The correct increasing order of stability of the complexes based on o value is: (I) [Mn(CN)6]3- (II) [Co(CN)6]4- (III)…

🧠 Stability ∝ CFSE ∝ Δₒ

Stability scales with CFSE. CFSE depends on:

• Metal d-configuration.
• Ligand field strength (here all CN⁻ — but $\Delta_o$ varies with metal OS).
• Spin state.

Higher metal oxidation state → higher charge → larger $\Delta_o$.

🗺️ Compute CFSE for Each

| # | Complex | Metal/d-config | LS Configuration (CN⁻ strong field) | CFSE (×$\Delta_o$) | |---|---|---|---|---| | (I) | $[\mathrm{Mn(CN)_6}]^{3-}$ | Mn(III) d⁴ LS | $t_{2g}^4 e_g^0$ | $-1.6$ | | (II) | $[\mathrm{Co(CN)_6}]^{4-}$ | Co(II) d⁷ LS | $t_{2g}^6 e_g^1$ | $-1.8$ | | (III) | $[\mathrm{Fe(CN)_6}]^{4-}$ | Fe(II) d⁶ LS | $t_{2g}^6 e_g^0$ | $-2.4$ | | (IV) | $[\mathrm{Fe(CN)_6}]^{3-}$ | Fe(III) d⁵ LS | $t_{2g}^5 e_g^0$ | $-2.0$ |

🗺️ Order by CFSE Magnitude

Less stable → more stable: $|-1.6| < |-1.8| < |-2.0| < |-2.4|$ $\text{(I)} < \text{(II)} < \text{(IV)} < \text{(III)}$

So increasing stability: I < II < IV < III.

⚡ CFSE Order Cheat (for LS oct)

| d-electrons | CFSE (×$\Delta_o$) | |---|---| | d⁴ LS | $-1.6$ | | d⁵ LS | $-2.0$ | | d⁶ LS | $-2.4$ ← maximum | | d⁷ LS | $-1.8$ | | d⁸ LS | $-1.2$ |

⚠️ Δₒ Differences Between OS States

Higher M oxidation state ⇒ larger $\Delta_o$ for same metal+ligand. So $[\mathrm{Fe(CN)_6}]^{3-}$ (Fe³⁺) has bigger $\Delta_o$ than $[\mathrm{Fe(CN)_6}]^{4-}$ (Fe²⁺) — but that's per-Δₒ, and CFSE in Δₒ units favours d⁶ over d⁵.

$\boxed{\text{Answer: (3) I < II < IV < III}}$