Magnetic Moment Calculation

The magnetic moment $ \mu $ of a complex is determined by the number of unpaired electrons using the formula:

$ \mu = \sqrt{n(n+2)} \, \text{BM} $

where $ n $ is the number of unpaired electrons.

Let's evaluate each complex:

1. $[\text{Fe}(\text{H}_2\text{O})_6](\text{NO}_3)_2$

Iron Oxidation State: +2

Electronic Configuration of $\text{Fe}^{2+}$: $[ \text{Ar} ] 3d^6$

Ligand Field: $\text{H}_2\text{O}$ is a weak field ligand, so no electron pairing occurs.

Unpaired Electrons: 4

$ \mu = \sqrt{4(4+2)} = \sqrt{24} \approx 4.90 \, \text{BM} $

2. $\text{K}_2[\text{MnCl}_4]$

Manganese Oxidation State: +2

Electronic Configuration of $\text{Mn}^{2+}$: $[ \text{Ar} ] 3d^5$

Ligand Field: $\text{Cl}^-$ is a weak field ligand, so no electron pairing occurs.

Unpaired Electrons: 5

$ \mu = \sqrt{5(5+2)} = \sqrt{35} \approx 5.92 \, \text{BM} $

3. $\text{K}_4[\text{Mn(CN)}_6]$

Manganese Oxidation State: +2

Electronic Configuration of $\text{Mn}^{2+}$: $[ \text{Ar} ] 3d^5$

Ligand Field: $\text{CN}^-$ is a strong field ligand, which causes electron pairing.

Unpaired Electrons: 1

$ \mu = \sqrt{1(1+2)} = \sqrt{3} \approx 1.73 \, \text{BM} $

4. $[\text{Ni}(\text{CO})_4]$

Nickel Oxidation State: 0

Electronic Configuration of $\text{Ni}$: $[ \text{Ar} ] 3d^8 4s^2$

Ligand Field: $\text{CO}$ is a strong field ligand, which causes electron pairing.

Unpaired Electrons: 0

$ \mu = \sqrt{0(0+2)} = 0 \, \text{BM} $

Conclusion

Among the complexes given, $\text{K}_4[\text{Mn(CN)}_6]$ has a magnetic moment closest to 2 BM (specifically, 1.73 BM), which arises from 1 unpaired electron.

Coordination Compounds

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