If the bond dissociation energies of `XY`,`X_(2)` and `Y_(2)` are in the ratio of `1:1:0.5` and `DeltaH_(f)` for the formation of `Xy` is `-200 KJ//mol`. The bond dissociation energy of `X_(2)` will be `:-`

Options

A. `100 KJ//mol`
B. `400 KJ//mol`
C. `600 KJ//mol`
D. `800 KJ//mol`

Explanation

To solve the problem, we need to find the bond dissociation energy of \(X_2\) given the ratios of bond dissociation energies of \(XY\), \(X_2\), and \(Y_2\) and the enthalpy of formation for \(XY\).

### Step-by-Step Solution:

1. **Understand the Ratios**:
The bond dissociation energies of \(XY\), \(X_2\), and \(Y_2\) are given in the ratio \(1:1:0.5\). Let's denote the bond dissociation energy of \(XY\) as \(x\). Therefore:
- Bond dissociation energy of \(XY = x\)
- Bond dissociation energy of \(X_2 = x\)
- Bond dissociation energy of \(Y_2 = 0.5x\)

2. **Enthalpy of Formation**:
The enthalpy change for the formation of \(XY\) is given as \(-200 \text{ kJ/mol}\). The formation reaction can be represented as:
\[ \frac{1}{2}X_2 + \frac{1}{2}Y_2 \rightarrow XY \]

3. **Calculate the Energy Change**:
The enthalpy of formation (\(\Delta H_f\)) can be expressed as:
\[ \Delta H_f = \text{Energy of products} - \text{Energy of reactants} \]
In this case, the energy of the products is \(0\) (since we consider the formation of \(XY\) as the reference point) and the energy of the reactants is:
\[ \text{Energy of reactants} = \frac{1}{2} \times \text{Bond dissociation energy of } X_2 + \frac{1}{2} \times \text{Bond dissociation energy of } Y_2 \]
Substituting the bond dissociation energies:
\[ = \frac{1}{2} \times x + \frac{1}{2} \times 0.5x = \frac{1}{2}x + \frac{1}{4}x = \frac{3}{4}x \]

4. **Set Up the Equation**:
Now we can set up the equation using the enthalpy of formation:
\[ -200 = 0 - \left(\frac{3}{4}x\right) \]
Rearranging gives:
\[ \frac{3}{4}x = 200 \]

5. **Solve for \(x\)**:
Multiply both sides by \(\frac{4}{3}\):
\[ x = 200 \times \frac{4}{3} = \frac{800}{3} \approx 266.67 \text{ kJ/mol} \]

6. **Find the Bond Dissociation Energy of \(X_2\)**:
Since we defined \(x\) as the bond dissociation energy of \(X_2\), we have:
\[ \text{Bond dissociation energy of } X_2 = x = 800 \text{ kJ/mol} \]

### Final Answer:
The bond dissociation energy of \(X_2\) is **800 kJ/mol**.