Question

The bond dissociation energy of X\(_2\), Y\(_2\) and XY are in the ratio of 1 : 0.5 : 1. \(\Delta H\) for the formation of XY is -200 kJ/mol. The bond dissociation energy of X\(_2\) will be

• A. 200 kJ/mol
• B. 100 kJ/mol
• C. 400 kJ/mol
• D. 800 kJ/mol

Hint:

The bond dissociation energy of a molecule is the energy required to break the bond between two atoms in a molecule.

Answer 1

The Correct Option is D

Step 1: {Using Given Data}
Let the bond dissociation energy of X\(_2\) be \(a\) kJ/mol. Thus, the bond dissociation energy of Y\(_2\) is \(0.5a\) kJ/mol and the bond dissociation energy of XY is \(a\) kJ/mol. The formation reaction is: \[ \frac{1}{2} {X}_2 + \frac{1}{2} {Y}_2 \rightarrow {XY}, \, \Delta H = -200 \, {kJ/mol} \] Step 2: {Bond Energy Formula}
The bond dissociation energy can be calculated using the formula for enthalpy change: \[ \Delta H = BE({Reactants}) - BE({Products}) \] \[ \Delta H = \left[\frac{1}{2} \, BE({X}_2) + \frac{1}{2} \, BE({Y}_2)\right] - BE({XY}) \] \[ \Delta H = \left[\frac{a}{2} + \frac{0.5a}{2}\right] - a \] \[ -200 = \frac{a + 0.5a}{2} - a \] \[ -200 = \frac{1.5a}{2} - a \] \[ -200 = 0.75a - a \] \[ -200 = -0.25a \] \[ a = 800 \, {kJ/mol} \] Thus, the correct answer is (D).

Answer 2

Step 1: Let the bond dissociation energies be
Let bond dissociation energy of X₂ = x kJ/mol
Then according to the given ratio:
- X₂ = x
- Y₂ = 0.5x
- XY = x

Step 2: Use bond enthalpy relation for reaction
The formation of XY from X₂ and Y₂ involves:
\[ \frac{1}{2} X_2 + \frac{1}{2} Y_2 \rightarrow XY \]
Using Hess’s law:
ΔH = Bonds broken − Bonds formed

Bonds broken = \( \frac{1}{2} \)X₂ + \( \frac{1}{2} \)Y₂ = \( \frac{1}{2}x + \frac{1}{2}(0.5x) = \frac{1}{2}x + \frac{1}{4}x = \frac{3}{4}x \)
Bonds formed = XY = x

So,
ΔH = (3/4)x − x = −(1/4)x
Given: ΔH = −200 kJ/mol

Step 3: Solve the equation
\[ -\frac{1}{4}x = -200 \Rightarrow x = 800 \text{ kJ/mol} \]

Final Answer: 800 kJ/mol