The bond dissociation energies of X₂, Y₂ and XY are in the ratio of 1 ∶ 0.5 ∶ 1. Δ H for the formation of X Y is −200 kJ mol⁻¹. The bond dissociation energy of X₂ will be

CONCEPT:

Bond Dissociation Energy

• Bond dissociation energy (BDE) is the energy required to break a bond in a molecule to form neutral atoms.
• The bond dissociation energies of X₂, Y₂, and XY are given in a ratio of 1 : 0.5 : 1.

EXPLANATION:

• Given the enthalpy change (ΔH) for the formation of XY is -200 kJ mol^-1.
• Let the bond dissociation energy of X₂ be E. Then:
  • Bond dissociation energy of Y₂ = 0.5E
  • Bond dissociation energy of XY = E
• Using the given ΔH for the reaction:

  X₂ + Y₂ → 2XY

  • ΔH = (Bond dissociation energy of X₂ + Bond dissociation energy of Y₂) - 2 × Bond dissociation energy of XY
  • -200 kJ mol^-1 = (E + 0.5E) - 2E
  • -200 kJ mol^-1 = 1.5E - 2E
  • -200 kJ mol^-1 = -0.5E
  • E = 400 kJ mol^-1

Therefore, the bond dissociation energy of X₂ is 400 kJ mol^-1, which corresponds to option 3.