Question

The complex(es) having metal-metal bond order \( \ge 3.5 \) is/are [Given: The atomic numbers of Mo, Cr, Mn, and Re are 42, 24, 25, and 75, respectively.]

• A. [Mo\( _2 \)(\(\mu\)-SO\( _4 )\)\(_4\)(H\( _2 \)O)\(_2\)]\(^{3-}\)
• B. [Mn\( _2 \)(CO)\(_{10}\)]
• C. [Cr\( _2 \)(\(\mu\)-O\( _2 \)CCH\( _3 \))\(_4\)]
• D. [Mo\( _2 \)(\(\mu\)-HPO\( _4 \))\(_4\)(H\( _2 \)O)\(_2\)]\(^{2-}\)

Hint:

To determine metal-metal bond orders, consider the number of valence electrons contributed by each metal, the oxidation state of the metal, and the electronic configuration. For transition metals, the d-electrons are primarily involved in metal-metal bonding. Common high bond order examples include Cr(II) carboxylates (quadruple bond) and some Mo and W complexes.

Answer 1

The Correct Option is A, C

To determine the metal–metal bond order, we need to consider the electronic configurations of the metal ions and the number of electrons available for metal–metal bonding.

(A) [Mo₂(μ-SO₄)₄(H₂O)₂]³⁻
The overall charge is 3−. Each sulfate (SO₄²⁻) has a charge of 2−, and two water molecules are neutral.
So, the charge on the Mo₂ core is: −3 − 4(−2) = +5 → Each Mo has an oxidation state of +2.5.
Mo (atomic) has configuration [Kr] 4d⁵ 5s¹; Mo^2.5+ effectively has d^3.5 configuration. So Mo₂ has 7 d-electrons.
Known quadruple bonded Mo₂ complexes have σ² π⁴ δ² configuration. Here: σ² π⁴ δ¹ → bond order = 3.5.
✅ Bond order ≈ 3.5

(B) [Mn₂(CO)₁₀]
Mn(0): [Ar] 3d⁵ 4s² → 7 valence electrons per Mn.
Each Mn is bonded to 5 CO ligands: 10 electrons total from COs + 1 from Mn–Mn bond = 18 electrons.
This implies a Mn–Mn single bond.
✅ Bond order = 1

(C) [Cr₂(μ-O₂CCH₃)₄]
Cr(II): [Ar] 3d⁵ 4s¹ → d⁴
Cr₂ = 8 d-electrons → Known to form a quadruple bond with σ² π⁴ δ²
✅ Bond order = 4

(D) [Mo₂(μ-HPO₄)₄(H₂O)₂]²⁻
Overall charge = 2−; each HPO₄²⁻ contributes 2− → core charge = −2 − 4(−2) = +6
Each Mo is in +3 oxidation state → d³ configuration → Mo₂: 6 d-electrons
Likely σ² π⁴ configuration → bond order = 3
✅ Bond order ≈ 3

Conclusion:
The complexes with metal–metal bond orders ≥ 3.5 are:
(A) [Mo₂(μ-SO₄)₄(H₂O)₂]³⁻ → BO = 3.5
(C) [Cr₂(μ-O₂CCH₃)₄] → BO = 4