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Use appropriate formulae to calculate the “spin-only” and “s+l” magnetic moments for: a. Cs2[Ni(CN)4]
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a. Cs2[Ni(CN)4]
Determining the oxidation state of Ni:
- Cyanide (CN-) has a charge of -1.
- Cesium (Cs) has a charge of +1.
- Therefore, the overall charge of the complex anion [Ni(CN)4]2- is -2.
- To balance the charge, Ni must have an oxidation state of +2.
Electronic configuration of Ni2+:
- Ni (atomic number 28): [Ar] 3d8 4s2
- Ni2+: [Ar] 3d8
Number of unpaired electrons:
- The 3d orbitals are filled in the following order: 3dxy, 3dxz, 3dyz, 3dx2-y2, 3dz2.
- Ni2+ has 8 electrons in its 3d orbitals, resulting in two unpaired electrons.
Spin-only magnetic moment (μs):
- μs = √(n(n+2)) BM, where n is the number of unpaired electrons.
- μs = √(2(2+2)) = √8 ≈ 2.83 BM
S+L magnetic moment (μs+l):
- This calculation requires the total spin angular momentum (S) and the total orbital angular momentum (L).
- For Ni2+, S = 1 (since there are 2 unpaired electrons with spin 1/2 each).
- The orbital angular momentum (L) is more complex to calculate and is often zero for transition metal ions due to ligand field effects.
- Therefore, μs+l ≈ μs ≈ 2.83 BM.
Determining the oxidation state of Ni:
- Cyanide (CN-) has a charge of -1.
- Cesium (Cs) has a charge of +1.
- Therefore, the overall charge of the complex anion [Ni(CN)4]2- is -2.
- To balance the charge, Ni must have an oxidation state of +2.
Electronic configuration of Ni2+:
- Ni (atomic number 28): [Ar] 3d8 4s2
- Ni2+: [Ar] 3d8
Number of unpaired electrons:
- The 3d orbitals are filled in the following order: 3dxy, 3dxz, 3dyz, 3dx2-y2, 3dz2.
- Ni2+ has 8 electrons in its 3d orbitals, resulting in two unpaired electrons.
Spin-only magnetic moment (μs):
- μs = √(n(n+2)) BM, where n is the number of unpaired electrons.
- μs = √(2(2+2)) = √8 ≈ 2.83 BM
S+L magnetic moment (μs+l):
- This calculation requires the total spin angular momentum (S) and the total orbital angular momentum (L).
- For Ni2+, S = 1 (since there are 2 unpaired electrons with spin 1/2 each).
- The orbital angular momentum (L) is more complex to calculate and is often zero for transition metal ions due to ligand field effects.
- Therefore, μs+l ≈ μs ≈ 2.83 BM.
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