:
\[ \Delta_f H^\circ = -90 \text{ kJ mol}^{-1} \]

### Step 3: Write the equation for bond enthalpy
Using the bond enthalpy concept, we can express the heat of the reaction in terms of bond energies:
\[ \Delta H = \text{(Bond energies of reactants)} - \text{(Bond energies of products)} \]
For our reaction:
\[ \Delta H = \left(\frac{1}{2} \times \text{Bond energy of } H_2 + \frac{1}{2} \times \text{Bond energy of } Cl_2\right) - \text{Bond energy of } HCl \]

### Step 4: Substitute the known values
Substituting the known bond energies:
- Bond energy of \(H-H\) = 430 kJ/mol
- Bond energy of \(Cl-Cl\) = 240 kJ/mol

The equation becomes:
\[ -90 = \left(\frac{1}{2} \times 430 + \frac{1}{2} \times 240\right) - \text{Bond energy of } HCl \]

### Step 5: Calculate the left-hand side
Calculating the left-hand side:
\[ \frac{1}{2} \times 430 = 215 \text{ kJ/mol} \]
\[ \frac{1}{2} \times 240 = 120 \text{ kJ/mol} \]
So,
\[ 215 + 120 = 335 \text{ kJ/mol} \]

### Step 6: Set up the equation
Now we can set up the equation:
\[ -90 = 335 - \text{Bond energy of } HCl \]

### Step 7: Solve for the bond energy of HCl
Rearranging gives:
\[ \text{Bond energy of } HCl = 335 + 90 = 425 \text{ kJ/mol} \]

### Conclusion
Thus, the bond enthalpy of HCl is:
\[ \text{Bond energy of } HCl = 425 \text{ kJ/mol} \]