Question

The complex with highest magnitude of crystal field splitting energy (Δ0) is

• A. \([Ti(OH)_2)_6]^{3+}\)
• B. \([C_r(OH)_2)_6]^{3+}\)
• C. \([m_n(OH)_2)_6]^{3+}\)
• D. \([F_e(OH)_2)_6]^{3+}\)

Answer 1

The Correct Option is B

The question asks about the complex with the highest magnitude of crystal field splitting energy \((\Delta_0)\). To determine this, we need to consider the factors affecting crystal field splitting energy:

• Nature of the Ligand: Strong field ligands cause greater splitting.
• Metal Ions: Different metal ions have different splitting capabilities based on their electronic configuration.

Given complexes are:

1. \([Ti(OH)_2)_6]^{3+}\)
2. \([Cr(OH)_2)_6]^{3+}\)
3. \([Mn(OH)_2)_6]^{3+}\)
4. \([Fe(OH)_2)_6]^{3+}\)

The ligand in each case is OH^{-}, which is a weak field ligand. Hence, the gain in splitting energy will primarily depend on the central metal ion.

The electronic configurations of the metal ions are:

• \(Ti^{3+}: [Ar] 3d^1\)
• \(Cr^{3+}: [Ar] 3d^3\)
• \(Mn^{3+}: [Ar] 3d^4\)
• \(Fe^{3+}: [Ar] 3d^5\)

Among these, the \(Cr^{3+}\) ion is known to cause greater crystal field splitting because:

• \(Cr^{3+}\) has a half-filled \(t_{2g}\) set of orbitals, which is relatively stable and tends to cause larger splitting.
• It also has a stronger ability to stabilize lower energy orbitals and allow greater splitting.

In contrast, the metal ions \(Ti^{3+}\), \(Mn^{3+}\), and \(Fe^{3+}\) do not have as significant stabilization trends as \(Cr^{3+}\) for this electron configuration.

Hence, the complex that exhibits the highest magnitude of crystal field splitting energy is:

Correct Answer: \([Cr(OH)_2)_6]^{3+}\)