Find crystal field stabilization energy in [ Ti ( L ) 6 ] 3 + in KJ / mole unit.

Question

Find crystal field stabilization energy in [ Ti ( L ) 6 ​ ] 3 + in KJ / mole unit.

TestHub · Accepted Answer

To find the Crystal Field Stabilization Energy (CFSE) for $[T i (L)_{6}]^{3 +}$ , we first determine the oxidation state of Ti and its d-electron configuration.

1. Oxidation state of Ti: Since the ligand (L) is neutral, Ti has an oxidation state of +3.

2. Electronic configuration of Ti³⁺: Ti is [Ar] 3d² 4s². So, Ti³⁺ is [Ar] 3d¹.

3. In an octahedral field, the single d-electron occupies the lower energy $t_{2 g}$ orbital.

4. CFSE calculation: CFSE = $n (t_{2 g}) (- 0.4 Δ_{O}) + n (e_{g}) (+ 0.6 Δ_{O})$

For Ti³⁺ (d¹), CFSE = $1 (- 0.4 Δ_{O}) + 0 (+ 0.6 Δ_{O}) = - 0.4 Δ_{O}$ .

5. Given $Δ_{O}$ for $[T i (H_{2} O)_{6}]^{3 +}$ is approximately $20300 c m^{- 1}$ .

To convert to kJ/mol: $20300 c m^{- 1} \times 0.01196 k J m o l^{- 1} / c m^{- 1} \approx 242.9 k J / m o l$ .

CFSE = $- 0.4 \times 242.9 k J / m o l = - 97.16 k J / m o l$ .

The closest option is -94 kJ/mol.

The final answer is $- 94$ .

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