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GATE 2026 CY – Question 15

Inorganic Chemistry · Organometallics: 18-Electron rule; metal-alkyl, metal-carbonyl, metal-olefin and metal-carbene complexes and metallocenes. Fluxionality in organometallic complexes. Types of organometallic reactions. Homogeneous catalysis – Hydrogenation, hydroformylation, methanol to acetic acid process, olefin metathesis and Wacker oxidation. Heterogeneous catalysis – Fischer-Tropsch reaction, Ziegler-Natta polymerization. · 1 mark · Multiple choice

The species that undergoes β-elimination is

  1. $[\mathrm{Rh}(\mathrm{C_5H_5})(\mathrm{PMe_3})(\mathrm{C_2H_5})]^+$
  2. $[\mathrm{Rh}(\mathrm{NH_3})_5(\mathrm{C_2H_5})]^{2+}$
  3. $[\mathrm{Pt}(\mathrm{PPh_3})_2(\mathrm{C_6H_5})\mathrm I]$
  4. $[\mathrm{Cr}(\mathrm{CH_2SiMe_3})_4]$

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Correct answer: (A) $[\mathrm{Rh}(\mathrm{C_5H_5})(\mathrm{PMe_3})(\mathrm{C_2H_5})]^+$

Explanation

**$\beta$-Hydride elimination** needs two things:
1. a hydrogen on the $\beta$ carbon of the metal-alkyl group, and
2. a **vacant coordination site** on the metal cis to the alkyl, where the hydride can go.

Check each complex:
- **A. $[\text{Rh(C}_5\text{H}_5)(\text{PMe}_3)(\text{C}_2\text{H}_5)]^+$:** the ethyl group has β-hydrogens, and the cationic 16-electron Rh centre is coordinatively unsaturated, so a vacant site is available. ✓
- **B. $[\text{Rh(NH}_3)_5(\text{C}_2\text{H}_5)]^{2+}$:** an 18-electron, coordinatively saturated Rh(III) complex with no vacant site. ✗
- **C. $[\text{Pt(PPh}_3)_2(\text{C}_6\text{H}_5)\text{I}]$:** the aryl group has no β-hydrogen that can be transferred (sp² C–H). ✗
- **D. $[\text{Cr(CH}_2\text{SiMe}_3)_4]$:** the alkyl has no β-hydrogens (the β atom is silicon). ✗

Answer **A**.