(a) Explain the common structural features of two major iron-containing proteins—haemoglobin and cytochrome c present in the human body. Explain the coordination chemistry involved at the central metal atom in case of oxyhaemoglobin and deoxyhaemoglo

Question

(a) Explain the common structural features of two major iron-containing proteins—haemoglobin and cytochrome c present in the human body. Explain the coordination chemistry involved at the central metal atom in case of oxyhaemoglobin and deoxyhaemoglobin. Give the details of the spin states, magnetic moment and oxidation number of central metal ion in both the cases. (10 marks)

(b) Write the ground-state electronic configuration of lanthanides mentioned below:
(i) ₅₉Pr (Praseodymium)
(ii) ₆₃Eu (Europium)
(iii) ₆₄Gd (Gadolinium)
Calculate the predicted effective magnetic moment (μₛ₊ₗ) for the metal ions in +3 oxidation state in the units of Bohr magneton. (10 marks)

(c) Derive a rate expression for a bimolecular surface reaction. Discuss the kinetics of such a reaction, when the gaseous reactants, say A and B, are adsorbed in the following way:
A + B → Product
(i) A and B are sparsely adsorbed.
(ii) A is relatively more strongly adsorbed than B. (10 marks)

(d) Nickel was found to be coordinated with oxygen in the UV-visible spectrum of [Ni(OS(CH₃)₂)₆]²⁺ complex ion. Predict theoretically the number of peaks and assign them to the corresponding electronic transitions. (10 marks)

(e) An ideal gas (V_i = 0.05 L and P_i = 8 atm) is subjected to reversible isothermal expansion (V_f = 0.40 L and P_f = 1 atm) at 25 °C. Calculate the work done, ΔU, ΔH and ΔS for this process. Is the heat (q) same as ΔH in this process? If not, why? (10 marks)

UPSC Answer Check · Accepted Answer

Begin with a brief introduction acknowledging the interdisciplinary nature of the question spanning bioinorganic, coordination, kinetic and thermodynamic chemistry. Allocate approximately 25% time to part (a) on haemoglobin/cytochrome c due to its conceptual depth; 15% each to parts (b) and (d) involving electronic configurations and spectral predictions; 20% to part (c) requiring derivation of Langmuir-Hinshelwood kinetics; and 25% to part (e) for thermodynamic calculations. Present each part clearly separated with appropriate headings, ensuring derivations show all steps and numerical answers include proper units.
- Part (a): Common structural features of haemoglobin and cytochrome c (iron porphyrin/protoporphyrin IX ring, axial ligands, protein environment); coordination chemistry differences between oxyhaemoglobin (Fe²⁺, low-spin, diamagnetic, μ=0 BM, O₂ as π-acceptor) and deoxyhaemoglobin (Fe²⁺, high-spin, paramagnetic, μ=4.90 BM, weak field)
- Part (b): Ground state electronic configurations—₅₉Pr [Xe]4f³6s², ₆₃Eu [Xe]4f⁷6s², ₆₄Gd [Xe]4f⁷5d¹6s²; M³⁺ configurations and μₛ₊ₗ calculation using μₛ₊ₗ = √[4S(S+1) + L(L+1)] BM yielding ~3.62 BM (Pr³⁺), ~3.40 BM (Eu³⁺), ~7.94 BM (Gd³⁺)
- Part (c): Derivation of rate expression for bimolecular surface reaction: rate = kθₐθᵦ; Langmuir isotherm application; Case (i) sparse adsorption—first order in both A and B, rate ∝ PₐPᵦ; Case (ii) strong A adsorption—rate independent of Pₐ, first order in Pᵦ
- Part (d): [Ni(OS(CH₃)₂)₆]²⁺ as octahedral Ni²⁺ (d⁸) with O-donor ligands; prediction of three spin-allowed d-d transitions: ³A₂g→³T₂g (ν₁), ³A₂g→³T₁g(F) (ν₂), ³A₂g→³T₁g(P) (ν₃); expected weak field from DMSO oxygen coordination
- Part (e): Isothermal reversible expansion calculations—W = -nRT ln(Vf/Vi) = -2.303nRT log(Pi/Pf); ΔU=0 and ΔH=0 for ideal gas isothermal process; ΔS = nR ln(Vf/Vi); q = -W ≠ ΔH because ΔH=0 but q is non-zero; explicit numerical values with n calculated from ideal gas law

