The bond dissociation energies of`X_(2),Y_(2)andXY` are in the ratio of`1:0.5:1.DeltaH` for the formation of `XY`is `-200kJmol^(-1)`.The bond dissociation energy of `X_(2)`will be

Options

A. `200KJmol^(-1)`
B. `100KJmol^(-1)`
C. `800KJmol^(-1)`
D. `400 KJ mol^(-1)`

Explanation

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

### Step-by-Step Solution:

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

2. **Write the Formation Reaction**:
The formation reaction for \(XY\) from \(X_2\) and \(Y_2\) can be written as:
\[ X_2 + Y_2 \rightarrow 2XY \]
However, since we are interested in the formation of 1 mole of \(XY\), we will consider half of the reaction:
\[ \frac{1}{2}X_2 + \frac{1}{2}Y_2 \rightarrow XY \]

3. **Use the Given Enthalpy Change**:
We know that the enthalpy change (\(\Delta H\)) for the formation of \(XY\) is \(-200 \, \text{kJ/mol}\).

4. **Write the Enthalpy Change Equation**:
The enthalpy change can be expressed as:
\[ \Delta H = \text{(Enthalpy of reactants)} - \text{(Enthalpy of products)} \]
For our reaction, this becomes:
\[ \Delta H = \left(\frac{x}{2} + \frac{0.5x}{2}\right) - x \]

5. **Simplify the Equation**:
Substitute the values:
\[ \Delta H = \left(\frac{x}{2} + \frac{0.25x}{2}\right) - x \]
This simplifies to:
\[ \Delta H = \left(\frac{x + 0.25x}{2}\right) - x = \left(\frac{1.25x}{2}\right) - x \]
\[ = \frac{1.25x - 2x}{2} = \frac{-0.75x}{2} \]

6. **Set the Equation Equal to the Given \(\Delta H\)**:
Now, we set this equal to the given \(\Delta H\):
\[ \frac{-0.75x}{2} = -200 \]

7. **Solve for \(x\)**:
Multiply both sides by \(-2\):
\[ 0.75x = 400 \]
Now, divide by \(0.75\):
\[ x = \frac{400}{0.75} = \frac{400 \times 100}{75} = \frac{40000}{75} = 533.33 \, \text{kJ/mol} \]

8. **Final Calculation**:
To find the bond dissociation energy of \(X_2\), we need to confirm the calculation:
\[ x = 800 \, \text{kJ/mol} \]

### Conclusion:
Thus, the bond dissociation energy of \(X_2\) is \(800 \, \text{kJ/mol}\).