The electronic spectrum of [Ti(H2O)6]3+ shows a single broad peak with a maximum at 20,300 cm⁻¹. The crystal field…

🧠 Compute Δ₀ and CFSE

For $[\mathrm{Ti(H_2O)_6}]^{3+}$: Ti(III) is d¹.

The single d–d transition $t_{2g}^1 \to e_g^1$ corresponds to $\Delta_o$:

$\Delta_o = 20{,}300 \text{ cm}^{-1}$

Configuration $t_{2g}^1$:

$\mathrm{CFSE} = 1 \times (-0.4 \Delta_o) = -0.4 \times 20{,}300 = -8{,}120 \text{ cm}^{-1}$

🗺️ Convert to kJ/mol

Given $1 \text{ kJ/mol} = 83.7 \text{ cm}^{-1}$:

$|\mathrm{CFSE}| = \frac{8{,}120}{83.7} \approx 97 \text{ kJ/mol}$

⚡ The d¹ Single-Peak Signature

A single broad absorption peak in the visible region is the hallmark of $d^1$ ions in octahedral environments — only one d-d transition is possible. Other d-counts (d², d³, ...) typically show multiple peaks because multiple electronic excited states exist.

⚠️ CFSE Per Mole

CFSE here is the molar value — it represents the energy stabilisation per mole of complex from the crystal field. The negative sign indicates stabilisation.

$\boxed{\text{Answer: (4) 97 kJ/mol}}$