Concept Explanation: Magnetic Moment (Spin Only) Calculation

The magnetic moment (spin only) is calculated using the formula: $\mu =\sqrt{n(n+2)}$ BM, where $n$ is the number of unpaired electrons. For coordination compounds, we first determine the oxidation state of the metal, its electron configuration, and the geometry (which affects splitting of d-orbitals) to find unpaired electrons.

Step-by-Step Solution for [NiCl₄]^2–

Step 1: Find oxidation state of Nickel (Ni)

Let oxidation state of Ni be $x$. Chlorine (Cl) has -1 charge. The complex has overall charge -2.

Equation: $x+4\times (-1)=-2$

Solving: $x-4=-2$ → $x=+2$

So, Ni is in +2 oxidation state.

Step 2: Write electron configuration of Ni²⁺

Atomic number of Ni is 28. Electronic configuration: [Ar] 3d⁸ 4s².

For Ni²⁺, two electrons are removed from 4s orbital first. So, configuration: [Ar] 3d⁸.

Step 3: Determine geometry and ligand field effect

Cl^– is a weak field ligand. [NiCl₄]^2– has tetrahedral geometry (common for Ni²⁺ with Cl^–).

In tetrahedral field, splitting is small (weak field), so electrons remain unpaired (high spin). For d⁸ in tetrahedral geometry, there are 2 unpaired electrons.

Explanation: The d orbitals split into e and t₂ in tetrahedral field. With 8 electrons, filling is: e⁴ t₂⁴. Since t₂ orbitals can hold 6 electrons, with 4 electrons, they are arranged with 2 unpaired (Hund's rule).

Step 4: Calculate number of unpaired electrons ($n$)

From above, $n=2$.

Step 5: Compute magnetic moment using spin-only formula

$\mu =\sqrt{n(n+2)}=\sqrt{2\times (2+2)}=\sqrt{2\times 4}=\sqrt{8}=2.828$ BM (approximately 2.82 BM).

Final Answer: 2.82 BM

Related Topics

• Crystal Field Theory
• Ligand Field Splitting in Tetrahedral vs Octahedral Complexes
• High Spin and Low Spin Complexes
• Electron Configuration of Transition Metals
• Oxidation State Determination

Important Formulae and Theory

Spin-only magnetic moment formula: $\mu =\sqrt{n(n+2)}$ BM, where $n$ is number of unpaired electrons.

For tetrahedral complexes: Splitting is smaller compared to octahedral. Weak field ligands often result in high spin complexes.

For Ni²⁺ (d⁸): In tetrahedral geometry, it has 2 unpaired electrons. In octahedral geometry with weak field ligands, it also has 2 unpaired electrons, but with strong field ligands (e.g., CN^–), it has 0 unpaired electrons.

Common weak field ligands: Cl^–, Br^–, I^–, H₂O. Strong field ligands: CN^–, CO, NH₃.