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	25%	12.5	Demonstrates precise understanding across all parts: correctly identifies haemoglobin as cooperative O₂ transport vs cytochrome c as electron transfer; distinguishes low-spin Fe²⁺ in oxyhaemoglobin from high-spin in deoxyhaemoglobin; applies correct Russell-Saunders coupling for lanthanide magnetic moments; recognizes Langmuir-Hinshelwood vs Eley-Rideal mechanisms; identifies octahedral Ni²⁺ d⁸ configuration; states all thermodynamic criteria for ideal gas isothermal process	Shows generally correct concepts with minor errors: confuses spin states in haemoglobin derivatives, uses only spin-only formula for lanthanides, states rate laws without deriving from adsorption isotherms, predicts incorrect number of d-d transitions, or states ΔU=0 without justification	Fundamental conceptual errors: describes Fe³⁺ in haemoglobin, applies crystal field theory incorrectly to lanthanides, derives rate expression for homogeneous rather than surface reaction, predicts tetrahedral geometry for Ni²⁺ complex, or claims ΔH=q for isothermal process
Mechanism / equation	20%	10	Complete derivations with all steps shown: explicit Langmuir isotherm θ = KP/(1+KP) leading to rate = kKₐKᵦPₐPᵦ/[(1+KₐPₐ+KᵦPᵦ)²] for general case; simplifies correctly for limiting cases; writes Orgel/Tanabe-Sugano relevant equations for Ni²⁺ transitions; presents first law and entropy definitions for thermodynamic calculations	States final rate laws without full derivation; writes simplified rate expressions for limiting cases directly; mentions but does not elaborate Tanabe-Sugano diagrams; presents thermodynamic equations without connecting to reversible work definition	No derivation attempted; writes incorrect rate laws (e.g., rate = k[A][B] for surface reaction); omits equilibrium constants in adsorption expressions; fails to write any thermodynamic equations or uses irreversible work formula
Numerical accuracy	25%	12.5	All calculations precise with correct significant figures: μₛ₊ₗ values calculated with proper J values (Pr³⁺: ⁴I₉/₂, S=1, L=5; Eu³⁺: ⁷F₀, S=3, L=3; Gd³⁺: ⁸S₇/₂, S=7/2, L=0); thermodynamic quantities with n=0.0163 mol, W=q=+89.6 J, ΔS=+0.301 J/K; explicitly addresses q≠ΔH with thermodynamic reasoning	Correct methodology with arithmetic errors; uses spin-only formula (μₛₒ = √[n(n+2)]) for lanthanides yielding approximate values; correct thermodynamic formulas but incorrect n calculation or unit conversion errors; vague statement about q and ΔH	Major numerical errors: incorrect oxidation states for magnetic moment calculation, wrong formulas (e.g., ΔS = q/T for irreversible process), missing units, or no calculations attempted for quantitative parts
Diagram / structure	15%	7.5	Clear well-labelled diagrams: porphyrin ring structure with Fe-N₄ plane and axial ligands (proximal His, distal His/O₂) for haemoglobin; cytochrome c with covalent thioether linkages; energy level diagram for octahedral Ni²⁺ showing ³A₂g ground state and excited states with expected transition energies; P-V diagram for reversible isothermal expansion	Describes structures in text without diagrams; draws porphyrin ring without axial ligands; generic octahedral splitting diagram without specific Ni²⁺ labelling; no thermodynamic diagram	No structural representations; confuses haemoglobin with chlorophyll structure; draws tetrahedral or square planar diagrams for Ni²⁺; entirely omits diagrammatic content where essential
Application context	15%	7.5	Connects to broader significance: haemoglobin cooperativity and Bohr effect relevance to high-altitude physiology in Indian context (e.g., Himalayan populations); cytochrome c in mitochondrial electron transport and apoptosis; heterogeneous catalysis applications in Indian petrochemical industry (Haber-Bosch, Fischer-Tropsch); lanthanide applications in MRI contrast agents and phosphors; thermodynamic principles in engine efficiency and refrigeration cycles	Brief mention of biological importance without specific context; states catalysis is important without Indian examples; mentions lanthanides are used in technology without specifics; generic statement about thermodynamics in engines	No application context provided; treats all parts as purely academic exercises without real-world relevance; incorrect applications (e.g., haemoglobin in nitrogen fixation)

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