Q1(a). Dissociation energies of N₂⁺ and O₂⁺
The dissociation energy decreases on going from N₂ to N₂⁺ whereas it increases on going from O₂ to O₂⁺. Explain.
Answer in brief
The electron lost from N₂ comes from a bonding MO (bond order 3 → 2.5), so the bond weakens. The electron lost from O₂ comes from an antibonding π* MO (bond order 2 → 2.5), so the bond strengthens.
Key points
- the larger the bond order, the stronger and shorter the bond. Ionisation removes the electron from the HOMO; its character decides the result.
- (σ2s)²(σ*2s)²(π2p)⁴(σ2p)², b=12(8-2)=3. The HOMO σ2p is bonding (s–p mixing places it above π2p).
- …(σ2p)¹, b=12(7-2)=2.5. Bonding density between the nuclei falls, so D falls: D(N₂)=945 → D(N₂⁺)=842 kJ mol⁻¹
- (σ2s)²(σ*2s)²(σ2p)²(π2p)⁴(π*2p)², b=12(8-4)=2. The HOMO π*2p is antibonding and holds two unpaired electrons.
The full model answer
Written out in full, as it should go in the answer booklet. The solution page with its diagrams follows it.
- Rule: the larger the bond order, the stronger and shorter the bond. Ionisation removes the electron from the HOMO; its character decides the result.
- N₂ (10 valence electrons): (σ2s)²(σ*2s)²(π2p)⁴(σ2p)², b=12(8-2)=3. The HOMO σ2p is bonding (s–p mixing places it above π2p).
- N₂⁺: …(σ2p)¹, b=12(7-2)=2.5. Bonding density between the nuclei falls, so D falls: D(N₂)=945 → D(N₂⁺)=842 kJ mol⁻¹
- O₂ (12 valence electrons): (σ2s)²(σ*2s)²(σ2p)²(π2p)⁴(π*2p)², b=12(8-4)=2. The HOMO π*2p is antibonding and holds two unpaired electrons.
- O₂⁺: …(π*2p)¹, b=12(8-3)=2.5. Removing an antibonding electron removes a destabilising contribution, so D rises above that of O₂ (497 kJ mol⁻¹) and the bond shortens: r(O-O): 120.8 pm (O₂) → 111.6 pm (O₂⁺)
- Magnetism follows the same diagram: N₂ diamagnetic → N₂⁺ one unpaired electron; O₂ two unpaired → O₂⁺ one unpaired. Both ions are paramagnetic.
General result: removing a bonding electron weakens a bond; removing an antibonding electron strengthens it. In the same way F₂⁺ (b=1.5) is more strongly bonded than F₂ (b=1), and C₂⁺ less than C₂.
Application. the dioxygenyl cation exists in solids such as O₂+[PtF₆]⁻, made by oxidising O₂ with PtF₆; the observation led Bartlett to the first noble-gas compound, since Xe has almost the same ionisation energy as O₂.
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All parts of Question 1
- 1(a) Dissociation energies of N₂⁺ and O₂⁺10 marks
- 1(b) Spacing of the (123) planes of an orthorhombic cell10 marks
- 1(c) C_V in terms of U; (∂ C_V/∂ V)_T=0 for an ideal gas10 marks
- 1(d) Phenol–water: two liquid layers and the phase rule10 marks
- 1(e) E°(Ag⁺/Ag) from the equilibrium constant10 marks