Q6(b)(ii). EAN rule; EAN of four complexes

1. EAN rule (Sidgwick). The effective atomic number is the total number of electrons around the metal in a complex, its own electrons plus those its ligands donate. A complex is expected to be stable when the EAN equals the atomic number of the next noble gas (36 for the 3d metals, krypton).
2. EAN =Z-x+2n, where x is the oxidation state of the metal and n the number of donor pairs (n=6 for each complex here, 2n=12).

Why the fourth complex still exists: Ni(II) is d⁸, t_(2g)⁶e_g²; the two electrons beyond 36 sit in the e_g orbitals. NH₃ is a moderate σ donor and no π acceptor, so e_g is only weakly antibonding and the complex is stable but labile. It has two unpaired electrons and is paramagnetic (μₛ=√8=2.83 μ_B). The EAN rule is a guide, not a law: [Zn(en)₃]²+ (EAN 40) is also stable.

Link with the 18-electron rule. Counting only valence electrons (metal d electrons + 12 from the ligands) gives 18 for the first three and 20 for [Ni(NH₃)₆]²+: the 18-electron rule is the EAN rule written for the valence shell. Nine bonding MOs (six σ, three t_(2g)) hold 18 electrons. It works best with strong σ-donor, π-acceptor ligands such as CO and CN⁻: Cr(CO)₆ is colourless, air-stable and sublimes unchanged, while the 17- and 19-electron ions [Cr(CO)₆]^(±) are much less stable.

Application. the rule predicts the formulas of metal carbonyls: Ni(CO)₄, Fe(CO)₅ and Cr(CO)₆ all have EAN 36. Ni(CO)₄, formed from Ni and CO at 50°C and 1 atm, is the basis of the Mond process for refining nickel.