Let's solve each part step by step using **Molecular Orbital (MO) Theory** (since Lewis is excluded): --- ### **a) F₂, F₂⁻, and F₂⁺: Bond Order, Magnetism, Bond Length & Dissociation Energy** #### **Step 1: Molecular Orbital Diagram for F₂ and its ions** For F (Z = 9), electronic configuration: 1s² 2s² 2p⁵ For F₂: Total electrons = 2 × 9 = **18** **Relevant MOs (valence only):** - σ(2s), σ*(2s) - σ(2pₓ), π(2p_y), π(2p_z) - π*(2p_y), π*(2p_z), σ*(2pₓ) **Filling order for p orbitals (for F₂ and beyond):** σ(2pₓ) < π(2p_y) = π(2p_z) < π*(2p_y) = π*(2p_z) < σ*(2pₓ) ##### **Electron Configuration for F₂:** - σ(2s)² σ*(2s)² σ(2pₓ)² π(2p_y)² π(2p_z)² π*(2p_y)² π*(2p_z)² = 2 + 2 + 2 + 2 + 2 + 2 + 2 = **14 electrons in valence MOs** #### **Step 2: Calculate Bond Orders** **Bond Order = (number of bonding electrons - number of antibonding electrons)/2** - **Bonding MOs:** σ(2s), σ(2pₓ), π(2p_y), π(2p_z) - **Antibonding MOs:** σ*(2s), σ*(2pₓ), π*(2p_y), π*(2p_z) | Molecule | Total e⁻ | Bonding e⁻ | Antibonding e⁻ | Bond Order | |----------|----------|------------|----------------|-------------------------| | F₂ | 14 | 8 | 6 | (8 - 6)/2 = **1** | | F₂⁻ | 15 | 8 | 7 | (8 - 7)/2 = **0.5** | | F₂⁺ | 13 | 8 | 5 | (8 - 5)/2 = **1.5** | #### **Step 3: Magnetic Properties** - **Paramagnetic**: At least one unpaired electron - **Diamagnetic**: All electrons paired Look at the last electron added: - **F₂:** All electrons paired → **Diamagnetic** - **F₂⁻:** 1 extra electron in π* orbital (unpaired) → **Paramagnetic** - **F₂⁺:** 1 electron missing from a paired π* orbital (all paired) → **Diamagnetic** #### **Step 4: Bond Length and Dissociation Energy** - **Bond order ∝ Bond strength ∝ 1/Bond length** - **Order (Bond order):** F₂⁺ (1.5) > F₂ (1) > F₂⁻ (0.5) - **Order (Bond length):** F₂⁻ > F₂ > F₂⁺ - **Order (Bond dissociation energy):** F₂⁺ > F₂ > F₂⁻ **Explanation:** Higher bond order means more bonding interactions (stronger, shorter bond). Lower bond order means weaker, longer bond. --- #### **Summary Table:** | Molecule | Bond Order | Magnetism | Bond Length | Dissociation Energy | |----------|------------|---------------|---------------------|----------------------| | F₂⁺ | 1.5 | Diamagnetic | Shortest | Highest | | F₂ | 1 | Diamagnetic | Intermediate | Intermediate | | F₂⁻ | 0.5 | Paramagnetic | Longest | Lowest | --- ### **b) N₂ Molecular Orbitals and Bonding** N (Z = 7): 1s² 2s² 2p³ N₂: 14 electrons **MO diagram for N₂ (for elements up to N, the order is different):** σ(2s) < σ*(2s) < π(2p_y) = π(2p_z) < σ(2pₓ) < π*(2p_y) = π*(2p_z) < σ*(2pₓ) **Filling:** σ(2s)² σ*(2s)² π(2p_y)² π(2p_z)² σ(2pₓ)² **Bond Order = (8 - 2)/2 = 3** (triple bond) **Schematic:** - **σ bond**: Head-on overlap of two 2pₓ orbitals - **π bonds**: Side-on overlap of 2p_y and 2p_z orbitals ``` N N 2p_x --- 2p_x => σ(2p_x) bond 2p_y --- 2p_y => π(2p_y) bond 2p_z --- 2p_z => π(2p_z) bond ``` ### **c) π-Back Bonding in Transition Metal Complexes** **Explanation:** - In π-back bonding, a filled metal d orbital donates electron density into an empty π* (antibonding) orbital of the ligand (often CO, CN⁻, etc.), while the ligand also donates lone pair into an empty metal orbital (σ bonding). - This strengthens the metal-ligand bond and weakens the ligand's internal bond. **Bonding Scheme (sketch):** ``` Metal dπ orbital ---> π* orbital of ligand (back donation) Ligand lone pair ---> empty metal s/p/d orbital (σ donation) ``` **Overlap:** ``` Metal dπ ---> π* (CO, etc) \ / ------ M ←→ L ------ / \ Ligand lone pair → M empty orbital ``` --- ## **Final Answers (Summary)** **a)** - **F₂:** Bond order = 1, diamagnetic, intermediate bond length and dissociation energy - **F₂⁻:** Bond order = 0.5, paramagnetic, longest bond, lowest dissociation energy - **F₂⁺:** Bond order = 1.5, diamagnetic, shortest bond, highest dissociation energy **b)** N₂ forms one σ and two π bonds via overlap of 2p orbitals, giving a triple bond. **c)** π-back bonding: Metal d orbitals donate electron density into ligand π* antibonding orbitals, strengthening the metal-ligand bond and weakening the ligand's own bond. (See sketch above.) --- Let me know if you want the MO diagrams drawn or further clarification!