GATE 2026 CY – Question 42

Inorganic Chemistry · Transition Metals: Coordination chemistry – structure and isomerism, theories of bonding (VBT, CFT, and MOT). Metal-metal multiple bonds. Energy level diagrams in various crystal fields, CFSE, applications of CFT, Jahn-Teller distortion. Electronic spectra of transition metal complexes: spectroscopic term symbols, selection rules, Orgel and Tanabe-Sugano diagrams, nephelauxetic effect and Racah parameter, charge-transfer spectra. Magnetic properties of transition metal complexes. Ray-Dutt and Bailar twists, Reaction mechanisms: kinetic and thermodynamic stability, associative, dissociative substitution and redox reactions. · 2 marks · Multiple choice

The pair of complex ions that exhibits the slowest outer-sphere electron-exchange reaction at 25 °C is

[Co(NH3)6]3+ and [Co(NH3)6]2+
[Fe(H2O)6]3+ and [Fe(H2O)6]2+
[Ru(NH3)6]3+ and [Ru(NH3)6]2+
[Mn(CN)6]3− and [Mn(CN)6]4−

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Correct answer: (A) [Co(NH3)6]3+ and [Co(NH3)6]2+

Explanation

The rate of an **outer-sphere electron-transfer** self-exchange reaction depends on how much each partner has to reorganise before the electron can move (the Franck-Condon barrier): changes in metal-ligand bond length and in spin state make the reaction slow.

**A. $[\text{Co(NH}_3)_6]^{3+/2+}$:** low-spin $d^6$ (Co(III), $t_{2g}^6$) and high-spin $d^7$ (Co(II), $t_{2g}^5e_g^2$). The electron must go into an antibonding $e_g$ orbital, the Co–N bond lengthens by about 0.18 Å, and the spin state changes. The reorganisation energy is large, so the exchange is **very slow** (about $10^{-9}$ M⁻¹ s⁻¹). ✓
**B. $[\text{Fe(H}_2\text{O)}_6]^{3+/2+}$:** high-spin to high-spin, moderate bond change; moderately fast (about 4 M⁻¹ s⁻¹).
**C. $[\text{Ru(NH}_3)_6]^{3+/2+}$:** both low-spin $t_{2g}$ configurations, very little bond change; fast (about $10^3$ M⁻¹ s⁻¹).
**D. $[\text{Mn(CN)}_6]^{3-/4-}$:** both low-spin with a $t_{2g}$ electron moving; fast.

Answer **A**.