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

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  1. 200 kJ mol−1
  2. 100 kJ mol−1
  3. 400 kJ mol−1
  4. 800 kJ mol−1

Answer (Detailed Solution Below)

Option 3 : 400 kJ mol−1
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Detailed Solution

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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.

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