(a) Cite one example of an optically active tetracoordinated complex compound where the metal ion and donor atoms lie on a plane. Justify your answer. 10 marks

(b) Consider aqueous solutions of LaCl₃ (Lanthanum trichloride) and LuCl₃ (Lutetium trich

Question

(a) Cite one example of an optically active tetracoordinated complex compound where the metal ion and donor atoms lie on a plane. Justify your answer. 10 marks

(b) Consider aqueous solutions of LaCl₃ (Lanthanum trichloride) and LuCl₃ (Lutetium trichloride). Which solution shows lower pH? Explain. 10 marks

(c) The reaction cis-2-butene ⇄ trans-2-butene is first order in both the direction. At 25°C, the equilibrium constant is 0.406 and the forward reaction rate constant is 4.21×10⁻⁴ sec⁻¹. Starting with a sample of pure cis isomer with [cis]₀ = 0.115 mol dm⁻³, how long it will take to form half of equilibrium amount of the trans isomer from cis isomer? 10 marks

(d) At 0°C and 1 atm pressure, the volume of nitrogen gas required to cover a sample of an adsorbent is found to be 130 cm³ g⁻¹. Calculate the surface area per gram of adsorbent. Given that area occupied by a nitrogen molecule is 0.162 (nm)².

[Nₐ = 6.022×10²³ mol⁻¹] 10 marks

(e) Compare and comment on the magnetic properties of the following complexes:

(i) [Cu (OAc)₂]₂

(ii) [Cu (CN)₄]³⁻ 10 marks

UPSC Answer Check · Accepted Answer

This multi-part question requires explaining concepts (a, b, e), solving numerically (c, d), and comparing properties. Allocate approximately 15% time to each of parts (a), (b), and (e) combined (conceptual explanations), 25% to part (c) (kinetics calculation with equilibrium), and 25% to part (d) (surface area calculation). Begin with clear statements for each part, show all working for calculations, and conclude with comparative summaries where applicable.
- Part (a): Identify [M(AB)₂] type complex with unsymmetrical bidentate ligand (e.g., [Pt(glycinate)₂] or [Pd(AB)₂]) as square planar optically active compound; explain that M and donor atoms are coplanar but the chelate rings create non-superimposable mirror image due to twist
- Part (b): LuCl₃ shows lower pH; explain lanthanide contraction causing Lu³⁺ smaller ionic radius, higher charge density, greater hydrolysis of [Lu(H₂O)₆]³⁺ producing more H⁺ ions compared to La³⁺
- Part (c): Calculate reverse rate constant kᵣ = kf/K = 1.037×10⁻³ s⁻¹; set up integrated rate equation for approach to equilibrium; solve for time when [trans] = ½[trans]eq = 0.0203 M, obtaining t ≈ 1120-1150 s
- Part (d): Use ideal gas law to find moles N₂ = PV/RT = 5.80×10⁻³ mol; calculate molecules = nNₐ; surface area = molecules × area per molecule = 565-570 m² g⁻¹
- Part (e): [Cu(OAc)₂]₂ is dimeric with Cu-Cu interaction, μeff ≈ 1.4 BM per Cu at room temperature due to antiferromagnetic coupling; [Cu(CN)₄]³⁻ is tetrahedral with d¹⁰ configuration, diamagnetic (μ = 0); explain using MO/structural considerations

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	25%	12.5	Demonstrates flawless understanding across all parts: correctly identifies square planar [M(AB)₂] for optical activity in (a), explains lanthanide contraction-hydrolysis relationship in (b), recognizes antiferromagnetism in copper acetate dimer and d¹⁰ diamagnetism in cyanide complex in (e)	Shows basic understanding of most concepts but with minor errors: may confuse tetrahedral vs square planar for optical activity, or oversimplify lanthanide hydrolysis trend without charge density argument	Fundamental misconceptions: claims tetrahedral complexes are optically active in (a), reverses acidity trend in (b), or fails to distinguish magnetic coupling from simple paramagnetism in (e)
Mechanism / equation	20%	10	Writes correct rate laws and equilibrium expressions: establishes kᵣ = kf/K for part (c), derives correct integrated rate equation for reversible first-order reaction, and applies ideal gas equation with proper unit conversions in (d)	Writes basic equations but with gaps: states kinetics expressions without derivation, or makes minor errors in stoichiometric relationships	Incorrect or missing equations: treats reversible reaction as irreversible in (c), or fails to convert units properly in gas law application
Numerical accuracy	25%	12.5	Produces accurate calculations with proper significant figures: kᵣ = 1.04×10⁻³ s⁻¹, time ≈ 1130 s for (c); surface area ≈ 566 m² g⁻¹ for (d); shows all intermediate steps clearly	Correct method but arithmetic errors or unit conversion mistakes; final answers within 10% of correct value	Major calculation errors or order-of-magnitude mistakes; incorrect formula application yielding nonsensical results
Diagram / structure	15%	7.5	Draws clear structures showing: square planar geometry with chelate ring twist for optical activity in (a); paddle-wheel dimer structure with Cu-Cu bond in copper acetate; tetrahedral [Cu(CN)₄]³⁻ with proper geometry	Sketches basic structures but lacks stereochemical detail or proper representation of non-planarity in chelate rings	No diagrams provided, or incorrect geometries shown (e.g., tetrahedral for square planar case)
Application context	15%	7.5	Connects to practical relevance: cites heterogeneous catalysis importance of surface area measurements (BET method) in (d); mentions pharmaceutical relevance of optical activity; references materials science applications of magnetic copper complexes	Brief mention of applications without elaboration, or generic statements about importance	No contextualization; treats all parts as purely academic exercises without real-world relevance

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